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ATLAS User's Manual

1. Table 3 30 Parameters for Equations 3 172 through 3 188 Statement Parameter Default Units OBILITY RN TAS 2 OBILITY RP TAS 3 OBILITY BETAN 2 OBILITY BETAP 1 OBILITY BETAN 2 OBILITY BETAP 1 OBILITY BETAN 1 5 OBILITY BETAN OBILITY MUBN TAS 1150 OBILITY MUBP TAS 270 OBILITY TMUBN TAS 2 5 OBILITY TMUBP TAS 1 4 MOBILITY DN TAS 3 2 107 OBILITY DP TAS 2 35 1079 OBILITY P1N TAS 0 09 OBILITY P1P TAS 0 334 OBILITY B1N TAS 1 75 OBILITY B1P TAS 1 5 OBILITY P2N TAS 4 53 1078 OBILITY PEP TAS 3 14 1077 OBILITY B2N TAS 0 25 OBILITY B2P TAS 0 3 OBILITY Z11N TAS 0 0388 OBILITY Z11P TAS 0 039 OBILITY Z22N TAS 1 73 10 5 OBILITY Z22P TAS 1 51 1075 OBILITY ESRN TAS 2 449 107 3 50 SILVACO International Physics Table 3 30 Parameters for Equations 3 172 through 3 188 Statement Parameter Default Units OBILITY ESRP TAS 10 108 OBILITY BETAN TAS 2 OBILITY BETAP TAS i OBILITY N2N TAS 1 1 10 1 OBILITY N2P TAS 1 4 1018 OBILITY 1N TAS 2 101 OBILITY 1P TAS 8 4 1016 OBILITY ALPHAN TAS 2 OBILITY ALPHAP TAS 3 4 Perpendicular Electric Field Dependent Mobility Models The Watt Model A surface mobility model derived by J T Watt 5 is available in ATLAS This mobility model is activated when the parameter surrmoB i
2. Table 3 52 User Specifiable Parameters for Equations 3 307 to 3 308 Statement Parameter Default Units MATERIAL FERRO EC 0 0 V cm MATERIAL FERRO EPS 1 0 MATERIAL FERRO PS 0 0 C sqcm MATERIAL FERRO PR 0 0 C sqcm Quantum Mechanical Models Self Consistent Schrodinger Poisson Model To model the effects of quantum confinement ATLAS also allows solution of Schrodinger s equation along with the fundimental device equations The solution of Schrodinger s equation gives a quantized description of the density of states in the presence of quantum mechanical confining potential variations The calculation of the quantized density of states relies upon a solution of Schrodinger s equation 1 Ving Vi Utot sk AG 3 311 where Cx and Me are the kt bound state wavefunction and energy level respectively and Utot is the total potential energy of the electron Utot qV E 3 312 where Ep the conduction band heterojunction discontinuity and is typically given by the difference in electron affinities Epi 3 313 X l p X lbotton SILVACO International 3 85 ATLAS User s Manual Volume 1 The quantized density of states subsequently has the form 41 me 2 h Sk ACE quantum E k 3 314 Ol k Using Fermi Dirac statistics the discrete nature of the quantised density of states reduces the inte gral over energy to a sum over bound state e
3. Trap Assisted Tunneling At high electric fields tunneling of electrons from the valence band to the conduction band via trap or defect trap assisted tunneling states can have an important effect on the current Trap assisted tunneling is modeled by including the field effect enhancement terms 125 Fn and Tp in the capture cross sections These enhancement terms modify the capture cross sections so that they include the effects of phonon assisted tunneling of the emission of electrons and holes from a trap This model is enabled by specifying TRAP TUNNEL is specified on the moDELs statement The electron and hole capture cross sections srcw and src in the previous equations are modified in the following manner g SIGN no 1 D 3 62 a SIGP 3 63 P EE i Sy replaces s en in equations 3 54 3 55 3 56 and 3 60 and o replaces src in equations 3 54 3 55 3 57 and 3 61 3 14 SILVACO International Physics NP 2AE bip For values of the electric field such that p gt r where 3 8m 2 MASS TUNNEL m AE p Sgen 3qhIE q is the electronic charge h is Planck s constant mg is the rest mass of an electron and mass TUNNEL iS the effective mass the parameter mass TUNNEL may be set on the vopgrs statement Theterm AE is given by KE Ec Erm ErSEm 4 65 ESSE Er gt Efn and Es E Ey gt E p V T 1 AE 3 66 P Ec Er Eq amp E where Ec is the condu
4. SILVACO International 2 13 ATLAS User s Manual Volume 1 The doping file filenamel must have been specified on the first DOPING statement with the OUTFILE parameter The results of the regrid are saved in the file filename2 The smooTH kEY parameter value selects a smoothing algorithm A value of 4 is typically best as this algorithm tends to produce the fewest obtuse triangles For a complete description of the various smoothing algorithms refer to Chapter 14 which describes numerical techniques TonyPlot 2 2 1 ATLAS INTIAL GRID JC SR WW Lev YA Ny Y A ESQ E RET E NJ ROS a y El it i LIA Jg E A WENN E E E E E E E A E O Y We A TA E O A E E E E A E A E Y 15 16 17 19 19 2 21 2 23 24 25 25 27 28 29 Microns Microns O SILVACO International 1994 4 Figure 2 6 Regrid on doping provides improved resolution of junction Regrid Using Solution Variables The REGRID statement can use a wide range of solution variables as the basis for mesh refinement Regrid on potential is often used for high voltage power devices Note that regrid on solution variables can only be used after a solution has already been obtained After a regrid on a solution variable the solution must be re solved at the same bias i
5. Statement Parameter Default IMPACT AN1 7T 03 109 gi IMPACT AN2 7 03 10 cm IMPACT AP1 6 71 10 cm IMPACT AP2 6 71 10 cm IMPACT BN1 1 131 10 v cm IMPACT BN2 1 231 10 V cm IMPACT BP1 1 693 106 V cm IMPACT BP2 2 036 106 V cm IMPACT BETAN 1 0 IMPACT BETAP 1 0 IMPACT EGRAN 4 105 V cm Table 3 43 Temperature Coefficient Parameters of the Selberherr Impact lonization Model for Silicon in Equations 3 238 to 3 241 Statement Parameter Default IMPACT A NT 0 588 IMPACT B NT 0 248 IMPACT A PT 0 588 IMPACT B PT 0 248 IMPACT M ANT 1 0 IMPACT M BNT 1 0 IMPACT M APT 1 0 IMPACT M BPT 1 0 3 68 SILVACO International Physics Grant s Impact lonization Model The second ionization model has the same form as the Selberherr model but a simpler implementation an ANexp HE 3 242 ag AP exp CE 3 243 This implementaion has three key differences e the model has a low field an intermediate field and a high field region e the coefficients for silicon are different e thereis notemperature dependence This model was developed after investigations by Baraff 128 suggested the existence of a low intermediate and high field response region for electron and hole ionisation rates The coefficients implemented into this model match the experimental data of Grant 2 which suggested that the three different regions existed This model
6. Table 5 1 User Specifiable Parameters for Equations 5 45 and 5 46 Statement Parameter Units MOBILITY MUN cm2 V s MOBILITY TMUN MOBILITY MUP cm2 V s MOBILITY TMUP SILVACO International 5 15 ATLAS User s Manual Volume 1 Parallel Electric Field Dependent Mobility Two types of electric field dependent mobility models are used in ATLAS BLAZE These models are a standard mobility model and a negative differential mobility model Both of these models contain appropriate default values of parameters for different materials The user must specify what type of mobility will be used for each material and what material parameters they wish to alter The standard mobility model that takes account of velocity saturation is defined according to 71 BETAN 1 H E Hno E BETAN d 1 Uno gt VSATN 4 1 BETAP 1 HCE Mpo BETAP e HpoE 1 VSATP where vsarN and vsatp are the saturation velocities for electrons and holes BETAN and BETAP are constants given in Table 5 2 and uno po are the electron and hole low field mobilities This model is activated by the parameter FLDMOB or EVSATMOD 0 of the MODEL statement Table 5 2 User Specifiable Parameters for Equation 5 47 and 5 48 Statement Parameter Units MOBILITY BETAN MOBILITY BETAP MOBILITY VSATN cm s MOBILITY VSATP cm s The negative differential mobility model of Barnes et al 24 has
7. method co mio Old Syntax V2 0 0 R New Syntax symbolic newton carriers 2 method newton symbolic newton carriers 1 elec method newton carriers 1 electron symbolic gummel carriers 0 method gummel carriers 0 symbolic newton carriers 2 method gummel newton method comb models lat temp models lat temp symbolic newton carriers 2 method block method comb models hcte models hcte symbolic gummel carriers 2 method block 2 30 SILVACO International Getting Started with ATLAS Obtaining Solutions ATLAS can calculate DC AC small signal and transient solutions Obtaining solutions is rather analogous to setting up parametric test equipment for device tests You usually define the voltages on each of the electrodes in the device ATLAS then calculates the current through each electrode ATLAS also calculates internal quantities such as carrier concentrations and electric fields throughout the device This is information that is difficult or impossible to measure In all simulations the device starts with zero bias on all electrodes Solutions are obtained by stepping the biases on electrodes from this initial equilibrium condition As will be discussed due tothe initial guess strategy voltage step sizes are limited This section concentrates on defining solution procedures Saving results using the LOG or SAVE statements and analysing and displaying these results is in the subsequent section DC Solutions
8. will begin with BLOCK iterations then switch to newton if convergence is still not achieved This is the most robust approach for many energy balance applications The points at which the algorithms switch is predetermined but can also be changed on the METHOD statement The default values set by Sil vaco work well for most circumstances Energy Balance Calculations with Lattice Heating When non isothermal solutions are performed in conjunction with energy balance models a system of up to six equations must be solved cumMEL Or NEWTON solve the equations iteratively or fully coupled respectively Brock initially performs the same function as with energy balance calculations then solves the lattice heating equation in a de coupled manner Setting The Number Of Carriers ATLAS can solve both electron and hole continuity equations or only for oneor none This choice can be made using the parameter carrTERS For example METHOD CARRIERS 2 specifies a solution for both carriers is required This is the default With one carrier the parameter ELEC Or HOLE is needed For example for hole solutions only METHOD CARRIERS 1 HOLE To select a solution for potential only specify METHOD CARRIERS 0 Note Setting the number of carriers uing the syntax MODEL NUMCARR n is obsolete and should not be used 2 28 SILVACO International Getting Started with ATLAS
9. gt gt J 2 2 Eee is oule heat qM n qHgp q R G 0 0 T P P is recombination and generation heating and cooling 3 E T J VP J VP accounts for the Peltier and Thomson effects A simple and intuitive form of H that has been widely used in the past is gt gt gt H J J E oN GIGA can use either Equation 6 8 or 6 9 for steady state calculations By default Equation 6 9 is used Equation 6 8 is used if the parameter HEAT FULL is specified in the MODELS statement The Peltier and Thomson terms are turned off by specifying the HEAT PETHOM parameter of the MODELS statement If the general expression shown in Equation 6 8 is used for the non stationary case the derivatives 9T 9T complete ionization 0 0 a and 2 are evaluated for the case of an idealized nondegenerate semiconductor and n p n p The heat generation term H is always set equal to 0 in isulators When carrier transport is modeled in the energy balance approximation the following expression is used for H SILVACO International 6 5 UTMOST User s Manual Volume 1 H Wah WW gt Be U 6 11 where U W and W are defined by formulas 3 94 through 3 96 Thermal Boundary Conditions At least one thermal boundary condition must be specified when the lattice heat flow equation is solved The thermal boundary conditions used have the general form d er s eu T TS 6 12 where is either
10. 1 200 2 x composition 0 46 0 5 x composition 1 0 In x Ga 1 x As y P 1 y System The In x Ga 1 x As y P 1 y material system is commonly used for the fabrication of heterojunction devices These indude laser diodes photodiodes Gunn diodes and high speed heterostructure transistors As a quaternary material two different mole fraction parameters x and y are necessary to specify any particular combination This produces a wide array of InGaAsP materials and characteristics Of particular interest in this system are materials that are lattice matched to InP The default material characteristics in BLAZE for the InGaAsP system correspond to composition fractions x and y that yield InGaAsP material that is lattice matched to InP The relationship between x and y that satisfy this condition is given by 5 22 SILVACO International BLAZE 0 1896 y composition X OTE 0 0123 y composition 0 lt y composition lt I 5 65 Many of the parameter models for the n x Ga 1 x As y P 1 y system are functions of the composition fraction y composition only The composition fraction x composition can be deduced from the preceeding relationship Again the default material characteristics in BLAZE for the InGaAsP system correspond to composition fractions x and y that yield InGaAsP material that is lattice matched to InP Note Users should not use this material system to form GaAs by setting x 0 and y 1 but
11. Egp and Ey are the p type and n type material bandgaps AE is the portion of the difference between E and E that appears between the valence bands at the heterojunction interface AE not labelled is the portion of the difference between E and E that appears between the conduction bands at the heterojunction interface qvo is the built in potential of the heterojunction X and x arethe electron affinities of the p type and n type materials m is the work function of the metal p is the barrier height between the metal and the semiconductor The basic band parameters for defining heterojunctions in BLAZE are bandgap parameter EG300 electron parameter AFFINITY and the conduction and valence band density of states NC300 and NV300 These parameters are defined for each material using the warERraL statement Other transport parameters relating these basic definitions to compound elemental concentrations x composition and y composition can also be defined See the MATERIALS section of this chapter for a description of these relationships for each material system and the Simulating Heterojunction Devices with Blaze section for their usage The work function of metals is defined using the contact statement Alignment As can be seen from figure 5 1 the difference in the two material bandgaps creates conduction and valence band discontinuities How the bandgap difference is distributed between the conductance and valenc
12. Table 9 1 User Specifiable Parameters for Equation 9 2 Statement Parameter Default Units ATERIAL ALPHAR 4 0 ATERIAL ALPHAA 0 0 ATERIAL EPSINF ATERIAL FCN 3 0e 18 cm ATERIAL FCP 7 0e 18 cm ODELS LAS ABSORPTION FALSE ODELS LAS FCARRIER FALSE Local Optical Gain The central model in semiconductor laser simulation is the optical gain model The optical gain is the ability of the semiconductor media to amplify light i e the number of photons generated per unit length LASER provides two models for local gain The first model is physically based It takes into account frequency dependence and can be used for spectral analysis 97 98 The optical gain using this model is given by 9 2 SILVACO International LASER ho E E Es GAMMA hO E c n 3 9 3 a g g x y GAINO T ET E Eg 1 GAMMA ho A kT Table 9 2 User Specifiable Parameters for Equation 9 3 Statement Parameter Default Units MATERIAL GAINO 2000 0 cm MATERIAL GAMMA where E fn and Er are the quasi F ermi levels for electrons and holes respectively Egis the band gap Ec is the conduction band edge energy Ey is the valence band edge energy and 1 f x expG 1 9 4 The user may specify the value of the parameter camma as shown in Table 9 2 If the parameter camma is not specified its value will be calc
13. 8 4 SILVACO International Luminous Sidewall Reflection By default the reflection from the sides of the device areignored Noreflected ray is traced back into the structure As above BACK REFL is used to enable the sidewall reflections assuming a vacuum outside the device Discontinuous Regions It is possibleto simulate devices electrically where a single region is defined as two or more separated areas However the ray tracing algorithm does not support such structures If a structure has two separate areas with the same region number the recommended approach is to use DpevEp r to renumber the regions perhaps even creating a new region number for each area Note this limitation is only for two separated areas with the same region number and not for two regions with different region numbers of the same material This latter case can be simulated Anti Reflective Coatings It is a popular strategy to place anti relective AR coatings on light detecting devices to improve device quantum efficiency Such coatings rely on coherence effects to reduce the reflection coefficient between the detecting device and the ambient i e air or vaccuum in the direction of the light source Typically these AR coatings are composed of one or more layers of insulating materials that are one quarter optical wavelength thick and optically transparent to the wavelength in question Coherence effects are not currently accounted for in Luminous
14. SILVAC ernationa ATLAS User s Manual DEVICE SIMULATION SOFTWARE Volume SILVACO International ric November 1998 n Telephone 408 567 1000 FAX 408 496 6080 ATLAS User s Manual Copyright 1998 SILVACO International 4701 Patrick Henry Drive Building 1 Santa Clara CA 95054 Phone 408 567 1000 FAX 408 496 6080 Notice The information contained in this document is subject to change without notice SILVACO International MAKES NO WARRANTY OF ANY KIND WITH REGARD TO THIS MATERIAL INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTY OF FITNESS FOR A PARTICULAR PURPOSE SILVACO International Inc shall not be liable for errors contained herein or for incidental or consequential damages in connection with the furnishing performance or use of this material This document contains proprietary information which is protected by copyright All rights are reserved No part of this document may be photocopied reproduced or translated into another language without the prior written consent of SILVACO International Simulation Standard TCADDrivenCAD Virtual Wafer Fab Analog Alliance Legacy ATHENA ATLAS FASTATLAS ODIN VYPER CRUSADE RESILIENCE DISCOVERY CELEBRITY Production Tools Automation Tools Interactive Tools TonyPlot DeckBuild DevEdit Interpreter ATHENA Interpreter ATLAS Interpreter Circuit Optimizer MaskViews PSTATS SSuprem3 SSuprem4 Elite Optolith Flash Silicides
15. The DeckBuild Command Menu The DeckBuiLD Command Menu can help you to create input files This menu is found under the Commands button on DeckBuiLD s main screen The Commands menu is configured for ATLAS whenever ATLAS is the currently active simulator in DEckBuiLD When ATLAS is active this is indicated in the lower bar of the DEckBuiLD application window and an ATLAS command prompt appears in the DEckBuiLD output section The DeckBuiLD Command Menu gives you access to pop up windows in which you type information When you select the Write button syntactically correct statements are written to the DEckBuiLD text edit region The DeckBuiLD Command Menu does not support all possible ATLAS syntax but aims to cover the most commonly used commands Quick Start for PISCES II Users This section is to provide quickstart instructions for users who may be familiar with the syntax and use of the Stanford University PISCES II program or other device simulators derived from this program The major differences between ATLAS and PISCES II are e all graphics are handled by a separate interactive graphics program TonyPLot The PISCES I graphics commands PLOT 1D PLOT 2D CONTOUR VECTOR etc are not required Using TonyPLot it is no longer necessary to run the device simulator simply to plot or alter graphics e thereis no need to separate individual ATLAS simulations into separate input files Multiple runs of ATLAS are possible in the same inp
16. Trap Implementation into Recombination Models To maintain self consistency it is necessary to take into account that electrons are being emitted or captured by the donor and acceptor like traps Therefore the concentration of carriers will be affected This is accounted for by a modification to the recombination rate in the carrier continuity equations The standard SRH recombination term is modified as follows k m o p R R Rp 3 58 a 1 B 1 where k is the number of donor like traps m is the number of acceptor like traps and the function R is SILVACO International 3 13 ATLAS User s Manual Volume 1 2 pn ni I P MMC M M MM MEE TAUN p n exp up TAUP n DEGEN FACn e a PEGEN FAC 3 59 The electron and hole lifetimes taun and taue are related to the carrier capture cross sections SIGN and stcp through the equations 1 TAUN gt z S SIGN V DENSITY e TAUP 3 61 SIGP Vp DENSITY li Table 3 6 User Specifiable Parameters for Equations 3 59 3 61 Statement Parameter Units TRAP TAUN S TRAP TAUP S The Tra statement activates the model and is used to e Specify the trap type DONOR Or ACCEPTOR e Specify the energy level E LEVEL parameter e Specify the density of the trap centers DENSITY e Specify the degeneracy factor DEGEN FAC e Specify either the cross sections sign and step or the electron and hole lifetimes Taun and TAUP
17. 0 116 y composition 0 03 x composition and the default heavy hole effective mass is a constant and is given by my 0 46 Dielectric Permittivity The default static dielectric constant for lattice matched InGaAsP toInP is given by EnmGaasp 14 6 1 x composition y composition 12 5 1 x composition 1 y composition 13 18 x composition y composition 11 11 x composition 1 y composition Low Field Mobility 5 69 5 70 5 71 5 72 The default low field mobility parameters for electrons and holes for lattice matched InGaAs are given by linear interpolations from the binary compunds GaAs and InP The following formulas are used 1 1 33000 8500 33000 x composition Mot 460 400 460 x composition Ha2 4600 300 4600 x composition Hp 150 100 150 x composition Hao May y composition 1 M 5 H4 Hpo Hpi y composition 1D Hp The Si 1 x Ge x System 5 73 5 74 5 75 5 76 5 77 5 78 Advances in the growth of Silicon and Si 1 x Ge x alloys have allowed the potential for using bandgap engineering to construct heterojunction devices such as HBTs and HEMTs using these materials 5 24 SILVACO International BLAZE BLAZE supports the SiGe material system by providing composition dependent material parameters These parameters are accessed by spedifying the material name SiGe Thefollowing sec
18. 2 Rgirect COPT pn nij 3 224 where the parameter cort is user definable on the MATERIAL statement Note In silicon direct band to band recombination is insignificant for almost every imaginable situation This model should therefore only be used for narrow bandgap materials Auger Recombination Auger recombination occurs through a three partide transition whereby a mobile carrier is either captured or emitted The underlying physics for such processes is unclear and normally a more qualitative understanding is sufficient 3 Standard Auger Model Auger recombination is commonly modeled using the expression 2 2 2 2 Rauger AUGN pn nnij AUGP np pni 3 225 where the model parameters aucn and avcr are user definable on the maTERIAL statement and have the silicon default parameters shown in Table 3 39 This model may be activated with the parameter AUGER Of the MODELS statement Table 3 39 User Specifiable Parameters for Equation 3 225 Statement Parameter Default Units MATERIAL AUGN 8 3e 32 cm s MATERIAL AUGP 1 8e 31 cm s Klaassen s Carrier Concentration Dependent Model The form of the Klaassen Auger recombination model 116 is Rauger Cn pn nnig Cy np Pnie 3 226 3 64 SILVACO International Physics where the Auger coefficients are concentration dependent according to T KAUGDN C P KAUGCN s 3 227 T KAUGDP C n
19. TIKF1 At TIKF2 TIKR1 At TIKR2 TIRB1 At TIRB2 At2 The following parameters are modified when corresponding temperature coefficients are specified At2 At2 10 119 10 120 10 121 regardless of the value of the parameter TEMPLEV BF t BF 1 TBF1 At TBF2 At2 10 122 BR t BR 1 TBR1 At TBR2 Dt2 10 123 VAF t VAF 1 TVAF1 At TVAF2 At2 10 124 VAR t VAR 1 TVARI At TVAR2 At2 10 125 ITF t ITF 1 TITF1 At TITF2 At2 10 126 F t TF 1 TIF1 At F2 At2 10 127 TR t TR 1 TTR1 Dt TTR2 Dt2 10 128 F t NE 1 TNFl At TNF2 At2 10 129 R t NR 1 NR At TNR2 At2 10 130 E t NE 1 El At TNE2 At2 10 131 C t NC 1 INC1 At TNC2 At2 10 132 S t NS 1 INS1 At TNS2 At2 10 133 JE t MJE 1 MJE1 At TMJE2 At2 10 134 JC t MJC 1 TMIC1 At TMJC2 At2 10 135 JS t MJS 1 TMJS1 At TMJS2 At2 10 136 SILVACO International 10 57 ATLAS User s Manual Volume 1 Capacitance Temperature Equations TEMPLEVC 1 CJE t CJE L t MJE 0 0004 Arz 1 CJC t VIC t CIC MIC 0 0004 Ato 3 CIS t CIS Mss 0 0004 ar T 1 VIS where t t t VJE t VIE vy 3 in Je zem n tnom tnom Vi znom Vit f Ts VIC VIC eyes l3 in
20. Uno Un 3 202 14 PETAD SUAM n Uno SSS SSS 3 203 14 ETA ETA p xBETAN _ o BETAN o2BETAN T T PETAN 7 BETAN T EN 3 204 BETAP 1 2BETAP BETAP BETAP Xp OBETAP o2BETAP T T 40 roe TO 3 205 kgu An a 3 206 QqVSATN TAUREL ElL 3 Kgl 3 207 2qVSATP TAUREL HO where uno and upo are the low field carrier mobilities and vsatn and vsarp are the saturated velocities for electrons and holes The parameters vsATN VSATP and BETAN and BETAP are user definable on the MOBILITY Statement The terms TAUREL EL and TAUREL HO are the energy relaxation times for electrons and holes and may be user defined on the maTERTAL statement Setting EvsarmoD 0 with the additional parameter MoBTEM sIMPL allows a simplified form of the above model to be applied This model has the form u Un ME SD s 3 208 ra pos u Hp i EQ 3 209 Ji ap Ty TL where uno and upo are again the low field carrier mobilities and a are as defined above Setting EVSATMOD 1 implements the GaAs carrier temperature dependent mobilty model This model is described in the BLAZE chapter of this manual Setting EvSATMop 2 will apply the simple velocity limiting model based upon the electric field n other words the temperature dependent mobility is turned off and the standard electric field based mobility model is applied SILVACO International 3 57 ATLAS User s Manual Vo
21. for the heterojunction between Materiall and Material2 and AE 5 X2 X3 Pi and AE 93 AE 73 AEG pet for the heterojunction between Material 2 and Material 3 SILVACO International 5 5 ATLAS User s Manual Volume 1 Using the AL cN parameter on the maTERTAL statement Notice that the reference material the material with the smallest bandgap in this case Material2 is located between the two larger bandgap materials Material 1 and Material 3 Let s assign 80 of the bandgap difference between Materiall and Material2 to the conduction band offset for this heterojunction Defining the aLtcn parameter on the varERrAL statement for Material 1 using MATERIAL NAME Materiall ALIGN 0 8 then Internally the affinity of Material 1 is adjusted so that AE equals this value Let s assign 70 of the bandgap difference between Material 3 and Material 2 to the conduction band offset for this heterojunction Defining the aLtcn parameter on the varERrAL statement for Material 3 using MATERIAL NAME Material3 ALIGN 0 70 then Internally the affinity of Material 3 is adjusted so that AE equals this value These new values of electron affinity for Materiall and Material3 will override any electron affinity specification for these materials This has an impact on any calculation where these materials electron affinity is used and must be considered when specifying Schottky barriers contacted to t
22. 00 cc cece eee eee eee eee eeaes 10 40 10 6 Base Width Modulation Parameters 0cce cece eee eee eee eee ene n eee eneeee 10 41 10 7 High Current Beta Degradation Effect Parameters cc cece cece eee eee eens 10 41 10 8 Parasitic Resistor Parameters 0c cece eet e eee eee Hn 10 41 10 9 Junction Capacitor Parameters sess 10 42 10510 Transit Time Parameters soins eae et RN oec cie waa eaae ea ease aaa 10 42 10 11 Temperature Effect Parameters ooooccocccccnccnrr Ie 10 43 10 12 MOSFET Model Parameters ooocooccccccccncn Inn 10 62 SILVACO International xxiii ATLAS User s Manual Volume 1 This page intentionally left blank xxiv SILVACO International Chapter 1 Introduction Overview of ATLAS ATLAS provides general capabilities for physically based two and three dimensional simulation of semiconductor devices ATLAS has a modular architecture that includes the following licensable tools and extensions ATLAS S PISCES BLAZE GIGA TFT LUMINOUS LASER MIXEDMODE QUANTUM SiC DEVICE3D BLAZE3D GIGA3D MIXEDMODE3D TFT3D QUANTUM3D THERMAL3D Supplies general capabilities that are accessed by all the device simulation products Simulates silicon devices Simulates devices fabricated using arbitrary semiconductors including II VI III V and I V I V materials and heterojunction devices Adds the ability to perform non isothermal calculations
23. Base Charge Equations The parameters VAF and VAR are forward and reverse early voltage The parameters IKF and IKR determine the high current BF roll off ISE NI ISC and NC determine the low current BF roll off qb base charge factor 10 33 q l 10 34 ee ee E 1 Voy B Vbe VAF VAR ISE NES ISC gis NF NR dou IER e al PR poro 10 35 eff eff q ae S q 7 10 36 SILVACO International 10 49 ATLAS User s Manual Volume 1 Substrate Current Equations The substrate current is substrate to collector for vertical transistors and substrate to base for lateral transistors jsover NS t is 2 substrate current area ISS are mer 1 10 37 For vertical transistors Vsc NS v isc 188 gre e when v sub sc 7 10 NS vt 10 38 isc 1SS eff when vsc lt 10 ns VT 10 39 For lateral transistors vbs NS v i is e 1 when vbs gt 10 NS vsubt 10 40 ibs 2ISSeff when vbs lt 10 NS vt 10 41 If both IBE and IBC are unspecified ISSeff 1SS area 10 42 Variable Base Resistance Equations MIXEDMODE provides a variable base resistance model that consists of a low current maximum resistance set by RB and a high current minimum resistance set by Rem IRB is the current at which the base resistance falls halfway to its minimum value If RBM is not specified it is defaulted to RB If IRB is not specified RB p RBM rbb RBM A 10 43 If IRB is specified H tan z z where i 1
24. In DC solutions the voltage on each electrode is specified using the SOLVE statement For example the statements SOLVE VGATE SOLVE VGATE 1 0 2 0 first solves a single bias point with 1 0V and then 2 0V on the gate electrode One very important rule in ATLAS is that when the voltage on any electrode is not specified in a given SOLVE statement the value from the last SOLVE statement is assumed In the following case the second solution is for a drain voltage of 1 0V and a gate voltage of 2 0V SOLVE VGATE 2 0 SOLVE VDRAIN 1 0 When the voltage on a particular electrode is never defined on any SOLVE statement that voltage is zero Therefore it is not necessary to explicitly state the voltage on all electrodes on all SOLVE statements n a MOSFET for example if VSUBSTRATE is not specified then Vbs defaults to zero Sweeping The Bias For most applications a sweep of one or more electrodes is usually required The basic DC stepping is inconvenient and a ramped bias should be used To ramp the base voltage from 0 0V to 1 0V with 0 05V steps with a fixed collector voltage of 2 0V the following syntax is used SOLVE VCOLLECTOR 2 0 SOLVE VBASE 0 0 VSTEP 0 05 VFINAL 1 0 NAME base The NAME parameter is required and the electrode name is case sensitive It is up to the user to ensure the initial voltage vs TEP and VFINAL are consistent A badly spec
25. Logicals can be explicitly set to false by preceding them with the symbol Any line beginning with a is ignored These lines are used as comments ATLAS can read up to 256 characters on one line However it is best to spread long input statements over several lines to make the input file more readable The character at the end of a lineindicates continuation The Order of ATLAS Commands The order in which statements occur in an ATLAS input file is important There are five groups of statements and these must occur in the correct order These groups are indicated in Figure 2 3 Each input file must contain these five groups in order Failureto dothis will usually cause an error message and termination of the program but it could lead to incorrect operation of the program For example material parameters or models set in the wrong order may not be used in the calculations The order of statements within the mesh definition structural definition and solution groups is also important Group Statements MESH REGION ELECTRODE DOPING 1 Structure Specification MATERIAL MODELS CONTACT INTERFACE 2 Material Models Specification 3 Numerical Method Selection METHOD LOG SOLVE LOAD SAVE 4 Solution Specification 5 Results Analysis EXTRACT TONYPLOT Figure 2 3 ATLAS Command Groups with the Primary Statements in each Group 2 6 SILVACO International Getting Started with ATLAS
26. Pon exp PATH N for 0 THETA N 3 301 P n 0 foro gt THETA N 3 302 DERE US Pop Coon for 0 gt THETA P 2 p 7 exp PATH P or 8 gt al 3 303 Pap 0 foro lt THETA P 3 304 where PATH N and PATH P are the electon and hole mean free path lengths within the oxide x is the oxide permittivity and E ox is the electric field in the oxide The angle introduces an angle dependence which is based upon the work of Wada 131 His experiments indicate a critical rejection angle THETA N and THETA P between the angle 0 formed between the semiconductor insulator interface and the electric field in the oxide If the angle 0 is less than the rejection angle thenthe electrons are repelled back to the substrate Note The current implementation of the Concannon model for hot carrier injection is that only carriers along the semiconductor insulator interface are significant and as a result the probability P4 is assumed unity This also means that the integration is only applied to those node points along the semiconductor insulator interface Two other parameters of the mopELs statement that may affect the result of the numeric integration are user definable The ENERGY STEP parameter specifies the energy step size in eV used during the numeric integration The default step size is 25 meV The INFINITY parameter sets the upper limit of the integration and specifies ratio of the increment added to the integral divided by the current value of
27. Volume 1 Modes of Operation ATLAS is normally used through the DeckBuiLD run time environment which supports both interactive and batch mode operation We strongly recommend that you always run ATLAS within DECKBUILD In this section we present the basic information you need to run ATLAS in the DECKBUILD environment The VWF INTERACTIVE TooLs manual provides a more detailed description of the features and capabilities of DECKBUILD Interactive Mode With DeckBuild To start ATLAS under DEckBuiLD type deckbuild as at the UNIX system command prompt The command line option as instructs DeckBuiLD to start ATLAS as the default simulator If you want to start from an existing input file you should start DEckBuiLD by typing deckbuild as input filename The run time output shows the execution of each ATLAS command and includes error messages warnings extracted parameters and other important output for evaluating each ATLAS run When ATLAS is run interactively run time output is sent to the output section of the DEckBuiLD application window and can be saved as needed You therefore do not need to save the run time output explicitly However the following command line specifies the name of a file that will be used for storing the run time output deckbuild as input filename outfile output filename In this case the run time output is sent to the output file and to the output section of the DEckBuILD window Batc
28. 17 3 iT 35 1 N 1 932 2 934 1 932 25 2 10 19 9 876 2 N 4 741 5 64 4 267 28 8 16 67 15 47 3 A 11 3 11 7 9 63 28 8 16 67 18 0 Electrode Va V Jn A um Jp A um Jc A um Jt A um gate 0 000e 00 0 000e 00 0 000e 00 0 000e 00 0 000e 00 source 0 000e 00 3 138e 13 1 089e 35 3 138e 13 3 138e 13 drain 1 000e 01 3 139e 13 1 076e 23 3 139e 13 3 139e 13 substrate 0 000e 00 6 469e 19 8 853e 17 8 918e 17 8 918e 17 The top left value proj indicates the initial guess methodology used Here it is the default projection method Alternatives are previous local or init The second value direct indicates the solver type This will either be direct or iterative The first three column headings i j m indicate the iteration numbers of the solution and the solution method i indicates the outer loop iteration number for decoupled solutions j indicates the inner loop number m indicates the solution method by a single letter these are G gummel B block N newton A newton with autonr S coupled Poisson Schrodinger solution The remaining column headings indicate which column lists the XNORM and RHSNORM errors for the equations being solved See the Numerical Methods Chapter for a full description of these errors The values printed in each error column under the hashed line are the logarithm to base 10 of the error Earlier PISCES versions would print the floating point value The values printed above
29. At the start of the solution the optical intensities of each optical source with a positive intensity is printed In addition the available photo current and source photo current are printed See the prior section on Photocurrent for a definition of these two quantities Internal and External Quantum Efficiency The available photocurrent divided by the source photocurrent is a measure of the external quantum efficiency of the detector The calculated terminal current can be divided by the source or available photocurrents is used to evaluate the internal quantum efficiency of the device SILVACO International 8 13 ATLAS User s Manual Volume 1 Obtaining Quantum Efficiency versus Bias The intensities specified in the SOLVE statement apply until another SOLVE statement changes the intensity of the beam Sequences of SOLVE statements can be used to vary the the optical intensity at arbitrary intervals The simple linear ramps of optical intensity can be abbreviated using the LIT STEP and NSTEP parameters of the SOLVE statement The LIT STEP parameter specifies the size of the DC step and NSTEP specifies how many steps are desired Another option for analyzing DC quantum efficiency is to fix the optical intensity and vary bias voltages The bias voltages can be varied in arbitrary discrete steps using several SOLVE statements or in a linear ramp using individual SOLVE statements This is useful for determining th
30. CA KLA NREFD KLA and NREFA KLA are user definable parameters as given in Table 3 27 Table 3 27 User Specifiable Parameters for Equation 3 155 and 3 156 Statement Parameter Default Units MOBILITY CD KLA 0 21 MOBILITY CA KLA 0 50 MOBILITY NREFD KLA 4 0e20 cm MOBILITY NREFA KLA 7 2e20 cm Note When the Klaassen low field mobility is used it should be remembered that it has been calibrated to work along with Klaassen s models for bandgap narrowing AUGER recombination and SRH recombination These models have been described in the carrier recombination section of this manual Inversion Layer Mobility Models Overview To obtain accurate results for MOSFET simulations it is necessary to account for the mobility degradation that occurs inside inversion layers The degradation normally occurs as a result of the substantially higher surface scattering near the semiconductor to insulator interface This effect is handled within ATLAS by three distinct methods asurface degradation model surrmoB atransverse electric field model sHIRAHATA e specific inversion layer mobility models cvr YAMAGUCHI and TASCH The cvt YAMAGUCHI and rascu models are designed as stand alone models which incorporate all the effects required for simulating the carrier mobility SILVACO International 3 43 ATLAS User s Manual Volume 1 The Lombardi CVT Model The inversion layer model from L
31. Example Qinv 2 5 7 O bjtmod1 20 R Resistor Syntax Rxxx n n value transient parameters Description Rxxx specifies the name of the resistor element It must begin with an R n n arethe positive and negative terminal node numbers value is the resistance in ohms transient parameters are described on page 10 22 Note Unlike the traditional SPICE program transient parameters are acceptable for resistor elements This allows simulation of different kinds of time dependent resistors and switches in a very simple way Example R12 4 5 100k T Lossless transmission line Syntax Txxx n1 n2 n3 n4 Z0 val TD val Description 10 18 SILVACO International MIXEDMODE Txxx specifies the name of the transmission line element It must begin with a T n1 n2 arethe nodes at port 1 n3 n4 are the nodes at port 2 ZO isthe characteristic impedance TD is the transmission delay Example T1102 0Z0 50 TD 10ns V Independent voltage source Syntax Vxxx n n value ac parameters transient parameters Description Vxxx specifies the name of the independent voltage source It must begin with a V n n are the positive and negative terminal node numbers ac parameters are described on page 10 21 value specifies the DC value of the source in units of volts transient parameters are described on page 10 22 Example VCC 5 0 10 Control and Analysis Statements BEGIN BEGIN indicates th
32. Heterojunction Charge Transport is covered next and includes the details of how BLAZE modifies the basic transport models to simulate heterodevices A section on the physical models unique to BLAZE is also included Detailed information about the material systems encountered in heterojunction simulation is covered in the subsequent maTERIALS section This includes the relationships bewteen the compound elemental concentrations and bandgap dielectric constant low field mobility and other important material and transport parameters Defaults for these parameters can be found in the Appendix B Finally the Simulating Heterojunction Devices with BLAZE section details a step by step approach to defining materials and models for simulation of heterojunction devices with BLAZE Basic Heterojunction Definitions Figure 5 1 Band Diagram of p n heterojunction Figure 5 1 shows the band diagrams and band parameters for a basic p n heterojunction device under equilibrium conditions This diagram illustrates two materials with different bandgaps and electron affinities and a Schottky barrier in contact to the n type material SILVACO International 5 1 ATLAS User s Manual Volume 1 Referring to figure 5 1 E x E x and E x are the spacially dependent conduction band valence band and intrinsic energy levels respectively Eg and E arethe Fermi and Vacuum level energies
33. In this case the parameters numa and NUMD DEFECTS Statement correspond to the number of acceptor and donor energy level intervals used in the integral Discrete Defects If CONTINUOUS is not specified on the DEFEcTs statement the equation is modeled using discrete energy levels The integrals terms in Equations 7 6 7 7 7 11 7 13 and 7 14 are replaced by summations which run over the number of discrete energy levels uma and NumD The acceptor and donor density of states terms are integrated separately For example the equation for the electron trap concentration Equation 7 6 is replaced by NUMA 00 4 co nr Y f Enp enGD dE f Esnp g6LE dE 7 17 i 0 oo SS SILVACO International 1 5 ATLAS User s Manual Volume 1 Table 7 3 Additional Parameters for the DEFECTS Statement Statement Parameter Default Units DEFEC FAST FALSE DEFEC CONTINUOUS FALSE DEFEC NUMA 12 DEFEC NUMD 12 Syntax for a typical defect states definition is given below DEFECTS NTA 1 12E21 NTD 4 E20 WTA 0 025 WID 0 05 NGA 5 E17 NGD 1 5E18 EGA 0 4 EGD 0 4 GA 0 1 WGD 0 1 SIGTAE 1 E 16 SIGTAH 1 E 14 SIGTDE 1 E 14 SIGIDH 1 E 16 SIGGAE 1 E 16 SIGGAH 1 E 14 SIGGDE 1 E 14 SIGGDH 1 E 16 Figure 7 1 shows how the syntax is used to define the peak
34. Note It is extremely important that no section of the origin plane of the beam intersects or is inside the simulation grid otherwise incorrect results will be obtained This is important to check in cases when ANGLE is not 90 or 270 Reflections The user can also specify whether to ignore the first reflection using the FRONT REFL and the backside and sidewall reflection using the BACK REFL It is useful toturn on the backside reflections for devices which use a back side reflector to improve collection efficiency The number of reflections solved is set by the REFLECTS parameter Typically BACK REFL should be used if the structure simulated is equivalent to the complete photodetector geometry as in a descrete device If the simulation structure is a section of a larger substrate as in CCD simulation then BACK REFL should not be used Since reflection and transmission coefficients are used in the ray trace for arbitrary angles of incidence the user should also specify the polarization using the POLARIZATION parameter SILVACO International 8 9 ATLAS User s Manual Volume 1 In complex structures it is useful to limit the ray tracing to trace only those rays with significant optical power The parameter MIN POWER is used to terminate ray traces that drop below MIN POWER optical source power Monochromatic or Multispectral Sources The optical source can be either monochromatic or multispectral For monochromatic sourc
35. SOLVE Bl 1 SILVACO International 8 15 ATLAS User s Manual Volume 1 Inthis statement it is assumed the source B1 has been already defined and the intensity is that which is expected in the actual device When a solution is obtained the terminal currents represent the short circuit current The open circuit voltage is obtained by defining one or more of the contacts as current controlled This is done using the CONTACT statement For example CONTACT NAME anode CURRENT defines that electrode number 1 is a current controlled electrode The open circuit voltage is then obtained by setting the current at this contact to zero and obtaining a solution The following statement illustrates this SOLVE I1 20 0 Bl 1 Once the solution is obtained the bias associated with 11 is the open circuit voltage Simulating LEDs LUMINOUS used with BLAZE can be used to extract certain parameters associated with light emitting devices Extraction of the integrated radiative recombination in the device provides an estimate of luminous intensity and extraction of integrated total recombination rate allows an estimate of luminous efficiency To calculate luminous efficiency all recombination models should be enabled using the appropriate MODEL and MATERIAL statements The device should be biased to its operating point The MEASURE statement should be used to obtain the integrated radiative recombination rate using the U RADIATIVE parameter The
36. Second order temp coeffi cient for BR 1 deg TIKF1 First order temp coefficient for IKF 1 deg SILVACO International 10 43 ATLAS User s Manual Volume 1 Table 10 11 Temperature Effect Parameters Parameters Description Units Default Area TIKF2 Second order temp coeffi 1 deg 0 cient for IKF TIKR1 First order temp coefficient 1 deg 0 for IKR TIKR2 Second order temp coeffi 1 deg 0 cient for IKRr TIRB1 First order temp coefficient 1 deg for IRB TIRB2 Second order temp coeffi 1 deg 0 cient for IRB TISCI First order temp coefficient 1 deg 0 for ISC TEMPLEV 3 enables TISCI TISC2 Second order temp coeffi 1 deg 0 cient for ISC TEMPLEV 3 enables ISC2 TIS1 First order temp coefficient 1 deg 0 for IS or IBE and IBC TEM PLEV 3 enables TIS1 TIS2 Second order temp coeffi 1 deg 0 cient For IS or IBE or IBC IEMPLEV 3 enables IS2 TISE1 First order temp coefficient 1 deg 0 for ISE TEMPLEV 3 enables TEISEL TISE2 Second order temp coeffi 1 deg 0 cient for SE TEMPLEV 3 enables ISE2 TISS1 First order temp coefficient 1 deg 0 for ISS TEMPLEV 3 enables TISS1 TISS2 Second order temp coeffi 1 deg 0 cient for ISS TEMPLEV 3 enables ISS2
37. The main problem is that the meshes required to resolve 2 D doping profiles and curved junctions are quite complicated and simple rectangular meshes require an excessive number of nodes to resolve such profiles If a device structure only includes regions of uniform doping there is usually no need to regrid However when realistic 2 D doping profiles are present a regrid may be necessary Note The recommended solution for defining complex mesh structures for ATLAS is to use the standalone program DEVEDIT Regrid On Doping ATLAS indudes a regridding capability that generates a fine mesh only in a localized region You specify a quantity on which the regrid is to be performed the mesh is then refined in regions wherethe specified quantity varies rapidly Whenever a specified quantity usually doping changes quickly the regridding will automatically grade the mesh accordingly A regrid on doping can be obtained before any solutions are obtained This can be accomplished with the statement REGRID LOGARITHM DOPING RATIO 2 SMOOTH KEY 4 DOPFILE filenamel OUTFILE filename2 This statement must be used after the MESH REGION MATERIAL ELECTRODE and DOPING statements described previously The effects of this REGRID statement on a simple Diode structure are shown in Figure 2 6 In this statement regridding will be done in such a way that the new mesh will resolve doping profiles to two orders of magnitude in change
38. Thus it is not a good idea for the user to place a layer of material explicitly into the simulated device structure to simulate an AR coating With the addition of this layer tuminous will not properly simulate the reflectivity of the layer In addition this will introduce many additional nodes into the mesh that will most likely have essentially no effect on the electrical performance of the device Instead there are two models that can be used to model the effects of the AR coating on the reflectivity of the device First there is a simple model for single layer AR coatings assuming no absorption in the AR coating This case is illustrated in the following figure Here n1 is the index of refraction in ambient outside the device n2 is the index of refraction in the device lambda is the source wavelength AR INDEX is the user specified index of refraction of the AR coating AR THICK is the user defined thickness of the AR coating In this case the reflection coefficient of the coating is given by Equation 8 15 where theta is defined below 2 2 pu AR INDEX n n5 cos 0 n n AR INDEx sin 0 2 2 232 AR INDEX n n5 cos 0 nyny an roux jin 0 2T AR INDEX AR THICK COS 0 I ee 8 10 The parameters AR INDEX and AR THICK are defined in the INTERFACE statement and is the angle of incidence The location of the interface must also be specified by the P1 x P2 x and P2 Y para
39. are the positive and negative terminal node numbers file name specifies the name of the text file that contains C source code for a user defined function that describes element behavior This file can contain more than one function description function name specifies the name of the function from the file Example B1 2 3 infile ud c function rc Note More detailed documentation on the user defined function is at the end of this chapter C Capacitor Syntax Cxxx n n value Description Cxxx specifies the name of a capacitor element It must begin with a C n n are the positive and negative terminal node numbers value is the capacitance in farads Example Cload 3 0 1pF D Diode Syntax Dxxx n n mname area Description Dxxx specifies the name of the diode element It must begin with a D n n are the positive and negative terminal node numbers mname is the diode model name It must refer to a diode model SILVACO International 10 13 ATLAS User s Manual Volume 1 area is the area factor The default is 1 0 Example D1 23 dmodel1 2 e3 E Linear voltage controlled source Syntax Exxx n n nc nc gain Description Exxx specifies the name of the linear voltage controlled voltage source It must begin with an E n n arethe positive and negative terminal node numbers A positive current flows from the node n through the source to the node n nc nc arethe positi
40. contributions from all mobile and fixed charges including electrons holes and ionized impurities The electric field is obtained from the gradient of the potential gt Carrier Continuity Equations The continuity equations for electrons and holes are defined by the equations A divi n Gs Re 3 3 d lom Se E gd p Gp Rp 3 4 gt gt where n and p are the electron and hole concentration J p and J p are the electron and hole current densities G and G are the generation rates for electrons and holes Ry and Ry are the recombination rates for electrons and holes and q is the magnitude of the charge on an electron SILVACO International 3 1 ATLAS User s Manual Volume 1 By default ATLAS includes both Equations 3 3 and 3 4 However in some circumstances it is sufficient to solve only one carrier continuity equation The specification of which continuity equations are to be solved is performed on the metHop statement by turning off any equation that is not to be solved The syntax ELECTRONS Or HOLES turns off the electron continuity equation and the hole continuity equation respectively The Transport Equations Equations 3 1 3 3 and 3 4 provide the general framework for device simulation However further gt gt secondary equations are needed to specify particular physical models for J nd p Gy Rn Gp and Ry The current density equations or charge transport models are usually obta
41. modelled as a sheet of charge at the interface and therefore is controlled by the interface boundary condition Interface traps and bulk traps will add space charge directly into the right hand side of Poisson s equation This section describes the definition of bulk trap states and the implementation of these bulk trap states into ATLAS for both steady state and transient conditions Semiconductor flaws have two possible states which are called empty and full When empty a flaw has a particular cross section for capturing an electron A flaw can only either emit or capture an electron When the charge on the centre has been changed by q by addition of an electron a flaw is full and has a new cross section for hole capture Two basic types of trap have been found to exist donor like electron traps and acceptor like traps hole traps The charge contained within each type of trap will depend upon whether or not an electron or hole fills thetrap A donor like trap similiar to ionised donor impurites Np are positively charged and therefore can only capture an electron This means that donor like traps are positive when empty of an electron but are neutral when filled An acceptor like trap similiar to ionised acceptor impurities Na are negatively charged so therefore they may only emit an electron Therefore acceptor like traps are negative when filled but are neutral when empty In a semiconductor there is a position of the Fermi level c
42. the parameter onefileonly can be added to the command The file lt filename gt sta will be over written at each solution point 2 42 SILVACO International Getting Started with ATLAS Structure files can be very large 1 2 MB depending on the mesh density and quantities saved It is recommended that unwanted structure files are deleted If many solution files have been written from a long simulation it is often confusing to find out which solution file belongs to which bias point or transient time A utility has been written by Silvaco to allow users to see the biasing conditions of each file To obtain this utility check the Silvaco internet web site or contact your local Silvaco support engineer The solution files should be plotted in TonyPLot Using ToNYPLor it is possible to create 2D contour plots and 1D cutlines To find out the bias of any solution file in ToNYPLor select the plot and press b on the keyboard Interpreting Contour Plots Most quantities saved in the solution files are never evaluated at the node points during solutions rather at the center of the side of each triangle in the mesh Values of quantities at each node are derived from averaging the values from the sides of triangles connected to that node The weighting method used to do the averaging can be selected by the user with options on the OUTPUT statement It is possible that for some meshes smoother contour plots can be obtained by choosing a non
43. vd id fes i Cathode Figure 10 3 Diode Equivalent Circuit Equations for the diode current id equations account for all the fundamental DC effects in the diode Capacitance effects are assumed to be separate from the id equations and are modeled independently The DC characteristics of the junction diode are determined by the parameters IS N and RS Charge storage effects are modeled by the transit time parameter rr and a nonlinear depletion layer capacitance is determined by the parameters co vg and m The reverse saturation current rs emission coefficient n and ohmic resistance rs are normally obtained from DC measurements of the forward biased diode characteristics N is determined from the slope of the diode characteristic in the ideal region In most cases the emission coefficient has a value of unity In practice at high levels of bias the diode current deviates from the ideal exponential characteristic This deviation is due to the presence of ohmic resistance in the diode and high level injection effects The deviation of the actual diode voltage from the ideal exponential characteristic at a specific current determines the value of RS In practice RS is estimated at several values of id and averaged since the value of RS can be dependent on the diode current Table 10 1 Diode DC Parameters Parameter Description Units Default x Area IS Saturation current A 1 10 14 RS Ohmic resistance ohm 1 10
44. 00ooooococcocrrran nh 3 60 Shockley Read Hall SRH Recombination 0 cece teen eae 3 60 SRH Concentrarion Dependent Lifetime Model 0 cece cece cece mnn 3 61 Klaassen s Concentration Dependent Lifetime Model 3 61 Trap Assisted Tunneling css odas dao cesis co a C e e ER Ode et 3 62 Radiative Direct B eC ODTDITId UD t urbs ch tt eden Mena debe P rte ir herr ob thi d est 3 64 Auger Recombination c5 rios ce decies d ss a ts tf eue ls e ld oil rus 3 64 Surface SCOTI QUOI acd cute pede utto ea ove rib ted bee pie ded ou p 3 65 Impact lonizatiori Models 54 vases aa a a ie a ae OCA EROR CECI 38 ee LC Ra 3 66 OVerVIBW s pce ri tala Ob RE EE REN URS KR NO A aa Rav lus de 3 66 Lotabeleciic Field Models oss oe ecco aote GE Srt tet ba ua M BST HERO Gre SERA 3 67 Selberherr s Impact Ionization Model ccc cece cece Hmm 3 67 Grants Impactlonizaton Modeli cues ota adest ater acie ae dade rs Ree ra nn 3 69 X SILVACO International Table of Contents Non Local Energy Dependent Models 0c cece e eee e eee eee nh 3 70 CrowellSze mpactlonizaton Model ese auti RERO Y oen PR b Aa bees iia 3 69 Toyabe Impact Ionization Model viste ex RR vox y er Eee Rd ees Ra Re RR 3 71 Concamnons Impact Ionization Model ta aet ee ha t dulce did 3 72 Band to Band Tunneling csie irere tane rit AAA 3 74 Gate Current Models ia ek tex dk euixb ed mes er ix rer xr vede nix RMUPe I a Eds 3 75 ONE 27 daa srta a mated RODA dass
45. 3 8 3 4 User Specifiable Parameters for Equations 3 121 and 3 122 cece eee eee eee eens 3 10 3 5 User Specifiable Parameters for Equations 3 51 to 3 57 cc cece cece eee eee nae 3 13 3 6 User Specifiable Parameters for Equations 3 59 3 61 cece eects 3 14 3 7 User Specifiable Parameters for Trap Assisted Tunneling Model sese 3 16 3 8 User Specifiable Parameters for Equations 3 95 and 3 96 iiuuslsesuueessseeese 3 21 3 9 User Specifiable Parameters for Variable Energy Relaxation Time 0 o oomomoo 3 21 3 10 User Specifiable Parameters for Equation 3 107 ccc cece cece teen eens 3 24 3 11 User Specifiable Parameters for Equations 3 108 to 3 109 0 ccc eee e eee eee eens 3 24 3 12 User Specifiable Parameters for Equations 3 110 to 3 111 0 0 cee ees 3 25 3 13 User Specifiable Parameters for Equation 3 114 2 0 cece eee e eee eee eee eens 3 25 3 14 User Specifiable Parameters for Figure 3 1 2 0 0 cece cece eee eee eee eee 3 28 3 15 User Specifiable Parameters for Equation 3 117 2 0 cece eee eee eee eee eens 3 30 3 16 User Specifiable Parameters for the Constant Low Field Mobility Model 3 32 3 17 Mobility of Electrtons and Holes in Silicon at T 300K oooooocooorrrrar 3 32 3 18 User Specifiable Parameters for Equations 3 121 and 3 122 cece eee eee eee eens 3 35 3 19 User Specifiable Parameters for Equations 3 123 a
46. 5 38 the following expressions for current densities can be obtained kT y kT a c L Jn kT u Yn aun y wu t B t a n 5 39 gt kT X E kT N Jp kT u Vn v Iny Eg In 5 40 p LH quyp V q Yp q q D SILVACO International 5 13 ATLAS User s Manual Volume 1 The Thermionic Emission Transport Model It is possible to activate an alternative current density expression Wu and Yang 72 which takes into account thermionic emission dominated current in abrupt heterojunctions This equation applies only at the node points along the interface of the heterojunction and takes the form T q kTi 4 on n ae Peer a Nnm m exp 5 41 2 3 m where 4 is the current density from the region to the region The and regions are defined such that x is less than X The variable n is a coefficient which accounts for quantum mechanical reflection and tranmission at the interface and m 5 42 where m is the effective electron mass in the region m is the effective electron mass in the region Expression 5 41 can be rewritten in the following form gt do 2 n n X X Jn A e Ti exp kT 5 43 Yn Nc C b where A S pu ALT x and A An is the effective Richardson constant which can be specified from input language in the MATERIAL Statement An analagous expression is used for holes The Physical Models In Cha
47. 6496 goes to the valence band If for example the band gap difference A Eg for this material system is 0 6 eV then the conduction band barrier height for this example is 0 216 eV and the valence band barrier height it 0 384 ev For heterojunction devices the transport models may be different for each material These models and their coefficients may be specified for each material using the mopEL statement Refer to the section Specifying Physical Models for a description of this option Specifying Interface Properties The INTERFACE Statement is used to define the interface charge density and surface recombination velocity at interfaces between semiconductors and insulators For example the statement INTERFACE QF 3e10 specifies that all interfaces between semiconductors and insulators have a fixed charge of 3 1019 cm In many cases the interface of interest is restricted to a specific region This can be accomplished with thex MIN X MAX Y MIN and Y MAX parameters on the INTERFACE Statement These parameters define a rectangle within which the interface properties apply The statement INTERFACE QF 23e10 X MIN 1 0 X MAX 2 Y MIN 0 0 Y MAX 0 5 restricts the interface charge to the semiconductor insulator boundary within the specified rectangle In addition to fixed charge surface recombination velocity and thermionic emission are enabled and defined with the INTERFACE Statement
48. A detailed description of the INTERFACE statement is given in the Statements Chapter Specifying Physical Models Physical models are specified using the MopELS and impact statements Parameters for these models appear on many statements including MODELS IMPACT MOBILITY and MATERIAL The physical models can be grouped into five classes mobility recombination carrier statistics impact ionization and tunneling The Physics chapter contains details of each model Tables 2 1 through 2 5 give summary descriptions and recommendations on the use of each model Table 2 6 is a guide for compatibility between models All models with the exception of impact ionization are specified on the MODELS statement Impact ionization is specified on the rmpact statement The statement MODELS CONMOB FLDMOB SRH FERMIDIRAC IMPACT SELB SILVACO International 2 21 ATLAS User s Manual Volume 1 specifies that the standard concentration dependent mobility parallel field mobility Schockley Read Hall recombination with fixed carrier lifetimes Fermi Dirac statistics and Selberherr impact ionization models should be used ATLAS also provides an easy method for selecting the correct models for various technologies The MOS BIP PROGRAM and ERASE parameters for the mMopELs statement configure a basic set of mobility recombination carrier statistics and tunneling models The parameters Mos and BIP enable the mo
49. Appendix B SILVACO International 5 17 ATLAS User s Manual Volume 1 Material Dependent Physical Models GaAs Bandgap Narrowing Following Lundstrom 71 the bandgap narrowing effects are important only for p type regions By default BLAZE uses the bandgap narrowing values shown in Table 5 4 Table 5 4 Default Bandgap Narrowing Values Concentration Bandgap Narrowing cm meV 1 0 1018 31 0 2 0 1018 36 0 4 0 1018 44 2 6 0 1018 48 5 8 0 1018 blu 1 0 1012 54 3 2 0 101 61 1 4 0 1012 64 4 6 0 10 9 61 9 8 0 1012 56 9 1 0 1029 53 2 2 0 1029 18 0 5 18 SILVACO International BLAZE Low Field Mobilty The mobility in GaAs can be made concentration dependent by setting the conmop parameter of the MODEL statement In this model mobility is interpolated from the values in Table 5 5 Table 5 5 Default Concentration Dependent Mobility for GaAs Mobility in GaAs cm v s Concentration cm 3 Electrons Holes 1 0 1014 8000 0 390 0 2 0 1014 7718 0 380 0 4 0 1014 7445 0 375 0 6 0 1074 7290 0 360 0 8 0 101 7182 0 350 0 1 0 1015 7300 0 340 0 or pq g 6847 0 335 0 4 0 1015 6422 0 320 0 6 0 101 6185 0 31540 8 0 1015 6023 0 305 0 pete 5900 0 302 0 rama ee 5474 0 300 0 LG OE SING aa 5079 0 285 0 6 0 1019 4861 0 ZT0S0 8 0 1016 4712 0 245 0 1 0 1017 4600 0 240 0 2 0 1017 3874 0 2
50. Chaltje ws opp UA crm a to Re RA Pc o e ni auton sana es 4 4 Single Cartier QUIONS desde cos ifte ds erint p ex d YT adr e s or Mao bl e etg 4 4 Energy Balance Solutions duae a RC a CARRETERA 4 4 ESMAS cir 4 4 Simulating Silicon Bipolar Devices 0oooooooccoccorco rar 4 5 Physical Models 305 B T5 oer ta dao 4 5 Meshing Issues for BINS iere hod ol ted Ede eL he Coo A E oa pA E D EAS 4 5 BJ TElecrode Naming v sue visos eke CER RARE SEA EXER ou MAL GM ea awa ta eee cares 4 5 Did Base BENS dana stad iia lene ad VER Ete boa de Ida s saie di ander AS 4 5 Creating an Open Circuit Electrode iiis sk Rhe RR RR a ERE 4 6 S lution Techniques for B TS asi med EA A A c 4 6 Simulating Non Volatile Memory Technologies EEPROMs FLASH Memories oaaae 4 6 Defining Floating AAA O dd a tele rae dre Ar Mira d 4 6 Gate CurrentModelS decumas uod meet tice uito sh pau id Vade SAC T dtt 4 Gate Current Assignment NEARFLG ccc ccc cece e nett cnet eens teens tennees 4 7 Siriuldtiig SOL Technolgies saat cote d Ge acid dic ders Rao wae dade o9 cada Cb Rea dart Rr cioe RUE 4 8 Meshing in SOI devices From uos us cod t ioo val post c dd tots banat de Dod etd 4 8 Physical Models TOF SOT S2 pavet tae o b e tO ti pU INDE de 4 8 SILVACO International Xi ATLAS User s Manual Volume 1 Numerical Methods for SOL s iunc RR A annie RC RR e 4 9 SOP MVSICd P henomena corro ds obe Dated Ur oS Lebens s hd 4 9 Chapter 5 BLAZE corone s AX siete VER ori
51. Equations 3 133 and 3 134 Statement Parameter Default Units MOBILITY MUMAXP KLA 470 5 cm V s MOBILITY THETAN KLA 2 285 MOBILITY THETAP KLA 2 247 Theimpurity carrier scattering components of the total mobility Eqs 3 131 and 3 132 are given by 3 135 MnpAP 7 MN n N Nacs NREF1N KLA ALPHAIN KLA er Te o tine nsc eff nsc eff N nsc RE IRKLAR PHAIP KLA N n p u mn 3 136 psc Be N u U PDAP N p psc eff psc eff where uy and up are the impurity scattering components of mobility and are given by Eq s 3 137 and 3 138 unc and upc are the carrier carrier scattering component of mobility given by Eqs 3 139 amd 3 140 Nnsc and N psc are given by Eqs 3 141 and 3 142 and N sc er and N psc er are given by Eqs 3 143 and 3 144 The parameters NREF1N KLA NREF1P KLA ALPHAIN KLA and ALPHA1P KLA are user definable model parameters which can be specified as in Table 3 22 Table 3 22 User Specifiable Parameters for Equation2 3 135 and 3 136 Statement Parameter Default Units MOBILITY ALPHAIN KLA 0 68 MOBILITY ALPHAIP KLA 0 719 MOBILITY NREFIN KLA 9 68e16 cm MOBILITY NREFIP KLA 2 23e17 cm The impurity scattering components uy n and Uy p are given by B MUMAXN KLA TL 3ALPHAIN KLA 1 5 HN n HUHAXN KLA MUMINN KER 300 MUMAXP KLA TE 3ALPHA1P KLA 1 5 ies HN p 7 MUMAXP RLA MUMINFKCA 300 where T is the temperature in
52. ITF1 First order temp coefficient 1 deg 0 for ITF ITF2 Second order temp coeffi 1 deg 0 cient for ITF EMPLEV Temperature equation level 0 selector 10 44 SILVACO International MIXEDMODE Table 10 11 Temperature Effect Parameters Parameters Description Units Default Area TEMPLEVC Temperature equation level 0 selector for junction capaci tances and contact potentials TMJC1 First order temp coefficient 1 deg for MJC TMJC2 Second order temp coeffi 1 deg 0 cient for MJC JE1 First order temp coefficient 1 deg 0 for MJE TMJE2 Second order temp coeffi 1 deg 0 cient for MJE TMJS1 First order temp coefficient 1 deg 0 for MJS TMJS2 Second order temp coeffi 1 deg 0 cient for MJS TNC1 First order temp coefficient 1 deg 0 for NC TNC2 Second order temp coeffi 1 deg 0 cient for NC El First order temp coefficient 1 deg 0 for NE TNE2 Second order temp coeffi 1 deg 0 cient for NE TNF1 First order temp coefficient 1 deg 0 for NF TNF2 Second order temp coeffi 1 deg 0 cient for NF TNR1 First order temp coefficient 1 deg 0 for NR TNR2 Second order temp coeffi 1 deg 0 cient for NR TNS1 First order temp coefficient 1 deg 0 for NS TNS2 Second order temp coeffi 1 deg 0 cient for NS TRB1 First order temp coefficient 1 deg 0 for RB T
53. Important Parameters Of the METHOD Statement It is possible to alter all of the parameters relevant to the numerical solution process This is not recommended unless you have expert knowledge of the numerical algorithms All of these parameters have been assigned optimal values for most solution conditions It is beyond the scope of this chapter to give more details Further information can be found in the Numerical Methods Chapter Two parameters however are worth noting at this stage 1 CLIMIT Or CLIM DD specify minimal values of concentrations to be resolved by the solver Sometimes it can be necessary to reduce this valueto aid solutions of breakdown characteristics A value of CLIMIT 1e 4 is recommended for all simulations of breakdown where the pre breakdown current is small cLIM DD is equivalent to CLIMIT but uses the more convienient units of cm for the critical concentration 2 pvmax controls the maximum update of potential per iteration of Newton s method The default corresponds to 1V For power devices requiring large voltages an increased value of DVMAX might be needed DVMAX 1e8 can improve the speed of high voltage bias ramps 3 CLIM EB controls the cut off carrier concentration below which the program will not consider the error in the carrier temperature This is applied in energy balance simulations to avoid excessive calculations of the carrier temperature at locations in the structure where the carrier concentration is
54. KSRHCP KSRHGN and KSRHGP are given in Table 3 37 These values may be modified on the maTERIAL statement Table 3 37 User Specifiable Parameters for Equations 3 215 to 3 216 Statement Parameter Default Units ATERIAL KSRHTN 2 5e 3 S ATERIAL KSRHTP 256 3 S ATERIAL KSRHCN 3 0e 13 cm s ATERIAL KSRHCP 11 76e 13 cm s ATERIAL KSRHGN dz ATERIAL KSRHGP 0 57 Trap Assisted Tunneling In a strong electric field electrons can tunnel through the bandgap via trap states This trap assisted tunneling mechanism which is enables by specifying TRAP TUNNEL on the mopELs statement is accounted for by modifying the Schockley Read H all recombination model 2 R 1 3 217 SRH TAUPO n ETRAP Y TAUNO 4 _ETRAP aca NieexP RT TT P igap Ha where I is the field effect enhancement functions for electrons and Tp is the corresponding function for holes If the concentration dependent lifetime is used the terms TAUNO and TAUPO are replaced by tp and tp as in equations 3 213 and 3 214 Two different enhancement functions are used one corresponding to low values of electric field and the other to high field values 67 2AE The low field case corresponds to K p gt pr where 8x J2 MASS TUNNEL m AE p np S3qhE 3 218 and q is the electronic charge h is Planck s constant mg is the rest mass of an electron and
55. MASS TUNNEL is the effective mass The parameter Mass TUNNEL may be set on the mopELs statement ThetermAE is given by Ecc ErSEm AE A Jb Sen 3 219 and 3 62 SILVACO International Physics ELSE Jere 3 220 BC EsES ESSE AE where Ec is the conduction band edge Ey is the valence band edge Eg is the electron quasi F ermi level Eg is the hole quasi F ermi level and Ex is the energy of the trap level The electron and hole field enhancement factors then become 25 E exp E E 3 221 where om a MASS TUNNEL m kT gt Er n and k is Boltzmann s constant and T is the lattice temperature and is the electric field 3 222 2AE p p At high values of electric field where Kp p lt SRT the enhancement terms becomes AEn p T b a b Ih p laa D xp erfd 3 223 where Table 3 38 User Specifiable Parameters for Equations 3 218 and 3 222 Statement Parameter Default Units MATERIAL MASS TUNNEL 02 25 SILVACO International 3 63 ATLAS User s Manual Volume 1 Radiative Direct Recombination Photon transitions occur when a direct transition from the valence band to the conduction band is possible This process normally only occurs in narrow bandgap materials such as GaAs The radiative or direct recombination model may be activated with the parameter opera on the wopErs statement This model has the form
56. N AALPHN CVT l cRN cvT Lp MUON CVT ex EET MUIN CVT csN cvr BETAN CVT 1 gt 3 162 3 44 SILVACO International Physics liiis MUOP CVTexp T GAMP CVT UR _ MUMAXP cvT 556 MUOP CVT N N AALPHP CVT 1 4 egp cvr MU1P CVT i CSP CVT BETAP CVT AA N 3 163 Where N is thetotal density of impurities and T is the temperature in degrees Kelvin Table 3 28 User Specifiable Parameters for Equations 3 158 to 3 163 Statement Parameter Default Units OBILITY BN CVT 4 75 107 cm s OBILITY BP CVT 9 925 10 cm s OBILITY CN CVT 1 74 105 OBILITY CP CVT 8 842 10 OBILITY TAUN CVT 0 125 unitless OBILITY TAUP CVT 0 0317 unitless OBILITY GAMN CVT 2 5 unitless OBILITY GAMP CVT 2 2 unitless OBILITY UON CVT 52 2 cm V s OBILITY UOP CVT 44 9 c V s OBILITY ULN CVT 43 4 cm V s OBILITY U1P CVT 29 0 cm2 V s OBILITY UMAXN CVT 1417 0 cm V s OBILITY UMAXP CVT 470 5 cm V s OBILITY CRN CVT 9 68 1019 Gn OBILITY CRP CVT 2 23 1017 cm OBILITY CSN CVT 3 43 102 9 cm OBILITY CSP CVT 6 10 102 cm OBILITY ALPHN CVT 0 680 SILVACO International 3 45 ATLAS User s Manual Volume 1 Table 3 28 User Specifiable Parameters for Equations 3 158 to 3 163 Statement Parameter Default Units OBILITY ALPHP CV
57. O E BALANCE EB OK O OK NO OK OK OK OK O OK 2 Key To Table Entries MODEL ABBREVIATION The model that supercedes when a combination is specified In some cases but not all a warning message is issued when a model is ignored OK This combination is allowed NO This combination is not allowed NOTES Uses internal model similar to FLDMOB 2 When models including a parallel electric field dependence are used with energy balance the electric field term is replaced by a function of carrier temperature Using The C Interpreter To Specify Models One of the ATLAS products is a C language interpreter that allows you to specify many of the models used by ATLAS To use these functions the user must implement the model in C as equations in a special file called an ATLAS lib file The default ATLAS template file can be accessed by typing atlas T filename at the UNIX command prompt This creates a default template file with the name specified by the filename parameter A listing of the default C I nterpreter functions can be found in the description section for the various ATLAS statements such as MAT ERIALS and MOBILITY Tousethe interpreter functions the corresponding parameters must be given on the statements with the name of the C language file containing the model given as the parameter value For example the statement MATERIAL NAMI E Silicon F MUNSAT munsat
58. October 30 1996 e Edition 5 April 30 1997 e Edition 6 November 1998 SILVACO International V This page intentionally left blank Table of Contents Chapter 1 INMOQUCUON Sack rex E EETINU E A AA d vanes 1 1 Overview Ol ATLAS ii iii oiia e Ip eie uo ARA AAA inte p Cr aia yi ae dp aloe 1 1 Organization Of This Manual 5c ore tee ry ci b x rh a x EAT A 1 3 Technical Support oci i vu xn E e Beko ARA AAA wir FUE TL Fx era x ede 1 3 Features And Capabilities of ATLAS 1 oreet eorr Iw A ex Re Ra 14 A Comprehensive Setof Models ovr vice descent o De Red OPE Eb 14 Fully Integrated Capabilities ias eres wb Cr ree EM Aere Y ai aay O Rte ay ate OU D Orr aw 14 Sophisticated Numerical Implementation 2 22 o oan aene da QURE ks 14 Using ATLAS With Other Silvaco Software sess 1 5 The Nature Of Physically Based Simulation sese 1 6 Chapter 2 Getting Started with ATLAS 0 ccc cece cece cee eee eee eee eee eeeeeeeees 2 1 OVEDWBW casta take Adda oco iau ra wie cas Meee M M nae aon T It E LE Eu 2 1 ATLAS Inputs and OUIDUIS Scone Verr IIR 3r xc Rr eee ar eed eh te Soe wee eee dr LE RE RS 2 1 Modes of Operation 5 s sese xt Rte e RARI ERE EI RR EY RERRER AREA 2 2 Interactive Mode With DeckBuild inuit ved uacepe ze ned re ao 2 2 Batch Mode With D ckBull 24 9 uix Y A ea DR YU eds 2 2 No Windows Batch Mode With DeckBuild iu i em eon rs ET Ie aa e a E ot a 2 3 Running ATLAS inside DSCKDH
59. Poisson equation see Chapter 3 are the same as for the homogeneous case Although the changing dielectric constant is taken into account However the current density expressions must be modified to take into account the nonuniform band structure This procedure starts with the current density expressions Jn u nV 9 5 28 gt Jp uynV 6 5 29 where bn and are quasi F ermi potentials 1 E 5 30 Da q FN 1 The conduction and valence band edge energies can be written as E q Wo W X 5 32 E q Vo V x E 533 5 12 SILVACO International BLAZE where Wo is some reference potential X isthe position dependent electron affinity Eg isthe position dependent bandgap Wo can be selected in the form X KT N X E a E gt 5 34 where ni is the intrinsic carrier concentration of the arbitrarily selected reference material and r is the index that indicates that all of the parameters are taken from reference material Fermi energies are expressed in the form Epy E kT Ing KT Inyn 5 35 C Epp E KT In kT In yn 5 36 V The final terms in Equations 5 35 and 5 36 are due to the influence of Fermi Dirac statistics These final terms are defined as follows F1 2 0 Ery E a fn da co crucem Fig 5 37 e L c F1 2 n E E p LEE CES ett D Yp ux Hp ERES Frog 9 98 where Nc and N are position dependent Yn Vp 1 for Boltzmann statistics By combining Equations 5 28 to
60. SPDB CMP MC Deposit MC Implant Process Adaptive Meshing S Pisces Blaze Device3D Thermal3D Interconnect3D Blaze 3D Giga3D MixedMode3D TFT Luminous Giga MixedMode ESD Laser FastBlaze FastMixedMode FastGiga FastNoise MOCASIM UTMOST UTMOST II UTMOST III UTMOST IV PROMOST SPAYN SmartSpice MixSim Twister FastSpice SmartLib SDDL EXACT CLEVER STELLAR HIPEX Scholar SIREN Escort Starlet Expert Savage Scout Guardian and Envoy aretrademarks of SILVACO International O 1990 1991 1992 1993 1994 1995 1996 1997 1998 by SILVACO International Inc SILVACO International ii Reader Comment Sheet We welcome your evaluation of this manual Your comments and suggestions help us to improve our publications If you have any responses to the questions below please let us know Write your observations complaints bug reports suggestions or comments below e Is this manual technically accurate e Are the concepts and wording easy to understand e Is the size of this manual convenient for you e Is the manual s arrangement convenient for you e Do you consider this manual to be easily readable e Please add any additional relevant comments Please fax your comments to SILVA CO International Attention Technical Publications at 408 496 6080 iv SILVACO International Introduction Intended Audience The information presented is based on the assumptions that the reader is 1 familiar with
61. These effects are modeled by the inclusion of two diodes In the forward active region these effects are represented by five parameters Is NF ISE NE and rkr They can be easily extracted from the forward Gummel Plot The forward Gummel Plot is defined as the plot of collector and base currents versus the intrinsic base emitter voltage In the reverse region the parameters BR NR ISC and NC model the reverse Gummel Plot var the forward early voltage and VAR the reverse early voltage are used to model the variations of finite output conductances TF is defined as the minimum value of the transit time at high collector emitter bias The parameter TF models the minimum value of TF at high currents and low collector emitter bias The parameter TF models the increase of TF with increasing collector current The parameter VTF controls the effect of the collector emitter bias at high collector currents x lt H The last area where the Gummel Poon model has made a contribution is the modeling of non linear effects of the base resistance variation with the base current The distributed nature of the base resistance makes it very difficult to model it Three parameters used to model base resistance are RB IRB and RBM MIXEDMODE models bipolar NPN and PNP devices the same way In the case of a PNP device the polarities of the node voltages vez and vec are reversed After computing the collector and base currents their signs
62. a Eder FA OR rte IER 5 1 Ier rei po A A A A pe cee 5 1 Basic Heterojunction Definitions aid Rad era dud I ESAE E DE RA CA eL PITE d s 5 1 PRUNE oos sero E E deri GIN ROSE RE GEM MEA 5 2 NETH ELITR RE a edo ria did 5 2 The ALIGN parameter on the MATERIAL statement ccc cece cect e ete mnn 5 2 Manually Adjusting Material Affinity ds v Rn E ve tet VARRO Y ente xk OR ee 5 3 EXAMPLES rca sia old clarita a Pn 5 3 Using the ALIGN parameter on the MATERIAL statement naua 5 4 Manually Adjusting Material Affinity a Eos tt d RS t e QR be SO RR Ee pe i ee a 5 4 EXA aie A sha Vota qutd ER OQ o desees fus 5 5 Manually Adjusting Material Affinity dcus deiode aue dre Mt reed ra n een oo oM ies An 5 6 EXAMPLES gt 2 vac tu Sette EE Aa dai ia dans 5 7 Manually Adjusting Material Affinity io da Re Rey Rh eet x Ra Y RR RE Rx 5 9 EXAMPLE AP cnc eran id ade Es a IR 5 10 Using the affinity rule for the heterojunction ooocooccoccoocco oro 5 10 The Drift Diffusion Transport Model S d EIE ERR ORA EI ER Padre O Nos 5 12 Drift Diffusion with Position Dependent Band Structure isssssssse e eee n eens 5 12 The Thermionic Emission Transport Model oec e RR RR ret Ee een 5 14 The Physica Models otr crea 5 14 Common Physical Models i e ce e Rene ER er eed eee diu DU pr RR ER e 5 15 LOW Fiet MODI MO td 5 15 Parallel Electric Field Dependent Mobility sse 5 16 Velocity Saturation with Energy Balance cede tre ted C CE D Ac ne e a 5 17 R
63. a mesh as described in the Getting Started Chapter of this manual When defining the material regions the following syntax may be used REGION Y MIN 0 05 Y MAX 0 OXIDE REGION Y MIN 0 Y MAX 0 2 SILICON REGION Y MIN 0 2 Y MAX 2 OXIDE Note that the region is defined as silicon It is also possible to define the material as polysilicon However users should note that it is the defect distribution rather than this initial material definition that will determine the electrical characteristics Defining The Defect States Disordered materials contain a large number of defect states within the band gap of the material In order to accurately model devices made of polycrystalline or amorphous materials it is necessary to use a continuous density of states The DerecT statement is used to specify the density of defect states DOS as a combination of exponentially decaying band tail states and Gaussian distributions of mid gap states90 SILVACO International 7 1 ATLAS User s Manual Volume 1 Density of States Model The total density of states DOS g is assumed to be composed of four bands two tail bands a donor like valence band and an acceptor like conduction band and two deep level bands one acceptor like and the other donor like which are modeled using a Gaussian distribution g E gpAUE gpp E 254 CE gg pCE 7 1 where E is the trap energy Ec is the conduction band ener
64. accounts for a broader set of effects and has been calibrated over a wider range of conditions than any other of the low field bulk mobility models As such it is the recommended model for both MOS and bipolar simulation and is the default model for silicon The model can be enabled or disabled using the kLa parameter on the MopELs statement or independently for electrons and holes by the kra N and kra P parameters of the moB1I11TY statement Thetotal mobility can be described by its components using Mathiesen s rule as 1 E Hal npAP 3 131 1 1 Ej Hn and p are the total low field electron and hole mobilities uy and up are the electron and hole mobilities due to lattice scattering unpap and uppap are the electron and hole mobilities due to donor D acceptor A screening P and carrier carrier scattering The lattice scattering components uy and pup are given as 300 THETAN KLA TET MUMAXN KLA 3 133 nL T 300 THETAP KLA u MUMAXP KLA 2 3 134 pL Ty where T is the temperature in degrees Kelvin MUMAXN KLA MUMAXP KLA THETAN KLA and THETAP KLA are user definable model parameters which can be specified as shown in Table 3 18 Table 3 21 User Specifiable Parameters for Equations 3 133 and 3 134 Statement Parameter Default Units MOBILITY MUMAXN KLA 1417 0 cm V s 3 38 SILVACO International Physics Table 3 21 User Specifiable Parameters for
65. and F owler N ordheim tunneling Hot carrier injection Thermionic emission currents Fully Integrated Capabilities ATLAS works well with other software from SI LVACO For example ATLAS Runs in the DEckBuiLD interactive run time environment Is interfaced to TonyPLoT the interactive graphics and analysis package Accepts input from the ATHENA and SSUPREM3 process simulators Is interfaced to UTMOST parameter extraction and device modeling software can be used in experiments with the VWF AUTOMATION TOOLS Sophisticated Numerical Implementation ATLAS uses powerful numerical techniques induding Accurate and robust discretization techniques Gummel Newton and block N ewton nonlinear iteration strategies Efficient solvers both direct and iterative for linear subproblems Powerful initial guess strategies Small signal calculation techniques that converge at all frequencies Stable and accurate time integration 14 SILVACO International Introduction Using ATLAS With Other Silvaco Software ATLAS should only be used in conjunction with the VWF INTERACTIVE TooLs These include DeckBUILD TonYPLOT DEVEDIT MaskViews and OPTIMIZER DECKBUILD provides an interactive run time environment ToNvPLor supplies scientific visualization capabilities DevEbIT is an interactive tool for structure and mesh specification and refinement and MaskViews is an IC Layout Editor The OPTIMIZER Supports black box optimization across
66. and error messages that were generated Provide us with the version number of ATLAS the version numbers of the VWF INTERACTIVE TOOLS that you are using and details of the hardware platform on which the problem was encountered Include your company affiliation business telephone number and fax number You will be contacted promptly and your problem will be resolved as quickly as possible User feedback drives the further development of ATLAS Please send your comments on the programs suggestions for improvements and additional feature requests to the electronic mail address given above SILVACO International 1 3 ATLAS User s Manual Volume 1 Features And Capabilities of ATLAS A Comprehensive Set of Models ATLAS provides a comprehensive set of physical models including DC AC small signal and full time dependency Drift diffusion transport models Energy balance and Hydrodynamic transport models Lattice heating and heatsinks Graded and abrupt heterojunctions Optoelectronic interactions with general ray tracing Amorphous and polycrystalline materials General circuit environments Stimulated emission and radiation Fermi Dirac and Boltzmann statistics Advanced mobility models Heavy doping effects Full acceptor and donor trap dynamics Ohmic Schottky and insulating contacts SRH radiative Auger and surface recombination Impact ionization local and non local Floating gates Band to band
67. and modal gain spectra for several longitudinal modes A basic familiarity with ATLAS and BLAZE is assumed You should read the Getting Started and BLAZE chapters before reading this chapter Physical Models In order to simulate semiconductor lasers the basic semiconductor equations Equations 3 1 to 3 4 in Chapter 3 of this manual are solved self consistently with an optical equation that determines the optical field intensity distribution LASER uses the following coordinate system e thexaxisis perpendicular to the laser cavity and goes along the surface from left to right e they axis is perpendicular tothe laser cavity and goes down from the surface e thezaxis goes along the laser cavity The x and y axes are the same as in other ATLAS products The electrical and optical equations are solved in the x y plane i e perpendicular tothe laser cavity LASER solves a two dimensional Helmholtz equation to determine the transverse optical field profile E x y 2 2 p 2 vien eo fon 0 9 1 C where 2 2 Vi E is the two dimensional Laplace operator x Oy Om is the frequency corresponding to longitudinal mode m m corresponds to Las omeGA on the MODELS Statement for single frequency simulations cis the velocity of light in vacuum e x y is the high frequency dielectric permittivity Equation 9 1 is a complex eigenvalue problem LASER solves this equation to determine the set of complex eigenvalues By and c
68. are also reversed for proper polarity The DC model is defined by the parameters Is BF NF IKF ISE and NE which determine the forward current gain characteristics Is BR NR IKR Isc and wc which determine the reverse current gain characteristics and var and var which determine the output conductance for forward and reverse regions Five ohmic resistances Rc RB IRB RBM and RE are included Base charge storage is modeled by forward and reversetransit times rr and rn and nonlinear depletion layer capacitances which are determined by cog vue and mse for the B E junction coc voc and mgc for the B C junction and cos vgs and uos for the C S junction The temperature dependence of the saturation current rs is determined by the energy gap EG and the saturation current temperature exponent xrr Base current temperature dependence is modeled by the sr temperature exponent xTB A complete Gummel P oon parameter list grouped according to basic effects is Table 10 3 A complete Gummel Poon parameter list Basic DC IBC IBE IS BF NF BR NR Degradation ISE NE ISC NC IKF IKR Resistor RC RB RBM IRB RE SILVACO International 10 39 ATLAS User s Manual Volume 1 Table 10 3 A complete Gummel Poon pa
69. are expressed in terms of the quasi F ermi levels 6 and as J n au4nVo9 3 5 gt J p 7 qupn Y Pp 3 6 where tin and up are the electron and hole mobilities The quasi F ermi levels are then linked to the carrier concentrations and the potential through the two Boltzmann approximations Q V 05 Nieexp RT 3 7 r q v 654 p N exp RT 3 8 where Nje is the effective intrinsic concentration and T is the lattice temperature These two equations may then be re written to define the quasi F ermi potentials 3 2 SILVACO International Physics KT n 0 qeu n 3 9 KT D By substituting these equations into the current density expressions the following adapted current relationships are obtained gt J q4D Vn qna Vy up n kT V Inn 3 11 gt J p GD Vp gp Vy ugp KT V Inn g 3 12 The final term accounts for the gradient in the effective intrinsic carrier concentration which takes account of bandgap narrowing effects Effective electric fields are normally defined whereby gt KT E n v y g Mie 3 13 gt KT Ep y Mnie 3 14 Which then allows the more conventional formulation of drift diffusion equations to be written gt gt Jn qna E qD yn 3 15 gt gt J p qPHpE 5 qD Vp 3 16 It should be noted that this derivation of the drift diffusion model has tacitly assumed that the Einstein relationship holds In the case of Boltzmann statistics this corr
70. are specified in the moB1L1TY statement The default parameters are for silicon at Tj 300K SILVACO International 3 35 ATLAS User s Manual Volume 1 Table 3 19 User Specifiable Parameters for Equations 3 123 and 3 124 Statement Parameter Default Units OBILITY UlN ARORA 88 0 cm V s OBILITY UlP ARORA 54 3 cm V s OBILITY U2N ARORA 1252 0 cm V s OBILITY U2P ARORA 407 0 cm V s OBILITY ALPHAN ARORA DD unitless OBILITY ALPHAP ARORA 0 57 unitless OBILITY BETAN ARORA 22 33 unitless OBILITY BETAP ARORA 2 23 unitless OBILITY GAMMAN ARORA 2 546 unitless OBILITY GAMMAP ARORA 2 546 unitless OBILITY NCRITN ARORA 1 432x10 7 cm OBILITY NCRITP ARORA 2 67x1077 cm The Carrier Carrier Scattering Model For Low Field Mobility The Dorkel and Leturq 66 model for low field mobility indudes the dependence on temperature doping and carrier carrier scattering This model is activated by specifying the ccsmoB parameter of the mopELs statement The parameters of the model are specified in the moBI1LTTY statement This model has the form 0 025 1 025 uL WB 1 E re u L is the lattice scattering is the ionized impurity scattering C is the carrier carrier scattering Ll Uno po Un p 3 125 where 3 36 SILVACO International Physics T 372 od wb g 1 04
71. be preferable for operating regimes where dl dV is large It is not uncommon for the negative resistance regime of a device to have a slope dl dV very dose to 0 Such behavior should be considered when using a current source to trace out an entire l V curve The curvETRACE option in ATLAS would be preferable in these cases Note When a current boundary condition has been specified it is necessary to choose the NEWTON numerical scheme on the metHop statement It is possible to perform ac small signal analysis with current boundary conditions Insulating Contacts Insulating contacts are contacts that are completely surrounded by insulator They may be connected to a voltage source tied contact or they may be floating Insulating contacts that are connected to a voltage source generally have a work function that dictates a value for ws similar to that shown in Equation 3 107 Electron and hole concentrations within the insulator and at the insulating contact are forced to be zero i e N D lt 0 Neumann Boundaries Along the outer non contact edges of devices homogeneous reflecting Neumann boundary conditions are imposed so that current only flows out of the device through the contacts In the absence of surface charge along such edges the normal electric field component becomes zero Current is not permitted to flow from the semiconductor into an insulating region except via oxide tunneling models At the interface bet
72. can be used to set the real and imaginary indices respectively of a specified material region or regions For example the statement MATERIAL MATERIAL Air REAL INDEX 1 0 IMAG INDEX 0 0 would set the index for all material regions composed of Air The statement MATERIAL REGION 1 REAL INDEX 1 0 IMAG INDEX 0 0 would set the index for region number 1 The statement MATERIAL REAL INDEX 1 0 IMAG INDEX 0 0 would set the index for all regions Setting A Wavelength Dependent Refractive Index The preceeding examples set the complex index of refraction for a material regardless of wavelength This is probably adequate for monochromatic sources For multispectral simulations the index of refraction should be modeled as having a dependence on wavelength There are two ways to do this ASCII File Input The first way is to spedify index versus wavelength in a file This is a text file that contains ordered triplets of wavelength real index and imaginary index The first entry in the table is the number of samples If the INDEX FILE parameter of the MATERIAL statement is set to the name of the index file Linear interpolation from this table will be done to obtain the index of refraction as a function of wavelength A valid index fileis shown below 2 0 45 2 0 0 0 0 6 3 0 0 02 In this example a real index of 2 5 and an imaginary index of 0 015 would be used for a wavele
73. completely arbitrary Doping profiles and the structure of the device may be obtained from analytical functions experimentally measured data or from process modeling programs SSUPREM3 and ATHENA Simulating Silicon Devices Using S PISCES Simulating MOS Technologies Physical Models for MOSFETs S PISCES provides special physical models tuned for simulating MOS devices Most of these models are accessed from the MODEL statement The mos parameter of the MODEL statement can be specified to turn on a default set of physical models that are most useful for MOS simulation The Mos parameter enables Shockley Read H all SRH Fermi statistics FERMI and the Lombardi mobility model CVT for transverse field dependence To sets the default MOS simulation models use MODEL MOS PRINT The transverse field dependent mobility models are of particular importance for simulating MOS devices S PISCES currently supports several different transverse field dependent mobility models The parameter cvT selects the Lombardi CVT model The parameter yama selects the Yamaguchi model The parameter Tasc selects the Tasch model and the parameter WATT selects the Watt surface model which can be operated in a more accurarate mode with the extra parameter MOD WATT on the MOBILITY statement Advanced users will find that the MOBILITY statement can be used to modify some of the parameters of the various models to apply different models to different regions or
74. default averaging method When interpreting the contour plots it is important for users to remember that the solution file contains values only at each node point The colour fills seen in Tonyplot are simply interpolations based on the node values This may lead to occasional strange contour values In these cases users should check the node values using the probe in TonYPLor The primary solution variables potential carrier concentration lattice temperature and carrier temperatures are calculated on the nodes of the ATLAS mesh and hence are always correct in TonYPLoT However since ATLAS does not use nodal values of quantities such as electric field and mobility the actual values being used in calculations cannot be determined from Tonyplot or the structure files The PROBE statement allows users to directly probe values at given locations in the structure This provides the most accurate way to determine the actual values used in ATLAS calculations Customizing Solution Files OUTPUT Statement Several quantities are saved by default within a structure file For example doping electron concentration and potential It is also possible to specify additional quantities with the output statement such as conduction band potential using the OUTPUT statement This must precede the SAVE Statement in question For example to save the conduction and valence band potentias the following command would be used at some point before the relevant SAV
75. density of states and distribution widths for the twotail states and two Gaussian distributions Plotting The Density Of States Versus Energy The parameters DFILE and AFILE were used to allow the user to specify output file names for capture of defect densities as a function of energy for donor states and acceptor states respectively For example if the user wants to look at the donor and acceptor defect distributions the following line could be specified DEFECTS DFILE donors AFILE acceptors Then the files donors and acceptors could be loaded into TonyPLot to look at the distributions of donor and acceptor defects as a function of energy Using the C Interpreter to define DEFECTS The C Interpreter can be used to define the defect states in the bandgap The r tFTrpon and F TFTACC parameters of the DEFEcT statement indicate the filenames containing the C functions See Appendix A for moreinformation on using the C I nterpreter DEFECTS F TFTDON mydefects c F TFTACC mydefects c The file mydefects c will contain C functions for donor and acceptor defect densities as a function of energy These user defined defects are added to the existing defect distribution If users wish to use only their own funcion they should set the gaussian and tail functions to zero In the following example defect states are defined in the file tft lib These are added to a zero background set using the tail
76. discrete segments which are based upon the mesh For each insulator semiconductor segment the Fowler Nordheim current is calculated as described above This current will then be added to a segment on the electrode insulator boundary Two schemes have been implemented to find out to which segment this current should be added The default model that calculates which electrode segment receives the hot carrier injected current follows the path of the electric field vector at the semiconductor insulator interface The first electrode insulator segment that is found along this trajectory provided no other semiconductors or metals are found along the trajectory will receive the current A second model may be chosen using the NEARFLG parameter of the MopELS statement In this case the electrode insulator segment found closest to the semiconductor insulator segment will receive the hot carrier injected current The total current on the gate electrode is then the sum of the currents from all the individual segements around the electrode boundary Note When simulating EPROM programming with this model the floating contact charging is simulated in the transient mode In this case the total current flowing into the floating electrode is multiplied by the time step to calculate the charge added to the electrode during that time step The new value of charge is then used as the boundary condition for the next time step SILVACO International 3 79
77. e eee eee eee eae 10 38 10 5 BJT Equivalent Circuit for DC and Transient Analysis eee eee eee eee 10 39 10 6 A Lateral Transistor os ccc essen sus ax ren nx hr Cede eee EE Rn e dans 10 48 10 7 A Vertical Transistor om won des ex UR US UO Rr Ra Oe E Re RA 10 49 10 8 Channel MOSFET Current Convention p channel currents are opposite oooooccoocccccnnc eee eee nee 10 62 10 9 MOSFET Equivalent Circuit for Transient Analysis 0c ee eee ee eee eee eee eee 10 63 XX SILVACO International List of Tables Figure Page No Table Title No 2 1 Carrier Statistics Models 5 due ri re Go els RE nado ae ta asta ea tees 2 23 2 2 Mobility Models Seier de eae ke etl eee eui maa recie per er x AR eee date EUR REY 2 23 2 3 Recombination Models 7 uou er ae rr o eee e ai a aa ec e eati 2 24 2 4 ImpactloniZalioli ossa Siesta acne cx dor d ad o d dc Aca v i EC LU RR Ata aea io ae s 2 25 2 5 Tunneling Models and Carrier Injection Models 0cceceeeee cette eee eee eee eeaee 2 25 2 6 Model Compatibility Chart eren oe rnnt A sie 2 25 2 7 Parameter Syntax Replacements 00sec cece eee eee eee Inn nnn 2 30 3 1 User Definable Parameters for the Density of States 0c cece cece eee eee eee 3 6 3 2 User Specifiable Parameters for Equation 3 36 cece cece eee eee eee teen eens 3 7 3 3 User Definable Parameters of Slotbooms Bandgap Narrowing Model lt lt
78. easily underflow Such situations were handled in the past by setting these concentrations to zero This method does not allow an accurate subsequent calculation of minority carrier quasi Fermi levels In order to accurately calculate quasi F ermi levels majority carrier concentration and the relation np njs is used to obtain minority carrier concentrations in case of an underflow Despite these efforts spurious glitches are occasionally observed at low temperatures in the minority quasi F ermi levels 3 10 SILVACO International Physics Traps and Defects Overview Semiconductor materials exhibit crystal flaws which can be caused by dangling bonds at interfaces or by the presence of impurities in the substrate The presence of these defect centers or traps in semiconductor substrates may significantly influence the electrical characteristics of the device Trap centers whose associated energy lies in a forbidden gap exchange charge with the conduction and valence bands through the emission and recombination of electrons The trap centers change the density of space charge in semiconductor bulk and influence the recombination statistics Device physics has established the existence of three different mechanism which add to the space charge term in Poissons equation in addition to the ionised donor and acceptor impurities These are interface trapped charge interface trap states and bulk trap states Interface trapped charge is
79. electric field dependence are used with energy balance the electric field term is replaced by a function of carrier temperature SILVACO International 3 59 ATLAS User s Manual Volume 1 Carrier Generation Recombination Models To put it simply carrier generation recombination is the process through which the semiconductor material attempts to return to equilibrium after being disturbed from it If we consider an homogeneously doped semiconductor with equilibrium concentrations ng an pg then at equilibrium a steady state balance exists according to 2 ha P ni 3 210 However semiconductors are under continual excitation whereby no and pg are disturbed from their equilibrium states For instance light shining on the surface of a p type semiconductor causes generation of electron hole pairs disturbing greatly the minority carrier concentration A net recombination results which attempts to return the semiconductor to equilibrium The processes responsible for generati on recombination are known to fall into six main categories e phonon transitions e photon transitions Auger transitions surface recombination impact ionization e tunneling The following sections will describe the models implemented into ATLAS that attempt to simulate these six types of generation recombination mechanisms Shockley Read Hall SRH Recombination Phonon transitions occur in the presence of a trap or defect within the forbidde
80. equations model the energy gap with temperature 2 tnom egnom EG GAPl s tnom GA P2 10 98 r eg t EG GAP1 74 GAP2 10 99 The basic BJ T temperature compensation equations for betas and the saturation currents are XTB BF t sr 10 100 tnom XTB BR t 10 101 tnom ISE facln NE ISE t Ea u 10 102 mom ISC facln NC ISC t XTB 10 103 mui ISS facln NS ISS t pe 10 104 mox S t IS d 10 105 facln IBE t IBE e 10 106 10 56 SILVACO International MIXEDMODE where IKF t IKF t IRB t TEMPL IBC t IBC e facln IKF IRE ERB EV 4 facin y 10 107 EG EG 22 XTI Inf 10 108 Vri nom Y t inom 1 TIKF1 At TIKF2 At2 10 109 1 TIKF1 At TIKF2 At2 10 110 1 TIRB1 At TIRB2 At2 10 111 The basic BJ T temperature compensation equations for the saturation currents when TEMPLEV 4 are ct ct O A CC ct cd Is 1 IBE 1 TIS1 At IBC 1 TIS1 At ISE 1 TISE1 At ISE 1 TISE1 At ISC 1 TISCI1 At ISS 1 TISS1 At TISC2 TISS2 TIS1 At TIS2 At2 TIS2 At2 TIS2 At2 ISEZ ISE2 At2 At2 10 112 10 113 10 114 10 115 10 116 10 117 10 118 The parameters IKF IKR and IRB are modified as follows IKF t IKR t IRB t IKF 1 IKR 1 IRB 1
81. essentially a modification of the density of states as a function of depth below the Si SiO interface and is given by Equation 3 319 MEE ARS LAMBDA Here Nc is the standard density of states z is the depth below the interface and LAMBDA is a user specifiable parameter on the MopEL statement Van Dort s Model In deep submicron MOS devices quantum effects in the channel can have significant effects on the device characteristics These effects are directly due to the increased doping levels and thinner gate oxide In the channel of such devices the potential well well formed during inversion is of dimensions where the effects of quantum confinement must be considered The direct effect of such quantum confinement is that the peak of the carrier concentration is shifted away from the interface and the thinner gate oxide can cause a marked difference in gate capacitance Consideration of the effects may be essential for accurate prediction of the device turn on voltage A full treatment of the quantum effects by solving for example Schrodinger s equation is not always desirable from a computational standpoint nor necessary A simpler approach has been suggested by Van Dort 123 In this model the effects of the quantum confinement are modeled by an effective broadening of the bandgap near the surface as a function of a perpendicular electric field and distance from the surface In Van Dort s model the change in bandgap is given by the
82. following formats V n n two nodes positive n and negative n Vxxxx where Vxxxx is the name of an existing voltage source The positive terminal of the source becomes the positive input port node and the negative terminal becomes the negative input node Ixxxx where Ixxxx is the name of an existing current source The positive terminal of the source becomes the positive input port node and the negative terminal becomes the negative input node Note If the nodes specified as the input port are the same nodes as an existing current or voltage source then the name of the source MUST be specified as inport outport is the output port description It should be in one of the following formats V n n two nodes positive n and negative n Vxxxx where Vxxxx is the name of an existing voltage source The positive terminal of the source becomes the positive output port node and the negative terminal becomes the negative output node Ixxxx where I xxxx is the name of an existing current source The positive terminal of the source becomes the positive output port node and the negative terminal becomes the negative output node Note If the nodes specified as the output port are the same nodes as an existing current or voltage source then the name of the source MUST be specified as outport Also all AC parameters should be removed from voltage or current sources before using the NET statement DEC specifies that the
83. for all simulations with floating regions such as SOI transistors A floating region is defined as an area of doping which is separated from all electrodes by a pn junction BLOCK is equivalent to NEWTON for all isothermal drift diffusion simulations Drift Diffusion Calculations with Lattice Heating When the lattice heating model is added to drift diffusion an extra equation is added The Brock algorithm solves the three drift diffusion equations as a Newton solution and follows this with a decoupled solution of the heat flow equation The wgEwrow algorithm solves all four equations in a coupled manner NEwTON is preferred once the temperature is high however Brock is quicker for low temperature gradients Typically the combination used is METHOD BLOCK NEWTON SILVACO International 2 21 ATLAS User s Manual Volume 1 Energy Balance Calculations The energy balance model requires the solution of up to 5 coupled equations GuMMEL and NEWTON have the same meanings as with the drift diffusion model i e GUMMEL specifies a decoupled solution and NEWTON specifies a fully coupled solution However Brock performs a coupled solution of potential carrier continuity equations followed by a coupled solution of carrier energy balance and carrier continuity equations It is possible to switch from BLOCK to NEWTON by specifying multiple solution methods on the same line For example METHOD BLOCK NEWTON
84. for the desired conduction band offset as calculated by the affinity rule that is relative to Materiall This value of electron affinity will override any electron affinity specification for Material2 This has an impact on any calculation where this materials electron affinity is used and must be considered when specifying Schottky barriers contacted to this materials See Example 4 for more details on Schottky barrier considerations Note Remember if the AL 1GN parameter is not specified on the MATERIAL statement BLAZE will use the Affinity Rule and either the default electron affinity or the affinity assigned using the AFFINITY parameter on the MATERIAL statement to calculate the conduction band offsets 5 4 SILVACO International BLAZE EXAMPLE 2 A A A qvo qVoo E x 4 X2 Xi Ec x y Be oL CUN REO F AEv23 ey I AE 12 t ea j t E X y Material 1 Material 2 Material 3 Figure 5 3 Band diagram of three material system lowest E in center Figure 5 3 details a heterostructure device consisting of three semiconductors with different bandgaps Eg Ej and E and electron affinities x1 x and x3 This is similiar to the band diagram of a Double Heterojunction Bipolar Transistor For this example E gt Ey2 lt Eg3 and X lt X2 7X5 Allocating the conduction band offsets using the affinity rule AE X2 X1 5 4 and
85. how these two syntax styles are joined in MIXEDMODE Each input fileis split in two parts The first part is SPICE like and describes the circuit netlist and analysis The second part is ATLAS like and describes the device simulation model parameters These two sections of an input file are separated as described in the next section The circuit description includes the circuit topology called netlist and the electrical models and parameters of the circuit components The simulation conditions specify the types of analysis to be performed These items are described using syntax based on SPICE The ATLAS device descriptions provide information about device geometry doping distribution meshes Device descriptions can be prepared using the built in ATLAS syntax the ATHENA process simulator or the DevEdit structure specification and meshing tool Previously calculated device solutions may optionally be read in The device data is read in from standard structure format files When a simulation has finished the following information is available e V data voltages in all circuit nodes and currents in all circuit branches nternal distributions of solution variables such as electron hole and potential distributions within the numerical devices Theresults of previous runs of MIXEDMODE can be used as initial guesses for future simulations This is particularly helpful when multiple simulations must be performed from the same starting
86. impact ionization coefficients as functions of the carrier temperatures rather than functions of the local electric field The Energy Balance Equations The energy balance model introduces two new independent variables T and Ty the carrier temperature for electrons and holes The energy balance equations consist of an energy balance equation with the associated equations for current density and and energy flux Sy p For electrons the energy balance model consists of 3k 9 gt gt ui divSn J nVy Wya cO NT 3 74 Es T Jn QD Vn up nVy qnD VT 3 75 gt k hn gt Sn Kw Td nTa 3 76 and for holes An i 3k ns _ divSp JJ pVw Wp 5 3r p pT 3 77 i T Jp qD V UpPVY qpD VT 3 78 gt k gt Sp KYT pTp 3 79 where gt gt Sn and Sp are the energy flux densities associated with electrons and holes Wp Wp are the energy density loss rates for electrons and holes Kw Kp are the thermal conductivities of electrons and holes SILVACO International 3 17 ATLAS User s Manual Volume 1 Dp Dp are the thermal diffusivities for electrons and holes and Hn Hp are the electron and hole mobilities Theremaining terms involving the electrons are defined by the following equations T ln q E 1 2 Mp AE p n n F 172 Q Nn kr vw T 3 k Dr Hon na Ja ET Fe 3 2 Np tan Ba 3 n JFE FTZ Fe 5 2 Np JE m n MES M REMOTA n 9n nta 37 2 F 1 2 0p H2n d
87. in MIXEDMODE These take the place of the SOLVE statements in a regular ATLAS input file At least one of these statements must appear in each MIXEDMODE input file e steady state analysis including loops DC transient analysis TRAN small signal AC analysis Ac small signal parameter extraction e g s parameters NET Special statements un Other statements than the control statements beginning with a dot specify special parameters for the circuit simulation These include numerical options and file input and output Full descriptions of each statement and associated parameters are found later in this chapter compact device models MODEL e the output files LOG SAVE e initial conditions settings NODESET IC SILVACO International 10 5 ATLAS User s Manual Volume 1 initial conditions from a file LOAD e numerics NUMERIC OPTIONS e miscellaneous OPTIONS Device Simulation Syntax The second part of a MIXEDMODE command file after END is used to define physical models material parameters and numerical methods for ATLAS devices referenced in the A element statements The following statements may appear in this part of the command file BEAM CONTACT DEFECT IMPACT INTERFACE INTTRAP MATERIAL MOBILITY METHOD MODELS OUTPUT PROBE TRAP and THERMCONTACT It is always necessary to include an indicator to
88. in terms of the intrinsic carrier concentration as q v 04 E Nieexp MET 3 34 qv p p Nj exp kr 3 35 where y is the intrinsic potential and y is the potential corresponding to the Fermi level i e Ep q 3 6 SILVACO International Physics The Energy Bandgap Thetemperature dependence of the bandgap energy is modeled in ATLAS as follows EGALPHA T 300 i E T1 E 0 TL V EGBETA EG300 EGALPHA Sorana Trimm 3 36 The parameters G300 EGALPHA and EGBETA can be specified by the user in the MATERIAL statement as indicated in Table 3 2 Table 3 2 User Specifiable Parameters for Equation 3 36 Statement Parameter Default Units ATERIAL EG300 1 08 ev ATERIAL EGALPHA 4 73e 4 eV K ATERIAL EGBETA 636 K ATERIAL C300 2 8e19 urs ATERIAL NV300 2 8e19 cm The default values are material dependent and may be found in Appendix B of this manual Table 3 2 displays the defaults for Silicon only Bandgap Narrowing In the presence of heavy doping greater than 1018cm3 experimental work has shown that the pn product in silicon decomes doping dependent As the doping level increases a decrease in the bandgap separation occurs where the conduction band is lowered by approximately the same amount as the valence band is raised In ATLAS this is simulated by a spatially varying intrin
89. including bipolar MOS IGBT and thyristor devices Another important application is the simulation of electrostatic discharge ESD protection devices Thermal effects are also important in SOI device operation due to the low thermal conductivity of the buried oxide and in devices fabricated in III V material systems due to the relatively low thermal conductivity of these materials Recent studies have demonstrated that accounting self consistently for lattice heating is necessary for accurate simulation of bipolar VLSI devices This is due to the sensitive temperature dependence of the carrier injection process Since bipolar devices are key components of CMOS technologies and because many devices can be impacted by parasitic bipolar effects the applications of GIGA are very general Numerics GIGA supplies numerical techniques that provide efficient and robust solution of the complicated systems of equations that result when lattice heating is accounted for These numerical techniques include fully coupled and block iteration methods When GIGA is used in conjunction with the energy balance equations the result is a six equation solver that defines the state of the art for general purpose device simulation SILVACO International 6 1 UTMOST User s Manual Volume 1 Physical Models The Lattice Heat Flow Equation GIGA adds the heat flow equation to the primary equations that are solved by ATLAS The heat flow equation has the f
90. instead specify GaAs as the material Bandgap The default energy bandgap for the InP lattice matched In x Ga 1 x As y P 1 y system used in BLAZE is given by E InGaAsP 1 35 x composition 0 642 0 758 x composition 5 66 0 101 y composition 1 101 y composition 0 28 x composition 0 109 y composition 0 159 x composition y composition Electron Affinity The electron affinities for materials in the InP lattice matched InGaAsP system are derived from conduction band offsets and from the assumption that the affnity of InP is 4 4eV The default conduction band edge offset between lattice matched InGaAsP and InP is then AE 0 268 y composition 0 003 y composition 5 67 Density of States and Effective Mass The density of states is defined as before as a function of the effective masses of electrons and holes according to Equation 3 29 For the InGaAsP system the default conduction and valence band effective masses for electrons and holes are given by the following For the conduction band m 0 08 0 116 y composition 0 026 x composition 5 68 0 059 x composition y composition 0 064 0 02 x composition y composition For the valence band the hole effective mass is defined by SILVACO International 5 23 ATLAS User s Manual Volume 1 2 1 5 1 5 3 my my my where the default light hole effective mass is given by my 0 120
91. lib specifies that the file munsat lib contains the C Interpreter function for the specification of the parallel field dependent electron mobility model 2 26 SILVACO International Getting Started with ATLAS Choosing Numerical Methods Numerical Solution Techniques Several different numerical methods can be used for calculating the solutions to semiconductor device problems Different solution methods are optimum in different situations and some guidelines will be given here Full details of the numerical solution techniques can be found in the Chapter on Numerical Techniques Numerical methods are given on the METHOD statements of the input file Different combinations of models will require ATLAS to solve up to six equations For each of the model types there are basically three types of solution techniques a de coupled cummeEL b fully coupled NEWTON and c BLOCK In simple terms the de coupled technique like the Gummel method will solve for each unknown in turn keeping the other variables constant repeating the process until a stable solution is achieved Fully coupled techniques such as the Newton method solve the total system of unknowns together The combined or block methods will solve some equations fully coupled while others are de coupled In general the Gummel method is useful where the system of equations is weakly coupled but has only linear convergence The Newton method is useful when the sy
92. low However if this parameter is set to too high so that the carrier temperature errors for significant carrier concentrations are being ignored unpredictable and mostly incorrect results will be seen Restrictions on the Choice of METHOD The following cases all require METHOD NEWTON CARRIERS 2 to be set for isothermal drift diffusion simulations Both BLOCK and or NEWTON are permitted for lattice heat and energy balance current boundary conditions distributed or lumped external elements AC analysis impact ionization Note Simulations using the GUMMEL method in these cases may lead to non covergence or incorrect results SILVACO International 2 29 ATLAS User s Manual Volume 1 Pisces Il Compatibility Previous releases of ATLAS 2 0 0 R and other PISCES II based programs use the SYMBOLIC command to define the solution method and the number of carriers to be included in the solution In this version of ATLAS the solution method is specified completely on the METHOD statement The COMB parameter which was available in earlier ATLAS versions is no longer required as it is replaced by either the BLOCK method or the combination of GUMMEL and NEWTON parameters The following table identifies direct translations of old syntax to new Note These are direct translations and not necessarily the best choices of numerical methods Table 2 7 Parameter Syntax Replacements
93. m The parameter LAS NEFF is user specifiable as shown in Table 9 4 Table 9 4 User Specifiable Parameters for Equation 9 7 Statement Parameter Default Units MODELS LAS NEFF 34 571 Photon Rate Equations Linkage between optical and electrical models is provided by the optical gain The optical gain depends on the quasi F ermi levels and in turn impacts dielectric permittivity see Equation 9 2 and by the coupling between the stimulated carrier recombination rate R t and the density of photons S as described by Equation 9 7 To determine S LASER solves the system of photon rate equations dSn c 1 c LAS LOSSES iS 9 8 dt LAS NEFF m Toh LAS NEFF m SPm where the modal gain Gm is given by 2 Gm fex y EG y dx dy 9 9 and the modal spontaneous emission rate R is given by 2 Ro fo y IEG y dx dy 9 10 LAS LOSSES is the internal losses and can be specified on the mopEL statement as shown in Table 9 5 E x y is the normalized optical field 9 4 SILVACO International LASER Table 9 5 User Specifiable Parameters for Equation 9 8 Statement Parameter Default Units MODELS LAS LOSSES 0 cm The modal photon lifetime in Equation 9 8 represents the losses in the laser The losses per mode are given by 6 1 c Toh LAS NEFF QA Og Qa 9 11 O is the bulk absorption loss af is the free carrier loss and aq
94. mobility model should be combined with FLDMOB to model velocity saturation For surface or lateral bipolar devices the Shirahata model SHI can be used to extend the Klaassen model with a transverse electric field dependence The most accurate and appropriate model statement for bipolar devices is therefore MODELS KLA FLDMOB KLASRH KLAAUGER BGN FERMI PRINT This set of models may be chosen with the parameter BIPOLAR2 of the MODEL statement Note For a complete syntax including description of models and method for simulating polysilicon emitter bipolar devices see the BJT directory in the on line examples Meshing Issues for BJTs The most important areas to resolve in bipolar transistors are the emitter base and base collector junctions Typically a very fine mesh throughout the base region is required The gain of the bipolar device is determined primarily by the recombination at the emitter base junction or inside the emitter Hencethese regions need to be resolved with a fine mesh BJT Electrode Naming S PISCES also provides special electrode names for bipolar simulation that can be used to ease confusion over electrode indices These electrode names include emitter base collector anode and cathode Electrode names can be defined in ATHENA or DEvEbDIT or in the ELECTRODE statement in ATLAS The electrode names are used on SOLVE statement for example SOLVE VBASE 1 0 VSTEP 1 0 VFINAL
95. mode ATLAS operates with x 0 as the axis of symmetry around which the cylindrical geometry is placed Many of the default units change when cylindrical coordinates are used The calculated current is in Amps rather than the usual Amps per micron External elements are specified in absolute units e g Farads not Farads micron for capacitors The MESH statement must be used to specify cylindrical symmetry The following statement creates a mesh which contains cylindrical symmetry There are 20 mesh nodes along the x axis and 20 mesh nodes along the y axis MESH NX 20 NY 20 CYLINDRICAL The following statement imports a mesh which contains cylindrical symmetry MESH INF mesh0 str CYLINDRICAL Note The CYLINDRICAL parameter setting is not stored in mesh files Therefore the parameter must be specified each time a mesh file which contains cylindrical symmetry is loaded Specifying Electrodes After you have specified the regions and materials you must define at least one electrode that contacts a semiconductor material This is done with the ELECTRODE statement ELECTRODE NAME electrode name position parameters Up to 50 electrodes may be specified The position parameters are specified in microns using the X MIN X MAX Y MIN and Y MAX parameters Multiple electrode statements may have the same electrode name Nodes that are associated with the same electrode name are treated as being e
96. model is activated on the MopELs statement using the quantum switch models quantum will activate the quantum moments equation for electrons and models h quantum will activate the quantum moments equation for holes Since the distributions of carriers given by the quantum moments model can vary significantly from the distributions predicted by the standard drift diffusion or energy balance models the standard initial guess strategies e g INIT typically are not suitable for obtaining solutions for quantum moments Until more suitable initial guess strategies can be devised for quantum moment modelling we have included a damping factor to gradually apply the quantum moment model This damping factor is specified by the oractor parameter of the soLve statement Theoracron is implemented as a prefactor to the expression for the quantum temperature in equation 3 17 As such a value of QFACTOR of 0 0 implies that the quantum moment model is turned off or is not being applied A value of oracron of 1 0 implies that the quantum moment model is turned on and is completely applied The user may smoothly vary the value of oracror between 0 0 and 1 0 to overcome the problems of initial guess During this ramping of oracron PR Evious should be used as an initial guess Also during such variation of oracron trapping is available should a given solution not converge In such cases the OFACTOR is reduced and solutions proceed un
97. no workfunction is specified in ATLAS irrespective of the material of the contact SILVACO International 3 23 ATLAS User s Manual Volume 1 Schottky Contacts Schottky contacts are defined by the work function of the electrode metal and an optional surface recombi nation velocity The surface potential at a Schottky contact is defined by Ey KT N V AFFINITY 7q Su ON WOREFUN applied 3 107 where ArFINITY is the electron affinity of the semiconductor material Eg is the bandgap Nc is the conduction band density of states Ny is the valence band density of states and T is the ambient temperature Table 3 10 User Specifiable Parameters for Equation 3 107 Statement Parameter Units CONTACT WORKFUN ev MATERIAL AFFINITY ev A finite surface recombination velocity can be imposed at a contact by specifying the parameter SURF REC on the CONTACT statement In this case the quasi F ermi levels n and bp are no longer equal to Vappliea nstead these parameters are defined by a current boundary condition at the surface 31 J sn AVSURFN N Neg 3 108 J sp qVSURFP p Peg 3 109 Table 3 11 User Specifiable Parameters for Equations 3 108 to 3 109 Statement Parameter Units CONTAC VSURFN cm s CONTAC VSURFP cm s where J s and J sp are the electron and hole currents at the contact ns is the surface electron concentration and p is the
98. of the ATLAS syntax used You should read this information before proceeding 8 Pressthe button Load Example The input command file for the example will be copied into your current working directory together with any associated files A copy of the command file will be loaded into DeckBuiLD Note that the Load Example button remains faded out until step 6 is performed correctly 9 To run the example press the Run button in the middle frame of the DeckBuiLD application window 10 Alternatively most examples are supplied with results that are copied into the current working directory along with the input file To view the results select highlight the name of the results file and select the DEckBuiLD menu option Tools Plot Details on the use of TonyPLoT can be found in the VWF INTERACTIVE TOOLS manual The ATLAS Syntax An ATLAS command file is a list of commands for ATLAS to execute This list is stored as an ASCII text file that can be prepared in DeckBuiLp or using any text editor Preparation of the input file in DECKBUILD is preferred and can be made easier by appropriate use of the DEckBuiLb Commands menu Statements and Parameters The input file contains a sequence of statements E ach statement consists of a keyword that identifies the statement and a set of parameters The general format is STATEMENT lt PARAMETER gt lt VALUE gt With very few exceptions the input syntax is not case sensi
99. of thelaser spectrumis desired specify the multiplelongitudinal modes model and additional parameters Specify 1MODES in the statement enables the multiple mode model Specify LAS EINIT LAS EFINAL in the mopELs statement These parameters set the photon energy range within which LASER will take into account multiple longitudinal modes Make surethat initial photon energy is within this range and that is specified for the active lasing region Specify the photon energy separation ras rEsEP If this is not specified LASER will automatically calculate the number of longitudinal modes based on the cavity length and the energy range It is recommended that LASER be allowed to choose the photon energy Separation Specify spectrum file name sezc savge on the mopELs statement LASER will produce a structure file containing spectrum data after calculation of each bias point LASER will automatically append dcN log to the specified file name where N is the number of the bias point for steady state solutions or trN log for a transient simulation The first bias point where LASER is active will have N 1 This is often not the first bias point during simulation These files can be examined using ToNvPLor If the parameter rAS SPECSAVE MopELS statement is specified the spectrum files will only be saved on every 1as specsave solution Note The index in the spectrum file name will still
100. part of the DeckBuiLD User Environment These include ser EXTRACT GO SYSTEM and SOURCE These commands can be interspersed inside ATLAS syntax e Variable substitution is supported for both numerical and string variables using the SET statement and symbol To avoid confusion the symbol is prefered to the symbol for comment statements In addition to these changes the physical models arein general different in ATLAS Most of the original PISCES II models have been preserved but often are not the default or the recommended models to use Consult the on line examples for technology specific information about models SILVACO International 2 7 ATLAS User s Manual Volume 1 Defining A Structure A device structure can be defined in three different ways in ATLAS 1 An existing structure can be read in from a file The structure can have been created by an earlier ATLAS run or by another program such as ATHENA or DEvEbIT A single statement loads in the mesh geometry electrode positions and DOPING of the structure This statement is MESH INFILE lt filename gt 2 The input structure can be transferred from ATHENA or DevEbiT through the automatic interface feature of DECKBUILD 3 A structure can be constructed using the ATLAS command language The first and second methods are more convenient than the third and are to be preferred whenever possible Interface From ATHENA
101. power law temperature dependence Concentration and ANALYTIC Caughey Thomas formula Tuned for Temperature Dependent 77 450K Arora s Model ARORA Alternative to ANALYTIC for Si Carrier Carrier Scatter CCSMOB Dorkel Leturq Model Includes n N ing and T dependence Important when carrier concentration is high e g forward bias power devices Parallel Electric Field FLDMOB Si and GaAs models Required to Dependence model any type of velocity satua tion effect Tasch Model TASCH Includes transverse field depen dence Only for planar devices Needs very fine grid Watt Model WATT Transverse field model applied to surface nodes only SILVACO International 2 23 ATLAS User s Manual Volume 1 Table 2 2 Mobility Models Model Syntax Notes Klaassen Model KLA Includes N T and n dependence Applies separate mobility to majority and minority carriers Recommended for bipolar devices Shirahata Model SHI Includes N E An alternative surface mobility model that can be combined with KLA Modified Watt MOD WATT Extension of WATT model to non surface nodes Applies constant E effects Best model for planar MOS devices Lombardi CVT Model CVT Complete model including N T E and E effects Good for non planar devices Yamaguchi Model YAMAGUCHI Includes N E and E effects Only for 300K Table
102. scaled to apply to a different length in the third dimension by simple multiplication This is not the case for Laser since the cavity length will determine energy spacing between longitudinal modes and will influence all other laser characteristics Be sure to specify the parameter cavITY LENGTH in the MopELS statement when the longitudinal mode spectrum is to be calculated SILVACO International 9 9 ATLAS User s Manual Volume 1 This page intentionally left blank 9 10 SILVACO International Chapter 10 MIXEDMODE Introduction The MIXEDMODE Concept MIXEDMODE is a circuit simulator that can indude elements simulated using device simulation as well as compact circuit models It combines different levels of abstraction to simulate relatively small circuits where compact models for single devices are not available or sufficiently accurate In addition MIXEDMODE allows the user to also do multi device simulations MIXEDMODE uses advanced numerical algorithms that are efficient and robust for DC transient small signal AC and small signal network analysis MIXEDMODE is typically used to simulate circuits that contain semiconductor devices for which accurate compact models do not exist or circuits in which devices that play a critical role must be modeled very accurately Applications of MIXEDMODE include power circuits that may include diodes power transistors IGBTs and GTOs optoelectronic circuits circuits su
103. syntax canbe used to link the voltages applied to the two electrodes CONTACT NAME basel COMMON base SOLVE VBASE 0 1 Here the electrode basel will be linked to the electrode base Later the applied 0 1V on base will also appear on basel However ATLAS will calculate and store separate currents for both base and basel This can be a useful feature However in some cases such as where functions of the currents are required in EXTRACT or TonYPLoT it is undesirable The parameter SHORT may be added to the CONTACT statement above to specify that only a single base current will appear combining the currents from base and basel When loading a structure from ATHENA or DEvEpiT where two defined electrode regions are touching ATLAS will automatically short these and use the electrode name that was defined first SILVACO International 2 19 ATLAS User s Manual Volume 1 Making an open circuit contact It is often required to perform a simulation with an open circuit on one of the defined electrodes From a device simulation viewpoint there are three different methods that will accomplish this These are Entirely deleting an electrode from the structure file Adding an extremely large lumped resistance for example 10200 onto the contact to be made open circuited Switching the boundary conditions on the contact to be made open circuited from voltage controlled to current controlled and then specifying a very sma
104. that include the effects of lattice heating and heat sinks Supports the simulation of devices that are based on polycrystalline and amorphous materials Supplies capabilities required to simulate optoelectronic devices including sophisticated ray tracing Allows the simulation of heterostructure lasers by self consistent solution of the Helmholtz equation for the optical field Offers circuit simulation capabilities that employ numerical physically based devices as well as compact analytical models enables simulation of quantum effects through a quantum moments solver and schrodinger solver enables simualtion of anisotropic material and device models Provides capabilities for three dimensional silicon device simulation Provides capabilities for three dimensional compound semiconductor and heterojunction device simulation Provides capabilities for non isothermal three dimensional device simulation Provides capabilities for mixed circuit simulation and three dimensional device simulation Provides capabilities for three dimensional polycrystalline and amorphous semiconductor device simulation Provides capabilities for three dimensional quantum effects Provides capabilities for three di mensional thermal analysis C INTERPRETER Allows inclusion of user defined equations into device simulation calculations ATLAS is designed to be used in conjunction with the VWF Interactive Tools The VWF Interactive Tools which inclu
105. the voltages on ATLAS device terminals to be referenced to the voltage on the first terminal From the physical point of view the state of the p n diode is the same for voltages of OV and 0 5V on the diode terminals with 1000V and 1000 5V but the first situation is better for numerical simulation RV defines the ohmic resistance that MIXEDMODE associates with all voltage sources and all inductances This value should never be set to O The default value is small enough to avoid errors due to the influence of the internal resistance Usually extremely small values of this parameters can cause convergence problems It is usually acceptable to decrease this parameter to the range of 1 10 1 107 This parameter should not be varied unless there is a compelling reason to do so SILVACO International 10 27 ATLAS User s Manual Volume 1 CNODE specifies a very small capacitance that is for algorithmic reasons automatically connected from each circuit node to ground This value can be set to 0 WRITE specifies how often the solution is to be saved in standard structure files during the simulation For example write 3 specifies that the solution will be saved at every third timestep Specifying this parameter can help avoid disk overflow CYLINDR activates the cylindrical coordinate system for all ATLAS devices LOADSOLUTIONS indicates that solutions as well as structures doping distributions and meshes are to be loaded from standar
106. the basic terminology of semiconductor processing and semiconductor device operation and 2 understands basic operation of the computer hardware and operation system being employed Introduction ATLAS is a modular and extensible framework for one two and three dimensional semiconductor device simulation It is implemented using modern software engineering practices that promote reliability maintainability and extensibility Products that use the ATLAS Framework meet the device simulation needs of all semiconductor application areas SILVACO International makes no warranty of any kind with regard to this material including but not limited to the implied warranty of fitness for a particular purpose SILVACO International shall not be liable for errors contained herein or for incidental or consequential damages in connection with furnishing performance or use of this material This document contains proprietary information protected by copyright All rights are reserved No part of this document may be photocopied reproduced or translated into another language without the prior written consent of SILVACO International Editions are recorded below under History and are individually listed as Edition 1 through 6 The basic issue of the manual is Edition 1 The date is also noted A completely revised manual results in a new edition History e Edition 1 July 1 1993 e Edition 2 March 1 1994 e Edition 3 June 1 1994 Edition 4
107. the charge added to the electrode during that time step The new value of charge is then used as the boundary condition for the next time step Lucky Electron Hot Carrier Injection Model In the lucky electron model it is proposed that an electron is emitted into the oxide by first gaining enough energy from the electric field in the channel to surmount the insulator semiconductor barrier Once the required energy to surmount the barrier has been obtained the electrons are redirected towards the insulator semiconductor interface by some form of phonon scattering When these 3 76 SILVACO International Physics conditions are met then the carrier travelling towards the interface will have an additional probability that it will not suffer any additional collision through which energy could be lost The model implemented into ATLAS is a modified version of the model proposed by Tam 30 and is activated by the parameter HEI and Hur for electron and hole injection respectively on the MODELS statement The gate electrode insulator interface is subdivided into a number of discrete segments which are defined by the mesh For each segment the lucky electron model is used to calculate the injected current into that segment The total gate current is then the sum of all of the discrete values If we consider a discrete point on the gate electrode insulator boundary we can write a mathematical formula for the current injected from the semicondu
108. to absorption over the ray path No is the internal quantum efficiency which represents the number of carrier pairs generated per photon observed y is a relative distance for the ray in question h is Planck s constant is the wavelength cis the speed of light a is given by Equation 8 12 8 6 SILVACO International Luminous where a is the absorption coeficient is the wavelength k istheimaginary part of the optical index of refraction Photogeneration on a Non uniform Mesh The photogeneration algorithm used integrates the optical intensity around each node point This is done to ensure that the total photogeneration rate is not grid sensitive A uniform photogeneration rate is defined as a constant value of photogeneration rate at any node element area around the node n ToyyPLor a uniform photogeneration rate may appear to vary across a non uniform mesh density Photogeneration at Contacts The photogeneration associated with nodes that are also defined as electrodes is a special case The electrical boundary conditions require that the carrier concentration at electrode nodes equals the doping level This means that photogeneration at nodes which are electrodes must be zero However just seting these nodes to zero photogeneration will typically cause an apparent drop in quantum efficiency The photogeneration rate at the contact nodes is calculated as usual However this photogeneration rate is applied
109. using a table of values This parameter is used as follows TABLE infile table file name where table file name is an ASCII text file that contains the tabulated time dependence of a variable in the following format EX ow t2 v2 E3 w3 tN vN end Each line contains two numbers The first number is the time in seconds The second number is the time dependent variable voltage in volts the current in amps or the resistance in ohms U p to 1000 lines can be used Input is terminated by the word end If during the simulation the transient time becomes larger than the last value in the table then the last value will be used for the remainder of the simulation AC Parameters 1 MIXEDMODE allows AC parameters to be specified for independent voltage Vxxx and current I xxx sources These parameters describe the AC behavior of the source Syntax AC value Description value specifies the AC source value in V for voltage sources and in A for current sources 10 32 SILVACO International MIXEDMODE Compact Device Models This section provides a detailed description of the models and parameters used to describe diodes bipolar transistors and MOS transistors Models are selected using the element and model statements Parameters associated with model equations are described here as part of the model description Diode Model The equivalent circuit for the diode model is shown on Figure 10 3 Anode
110. 0 348 3 1 0407 675 0 331 5 2 010 524 0 219 0 4 0107 385 0 220 8 6 010 321 0 2103 8 8 0410 279 0 186 9 1 0 x1018 252 0 178 0 2 0x1018 182 5 130 0 4 0 1018 140 6 90 0 6 0 1018 113 6 74 5 8 0101 99 5 66 6 1 040 90 5 61 0 2 0107 86 9 55 0 4 0107 834 53 7 6 0 10 78 8 52 9 SILVACO International 3 33 ATLAS User s Manual Volume 1 Table 3 17 Mobility of Electrtons and Holes in Silicon at T 300K Continued Concentration cm Mobility cm2 v s Electrons Holes 8 051012 71 6 524 1 03102 67 8 52 0 2 03020 52 0 50 8 4 0 1020 35 5 49 6 6 0 1020 23 6 48 9 8 0 1020 19 0 48 4 1 04021 17 8 48 0 The Analytic Low Field Mobility Model The following analytic function based upon the work of Caughey and Thomas 22 can be used to specify doping and temperature dependent low field mobilities T ALPHAN CAUG Ung MU1N CAUG sso 3 121 T BETAN CAUG T ALPHAN CAUG MU2N CAUG soi MU1N CAUG soo Tn GAMMAN CAUG N o 500x NCRITN CAUG T L ALPHAP CAUG Hpo mu1p caus so 3 122 T BETAP CAUG T ALPHAP CAUG L L MU2P CAUG scar MU1P CAUG soar Tj GAMMAP CAUG N DELTAP CAUG d s00K l ucxrss cuss where N is the local total impurity concentration in cm and T is the temperature in degrees Kelvin 3 34 SILVACO International Physics This model is activated by specifying both the coxmoB and anaLytic parameters in
111. 0157 KLA S6 KLA S2KLA Pgy 7300 e n m T 3 145 3 40 SILVACO International Physics G P 21 SLKLA S5 KLA is m T S4KLA S3 KLA m 300 97 KLA S6 KLA S2KLA Pss des BH p m T 3 146 where T is the temperature in degrees Kelvin me and mj are the electron and hole masses and the parameters s1 kLA through s7 kLA are user specifiable model parameters as shown in Table 3 24 Table 3 24 User Specifiable Parameters for Equations 3 145 and 3 146 Statement Parameter Default Units OBILITY S1 KLA 0 89233 OBILITY S2 KLA 0 41372 OBILITY S3 KLA 0 19778 OBILITY S4 KLA 0 28227 OBILITY S5 REA 0 005978 OBILITY S6 KLA 1 80618 OBILITY S7 KLA 0 72169 The functions F P and F Pp in equations 3 143 and 3 144 are given by Me RLKLA PROKLA R2 KLA R3 KLA gx h 3 147 pR6 KLA R4 KLA R5 KLA mn m R1 KLA PRO KLA R2 KLA R3 KLA CENA CETERI 3 148 F P m pR6 KLA RA KLA R5 KLA p me p where the parameters r1 kLA through r6 kLA are user specifiable model parameters as shown in Table 3 25 Table 3 25 User Specifiable Parameters for Equations 3 147 and 3 148 Statement Parameter Default Units MOBILITY R1 KLA 0 7463 MOBILITY R2 KLA 2 2999 MOBILITY R3 KLA 6 5502 SILVACO International 3 41 ATLAS User s Manual Volume 1 Table 3 25 User Specifiable Parameters for Eq
112. 10 0 4 0 1017 3263 0 205 0 6 0 1017 2950 0 200 0 8 0 1017 2747 0 186 9 1 0 1018 2600 0 170 0 2 0 1018 2060 0 130 0 SILVACO International 5 19 ATLAS User s Manual Volume 1 Table 5 5 Default Concentration Dependent Mobility for GaAs Mobility in GaAs cm v s Concentration cm 3 Electrons Holes 4 0 1018 1632 0 90 0 6 0 1018 1424 0 74 5 8 0 1018 1293 0 66 6 1 0 1012 1200 0 61 0 If MODEL ANALYTIC is specified the program will use 8000 940 0 75 TAR 2 8 10 where Nt is the total impurity concentration lll V and II VI Materials Ly p 940 5 52 Al x Ga 1 x As System The Al x Ga 1 x As material system is commonly used for the fabrication of heterojunction devices These materials are available in BLAZE by specifying the material name GaAs AlGaAs or AlAs Asa ternary material system different material properties are obtained by adjusting the molar fraction of Aluminum and Gallium This mole fraction is represented by the x as written in Al x Ga 1 x As GaAs material parameters are identical to the those of AlGaAs with mole the fraction x set equal to zero AlAs material parameters are identical to the those of AlGaAs with mole the fraction x set equal to one Fundamental in the proper simulation with the AlGaAs material system is the relationship between this mole fraction x and the material parameters for that composition In the following secti
113. 10 505 pq a rom 3 126 Jnpin 1 7 45 10P npy 300 AN CCS TL D esx a y _ CCS EA 300 300 Hn c MN a E Sed T 3 2 T AP CCS 3 Jens Hp AN n Sen where x 7 f x ma x TA The values of the lattice scattering terms TN are defined by T 122 Lo L T 22 Lo L Hp MP xs 3 130 Table 3 20 User Specifiable Parameters for Equations 3 127 and 3 128 Statement Parameter Default Units OBILITY AN CCS CCS EA 4 61 1017 cm OBILITY AP CCS 1 0 1077 eu OBILITY BN CCS 1 52 1015 cm OBILITY BP CCS 6 25 1014 cm SILVACO International 3 37 ATLAS User s Manual Volume 1 Klaassen s Unified Low Field Mobility Model The model by D B M Klaassen 114 115 provides a unified description of majority and minority carrier mobilities In so doing it includes the effects of lattice scattering impurity scattering with screening from charged carriers carrier carrier scattering and impurity clustering effects at high concentration The model shows excellent agreement between the modeled and empirical data for majority electron mobility as a function of donor concentration over the range of 101 cm to 1022 em e minority electron mobility as a function of acceptor concentration over the range of 10 cm to 102 cm e minority hole mobility as a function of donor concentration from 101 cm to 10 am temperature dependence over the range of 70 K to 500 K 3 The Klaassen model
114. 11 1 expl t td1 taul 11 12 l exp t td2 tau2 GAUSS GAUSS is used to define a Gaussian waveform The waveform is specified as follows GAUSS i1i2td1 taul td2 tau2 where 10 30 SILVACO International MIXEDMODE ilistheinitial value i2is the pulsed value td1 is the rise delay time td2 is the fall delay time taul is the rise time constant tau2 is the fall time constant The transient behavior will be Time Value 0 lt t lt tdl il tdist lt td2 ilc i2 i1 1 exp t td1 tau1 td2st 11 12 11 1 exp t td1 taul 11 12 1 expl t td2 tau2 SFFM SFFM is used to define a modulated sinusoidal waveform The waveform is specified as follows SFFM io ia fc mdi fs where io is the DC offset ia is the amplitude fc is the carrier frequency mdi is the modulation index fs is the signal frequency The transient behavior will be value t 30 ia sin r fc t mdi sin 2z fs t SIN SIN is used to define a sinusoidal waveform The waveform is specified as follows SIN io ia freq td theta where io is the offset ia is the amplitude freq is the frequency td is the delay theta is the damping factor SILVACO International 10 31 ATLAS User s Manual Volume 1 Thetransient behavior will be Time Value Eyed value t io t 2 td value t iO0ria exp t td THETA sin 2m freq t td TABLE TABLE is used to define a waveform
115. 2 Hue E T IRB sy z C r d WES 10 45 nm C 10 50 SILVACO International MIXEDMODE Capacitance Equations The total capadtance for all junctions contains two terms depletion capacitance and diffusion capacitance The depletion capacitance dominates low frequency behavior The diffusion capacitance dominates high frequency behavior Base Emitter Capacitance Equations The base emitter capacitance contains a complex diffusion term with a standard depletion capacitance formula The diffusion capacitance is modified by model parameters TF XTF ITF and vrr The base emitter capacitance is determined by cbe cbediff cbedep 10 46 where cbediff is the base emitter diffusion capacitance and cbedep is the base emitter depletion capacitance Base Emitter Diffusion Capacitance d ibe E cbediff TF 75 for ibex 0 10 47 bediff TE 14 He ap these 10 48 cbediff 3l arg 71 or ibe where 2 Vpc ibe 144 VTF argtf XTF TETT 10 49 Internal base emitter current is determined by q Vbe be ISE op En 10 50 e Base Emitter Depletion Capacitance There are two different equations for modeling the depletion capacitance The desired equation is selected by specifying the option capmop in the optrons statement CAPMOD 1 yy MIE cbedep CIE orp 1 v for vbe lt FC VJ E 10 51 Vbe FC 1 MJE MJE WE cbedep CIE orp RC TXJE for Vbe 2 FC VJ E 10 52 CAPMOD 2 The base emitter depletion capacitan
116. 2 3 Recombination Models Model Syntax Notes Shockley Read Hall SRH Uses fixed minority carrier life times Should be used in most simu lations Concentration Dependent CONSRH Uses concentration dependent life times Recommended for Si Auger AUGER Direct transition of three carriers Important at high current densities Optical OPTR Band band recombination For direct materials only Recombination at semiconductor to insulator interfaces Set on the INTERFACE statement n zZ Surface n HU 2 24 SILVACO International Getting Started with ATLAS Table 2 4 Impact lonization Model Syntax Notes Silberrherr s Model IMPACT SELB Recommended for most cases Includes temperture dependent param eters Grant s Model IMPACT Similiar to Selberrherr s model but with different coefficients Crowell Sze IMPACT CROW Uses dependence on carrier scatter ELL ing length Toyabe Model Non local model used with Energy Balance Any IMPACT syntax is accepted Concannon N CONCAN Non local model developed in Flash P CONCAN EEPROM technologies Table 2 5 TUnneling Models and Carrier Injection Models Model Syntax Notes Fowler Nordheim elec FNORD Self consistent calculation
117. 2 4 ATLAS User s Manual Volume 1 AC Parameter Extraction Basic analysis of the capacitance and conductance matrix produced by ATLAS can be done using DECKBUILD or TonYPLoT The capacitance between gate and drain will be labeled as C gate drainin Tonyplot or c gate drain in DECKBUILD S EXTRACT The total capacitance on any electrode is defined as C electrode gt electrode Thus the magnitude of C gate gt gate is total gate capacitance The roc statement also includes options for small signal two port RF analysis including s parameter extraction The solutions are saved into thelog file and alsoin the run time output The list of options for RF analysis is S param y param h param z param abcd param gains Terminal impedance and parasitics are accounted for by adding any of the following impedance lt val gt rin lt val gt rout lt val gt rcommon lt val gt or rground lt val gt lin lt val gt lout lt val gt lcommon lt val gt or lground lt val gt width lt val gt The width defaults to lum and impedance defaults to 50Q All parasitics default to zero The Stern stability factor k is calculated along with current gain h21 GUmax and GTmax when the GAINS option is added to the Loc statement The run time output for AC analysis has been modified to only list the analysis frequency and electrode conductance capacitance values f one of the two port options is added to the Loc statement such as s PA
118. 2 KAUGCP sy 3 228 where the model parameters KAUGCN KAUGCP KAUGDN and KAUGDP are user definable on the MATERIAL Statement and have the defaults shown in Table 3 40 This model is activated by spedifying the kLAAuG paramater of the MopELs statement Table 3 40 User Specifiable Parameters for Equation 3 227 and 3 228 Statement Parameter Default Units MATERIAL KAUGCN 1 83e 31 cm s MATERIAL KAUGCP 2 78e 31 cm s MATERIAL KAUGDN 1 18 MATERIAL KAUGDP 0 72 Narrow Bandgap Auger Model An alternative model for the Auger recombination coefficients that is more suitable for modelling Auger processes in narrow bandgap semiconductors can be enabled by setting the parameters kAGUN and kacup on the MopELs statement The model in ATLAS is a simplification of that by Beattie 146 and takes the form Rauger Ca pn nni C np Prie 3 229 where the Auger coefficients are concentration dependent according to AUGN n 1 AUGKNn 3 230 AUGP 231 P 1 AUGKP p vis where n and p are the electron and hole carrier concentrations and the new parameters auckn and AUGKP are user definable on the mopELs statement Surface Recombination In addition to generation recombination within the bulk of the semiconductor electrons or holes may recombine or be generated at interfaces The rate of surface recombination may be even greater than within the bulk The standard method is to model
119. 3 eV Alternatively it is possible to use the C interpreter to apply a user defined model for energy relaxation time as a function of carrier energy On the mopeLs statement the parameter F TAURN and F TAURP should be assigned the names of external files that contain the user defined C interpreter function for the energy relaxation time The flag TAUR VAR and H TAUR VAR should also be specified in the MODELS statement when using C interpreter functions for the energy relaxation times Energy Dependent Mobilities The energy balance transport model requires the carrier mobility to be related to the carrier energy This has been achieved through the homogeneous steady state energy balance relationship that pertains in the saturated velocity limit This allows an effective electric field to be calculated which is the uniform electric field value which causes the carriers in an homogeneous sample to attain the same temperature as at the node point in the device The effective electric fields E gp and E ef y are calculated by solving the equations 2 3 KT T1 HACE err nE ff n 2TAUREL EL lm k T T 3 p L he Atty E err pE eft p STAUREL HO TE for E eff y and E eff These equations are derived friom the energy balance equations by stripping out all spatially varying terms The effective electric fields are then introducecd into the relevent field dependent mobility model A full
120. 4 K Electron Affinity As indicated in the introduction the semiconductor electron affinity x is a key parameter for determining the alignment of heterojunctions For AlGaAs x is a function of E gr and is given by XAIGaAs 4 07 0 85 E r x composition E GaAs 5 57 Density of States and Effective Mass The valence and conduction band densities of states Nc and Ny are calculated from the effective masses according to the following equations 3 2nm kT Y N 3 5 58 h 3 2nm kT Y N gt T h For the AlGaAs system the conduction band and valence band effective masses for electrons and holes are given by m 0 067 5 60 SILVACO International 5 21 ATLAS User s Manual Volume 1 2 1 5 1 5 3 where mp and mg represent the light hole and heavy hole effective masses which for this system are my 0 082 5 62 Dielectric Permittivity The default static dielectric constant for AlGaAs is given by AlGaAs 13 8 2 9 x composition 5 64 Low Field Mobility The default low field electron mobility for AlGaAs is a function of the composition fraction x within the system The following equations outline this relationship AlGaAs Low Field Mobility Mole Fraction Range Ha 8000 1818x104 X composition 0 x composition 0 429 u 90 1435510 composition oa 0429 composition 0 49 u 90 375x107 x composition 0 46 0 46 x composition 0 5
121. 5 0 NAME BASE Dual Base BJTs It is possible in S PISCES to tie two or more contact together so that voltages on both contacts are equal This is useful for many technologies for example dual base bipolar transistors There are several methods for achieving this depending on how the structure was initial defined If the structure is defined using ATLAS syntax it is possible to have multiple ELECTRODE statements with the same NAME parameter defining separate locations within the device structure In this case the areas defined to be electrodes will be considered as having the same applied voltage A single current will appear combining the current through both ELECTRODE areas Similarly if two separate metal regions in ATHENA are defined using the ATHENA ELECTRODE statement to have the same name then in ATLAS these two electrodes will be considered as shorted together If the electrodes are defined with different names the following syntax canbe used to link the voltages applied to the two electrodes SILVACO International 4 5 ATLAS User s Manual Volume 1 CONTACT NAME basel COMMON base SOLVE VBASE 0 1 Here the electrode basel will be linked to the electrode base Later the applied 0 1V on base will also appear on basel However ATLAS will calculate and store separate currents for both base and basel This can be a useful feature However in some cases such
122. 74 i N Emission coefficient L SILVACO International 10 33 ATLAS User s Manual Volume 1 Note RS should never be set to 0 in MIXEDMODE Table 10 2 Diode Capacitance Parameters Parameter Description Units Default x Area TT Transit time sec 0 FC Coefficient for the forward bias 0 5 depletion capacitance formula CJO Zero bias junction capacitance F 0 Ls M Junction grading coefficient 0 5 VJ Junction potential V 0 8 DC Current Equations This diode model is based on the original Berkeley model kT Define Vie N gt vc v q For forward bias defined as vg gt 10 v ig IS opp on Sd IS E Va Va te e te 10 1 10 2 10 3 In cases of reverse bias node 1 anode is more negative than cathode The diode is turned off and conducts a small leakage current For reverse bias ig Ser Capacitance Equations 10 4 The diode capacitance is modeled by the parameter cy This capacitance is a combination of diffusion capacitance cgi and depletion capacitance Cyep Ca Caiff Cdep 10 5 10 34 SILVACO International MIXEDMODE Diffusion Capacitance Equations The diffusion capacitance due to the injection of minority carriers is modeled by the transit time parameter TT In practice TT is estimated in time domain from time delay measurements di Depletion Capacitance Equations The follow
123. AP CAUG 3 BETAP CAUG 3 5 28 SILVACO International BLAZE Impact lonization and Thermal Parameters The equations governing these effects are identical to those for Silicon but with adjusted coefficients Please refer to Appendix B for a list of all these parameters Simulating Heterojunction Devices with Blaze Defining Material Regions with Positionaly Dependent Band Structure Step Junctions The easiest way to define a device with positionally dependent band structure is to specify two adjacent semiconductor regions with dissimilar bandgap In this case BLAZE would simulate an abrupt heterojunction between the two materials As an example suppose the user wanted to simulate an abrupt heterojunction parallel to the x axis at a location of y 0 1 microns For values of y greater than 0 1 the user might specify for example GaAs For values of y less than 0 1 the user might specify AlGaAs with a composition fraction of 0 3 The following statements would specify this situation REGION Y MIN 0 1 MATERIAL GaAs REGION Y MAX 0 1 MATERIAL Al1GaAs X COMPOSITION 0 3 This fragment specifies that the two regions form an abrupt heterojunction at Y 0 1 The first region is composed of GaAs while the second is composed of AlGaAs These two material names are used by BLAZE to choose default material models for the two regions A complete list of the materials which are available in ATLAS BLAZE is given in Ap
124. AS User s Manual Volume 1 Regrid On DOPING is is Ce OU RR bs Aue lcs aac Ree ies 2 13 Regrid Using Solution Variables A ad 2 14 Specifying 3D Structures codec sse eu a Re mu e ER PERI Ede wees ae ede e 2 15 General Comments Regarding Grids cose dada td 2 15 Maximum Number Of A O 2 16 Defining Material Parameters And Models ccc cece eect e eee eee eee teens 2 17 Specifying Contact Characteristics eco Patet es pr ctt Le peti ear picti bep RS Diet ees 2 17 Workfunction for Gates or Schottky Contacts ecc k rt n t n RR n 2 17 Setting Current Boundary Conditions v ure nt tea ta n Pe oce A E E te es 2 18 Defining External Resistors Capacitors or Inductors 2 0 0 cece cect rr 2 18 Floating Contact O E 2 18 Shorting two contacts together ocio secus Re DEN 2 19 Making an open circuit contact 1 a a Wea da ai 2 20 Specifying Material Properties ecards add cri seda 2 20 SSItng Paramelels at Pee cfc e AOS ad o IS eb Ls 2 20 Heterojunction A Pete e pto tcu ede sapo te avc Ranae e aa 2 21 Specifying Interface Properties 0 0cooooccooccooco rr Hmmm 2 21 Specifying Physical Models s cusctsctiidanaiave RR eR ERE ti a cda 2 21 Energy Balance MOUGIS iei rd trt trcs V Beo bw b eS e RIVE Rare e ans 2 22 Summary Of Physical Models ics di dics eder ee RR vane ee rp x de das 2 23 Using The C Interpreter To Specify Models tna cs Lat eae e rc t af e deat 2 26 Choosing Numerical Methods ccc cece cece e cece eee II nn 2 27 Numerica
125. AS User s Manual Volume 1 rs Source Gate ggs ps ggd CGD a Mis ji o wn N 0 Drain Figure 10 9 MOSFET Equivalent Circuit for Transient Analysis Table 10 12 MOSFET Model Parameters Parameters Description Units Default Area TOX Oxide thickness meter m 1 0 1077 KP Transconductance parameter A V 2 0 1075 NSUB Substrate doping 1 cm 0 GAMMA Bulk threshold parameter V0 5 0 THETA Mobility modulation 0 0 KAPPA Saturation field factor 0 2 PHI Surface potential v 0 6 DELTA Width effect on threshold voltage 0 ETA Static feedback 0 VTO Zero bias threshold voltage v 0 RD Drain ohmic resistance ohm 0 RS Source ohmic resistance ohm 0 RSH Drain and source diffusion sheet resistance ohm sq 0 10 62 SILVACO International MIXEDMODE Table 10 12 MOSFET Model Parameters Parameters Description Units Default Area CGDO Gate drain overlap capacitance per meter F m 0 channel width CSDO Gate source overlap capacitance per meter F m 0 channel width CGBO Gate source overlap capacitance per meter F m 0 channel width CJ Zero bias bulk junction bottom cap per F m2 0 meter of junction area PB Bulk junction potential v 0 8 MJ Bulk junction bottom grading coef 0 5 CJSW Zero bias bulk junction sidewall cap per F m 0
126. ATLAS User s Manual Volume 1 Concannon s Injection Model The implicit assumption in the lucky electron approach is a Maxwellian shape for the energy distribution of the hot carriers Recent work by Fiegna 129 using Monte Carlo simulations suggests a non M axwellian high energy tail tothe distribution function To more accurately model these effects a non M axwellian based model from Concannon 112 has been implemented This model requires the solution to the energy balance equation for the carrier temperatures but has been implemented in a similaiar manner to the lucky electron model The Concannon gate injection model may be specified with the parameters N coNCANNON and P CONCANNON on the mopeLs statement This choice of parameters will automatically activate the energy balance model The Concannon injection model has a similiar form to the lucky electron model The injected current is calculated according to li JP cx y n x y dx dy Ps y p x y dx dy 3 287 where n x y and p x y are the carrier concentrations within the semiconductor The probability functions P x y and P x y are now defined by Pa X y q CGATE N Po Pi P 3 288 Pp X y q CGATE P Po Pi pPap 3 289 where q is the electronic charge and the parameters ccaTE N and ccATE P are user definable on the MODEL Statement The three probability functions in equations 3 288 and 3 289 shall now be described The probability that a carrier has sufficie
127. E OUTPUT CON BAND VAL BAND Saving Quantities from the Structure at each Bias Point PROBE statement Structure files provide all data from the structure at a single bias point The Log files provide terminal characteristics for a set of bias points To combine these and allow certain structural quantities to be saved at each bias point the PROBE statement is used The PROBE statement allows the user to specify quantities to be saved at given XY locations There is also a facility to save the maximum or minimum of certain quantities The value from the PROBE at each bias point in DC or timestep in transient mode is saved to the log file The syntax PROBE NAME mycarriers N CONC X 1 Y 0 1 will save the electron concentration at 1 0 1 for each solution in the log file When the log file is displayed in TonYPLoT the value will be labelled mycarriers It will be possible to plot mycarriers versus terminal bias or current or other probled quantities SILVACO International 2 43 ATLAS User s Manual Volume 1 Certain directionally dependent quantities such as electric field and mobility can be probed In these cases a direction for the vector quantity must be specified using the DIR parameter The PROBE statement provides the only way to extract the actual values of quantities that are calculated along the sides of each triangle in ATLAS The PROBE statement actually stored the triangle side value closest t
128. FSTEPS 10 2 SOLVE VBASE 0 7 AC FREQ 1e6 FSTEP 2 MULT F NFSTEPS 10 The first case ramps the frequency from 1GHz to 11GHz in 1GHz steps A linear ramp of frequency is used and FSTEP is in Hertz In the second example a larger frequency range is desired and so a geometrical step of frequency is used The MULT F parameter is used to specify that rsTEP is a unitless multiplier for the frequency This doubles the frequency in successive steps from 1Mhz to 1 024GHz The syntax described here for ramping the frequency of the AC signal can potentially be combined with that for ramping the bias The frequency ramps are done as inner loops tothe DC ramping SOLVE VBASE 0 0 VSTEP 0 05 VFINAL 1 0 NAME base AC FREQ 1 0e6 FSTEP 2 MULT F NFSTEPS 10 2 34 SILVACO International Getting Started with ATLAS Transient Solutions Transient solutions can be obtained for piecewise linear exponential and sinusoidal bias functions Transient solutions are used when a time dependent test or response is required To obtain transient solutions for a linear ramp the TSTART TSTOP TSTEP and RAMPTIME parameters should be specified The TSTART parameter specifies the time that the linear ramp should start The RAMPTIME specifies the time that the linear ramp should obtain its final value TsTOP specifies the time that solutions will stop TsTEP specifies the initial step size Subsequent time steps are calcu
129. Fermi level is calculated from the local elec tron density via Equation 3 9 FALSE TRUE Quasi Fermi level is uniform across Y slice and is calculatd to match the classical and quantum mechan ical sheet charge RUE FALSE Quasi Fermi level is uniformly zero RUE TRUE Quasi Fermi level varies with Y position and is cal culated to match the local classical and quantum mechanical charge concentration Quantum Moments Model The quantum module in ATLAS is applicable to several different types of problems 1 HEMT channel confinement simulation 2 Thin gate oxide MOS capacitors and transistors 3 Other problems such as small geometry MESFETs and Heterojunction diode The effects due to comfinement of carriers associated with variations of local potential on the scale of the electron wave functions i e quantum effects can be modeled in ATLAS using a quantum transport model This model is based on moments of the Wigner function equations of motion 120 121 consists of quantum correction to the carrier temperatures in the carrier current and energy flux equations Equations 3 74 3 75 3 77 and 3 78 The quantum correction tothe carrier temperature is given by 2 lg sra 3 317 where Tq is the quantum corrected carrier temperature T is the carrier temperature and Uq is the quantum potential When the quantum moment model is enabled the carrier temper
130. For example MODEL HCTE EL enables the energy balance model for electrons ESD Simulation In some cases lattice heating may be of importance for MOS simulation This typically occurs in cases with very high currents as is the case with ESD simulation In these cases GIGA should be used to simulate the heatflow in the device To enable heat flow simulation the LAT TEMP parameter of the MODEL Statement should be set a licensefor GIGA is required For example the statement ODEL LAT TEMP enables heatflow simulation 4 4 SILVACO International S PISCES Simulating Silicon Bipolar Devices Physical Models for BJTs S PISCES provides special physical models for bipolar device simulation These models can be selected using the MODEL statement The BIPOLAR parameter of the MODEL statement enables a reasonable default set of bipolar models These include concentration dependent mobility conmoB field dependent mobility FLDMOB band gap narrowing BGN concentration dependent lifetime CONSRH and Auger recombination AUGER For the most accurate bipolar simulations the recommended mobility model is the Klaassen Model KLA This includes doping temperature and carrier dependence It applies separate mobility expressions for majority and minority carriers This model should also be used with Klaasen s Auger model KLAAUG and Klaassen s concentration dependent SRH model kLasrH The
131. H P are user specifiable parameters as given in Table 3 46 3 72 SILVACO International Physics Table 3 46 User Specifiable Parameters for Equations 3 262 and 3 263 Statement Parameter Default Units IMPACT CSUB N 2 0e14 IMPACT CSUB P 4 0e14 IMPACT ETH N 148 eV IMPACT ETH lt P DS eV The function F e T in Equations 3 262 and 3 263 is given by the product of the density of states function g e and the energy distribution function f e as Eo g e f e 3 264 f eof The density of states function is given by g e e 3 265 The energy distribution functions for electrons and holes are CHIA e CHIB e f e exp 3 COexp 3 3 266 Ta Te f CHI HOLES fp amp exp T 3 267 XE p where is energy Th are the carrier temperatures CHIA CHIB and co are user specifiable parameters as given in Table 3 47 Table 3 47 User Definable Parameters for the Energy Distribution Functions Statement Parameter Default Units IMPACT CHIA 3 0e5 IMPACT CHIB 5 0e4 IMPACT CO 2 5e 10 IMPACT CHI HOLES 4 6e4 Two other parameters of the impact statement are user definable that may effect the result of the numeric integration The ENERGY STEP parameter specifies the energy step size in eV used during the numeric integration The default step size is 25 meV The INFINITY parameter sets the u
132. II 2 cna aed a cate e oct 2 3 Running a given version number of ATLAS oc cct et cute oe ek to I MT A 2 3 Star ng Parallel ATLAS cosas a decent aig ROLE wan write ues ic ARA actas 2 3 Batch Mode Without DeckBulld socias Roe Re che ERI a EC ERROR RR 2 3 Accessing The Examples 155 4150 35 44 1a ER a ak dead Wa LT dia cwm a 2 4 Me ATLAS Syntax ii AAA AA AA 2 5 Statements and Parameters acc ttre nan d aos to de on d eec dM eto Dra dE 2 5 The Order of ATLAS CommandS iussa ERR dare der ote SIR dran stack tco Rcx og V ar DV Rod 2 6 The DeckBuild Command Menu enero rix XR RR RR beh Rer a EERRPERE PREGA 2 7 Dick Start Tor PISCES PUSE eat ance is is a Re aed ena Dd 2 7 Defining A Struct r sc oorr e geh rd 2 8 Interface Pro ATHENA ti a A tet d a a i Pb 2 8 Interface From DEE rabia X Pobre dba afecten DU Dex pardas 2 9 Using The Command Language To Define A Structure ssssssssssss 2 9 Specifying The Initial Mesh 2 rues uet dois E ON S ey LE SI a Men s i mae 2 9 Specifying Regions And Materials 0 isses Hmmm 2 10 EXI CCOO S s 2 004 Diete a Sr AS alg dut A A dr Alea hk AAR ae etin 2 11 Specifying Electrodes o Fe osos oat dab ok Li dale vost erii qp A anu 2 11 5pecitying DOPING 5 ose est rei dd edat 2 11 Analytical Doping TOMES ara a tddi os ro MC 2 12 Importing 1D SSUPREM3 Doping Promesa c rer t S Lees s 2 13 Remeshing Using The Command Language 225 eque p De e CE EON he ole oh dtt tic ts 2 13 SILVACO International vii ATL
133. LVACO International TFT Ec E E R G y oir i 1 E Y 0xp p g E dE 7 14 k Ey The summation in Equation 7 13 runs over all acceptor bands j stands for TA and GA and the summation in Equation 7 14 runs over all donor bands k stands for TD and GD A transient trap simulation using this model is more time consuming than using the static model but gives a much more accurate description of the device physics It may sometimes be acceptable to perform transient calculations using the static trap distribution and assume that traps reach equilibrium instantaneously Specifying Fast on the DEFECTS statement will neglect the trap rate equation from the simulation Trap Assisted Tunneling Thetrap assisted tunneling models can be used to include the effects of electrons tunneling through the bandgap via defects This model is enabled by specifying rRaP TUNNEL on the moDELs statement The capture cross sections 6 and op enhanced by the field effect terms rh and I as given by Hurkx et al 134 in the following manner o gS 7 15 no TE Oo P 7 16 OPTED P o n and o p replace op and op in the previous equations Equations 7 8 to 7 14 Ta and T are given by Equations 3 67 and 3 69 in Chapter 3 Continuous Defects If continuous is specified on the pgrecrs statement then the integral equations for the charge and recombination are evaluated using a numerical integral scheme
134. NET I1 V2 DEC 10 1e6 1e10 ZO 5 RSOUT 2 100 NET V 1 0 V 2 3 DEC 10 1e6 1e10 TRAN TRAN specifies that a transient analysis is to be performed Syntax TRAN tin tstop Parameter Type Default Units tin Real S tstop Real S 10 22 SILVACO International MIXEDMODE Description tin is the initial timestep tstop is the final time value for which the simulation is to be performed Transient analysis is performed only after the execution of all DC statements If no DC statements are used the transient starts after the calculation of the initial circuit state with the values of the independent sources given in the descriptions of those sources Multiple TRAN statements are supported The TSTOP parameter is NOT reset between each TRAN statement Example TRAN 1ns 100ns LOAD LOAD loads a solution file Syntax LOAD INFILE lt filename gt Description INFILE specifies the name of a file to be loaded as an initial guess for further simulation This file must have been saved during a previous run of MIXEDMODE using the SAVE statement Example LOAD INFILE pdsave Note This statement is not used to load SSF format solution files from ATLAS see OPTIONS LOADSOLUTIONS SAVE SAVE saves simulation results into files for visualization or for future useas an initial guess Syntax SAVE outfile name master mname Description outfile specifies that after the simulation is finished the solution i
135. NIN A A tuat fro i prd IS 10 29 Pda ra ets ale dada webs Ea 10 30 GAUSS Lar adds teins AAA Sd da e da wena AA Kup Sa 10 30 SRF pe TEE 10 31 SNP Eos ossis uid uie ta eal oad vitate dte rate peti lus c c Sod fai are AN 10 31 TABLE M TM 10 32 AC Parametros 10 32 Compact Device Models iii aae Y cv xr aat Er YAE eX acd seas 10 33 Dioda Model rs de cil caes lacio 10 33 BIT Model acts AOS 10 35 BTModelP arme a ii CR 10 40 BJT Model Equations beer ibid pr toe e 10 48 DC Current Equations vu ose rere oe soria dors RC ERR DR OT 10 49 Base Charge Equations utc ters ectetuer edat A dub ANI IN E Rat 10 49 Variable Base Resistance Equations 10 50 Capacitance Equations i isis eme eR da inh bug ea Exc near ene 10 51 Temperature Effects Equations as x Test dco bs troverete t sies A etude foe at ra 10 54 Capacitance Temperature Equations ccc c e 10 58 Parasitic Resistor Temperature Equations i sce reca Le Co bal ec t etin 10 60 MOS FET Model tad et m A eet heo tla etd da a eoi aos 10 60 DC Current EU vot a Pei clau E NEA CQ ames a Aet dictt n cat diei us ias 10 64 User Defined Two Terminal Elements 149 secessit pp xv e cda ker ER nd Rs 10 68 D VOIVIGIN usted o an e p tun ACIDS KORR shane eaten RAUS si Rp eta 10 68 User Defined Model ac seva E Seton deter eot i drea genio 10 68 Input Parameglels cs dai n Gi VE Idee kg aie CAI dort RUNI e IS ani ee GENAN 10 69 Xvi SILVACO International Table of Contents Output Parameters
136. NIX usethe command atlas input filename To save the run time output to a file do not use the UNIX redirect command gt simply specify the name of the output file atlas input filename logfile output filename SILVACO International 2 3 ATLAS User s Manual Volume 1 Note The standard examples supplied with ATLAS will not run correctly outside of DECKBUILD Accessing The Examples ATLAS is supplied with morethan 300 standard examples that demonstrate the way that the program is used to simulate many different technologies The examples are instructional and it is strongly recommended that new users use these examples as a starting point for creating their own simulations One of the first things you should learn is how to access load and run these examples The examples are accessed from the menu system in DECK BUILD To select and load an example 1 Start DeckBuiLD with ATLAS as the simulator as described in the previous section 2 Pull down the MainControl menu using the right hand mouse button There are options on this menu for MainControl Optimizer Examples Help etc 3 Select Examples An index will appear in a DEckBuiLb Examples window see below 3 Deckbuild Examples Index T Section T zl Index v 1 MOS1 MOS Application Examples 2 MOS2 Advanced MOS Application Examples 3 BJT Bipolar Application Examples 4 DIODE Diode Application Examples 5 SOI Application Exampl
137. O or 1 J tot is thetotal energy flux and s is theunit external normal of the boundary The projection of the energy flux onto s is Gs 3 Kon T P F In St TP Pp Cp s 6 13 When o 0 Equation 6 12 specifies a Dirichlet fixed temperature boundary condition Tq TEMPER 6 14 where TEMPER may be defined on the THERMCONTACT Statement as shown in the next section Dirichlet boundary condtions may be specified for an external boundary which may coincide with an electrode or for an electrode that is inside the device When o 1 Equation 6 12 takes the form BE T 6 15 Jas R L TEMPER where the thermal resistance Ryp is given by 1 Rth ALPHA and ALPHA is user definable on the rHERMCONTACT statement Specifying Thermal Boundary Conditions Setting thermal boundary conditions is similar to setting electrical boundary conditions The THERMCONTACT statement is used to specify the position of the thermal contact and any optional properties of the contact Thermal contacts may be placed at any position in the device including sidewalls Equation 6 15 is used if a value is specified for a otherwise Equation 6 14 is used The following command specifies that thermal contact number 1 is located between x 0 um and x 2 um at y 0 um and that the temperature at the contact is 300K THERMCONTACT NUM 1 X MIN 0 X MAX 2 Y MIN 0 Y MAX 0 TEMP 300 A simpler statemen
138. ONTAC INDUCTANCE Hum Resistance is specified in Q m capacitance is specified in F um and inductance is specified in H um The following combinations are possible resistance only resistance and capacitance inductance and resistance inductance capacitance and resistance For the case of inductance or capacitance only ATLAS adds a small resistance as well For more complicated circuit configurations it is necessary to use the MIXEDMODE module of ATLAS Note Capacitance increases with device width into the z plane while resistance decreases Except for the case of extremely large resistances where the arrangement becomes similar to a pure current 3 28 SILVACO International Physics Source no convergence degradation has been observed for a lumped element boundary in comparison to a simple ohmic contact Transient simulation therefore becomes easier and is more well defined It is a good idea to use the simulator to calculate any resistance or capacitance components that might be included as lumped elements When peforming CMOS simulations you could simulate just the p tub with ohmic contacts at either end From the plot of terminal current in A nm versus voltage resistance can be directly extracted from the slope Be very careful to consider any three dimensional effects e g current spreading before using a resistance value in further simulations When looking at the results of simulation w
139. ORCHID The Orchid module in ATLAS allows users to simulate total radiation dose effects on reliability in MOS devices These effects are treated by modelling the gate oxide as a semiconductor The user does this by adding a MATERIAL statement identifying the gate oxide region using the REGION parameter and adding the parameter SEMICONDUCTOR to the statement This MATERIAL statement should immediately follow the structure definition or mesu statement if the structure is read in Next the user must specify a C interpreter function F OXGENERATE On the Beam statement This function specifies the generation rate of electron hole pairs in the oxide as a function of position time and electric field The user must also specify a C interpreter function F oxCHARGE on the popING statement This function specifies the oxide charge density as a function of position field electron and hole currents and time The user then runs the simulation in the time domain capturing the state of the structure at various times of interest These structures can then be simulated to extract the ID VG characteristics to examine the threshold shifts as a function of exposure The Ferroelectric Permittivity Model Ferroelectric materials exhibit high dielectric constants polarization and hysterisis Such materials are finding more and more applications in integrated memory devices To allow simulation of these effects a modified vers
140. P WA 92 8 cm2 V s OBILITY REF2N WA 591 0 cm2 V s OBILITY REF2P WA 124 0 cm2 V s OBILITY REF3N WATT 1270 0 cm2 V s OBILITY REF3P WA 534 0 cm2 V s OBILITY ALIN WA 0 16 OBILITY AL1P WA 0 296 3 52 SILVACO International Physics Table 3 31 User Specifiable Parameters for Equations 3 189 3 192 Statement Parameter Default Units MOBILITY AL2N WA 2 17 MOBILITY AL2P WATT 1 62 MOBILITY AL3N WA 1 07 MOBILITY AL3P WA 1 02 Modifications to Watt s Model By default the Watt mobility model is a surface model that applies only to those grid points on the silicon oxide interface A modification has been added that now applies the Watt model to points below the interface This extension to the Watt model is enabled using the moD wATT N and MOD WATT P parameters of the MoBILITy statement The distance over which the model is applied can be controlled by using the ymaxn watt and the YMAXP WATT parameters of the moBILITY statement These parameters specify the maximum value of the y coordinate over which the model is applies below the interface for electrons and holes respectively The xMINN WATT XMINP WATT XMAXN WATT and xMAXP WATT Of the moBILITY statement can be used to limit the range of the model in the x direction to prevent the model from applying to the source and drain regions The rx sunr parameter of the MopELs stat
141. RAM the two port parameters are also included in the run time output The UTMOST statement AC parameter conversion utilities have been discontinued UTMOST Interface ATLAS log files can be read directly into batch mode UTMOST The following commands in UTMOST are used to read in a set of IV curves stored in separate log files INIT INF lt filename gt MASTER INIT INF filename MASTER APPEND Use of the older urTMOsT statement in ATLAS is no longer recommended for interfacing to UTMOST Solution Files Solution files or structure files provide a snap shot of the device at a particular bias point DC solution or transient solution point This gives the user the ability to view any evaluated quantity within the device structure in question from doping profiles and band parameters to electron concentrations and electric fields These files should be plotted using TonYPLorT The syntax used to generate these files is of two forms 1 SAVE OUTFILE lt filename gt Here a file named filename will be saved with data from the previously solved bias point 2 SOLVE OUTFILE filename sta MASTER ONEFILEONLY In this case a structure file will be saved at each bias point solved in the solve statement The last letter of thefile name will be automatically incremented alphabetically sta stb stc and soon If the solution for the last bias point only is required
142. RB2 Second order temp coeffi 1 deg 0 cient for RB SILVACO International 10 45 ATLAS User s Manual Volume 1 Table 10 11 Temperature Effect Parameters Parameters Description Units Default Area TRC1 First order temp coefficient 1 deg 0 for RC TRC2 Second order temp coeffi 1 deg 0 cient for RC REI First order temp coefficient 1 deg 0 for RE RE2 Second order temp coeffi 1 deg 0 cient for RE TRM1 First order temp coefficient 1 deg 0 for RM TRM2 Second order temp coeffi 1 deg 0 cient for RM F1 First order temp coefficient 1 deg 0 for TF F2 Second order temp coeffi 1 deg 0 cient for TF R1 First order temp coefficient 1 deg 0 for TTR R Second order temp coeffi 1 deg 0 cient for TTR TVAF1 First order temp coefficient 1 deg 0 for VAF TVAF2 Second order temp coeffi 1 deg 0 cient for VAF TVAR1 First order temp coefficient 1 deg 0 for VAR TVAR2 Second order temp coeffi 1 deg 0 cient for VAR TVJC Temp coefficient for V deg 0 VJE Temp coefficient for V deg 0 TVJS Temp coefficient for V deg 0 tnom Parameter measurement C tem perature 27 10 46 SILVACO International MIXEDMODE Lateral and vertical transistors are shown in Figures 10 6 and 10 7 AREAB Overhead View of Lateral Transistor AREAE AREAC Y
143. S 555 E eit p Z22P TAS E 3 178 eff p 3 48 SILVACO International Physics 7 Brus RN TAS 1 Ej 3 179 eff n 7 RN TAS E Prap URE TRS oT Bg 3 180 eff p RP TAS T BIN TAS T Y PIN TAS P2N Tas n PWTAS LN 3 181 n 300 300 f T BIP TAS Ted Y PIP TAS 305 P2P TAS p PAP TAS N 3 182 Mobility degradation due to surface roughness is accounted for by the term usr which is calculated according to BETAN TAS Usp n ESRN TAS E ef n 3 183 Hsr p ESRP TAS E py ARAS 3 184 Thefinal term uc models Coulombic scattering with the expressions T 45 T N2N TAS 505 uu ud Na In 14 y ys BHn A BH n 1 Yan T 35 N2P TAS 505 EM C j Np Ind Ygu e HBO P 1 Bu p where N1N TAS T ALPHAN TAS YBH n qa 300 3 187 N1P TAS du ALPHAP TAS YBH p p S 300 3 188 In the above equations T is the lattice temperature in degrees Kelvin Nf is the fixed interface charge at the gate dielectric silicon interface cm NA is the channel acceptor doping concentration in cm Np is the channel donor doping concentration in cm n and p are the electron and hole SILVACO International 3 49 ATLAS User s Manual Volume 1 concentrations per unit volume in the inversion layer cnY 3 The default parameters within each equation may be defined on the MOBILITY statement The default parameters are shown in Table 3 30
144. SAVE 1 MODELS LAS MULTISAVE TRUE ATERIAL LAS TOLER 0 01 ATERIAL LAS ITMAX 30 ATERIAL LAS SIN 100000 cm ATERIAL LAS TAUSS 0 05 ATERIAL LAS MAXCH 2 25 Semiconductor Laser Simulation Techniques The most common technique for simulating laser diodes is to simulate forward characteristics with gradually increasing bias The forward voltage is usually specified but current boundary conditions can be used and external elements can be included 9 8 SILVACO International LASER To save computational time we recommend that you do not enable LASER models at the start of the simulation Ramp the device bias first and then enable LASER simulation using the LASER parameter in an additional mopELs statement In general the single frequency Laser model which does not take into account the longitudinal mode spectrum is faster This model provides good results very reliably and is recommended for use if the lasing spectrum is not the subject of interest If the multiple longitudinal mode model is used computational time will be longer and strongly dependent on the number of longitudinal modes involved in the calculation Although ATLAS is a two dimensional simulation framework the laser spectrum and all other laser results are strongly dependent on cavity length which is effectively the device length in the z direction This situation is different than for other ATLAS simulators For example terminal currents can normally be
145. ST a swept DC variable VAR 1 a stepped DC variable VAR2 or a transient solution PULSE The remaining cells specify the parameter values that are required for the type of solution desired The pop up window to specify the solution file names are accessed through the Props button Several solve statements may be constructed to create solve sequences which define a test This test may be saved in a file and read in using the Save and Load buttons A powerful features of the DEckBuiLD SOLVE menu is the ability to generate a family of curves using the sweep and step variables Interpreting The Results As indicated in Figure 2 1 ATLAS produces three different types of output To recap these are RUN TIME OUTPUT This stores the run time messages produced by ATLAS These messages typically indude impor tant values extracted from the simulation All error messages go to the run time output If a simu lation fails it is extremely important to check the run time output for error and warning messages LOGFILES Storethe DC small signal AC and transient terminal characteristics for a sequence of SOLVE statements They are loaded into ToNvPLor to visualize the device behavior SOLUTION FILES These store physical quantities of the structure at each grid node for a single bias point These can be viewed in TonyPLot to see the internal distributions of parameters eg potential electric field They can also be loaded into other A
146. T 0 71 OBILITY BETAN CVT 2 00 OBILITY BETAP CVT 2 00 OBILITY PCN CVT 0 0 cm OBILITY PCP CVT 0 23 1016 cm 3 OBILITY DELN CVT 5 82 1014 V s OBILITY DELP CVT 2 0546 10 4 v s Note The cvr model when activated will also by default apply the parallel electric field mobility model which is described in a later section of this chapter In this model the low field mobility is supplied from the cvr model The Yamaguchi Model The Yamaguchi model is selected by setting vavacucnr on the mopELs statement This model overrides any mobility model specifications other than the cvr model The model consists of calculating the low field doping dependent mobility Surface degradation is then accounted for based upon the transverse electric field before including the parallel electric field dependence Thelow field part of the Yamaguchi model is given as follows N 2 l uno MULN YAMA 1 y SN YAMA NREFP YAMA 3 164 N E u MULP YAMA 1 4 A 3 165 po N sp YAMA NREFP YAMA where N is the net impurity concentration The equation parameters MULN YAMA MULP YAMA SN YAMA SP YAMA NREFP YAMA and NREFP YAMA are user definable on the moBIL1TY statement and have the defaults shown in Table 3 29 Thetransverse electric field dependence is accounted for as follows 1 2 Hs n Hpo t ASN YAMA E 3 166 3 46 SILVACO International Physics 1 2 Hs p Hpo 1 ASP YAMA E 3 167 w
147. T NAME source CON RESISTANCE 0 01 specifies that the source contact has a distributed resistance of 0 01 Qam Note Simulations with external resistors capacitors or inductors must be solved using the BLOCK or NEWTON solution method Floating Contacts The CONTACT statement is also used to define a floating electrode There are two distinctly different situations for which floating electrodes are important The first is floating gate electrodes used in EEPROM and other programmable devices The second is for contacts directly onto semiconductor materials such as floating field plates in power devices Floating gates are enabled by specifying the parameter FLOATING on the CONTACT statement The statement CONTACT NAME fgate FLOATING specifies that the electrode named fgate will be floating and that charge boundary conditions will apply For contacts directly onto semiconductor the FLOATING parameter cannot be used This type of floating electrode is best simulated by specifying current boundary conditions on the CONTACT statement The statement CONTACT NAME drain CURRENT 2 18 SILVACO International Getting Started with ATLAS specifies current boundary conditions for drain electrode On subsequent SOLVE statements the drain current boundary condition will default to zero current hence floating the contact It is also possible make a floating contact to a semiconductor using a very large resistor attache
148. TLAS device must have at least two electrodes The maximum number of electrodes allowed in ATLAS is 50 This means that up to 25 ATLAS devices can be specified for example 25 devices with 2 electrodes each or 10 devices with 5 electrodes each may be specified The use of ATLAS device models should be sparing since it can be very time consuming Use circuit models for less important circuit components to conserve CPU time infile specifies the name of standard structure format file with device geometry mesh doping electrodes names etc The number of electrodes and their names should match those mentioned in this statement Optionally this file can contain a solution which MIXEDMODE will use as an initial guess see the OPTIONS statement for more details width is an optional parameter default 1 All currents through ATLAS device terminals calculated using the 2 D ATLAS model will be multiplied by this parameter to account for the third dimension of the device Width can still be used as a multiplier to the ATLAS current if a 3D ATLAS structure is used in MIXEDMODE3D Example ABJT1 3 EMITTER 4 BASE 6 COLLECTOR INFILE BJT1 STR WIDTH 10 10 12 SILVACO International MIXEDMODE B User defined two terminal element Syntax Bxxx n n INFILE file name FUNCTION function name where Bxxx specifies the element name of a user defined two terminal device It must begin with a B n n
149. TLAS runs tore initialize ATLAS at non zero biases Run Time Output Run time output is provided in the bottom of the Deck BuiLD window If run as a batch job the run time output can be stored to a file Errors occuring in the run time output will be displayed in this window Note that not all errors will be fatal as deckbuild tries to interprete the users file and continue This may cause a statement to be ignored leading to unexpected results It is recommended that the user check the run time output of any newly created input file the first timeit is run tointercept any errors If the user specifies the PRINT option within the MODELS statement details of material parameters constants and mobility models will be specified at the start of the run time output This is a useful way of checking what has been spedified and which mobility parameters apply to which regions It is recommended that the user always specifies MODELS PRINT in input files During soLve statements the error numbers of each equation at each iteration are displayed This is a change from the previous ATLAS version It is is not vital for users to understand the iteration information but it may provide important insights in the case of convergence problems 2 38 SILVACO International Getting Started with ATLAS The output can be interpreted as follows proj psi n p psi n p direct x x x rhs rhs rhs i j m 95400 5 00 5 00 26 0
150. TS i is used to set an integer number of reflections to consider Users should note that setting a very large number of reflections can lead to extremely long simulation times for the ray trace One very convienient way to overcome the long CPU times is to use the parameter MIN POWER This terminates each ray when the optical power falls to the fraction ofthe original power defined by this parameter Front Reflection By default reflection and refraction at the first interface the initial interface with the device are ignored The first reflection coefficient is zero and the transmission coefficient is one The polarization and angle of the transmitted ray at the first interface is identical to the polarization and angle of the incident beam If the FRONT REFL parameter of the BEAM statement is specified the transmission coefficient is calculated using Equations 8 1 to 8 6 When the transmission coefficient is calculated it is assumed that the material outside the device domain is a vacuum The transmitted rays are attenuated by the transmission coefficient but the reflected ray is not traced Back Reflection By default the reflection at the back of the device are ignored No reflected ray is traced once the back of the device is reached If the BACK REFL parameter is specified the backside reflection coefficient is calculated again assuming a vacuum outside the device and the back side reflected ray is traced
151. These names can be used in the SOLVE statements for setting bias voltages such as SOLVE VGATE 1 0 VSTEP 1 0 VFINAL 5 0 NAME GATE Gate Workfunction In MOS simulations the workfunction of the gate is an important parameter This must be set in each input deck using the work parameter of the contact statement For example CONTACT NAME GATE WORK 4 17 would set the workfunction on the gate at 4 17 eV Certain material names can also be used to set the workfunction of common gate materials For example CONTACT NAME GATE N POLY would set the workfunction on the gate to that of n type polysilicon Note The gate workfunction should be set on a contact statement even though the material or workfunction might be set from ATHENA or DEVEDIT SILVACO International 4 3 ATLAS User s Manual Volume 1 Interface Charge For accurate simulation of MOS devices the interface charge at the oxide semiconductor interface should be specified This can be done by setting the or parameters for the INTERFACE statement Typically a value of 3e10 is representative for the interface charge found in silicon MOS devices The proper syntax for setting this valuefor interface fixed charge is INTERFACE QF 3e10 The user may also choose to try to model the fixed charge more directly by using interface traps to simulate the surface states This can be done using the INTTRAP s
152. UNCTION MAX DOPING LEVEL CONC Net Do in ems s Nel Doping 2 15 1 05 o 0 5 1 1 5 2 2 5 Microns SILVACO International 1994 f Figure 2 5 Analytical specification of a 2D Profile Position parameters X MIN X MAX Y MIN and Y MAX may be used instead of a region number The second statement specifies a p type Gaussian profile with a peak concentration of 1018 cm DOPING GAUSSIAN CONCENTRATION 1E18 CHARACTERISTIC 0 05 P TYPE X LEFT 0 0 X RIGHT 1 0 PEAK 0 1 This statement specifies that the peak doping is located along a line from x 0 to x 1 microns Perpendicular to the peak line the doping drops off according to a Gaussian distribution with a standard deviation of 0 05 mm At x lt 0 or x gt 1 the doping drops off laterally with a default standard deviation that is 7096 of CHARACTERISTIC This lateral roll off can be altered with the RATIO LATERAL parameter If a Gaussian profile is being added to an area that was already defined with the opposite dopant type then the JUNCTION parameter may be used to specify the position of the junction depth instead of specifying the standard deviation using the CHARACTERISTIC parameter 2 12 SILVACO International Getting Started with ATLAS Importing 1D SSUPREM3 Doping Profiles One dimensional doping profiles can be read into ATLAS from a SSUPREM3 output file The doping data must have been saved from SSUPREM3 using the sta
153. UNO 2e 7 TAUPO 1e 5 sets the electron and hole Shockley Read Hall recombination lifetimes for region number two If the name base has been defined using the NAME parameter in the REcron statement then the statement MATERIAL NAME base NC300 3e19 sets the conduction band density of states at 300 K for the region named base The description of the MaTERIAL statement in the Statements Chapter provides a complete list of all the material parameters that are available 2 20 SILVACO International Getting Started with ATLAS Heterojunction Materials The material properties of heterojunctions can also be modified with the MATERIAL statement n addition to the regular material parameters compositionally dependent material parameters can be defined These include compositionally dependent band parameters dielectric constants saturation velocities and so on For heterojunction material systems the bandgap difference between the materials is divided between conduction and valence bands The ALIGN parameter specifies the fraction of this difference that is applied to the conduction band edge This determines the electron and hole barrier height and overrides any electron affinity specification The statement MATERIAL MATERIAL InGaAs ALIGN 0 36 MATERIAL MATERIAL InP ALIGN 0 36 specifies that 36 of the band gap difference between InGaAs and InP goes to the conduction band and
154. User s Manual Volume 1 Table 6 5 User Specifiable Parameters for Equations 6 16 and 6 17 Statement Parameter Default Units MATERIAL TAUNO 1e 7 S MATERIAL TAUPO 1e 7 S MATERIAL LT TAUN 0 MATERIAL LT TAUP 0 See Equations 3 213 and 3 214 for information regarding concentration dependent lifetimes C interpreter Defined Peltier Coefficients A C interpreter functions is available that can be used to define the Peltier coefficient ksn and ksp as a function of the electron and hole carrier temperatures T and Tp This is defined using the syntax MODELS F KSN filename F KSP filename where the lt filename gt parameter is an ascii file containing the c interpreter function See Appendix A for more information regarding the c interpreter Applications of GIGA Power Device Simulation Techniques This section contains a series of techniques which you may find useful when simulating typical power device structures Not all of the features described below are specific to GIGA and are common to the ATLAS framework Floating Guard Rings No special syntax is needed for the simulation of un contacted doping areas used in floating guard rings The program is able to simulate guard ring breakdown with the standard impad ionization models n some extreme cases convergence may be slow due to poor initial guesses If convergence is slow both GUMMEL and NEWTON should be specified in the METHOD statem
155. VACO International MIXEDMODE Parameter Type Default Units RELPOT Logical False NOSHIFT Logical False RV Real 1 1074 W CNODE Real 1 10 19 F WRITE Integer 1 LOADSOLUTIONS ogical False CYLINDER iogical False Z PARA jogica False Y PARA ogical False H PARA jogica False ABCD PARAM jogica False GAINS jogica False Description TNOM specifies the circuit temperature to be use during the simulation FULLN M2LN specifies the solution method to be used during steady state simulation FULLN specifies the full Newton method M2LN specifies the modified two level Newton method The full Newton method provides faster solution than the modified two level Newton method when a good initial guess is available The modified two level method is more reliable when the initial guess is far from the solution The default is the full Newton method PRINT enables printing of circuit nodes voltages after the calculation for each bias point DC analysis or time step transient the analysis RELPOT enables the use of relative convergence criteria for potential for ATLAS models By default ALTAS models use absolute convergence criteria for potential When bias voltages are large a common situation for power devices then absolute convergence criteria are not appropriate and this parameter should be specified NOSHIFT disables the shift of voltages for ATLAS device models MIXEDMODE normally shifts
156. When ATHENA and ATLAS are run under DeckBuiLpD users can take advantage of an automatic interface between the two programs Use the following steps to load the complete mesh geometry and DOPING from ATHENA to ATLAS 1 Deposit and pattern electrode material in ATHENA 2 Use the ELECTRODE statement in ATHENA to define contact positions Specify the x and y coordinates as cross hairs to pin point a region The whole region is then turned into electrode In many cases only the x coordinate is needed ECTRODE NAME gate X 1 3 Y 0 1 3 Thereis a special case to specify a contact on the bottom of the structure LECTRODE NAME substrate BACKSIDE 4 Savea structure file while ATHENA is still the active simulator STRUCTURE OUTF nmos str 5 Start ATLAS with the command go atlas This will automatically load the most recent structure from ATHENA into ATLAS Note Do not specify a mzsH command in ATLAS If you subsequently need to load the structure saved in step 4 into ATLAS without using the auto interface capability use the MESH command eg MESH INF nmos str ATLAS inherits the grid used most recently by ATHENA With a careful choice of initial mesh or by using the grid manipulation techniques in ATHENA it is possible to produce a final mesh from ATHENA that will give good results in ATLAS However a grid that is appropriate for process simulation is not always appropriate for device simulati
157. a ISC 10 13 IKF of area IKF 10 14 IKRef area IKR 10 15 IRB off area IRB 10 16 For vertical and lateral devices the resistor model parameters RB RBM RE and rc are scaled according to the following equations RBer RB area 10 17 RBM ag RBM area 10 18 RE oe RE area 10 19 RCeff RC area 10 20 BJT Current Convention Figure 10 4 shows the direction of current flow through a bipolar NPN device For a bipolar PNP device polarities of the terminal voltages gate junction directions and the direction of the current sources are reversed 10 36 SILVACO International MIXEDMODE Collector lio Q2N2222 ib Q2N2222 is Q2N2222 SE Base Bn oubstrate 2N2222 lie Q2N2222 Emitter Figure 10 4 NPN BJT Current Convention PNP are opposite BJT Equivalent Circuit MIXEDMODE uses two equivalent circuits for analysis of bipolar devices DC and transient The fundamental components in the equivalent circuit are the collector i and base ip currents and their partial derivatives with respect to terminal voltages Vp and Vpe The ic and ip equations account for all DC effects of the BJ T The names of the partial derivatives are Output conductance di di 8 A Eo Vp const 10 21 Vee Vg const OVpe Transconductance di di di di Em Dube Ov dvp vbe 6 10 22 Forward bias conductance di Sz Ovbe 10 23 Vie const Reverse bias conductance SILVACO Interna
158. a n Kg Similar expressions for holes are H kT D q A Fay a p n FAY IP V VAN T 3 k Dp tas 5g Ja zu un Ip Hop 7 Mp3 p JF 172015 k 2 P gp mola App 3 80 3 81 3 82 3 83 3 84 3 18 SILVACO International Physics s aJ t gp P POr 2 F 3 2 Mp PP 2 F amp 172 m p 2 p pap 3 85 Hp If Boltzmann statistics are used in preference to Fermi statistics the above equations simplify to An Ap 1 3 86 5 Ap n 3 3 87 5 Ap Sp 5 65 3 88 7 d inu Th Oly ies E d Inpp E Tp OH oe P dnp Mp OT The parameters and are dependent on the carrier temperatures Different assumptions concerning and p correspond to different non local models In the high field saturated velocity limit that corresponds to velocity saturation the carrier mobilities are inversely proportional to the carrier temperatures n Sp 1 3 91 and this corresponds to the Energy Balance model If instead the choice 0 was chosen this would correspond to the simplified Hydrodynamic model The parameters and p may be specified using the parameters ksn and ksp on the MODELS statement Boundary conditions for n p and y are the same as for the drift diffusion model Energy balance equations are solved only in the semiconductor region Electron and hole temperatures are set equal to the lattice temperature on the contacts On the other part of the boundar
159. a Emitter Collector Emitter Collector Base Cross section of Lateral Transistor Figure 10 6 A Lateral Transistor SILVACO International 10 47 ATLAS User s Manual Volume 1 AREAE Overhead View of Vertical Transistor AREAB AREAC Base E Emite y Base Collector lt Buried Collector y Base Collector lt Buried Collector Cross section of Vertical Transistor Figure 10 7 A Vertical Transistor BJT Model Equations The DC characteristics of the BJ T transistor are determined by twenty model parameters Define Belma NF v i pr forward diffusion current BEC e hes 10 25 Vbe NE v ibe non ideal base emitter current ISE e 2 10 26 Voc 1 P IS NR Vi pr reverse diffusion current BR 1 10 27 Vpc NC v ig non ideal base collector current ISC e 10 28 10 48 SILVACO International MIXEDMODE DC Current Equations Current equations for the collector current i and the base current ip are Ib I bf tibe lbr tipc 10 29 Vbe Vbc Voc o Seg NF NR V Pep NRO y s ETE e BR e If IBE and IBC are both specified instead of IS Vp Vp IBE IBC a Pe e Sf NF Nis 7 eff NR vp E i ab e 3b e 10 31 IBC Voce Voce eff NR y NC y Tu 1 15 y Z IBE eq IBC 400 aa NF NR pus e A a ed 10 32 BF BR Vp c Vbc NR y NC y
160. a btt ON 6 5 Thermal Boundary Conditions 1225 ace E CREE Pr eT Rad Hebr ER COE IY aran 6 6 Temperature Dependent Material Parameters 0 ccc cee teeter me 6 7 C interpreter Defined Peltier Coefficients 20 isses Hmm 6 8 Applications of GIGA 00 ole EN IR eat mu pM UN EM E Bote IUE 6 8 Power Device S THU ladori TechiniQ les a cute cct Lon atar PERS RET RET Eres pd ehe 6 8 Moreiintormaton do ast acid ducto artt hay vC AUS Pea aa DDR do SUC A a Foe oe 6 9 Chapter 7 CE Wied tele atado O AAN T 1 Polycrystalline and Amorphous Semiconductor Models 00oocoocoocccrrrcr o 7 1 nioduction Serai O A a alk atte Saas 7 1 Simulating WET DEVICES A NA Iram dow ware dr Ar Aot Pts usa e aa 7 1 Defining The Materials c ous ser actress 29 ub O O 7 1 Defining The Defect States uiui stos as e e en 7 1 SILVACO International Xiii ATLAS User s Manual Volume 1 Density of States Model e cocodrilo Ae RC RR e 1 2 Trappedd ater Densi cios suce A E reddituri did ceri teg 1 3 Steady state Trap Recombination rk RR x er RR bees bey rd ed dae 7 4 MASIA a a tio odia la 7 4 Trap Assisted A E dod id 7 5 Continuous Defect duas toov rante at than ede be etat Rant tat pup ca pid et aan i 1 5 Discrete Defects aida rr ia AO sani ee Fe Rua Wei Fede ee oa eb 1 5 Plotting The Density Of States Versus Energy sssssssssssses nn 1 6 Using the C Intemreter to define DEFECTS 5 ien rana Feeder ies vif pics 1 6 Setting Mobility and Other Model
161. active Tools manual Using MIXEDMODE inside the VWF Automation Tools Like all other Silvaco products MIXEDMODE is fully integrated into the VWF framework and can be used for automated experiments There are some points however to take into account a The auto interface feature does not work with MIXEDMODE All structures have to be explicitly saved in unique files previous to the MIXEDMODE runs and referred toin the A element statements b MIXEDMODE is not re entrant which means that splits within MIXEDMODE runs are not possible To overcome this problem the SET statement should be used to define a variable in a process simulator or in the dummy internal run This variable is used to parameterize the input file Example Capacitance as an independent split variablein a VWF experiment go internal define the independent split variable in a re entrant simulator set cap 5e 9 go atlas BEGIN use the variable as parameter in MIXEDMODE El 2 3 cap c The automation tools only store files opened by the normal ATLAS Loc statement in the VWF database but ignore those defined by LoG To overcome this re initialize ATLAS open the relevant log file of the previous MIXEDMODE run again with log with the append option in order not to reset it Example MIXEDMODE log file definition LOG OUTFILE hallo Re opening the second DC log file and the transient log file to get them stored in the VWF database g
162. affinities x and x This example is similar to the bandstructure of a HFET or HEMT For this example Eg Eg and x x Allocating the conduction band offsets using the affinity rule and AE AE AE 5 2 SILVACO International 5 3 ATLAS User s Manual Volume 1 AE is the amount of the conduction band discontinuity at the heterointerface and AE is is the amount of the valence band discontinuity Note Remember the Affinity Rule is invoked to calculate the conduction band offset for a material as long as the ALIGN parameter is NOT specified on the MATERIAL statement for that material Using the ALIGN parameter on the MATERIAL statement Let s assign 80 of the bandgap difference between Materiall and Material2 to the conduction band offset Define the a cw parameter on the maTERIAL statement for Material 2 using MATERIAL NAME Material2 ALIGN 0 80 Then AE Ej E 1 0 80 5 3 Internally the affinity of Material 2 is adjusted so that AE equals this value This value of electron affinity will override any electron affinity specification for Material 2 This has an impact on any calculation where this materials electron affinity is used and must be considered when specifying Schottky barriers contacted to this materials See Example 4 for more details on Schottky barrier considerations Manually Adjusting Material Affinity MATERIAL NAME Material2 AFFINITY VALUE where VALUE is adjusted to provide
163. al Electric Field Models Selberherr s Impact lonization Model The ionization rate model proposed by Selberherr 3 is a variation of the classical Chynoweth model 127 It is activated by the sers parameter of the rmpact statement and is based upon the following expressions BETAN 0 AN ep HE l 3 236 BETAP ap APex l 3 237 where E is the electric field in the direction of current flow at a particular position in the structure and the parameters AN AP BN BP BETAN and BETAP May be defined on the impact statement and have the default values shown in Table 3 42 In the case of an AP Bw and Bp it is also possible to define a value of electric field Ecran V cm where for electric fields lt zcran V cm the parameters are AN1 AP1 BN1 BP1 Whilst for electric fields gt cran V cm the parameters become an2 AP2 BN2 and BP2 The an and BN parameters are also a function of the lattice temperature in this model The temperature dependence of these coefficients is defined as follows T M ANT AN AN Z1 A NT 355 Al 3 238 T M APT AP AP Z1 A PT 35 al 3 239 T M BNT BN BN Z1 B NT 355 Al 3 240 T M BPT BP BP Z1 B PT 3c Al 3 241 The parameters associated with these equations are shown in Table 3 43 SILVACO International 3 67 ATLAS User s Manual Volume 1 Table 3 42 User Definable Parameters in the Selberherr Impact lonization Model
164. al variations in composition the standard modifications to the drift diffusion equations can be considered adequate for simulation purposes For abrupt heterojunctions it has been suggested that thermionic emission may be the dominant factor in the behavior of heterojunction behavior Individual material parameters and models can be defined for each material or region These models are set in the MATERIAL MODEL and Impact statements This statement uses the MATERIAL parameter to select all regions composed of the material InP The bandgap in these regions will be set to 1 35 The parameters of a particular region can be set in two ways The first is by way of the region index as in MODEL REGION 1 BGN In this case the band gap narrowing model is enabled in the region indexed number 1 The region name may also be used as in the following IMPACT NAME substrate SELB This example turns on the Selberherr impact ionization model in the region named substrate Finally parameters can be set for all regions and materials by omitting the MATERIAL REGION Or NAME parameters as in the following MODEL BGN This statement sets the bandgap narrowing model for all regions and materials Parser Functions The use of parser functions requires knowledge of the C programming language please consult Appendix A for a description of the parser functions To specify completely arbitrary spatial variation o
165. ally with the substrate and the gate biased the drain potential is added and the system solved again The advantage of this method over the first case is that the small incremental changes in voltage allow for better initial guesses at each step Generally the projection method for the initial guess gives good results when the I V curve is linear However it may encounter problems if the IV curve is highly non linear or if the device operating 2 32 SILVACO International Getting Started with ATLAS mode is changing Typically this might occur around the threshold or breakdown voltages At these biases smaller voltage steps are required to obtain convergence As will be described ATLAS contains features such as the TRAP parameter and the curve tracer to automatically cut the voltage steps in these highly non linear area Numerical methods are described earlier in this chapter In many cases these methods are designed to overcome the problems associated with the initial guess This is particularly important in simulations involving more than the three drift diffusion variables In general coupled solutions require a good initial guess whereas de coupled solutions can converge with a poor initial guess The Initial Solution When no previous solutions exist the initial guess for potential and carrier concentrations must be made from the doping profile This is why the initial solution performed must be the zero bias or thermal equilibriu
166. alternative surface mobility model that can be combined with KLA Modified Watt MOD WATT Extension of WATT model to non surface nodes Applies constant E effects Best model for planar MOS devices Lombardi CVT Model CVT Complete model including N T E and E effects Good for non planar devices Yamaguchi Model YAMAGUCHI Includes N E and E effects Only for 300K SILVACO International Physics CONMOB BLDMOB TFLDMB2 YAMAGUCHI CVT ARORA ANALYTIC CCSMOB SURFACE LATTICE H E BALANCE CONMOB CM OK OK YA CV AR AN CC OK OK OK FLDMOB FM OK TF YA CV OK OK OK OK OK OK TFLDMB2 TF OK TF YA CV OK OK TE TF OK OK YAMAGUCHI YA YA YA YA CV YA YA YA YA NO NO CVT CV CV CV CV CV CV CV CV CV OK OK ARORA AR AR OK OK YA CV AR CC OK OK OK ANALYTIC AN AN OK OK YA CV CC OK OK OK CCSMOB CC cc OK TF YA CV CC cc OK OK OK SURFMOB SF OK OK TE YA CV OK OK OK OK OK LATTICE H LH OK OK OK NO OK OK OK OK OK OK E BALANCE EB OK OK OK NO OK OK OK OK OK OK 2 Key to Table Entries MODEL ABBREVIATION The model that supercedes when a combination is specified In some cases but not all a warning message is issued when a model is ignored OK This combination is allowed NO This combination is not allowed NOTES 1 Uses internal model similar to FLDMOB 2 When models including a parallel
167. ame width at the beam origin and the sum of the rays will cover the illumination window Even when the RAYS parameter is specified ATLAS will automatically split the rays in order to resolve the device geometry Ray Splitting At Interfaces Rays are also split at interfaces between regions into a transmitted ray and a reflected ray Figure 8 2 illustrates the difference between rays that are split to resolve the geometry and transmitted reflected rays split at a region interfaces SPLIT INCIDENT REFLECTED HAYE RAYS INTERFACE GEOMETRA Y POHNT TRANSMITTED HAYES Figure 8 2 Reflected and Transmitted Rays In Figure 8 2 the incident rays come in from the top left They intersect an interface between two material regions with differing refractive indices Within this interface lies a geometric point where 8 2 SILVACO International Luminous the normal tothe interface changes This implies that the angles of reflection and transmission will be different for light incident to the left of the point from light incident on the right Thus the incident rays are split to resolve the interface point The second level of splitting occurs at the interface itself Herethe incident rays are split into reflected and transmitted rays Reflection and Transmission Figure 8 3 shows the relationship between the angles of incidence 6 reflection 8 and transmission 6 at the interface between two media These coefficients are calculate
168. and gaussian state syntax Theresultant distribution of defects versus energy can be plotted in the files don dat and acc dat DEFECTS F TFTDON tft lib F TFTACC tft lib DFILE don dat AFILE acc dat NTA 0 NID 0 WTA 1 0 WID 1 0 NGA 0 NGD 0 EGA 0 6 EGD 0 6 WGA 1 WGD 1 1 6 SILVACO International TFT SIGTAE 1 E 16 SIGTAH 1 E 14 SIGTDE 1 E 14 SIGTDH 1 E 16 SIGGAE 1 E 16 SIGGAH 1 E 14 SIGGDE 1 E 14 SIGGDH 1 E 16 Setting Mobility and Other Models TFT uses adaptations of the standard models of S PISCES or BLAZE An example of how to select the models and material parameters for polysilicon is MATERIAL MUN 300 MUP 30 MODELS SRH Note Concentration dependent mobility models CONMOB ANALYTIC ARORA KLA should not be used as this will overwrite the low field mobilities set in the MATERIAL statement Typical mobility values for amorphous silicon can be set by MATERIAL MUN 20 MUP 1 5 Other models are also available in TFT These include impact ionization and tunneling These can be set by MODELS BBT STD IMPACT SILVACO International 1 1 ATLAS User s Manual Volume 1 TFT TRAP DESCRIPTION TAIL AND GAUSSIAN DEFECT STATES Density of States Ev Energy ev Ec Figure 7 1 Syntax Guide to Define Two Tail States and Two Gaussian Distributions NGA and NDG are the integrated values of the Gaussian distributions Gaussians ar
169. and sIGMAH are the capture cross section of electrons and holes To activate this model the parameters DEVDEG DEVDEG E and DEVDEG H may be used in the MODELS statement to account for both hot electron and hole injection hot electron or hot hole injection respectively The model parameters are user definable on the DEGRADATION statement Table 3 51 User Definable Parameters for Equations 3 305 and 3 306 Statement Parameter Units DEGRADATION SIGMAE cm DEGRADATION SIGMAH cm DEGRADATION NTA F NTA cm DEGRADATIO NTD F NTD cm Theresults of stress simulation can be used to calculate the characteristics of the degraded device the shift of the threshold voltage transconductance degradation etc The distribution of traps hot electron hole current density and trapped electron hole distribution can be easily visualized using TONYPLOT SILVACO International 3 83 ATLAS User s Manual Volume 1 The model parameters NTA NTD SIGMAE and sIGMAH may also be defined through the C interpreter functions F NTA F NTD F SIGMAE and F sIGMAH This allows these values to be defined as functions of their position x y along the insulator semiconductor interface These C function libraries are also defined on the DEGrRADATION statement More information on the C interpreter functions can be found in Appendix A
170. arameter NOD 11 0 7 I gate use extracted gate bias and other expressions to calculate the set set v7 V gate I gate Rgl ES node settings Rgl 10 5 V 6 15 V 7 v7 A Sample Command File A sample MIXEDMODE command file is shown below This file was used to simulate the reverse recovery of a power diode Several MIXEDMODE examples are provided with the product which can be accessed using DECKBUILD B V1 R1 L1 R2 IL O 0 4 oO OC BF WN Pp 5 5 5 FPF OO DANA O O1 4 WN FP O N N 1 1 2 4 0 ADIO NUM OPTIONS PRINT RELPOT WRITE 10 LOAD LOG SAVE MOD MAT 0 2 3 0 4 DE go atlas EGIN 1000 im 2nH 1MG 300 EXP 1MG 1E 3 0 20NS 10 200 3 cathode 4 anode WIDTH 5 E7 INFILE pd str ER IC LT E 0 Ira Z 3 TOLTR 1 E 5 VCHANGE 10 EL S D E pdsave TRAN 0 1NS 2US EVIC E ADIODE REG 1 CONMOB FLDMOB CONSRH AUG ER IAL D EVIC E ADIODE REG 1 TAUNO 5E 6 TAUP 2E 6 ve ET V 1 2000 V 2 S Von V 3 S V_gate V 4 V_gate V 5 25 ER BGN 10 10 SILVACO International MIXEDMODE 22 1MPACT DEVICE ADIODE REG 1 SELB lt 23 24 METHOD CLIM DD 1 E8DVMAX 1 E6 25 26 go atlas 27 TONYPLOT pd tr log Line by Line Description Line 1 All ATLAS input files s
171. arge density and E ff is the effective electric field given by E E ETAN WATT Eg E 3 191 eff n E E FETAP WATT E E 3 192 eff p where E is the electric field perpendicular to the current flow and Eg is the perpendicular electric field at theinsulator semiconductor interface The equation parameters and their defaults are listed in Table 3 31 In Equations 3 191 and 3 192 E ff represents the effective electric field The terms on the right side of Equation 3 189 describe in order the three scattering mechanisms previously discussed Each component contains two constants a pre exponential factor and the exponent of the principal independent parameter The charge impurity scattering component is assumed to be inversely proportional to doping density The expression for effective mobility contains a number of normalizing constants These normalizing constants are included to allow easy comparison of constants The first two terms in this mobility model are dependent on E ff and represent the universal mobility field relationship The third term accounts for deviation from the universal relationship resulting from charged impurity scattering Table 3 31 User Specifiable Parameters for Equations 3 189 3 192 Statement Parameter Default Units OBILITY ETAN WATT 0 50 OBILITY ETAP WATT 0 33 OBILITY REFIN WA 481 0 cm2 V s OBILITY REFI
172. aries in the y direction Position parameters for the z direction z mIN and z Max arealsoused on REGION ELECTRODE or DOPING Statements General Comments Regarding Grids Specifying a good grid is a crucial issue in device simulation There is a trade off between the requirements of accuracy and numerical efficiency Accuracy requires a fine grid that resolves the strucure in solutions Numerical efficiency is greater when fewer grid points are used The critical areas to resolve are difficult to generalize since they depend on the technology and the transport phenomena The only generalization possible is that most critical areas tend to coincide with reverse biased metallurgical junctions Typical critical areas are High electric fields at the drain channel junction in MOSFETs Thetransverse electric field beneath the MOSFET gate e Recombination effects around the emitter base junction in BJ Ts Areas of high impact ionization e Around heterojunctions in HBT s HEMTs The cpu time required to obtain a solution is typically proportional to N where N is the number of nodes and a varies from 2 to 3 depending on the complexity of the problem Thus it is most efficient to allocate a fine grid only in critical areas and a coarser grid elsewhere Thethree most important factors to look for in any grid are Ensure adequate mesh density in high field areas e Avoid obtuse triangles in the current path or high field are
173. arrier considerations 5 6 SILVACO International BLAZE Note The band offsets are always defined with reference to the conduction band Therefore if a specific valence band offset is required the appropriate conduction band offset should be calculated from the desired valence band offset and the materials bandgap EXAMPLE 3 qvo Materiall Material2 Material3 Figure 5 4 Band diagram of three material system lowest E not in center Figure 5 4 details a heterostructure device consisting of three semiconductors with different bandgaps Ey1 Ey2 and E and electron affinities x1 x and x3 Thisis similiar tothe Example 2 except that the narrow bandgap material is not located in between the other larger bandgap materials As will be seen this adds extra complexity to the conduction and valence band offset calculations For this example Ey E lt E and X3 x x Allocating the conduction band offsets using the affinity rule AE 1 X1 X2 PM and for the heterojunction between Materiall and Material2 and AE 5 X2 X3 se SILVACO International 5 ATLAS User s Manual Volume 1 and for the heterojunction between Material2 and Material3 Using the ALIGN parameter on the MATERIAL statement Notice that the reference material the material with the smallest bandgap in this case Material2 is not shared between the two larger bandgap materials M
174. arrier considerations Manually Adjusting Material Affinity Assigning the conduction band offsets for each heterojunction is accomplished by setting the electron affinities for Material2 and Material3 using the AFFINITY parameter on the MATERIAL statement The electron affinity for Material2 is adjusted relative to Material land Material3 is adjusted relative to Material2 by the amount of the desired conduction band offset for each heterojunction Since Materiall affinity is larger than that for Material2 and Material2 affinity is larger than that for Material3 the affinities for Material2 and Material3 are reduced to provide the desired conduction band offsets Let s assume an electron affinity for Material 1 of 4eV that of GaAs Let s decide that between Materiall and Material2 the conduction band offset is 0 3eV and that between Material 2 and Material 3 the conduction band offset is 0 2eV Then for Material 2 MATERIAL NAME Material2 AFFINITY 3 7 and for Material 3 MATERIAL NAME Material3 AFFINITY 3 5 This is the easiest method to define the conduction band offsets for multiple materials This value of electron affinity will override any electron affinity specification This has an impact on any calculation where this materials electron affinity is used and must be considered when specifying Schottky barriers contacted to this materials See Example 4 for more details on Schottky barrier consideration
175. as e Avoid abrupt discontinuities in mesh density More information concerning grids is provided in the Numerical Techniques chapter SILVACO International 2 15 ATLAS User s Manual Volume 1 Maximum Number Of Nodes ATLAS sets some limits on the maximum number of grid nodes that may be used H owever this should not be viewed as users as a bottleneck to achieving simulation results In the default version e 2 D ATLAS simulations have a maximum node limit of 9 600 e 3 D ATLAS simulations have an upper limit of 200 000 nodes with no more than 20 000 in any one plane This limit is high enough that for almost all simulations of conventional devices running out of nodes is never an issue For most 2 D simulations accurate results can be obtained with somewhere between two thousand and four thousand node points properly located in the structure If the node limits are exceeded error messages will appear and ATLAS will not run successfully Decreasing the mesh density is the first option since simulations with the maximum nodes will take an extremely long time to complete However if it is deemed absolutely necessary to include more than the maximum number of nodes please contact your local Silvaco office to describe your needs so that Silvaco may be better able to meet them A version of each ATLAS release with 20 000 nodes is routinely available Versions of 2 D ATLAS up to 100 000 nodes have been distributed A node point limita
176. as where functions of the currents are required in EXTRACT or TonYPLoT it is undesirable The parameter SHORT may be added to the CONTACT statement above to specify that only a single basecurrent will appear combining the currents from base and basel When loading a structure from ATHENA or DEvEpiT where two defined electrode regions are touching ATLAS will automatically short these and use the electrode name that was defined first Creating an Open Circuit Electrode It is often required to perform a simulation with an open circuit such as for an open base breakdown voltage simulation on one of the defined electrodes From a device simulation viewpoint there are three different methods that will accomplish this These are Entirely deleting an electrode from the structure file e Adding an extremely large lumped resistance for example 10790 onto the contact to be made open circuited e Switching the boundary conditions on the contact to be made open circuited from voltage controlled to current controlled and then specifying a very small current through that electrode Each of these methods are feasible but if in doing so a floating region is created within the structure then numerical convergence may be affected As a result it is normally recommended that the second method that of a lumped resistance be used as it ensures that nofloating region is created Solution Techniques for BJTs To obtain bipolar solutions it is almos
177. assen s model beneath the same perpendicular field model used in the original paper The Shirahata model is enabled by the sa parameter of the mopELs statement or can be enabled individually for electrons and holes using the sur w and sur P parameters of the moBI11TvY statement If a low field mobility model is also chosen such as xia then Mathiessens rule is used to combine the two models The following paragraphs describe the analytic form of the Shirahata mobility model The Shirahata model for electrons and holes are given by 7 MUON SHI nas Hh E P1N SHI E P2N SHI E1 sHI 2N SHT MUOP SHI Hp E PIPSHI E P2P SHi 3 196 1 IP SHI ESP SHIT where E is the perpendicular electric and the equation parameters MUON SHI MUOP SHI ElN SHI ElP SHI E2N SHI E2P SHI P1N SHI P1P SHI P2N SHI and 2P sHi are user definable on the OBILITY Statement and have the defaults shown in Table 3 32 Table 3 32 User Specifiable Parameters for Equations 3 195 and 3 196 Statement Parameter Default Units OBILITY UON SHI 1400 0 cm V s OBILITY UOP SHI 500 0 cm V s OBILITY E1N SHI 8 9x10 V cm OBILITY E1P SHIO 8 0x103 V cm OBILITY E2N SHI 1 22x109 V cm OBILITY E2P SHI 3 9x10 V cm OBILITY PIN SHI 0 28 OBILITY P1P SHI 0 3 OBILITY P2N SHI 2 9 OBILITY P2P SHI 1 0 3 54 SILVACO International Physics Note If the maximum lo
178. ate velocity overshoot in GaAs this is described in the BLAZE chapter Carrier Temperature Dependent Mobility The energy balancetransport model allows the carrier mobility to berelated tothe carrier energy This has been achieved through the homogeneous steady state energy balance relationship that pertains in the saturated velocity limit This allows an effective electric field to be calculated which is theuniform electric field value which causes the carriers in an homogeneous sample to attain the same temperature as at the node point in the device The effective electric fields E efn and Ee are calculated by solving the equations 2 3 k T T QUE erc n E efen 2TAUREL EL 3 200 ES 3 KTp T Ql E err p Ert p 2YAUREL HO ce for E eff y and E eff These equations are derived friom the energy balance equations by stripping out all spatially varying terms The effective electric fields are then introducecd into the relevent field dependent mobility model Four different models have been implemented into the ATLAS energy balance model which can be chosen by the parameter Evsatmop on the mopELs statement These four models shall be described next Setting EvsarmoD 0 implements the default model for silicon based upon the Caughey Thomas field dependent mobility model in Equation 3 197 The resultant relationship between the carrier mobility and the carrier temperature is of the form 3 56 SILVACO International Physics
179. ateriall and Material3 This will be important in calculating the conduction band offsets for the heterojunction formed by Material3 and Material 2 the one in which the reference material is not present Let s assign 8096 of the bandgap difference between Material 1 and Material 2 to the conduction band offset for this heterojunction Since the reference material is one of the materials of this heterojunction we can procede as before Defining the aLIcn parameter on the maTERTAL Statement for Material 2 using MATERIAL NAME Material2 ALIGN 0 8 then Internally the affinity of Material 2 is adjusted so that AE equals this value Let s assign 70 of the bandgap difference between Material3 and Material2 to the conduction band offset for this heterojunction Since the reference material is not one of the materials in this heterojunction another procedure will be used Since BLAZE always uses the bandgap of the reference material the smallest bandgap material in overall structure when calculating the conduction band offset using the ALicN parameter on the MATERIAL statement the actual value for the ALIGN parameter needs to be calculated as follows ALIGN AE NE 31 FRACTION 5 15 g32 where FRACTION is the desired fraction of the bandgap difference between Material3 and Material2 that will appear in the conduction band AE 23 is the bandgap difference for the actual heterojunction and AE is the bandgap difference us
180. ations 7 8 to 7 10 Statement Parameter Default Units DEFEC SIGTAE 1 0 10 18 cm DEFEC SIGTDE 1 0 10724 ae DEF EC SIGGAE 1 0 10718 cm DEFEC SIGGDE 1 0 10714 am DEFEC SIGTAH 1 0 10714 M DEFEC SIGTDH 0 107 6 cm DEFEC SIGGAH 1 0 10714 m DEFEC SIGGDH 1 0 10716 in Steady state Trap Recombination The Schockley Reed H all model is used to determine the recombination rate due to the defect states V y 5 nF pM p 1n21p Ec R n p EEEE Fop ten eee dE 7 11 Ey where the summation runs over all the donor and acceptor bands stands for TA TD GA GD Transient Traps An additional differential rate equation is solved whenever a transient simulation is performed This takes into account the time required for electron and hole to be emitted or captured The probability of occupation becomes linked to the time dependent emission of electrons through the rate equation Equation 7 12 and is no longer given by Equation 7 8 The rate equation is given by d Jen GO 7 G 0 7 R GC 7 12 where Cy is the trap concentration R t and R t are the recombination rates of electrons and holes respectively while G t and G t are the electron and hole generation rates Cy is equal to ny when evaluating the electron current continuity equation and equal to py for the hole continuity equation E i E E R G de v Oj n l zy fy Vl exp Ep amp E dE 7 13 j Ey 7 4 SI
181. ature Ey is the bandgap T is the elevated temperature T is the operating temperature V is the operating bias voltage and J is the current estimate at the operating temperature Oncethe user has obtained estimates of the recombination and diffusion contributions the total leakage current can be obtained by summing the two contributions Numerical Solution Parameters ATLAS uses a cut off value of carrier concentration below which solutions are not required to converge This limit is set by the parameter CLIM DD Seethe Numerical Methods chapter for more detail on CLIM DD For photodetectors it is often necessary to reduce CLIM DD to 10 in order to resolve carrier concentrations in depleted regions before illumination Extracting Detection Efficiency One of the simpler tasks in characterizing a photodetector design is to measure DC detection efficiency This will be typically done as a function of bias voltage optical intensity or wavelength Each of these analyses can be performed using the SOLVE statement The Bn parameter can be used to set the optical intensity of the optical sources described in the previous section The following example illustrates obtaining a solution with a specified optical intensity SOLVE B1 1 0 This specifies that a solution is to be obtained for an optical intensity in the beam numbered 1 of 1 0 Watt cm If this were the first SOLVE statement specified the ray trace in LUMINOUS would be initiated
182. atures appearing in equations 3 74 3 75 3 77 and 3 78 are replaced by the quantum corrected temperature Tq The quantum potential Ug is given by 2 h U V In n 3 318 sm wheren is the carrier concentration Equations 3 317 and 3 318 apply to both electrons and holes In ATLAS the quantum transport model is enabled for electrons by specifying E guaxTuM on the mopEL statement and is enabled for holes by specifying H QUANTUM on the MODEL statement The quantum temperatures can be written to the standard structure file by specifying r ouaNTUM on the output statement Once written the quantum temperature distribution can be examined using TONYPLOT SILVACO International 3 87 ATLAS User s Manual Volume 1 Note In equating Equation 3 318 the quantum potential is proportional to the gradient squared of the log of the carrier concentration the quantum temperature tends to increase the thermal diffusivity around sharp peaks in the concentration distribution and tends to smear out such peaks This effect tends to draw carriers away from the Si Si02 interface in MOSFETS In HEMTS it helps move carriers away from the hetero interface and into the narrow bandgap channel Syntax As discussed in the previous section the quantum model uses a quantum moments function added to the standard drift diffussion current continuity equation As such the model for electrons and holes can be activated independently The quantum
183. avers sieve ark RR rd AA A RAE ERR AE 3 31 O a ae al a ANIMS a o dl uo MM USE Rosa toad 3 31 Low Field Mobility Models tor A X e Cede ik cede YD S DR c lg 3 31 Constant Mobily e to ae ii a aida 3 32 Concentration Dependent Low Field Mobility Tables 0 ccc csc cece cece aa 3 32 The Analytic Low Field Mobility Model 5 ote e ec ek p CA CIC ER 3 34 The Arora Model for Low Field Mobility 0 ccc cece cece eee eee eee e eee teen eens 3 35 The Carrier Carrier Model Scattering for Low Fleld Mobility ccc cece eee ee ee eee eens 3 36 Klaassen s Unified Low Fleld Mobility Models 0 ccc cece cece eee n eee e eae 3 38 Inversion Layer Moblity Models 0cce ccc eee e eene IH 3 43 OIN M LT 3 43 Thekombardi CVT Modela 4 eot A ce tha tis EDU PLU LL 3 44 Tile AMA UCA Modelis cuneo enden Cote A A NI Bebo DAC SDN e ui enl 3 46 iU cac b rn 3 48 Perpendicular Electrid Field Dependent Moblity Models seen ene 3 51 The Watt Model v eret Eos TORT t erts cete a uda e UN cu TS 3 51 Modifications to Watt Model reg ace de det a erect tob eb wr EE E c Pte et Ret ied 3 53 Shirahata s Mobility Model iro re ke eR hg RA Ra e eben 3 54 Parallel Electric Field Dependent Mobility oooooooocrocrcrnco eee een eee 3 55 Carrier Temperature Dependent Mobility 0 cece cece e eee 3 56 Mobility Model SUMMARY Gh A A cote et aa 3 58 Carrier Generation Recombination Models
184. b 10 202 Capacitances For CBS 0 and CBD 0 10 203 Cbs AS CJ Cbsj PS CJ SW Cbss 10 204 Cbd AD CJ Cbdj PD CJ SW Cbds 10 205 Otherwise Cbs CBS Cbsj PS CJ SW Cbss 10 206 Cbd CBD Cbdj PD CJ SW Cbds 10 207 For Vbs lt FC PB Cbsj 1 FC PMJ 1 FC 1 Mj MJ Vbs PB 10 208 Cbds 1 FCyM SW 10 209 For Vbd lt FC PB Cbdj 1 Vbd PByM 10 210 Cbds 1 Vbd PBSW SW 10 211 For Vbd FC PB Cbsj 1 FC MD 3 FC 1 2 MJ MJ Vbd PB 10 212 Cbds 1 FCyM SW 1 FC 1 MJ SW MJ SW Vbd PB 10 213 Gate Overlap Capacitances Cgs CGSO W 10 214 Cgd CGDO W 10 215 Cgb CGBO L 10 216 Gate Capacitance Calculation Define cap COX sclegd Weft ler 10 217 SILVACO International 10 67 ATLAS User s Manual Volume 1 Gate Bulk Capacitance cgb Accumulation cgb cap for vgs lt von PHI 10 218 von v Depletion cgb cap PHT for vgs von 10 219 Strong inversion cgb 0 for vgs 2 von 10 220 Gate Source Capacitance cgs Accumulation cgs 0 for vgs lt von PHI 2 10 221 Depletion y Voy vth f cgs CF5 cap Spm 1 or vgd lt von 10 222 Strong inversion saturation region cgs 2 3 cap for vgs gt von and vds vdsat 10 223 Strong inversion linear region For vgs gt von and vds lt vdsat PSY cgs 2 3 cap fi MT 10 224 Gate Drain Capacitance cgd The gate drain capacitance has value only in the linear region Strong in
185. back mechanisms such as avalanche gain Luminous does not directly calculate quantum efficiency but does calculate two useful quantities printed to the run time output and saved to the log file These quantities are source photo current and available photo current and can be viewed in ToxvPzor from log files produced using Luminous Definition of Source Photocurrent The source photocurrent for a monochromatic source is given in the equation below Here B is the intensity in beam number n set by the user on the SOLVE statement A is the source wavelength specified by the WAVELENGTH parameter of the BEAM statement h is Planck s constant c is the speed of light and W is the width of the beam including the effects of clipping see section on Ray Tracing This can be considered as a measure of the rate of photons incident on the device expressed as a current density B I dc Wi 8 13 Definition of Available Photocurrent The available photo current for a monochromatic source is given by the equation below Here all the terms in front of the sumation have the same definitions as for the source photo current The sum is taken over the number of rays traced NR We is the width associated with the ray The integral is taken over the length Yi associated with the ray P accounts for the attenuation before the start of the ray due to non unity transmission coefficients and absorption prior to the ray start And oj is the absor
186. been implemented to account for certain devices where the carrier drift velocity peaks at some electric field before reducing as the electric field increases This model takes account of this through the carrier mobility with equations of the form Hno t E ECRITN BE R 5 49 E GAMMAN 1 scars x E pe ECRITN VSATP E pot E ECRITP RE Dem 5 50 E GAMMAP l s CRITP Je 5 16 SILVACO International BLAZE where VSATN and VSATP are the electron and hole saturation velocities Ey is a constant and lino po are the low field electron and hole mobilities Table 5 3 User Specifiable Parameters for Equation 5 49 and 5 50 Statement Parameter Default Units OBILITY ECRITN 4 0 103 V cm OBILITY ECRITP 4 0 103 V cm OBILITY GAMMAN 4 0 OBILITY GAMMAP 1 0 OBILITY VSATN Eq 5 20 cm s OBILITY VSATP Eq 5 20 cm s Note The negative differential mobility model introduces an instability in the solution process and is not recommended for general use Only activate this model in cases where the device operation directly depends on negative differential mobility e g a Gunn diode For both the standard and negative differential models an empirical temperature dependent model for saturation velocity in GaAs 13 is implemented according to VSATN VSATP 11 3x10 12x10 Ti 5 51 where VSATN and VSATP are expressed in cm sec and T
187. being used for the simulation of substrate current Device Level Reliability Modeling Hansch MOS Reliability Model The Hansch Reliability Model 88 can be used to simulate MOS transistor degradation under stress conditions The causes of device characteristic degradation are the hot electron hole injection into gate oxide and the trapping of electron hole charge on the effective interface acceptor donor like traps The model calculates hot electron hole injection current according to the lucky electron model The arbitrary position dependent distributions of acceptor and donor like traps are specified on the oxide semiconductor interface as a priori knowns with corresponding capture cross sections The device degradation is calculated as a function of stress time by performing transient calculations The trap rate equation is solved on every time step and thus the trapped electron hole concentration is calculated The rate of electron trapping can be descri bed by the equations QNQOG SIGMAE dt oe J inj nX t NTA X N 0 3 305 dN Xt SIGMAH dt d gt J inj pQst E NTD X N x t 3 306 where N x t represents the trapped electron hole density at the interface point x at time t during a transient simulation The nra and wrp parameters represent the acceptor and donor like trap densities at time 0 The J inj nt and J inj p x t parameters are the injected electron and hole current densities sIcMAE
188. bject to single event upset thin film transistor circuits high frequency circuits precision analog circuits and high performance digital circuits MIXEDMODE circuits can include up to 100 nodes 300 elements and up to ten numerical simulated ATLAS devices These limits are reasonable for most applications however they can be increased in custom versions on request to Silvaco The circuit elements that are supported include dependent and independent voltage and current sources as well as resistors capacitors inductors coupled inductors MOSFETS BJ Ts diodes and switches Commonly used SPICE compact models are available and the SPICE input language is used for circuit specification Organization of this Chapter This chapter describes circuit simulation capabilities rather than device simulation capabilities It is therefore organized differently than the chapters that describe other ATLAS products The first part of the chapter contains introductory and background information The middle section presents and explains MIXEDMODE syntax This is followed by some sample input decks The final sections contain a statement reference and a detailed description of the provided electrical compact models for diodes BJ Ts and MOSFETs Background Circuit simulators such as spice solve systems of equations that describe the behavior of electrical circuits The devices that are of interest to circuit designers are normally well characterized Com
189. breakdown curve up to high current values more advanced techniques than the simple voltage ramp must be used Two of them are described below curve tracer and current boundary conditions The expense of these methods might be extra CPU time Using Current Boundary Conditions In all of the examples considered in the basic description of the soLve statement it was assumed that voltages were being forced and currents were being measured ATLAS also supports the reverse case through current boundary conditions The current through the electrode is specified in the sorve statement and the voltage at the contact is calculated Current boundary conditions are set using the CONTACT Statement as described earlier in this chapter The syntax of the soLve statement is altered once current boundary conditions are specified SOLVE IBASE 1e 6 The syntax above specifies a single solution at a given current SOLVE IBASE 1e 6 ISTEP 1e 6 IFINAL 5e 6 NAME base This sets a current ramp similar in syntax to the voltage ramp described earlier SOLVE IBASE 1e 10 ISTEP 10 IMULT IFINAL 1e 6 NAME base 2 36 SILVACO International Getting Started with ATLAS This is similar to the previous case but the 1muLT parameter is used to specify that ISTEP should be used as a multiplier for the current rather than a linear addition This is typical for ramps of current since linear ramps are inconvenient when several orders of
190. c accesso regu DR Dad Ra x RU e RO C ad Io CRURA RON AU ECONTRA 10 69 Example a ed 10 70 Bibliography See Volume 2 Index See Volume 2 SILVACO International xvii ATLAS User s Manual Volume 1 This page intentionally left blank xviii SILVACO International List of Figures Figure Page No Caption Title No 2 1 ATLAS Inputs and OUTPUTS rli iieeimiertatxezki ts tra 2 1 2 2 Examples Index in DeckBuild ooococooccccccccnrcn He 24 2 3 ATLAS Command Groups with the Primary Statements in each Group o oooooooomm 2 6 2 4 Non uniform Mesh Creation using ATLAS Syntax sese eee eens 2 10 2 5 Analytical specification of a 2D Profile ooooooocoooornrrcarnr ca 2 12 2 6 Regrid on doping provides improved resolution of junction oooocoooooommmmmmmm 2 14 2 7 Diagram showing syntax of Transient Voltage Ramp in ATLAS eeseeee 2 35 3 1 Definition of the trap energy level for acceptor and donor traps in reference to the conduction and valence band edges cc ccc cece eee eee n n 3 12 3 2 The lumped elements supported by ATLAS sess Ine 3 28 4 1 Effect on MOS IV curve of progressive refinement of the vertical mesh spacing at the surface ol ihe MOS ch ritel s s 5 33 react moria auta too Leu RES REA PERO GU READS Tad ad 4 2 4 2 Effect of surface mesh spacing on simulated current for several MOS Mobility Models e
191. c Ec np gr E f Gs n p dE 8402 f En p dE 7 6 Ey Ey Ec Ec pp 85ptE f E n p dE ggp E f E n p dE 7 7 E Ey f E n p and f Enp are probabilities of occupation for the tail and Gaussian acceptor DOS while ft Enp and f E n p are the equivalent for the donors In the steady state case the probability of occupation of a trap level at energy E is given by VO e SAE n p St ee a ae 7 8 v O n HVO P e e where v is the electron thermal velocity v is the hole thermal velocity o is the capture cross section for electrons and op is the capture cross section for holes The emission rates for the electrons and holes e and ey are shown in equations 7 9 and 7 10 E E v O n exp lr 7 9 E E 2 7 yn exp IT 7 10 nj is theintrinsic carrier concentration A different value of op can be specified for each acceptor and donor tail and deep level state These are specified on the DEFEcTs statement as shown in Table 7 2 The values of o are sIcTAE is the acceptor tail state srcrpzg is the donor tail state srccaz is the deep level Gaussian state and srccpz is the Gaussian donor state Similar expressions are used for o SIGTAH SIGTDH SIGGAH and SIGGDH SILVACO International 1 3 ATLAS User s Manual Volume 1 Table 7 2 User Specifiable Parameters for Equ
192. cal ray trace using real component of refractive index to calculate the optical intensity at each grid point 2 Absorption or photogeneration model using the imaginary component of refractive index to calcu late a new carrier concentration at each grid point This is followed by an electrical simulation using SPISCES or BLAZE to calculate terminal currents Ray Tracing Defining The Incident Beam An optical beam is modeled as a colli mated source using the BEAM statement The origin of the beam is defined by parameters x ORIGIN and Y ORIGIN see Figure 8 1 The ANGLE parameter specifies the direction of propagation of the beam relative to the x axis ANGLE 90 is vertical illumination from the top MIN WINDOW MAX WINDOW parameters specify the illumination window As shown in Figure 8 1 the illumination window is dipped against the device domain so that none of the beam bypasses the device The beam is automatically split into a series of rays such that the sum of the rays covers the entire width of the illumination window When the beam is split ATLAS automatically resolves discontinuities along the region boundaries of the device SILVACO International 8 1 ATLAS User s Manual Volume 1 Y ORIGIN X ORIGIN Figure 8 1 Optical Beam Geometry Although the automatic algorithm is usually sufficient the user may also split the beam up into a number of rays using the RAYS parameter Each ray will have the s
193. calculation significantly Using a larger value will result in faster but less accurate calculations LAS ITMAX Set maximum number of external Laser iterations during photon density calculation The default value is 30 e LAS SIN Thisistheinitial photon density used only with simple aser models LASER starts the iteration process for photon density calculation from this value This parameter SILVACO International 9 7 ATLAS User s Manual Volume 1 influences only the calculation time for the first bias point after the laser threshold is reached LAS TAUSS Thisisaniteration parameter used in thecalculation of photon densities Usinga larger value of this parameter can speed up the calculation but may cause convergence problems LAS MAXCH This is the maximum allowable relative change of the photon density between LASER iterations Using a larger value of this parameter can speed up the calculation but may cause convergence problems Table 9 7 LASER Parameters Statement Parameter Default Units MODELS GAINMOD MODELS CAVITY LENGTH 100 cm MODELS PHOTON ENERGY MODELS LAS OMEGA 2 16615 Hz MODELS LAS MIRROR 90 MODELS LAS FCARRIER FALSE MODELS LAS ABSORPTION FALSE MODELS LAS LOSSES 0 MODELS LAS EINIT 0 MODELS LAS EFINAL 0 MODELS SPEC NAME spectrum log MODELS LAS SPEC
194. carriers that gain energy can take part in a wider range of scattering processes The mean drift velocity no longer increases linearly with increasing electric field but rises more slowly Eventually the velocity does not increase any more with increasing field but saturates at a constant velocity This constant velocity is commonly denoted by the symbol Vsa Impurity scattering is relatively insignificant for energetic carriers and so Vsat is primarily a function of the lattice temperature Modeling mobility in bulk material involves i characterizing uno and upo as a function of doping and lattice temperature ii characterizing Vsat as a function of lattice temperature and iii describing the transition between the low field mobility and saturated velocity regions Modeling carrier mobilities in inversion layers introduces additional complications Carriers in inversion layers are subject to surface scattering extreme carrier carrier scattering and quantum mechanical size quantization effects These effects must be accounted for in order to perform accurate simulation of MOS devices The transverse electric field is often used as a parameter that indicates the strength of inversion layer phenomena It is possible to define multiple non conflicting mobility models simultaneously It is also necessary to know which models are over riding when conflicting models are defined Low Field Mobility Models Thelow field carrier mobility may be de
195. ce eee e 9 8 Chapter 10 MIXEDMODE consta cort err aos 10 1 hte reip DET a a a 10 1 The MIXEDMODE CONCEDE ves cra vies xim eed Rare Ec xb esi knit Baas aw eb p Ede Monee 10 1 Organization A TOP sos uaa A ace ba cede dog E elaine tein d 10 1 Pd ded ete tien A o Pu bulbi eo pa a 10 1 Advantages of MIXEDMODE Simulation o ucc e edere Re e om e Rel e 10 2 Using MIXEDMODE casio avant donor do nac Sa Y CRT S ASH A LU LE LATI PU yaa aaa 10 2 SYNTAX OVerVIBW ri cp ER casa HERR ERRORI Yea CENE AA KE e RET EE RA 10 2 General Syntax RUES DUE ADMONERE LE 10 3 Circuit and Analysis Specification E aoe deen rari OR A ADIOS Y Ed 10 3 Netist Statement ia e T 10 3 COMO EME P 10 5 Special Statements anna ER E ME Reza 10 5 Devi e Simulation S MIA Ce snes aden E Pad nra eda Spr epa la 10 6 Recommendations tei sb eias pvo aod eta e dro p ote ios Yo s 10 6 aes edo P RI Ux UE 10 6 Scale OSMOSIS oet aru cds aire Sn ach IA disi 980 am at 10 6 NUMETICS ace tore obo dla e Rae S ta RR RU e Rd o o o ina Eo nA de AC ac 10 7 Multi Device Structure Representation sssssse mmn 10 7 Extraction OT Rel xus eus sit da Edo 10 8 Using MIXEDMODE inside the VWF Automation Tools 0 c cece eee eect aaan 10 9 e A A ee ee oe ee EET IP 10 9 ASample Command Fil 2 ns is iR EE E uER re A ae Ua uio tax OD M E 10 10 MIXEDMODE Syntax Gs 10 12 A ATLAS device to be simulated using device simulation 10 12 B User defined two terminal element z 1 ez Wine Er
196. ce is determined as follows SILVACO International 10 51 ATLAS User s Manual Volume 1 yy MIE cbedep CIE op VIE for Vpe lt 0 10 53 cbedep CIE op 1 t MJE ae for vg gt 0 10 54 Base Collector Capacitance Equations The base collector capacitance contains a complex diffusion term with a standard depletion formula The diffusion capacitance is modified by model parameter TR The base collector capacitance cbc is determi ned by cbc cbcdiff cbcdep 10 55 where cbcdiff is the base collector diffusion capacitance and cbcdep is the depletion capacitance Base Collector Diffusion Capacitance cbcdiff 2 TR ibc 10 56 Voc where the internal base collector current ibc is be NR ibe ISo des 10 57 Base Collector Depletion Capacitance There are two different equations for modeling the depletion capacitance Select the desired equations by specifying the option caewop in the oprIows statement CAPMOD 1 vy MIC cbcdep XCJC CIC y 1 vc for Vec lt FC VJC 10 58 Voe 1 FC 1 MIC MIC VIC cbcdep XCJC CIC oy Ss TEMP 10 59 1 FC CAPMOD 2 Voc cbcdep XCJC CIC oy 1 v for Vi 0 10 60 cbcdep XCJX CIC oy 1 MJC vc for v 2 0 10 61 10 52 SILVACO International MIXEDMODE External Base Internal Collector Junction Capacitance The base collector capacitance can be modeled as a distributed capacitance by setting parameter xcuc When xcuc is one set
197. ch are termed aSiC and bSiC for 6H SiC and 4H SiC respectively Thefollowing paragraphs describe the material defaults for these materials 5 26 SILVACO International BLAZE Band Parameters for SiC SiC band parameter equations are identical to those used for Silicon but with the values adjusted for 4H and 6H SiC The physical band parameter values are summarised in Tables B 18 and B 19 of Appendix B SiC Mobility Parameters Isotropic Mobiliy By default mobility is assumed to be entirely isotropic in nature that is there is no directional component The default low field mobilities of electrons and holes for 4H and 6H SiC are shown in Table 5 6 and 5 9 below Table 5 6 6H SiC Low Field Mobility Statement Parameter Default Units MOBILITY MUN 330 cm2 V s MOBILITY TMUN MOBILITY MUP 60 cm2 V s MOBILITY TMUP Table 5 7 4H SiC Low Field Mobility Statement Parameter Default Units MOBILITY MUN 1000 cm2 V s MOBILITY TMUN MOBILITY MUP 50 cm2 V s MOBILITY TMUP SILVACO International ATLAS User s Manual Volume 1 Anisotropic Mobility The mobility behaviour within SiC is now known to be anisotropic in nature which dramatically alters the electrical performance of a device An isotropic model has been implemented into ATLAS to correctly model this behaviour Following the ideas of Lindefelt 136 and Lades 137 the mobility within the dr
198. chu e CR CR vein bu Ote ets 2 44 Chapter 3 PHUSICS o coitu etit Eb bove ttu Eod cs ecc siu e tue tu bd vba av eros 3 1 Basic Semiconductor Equations ooooccccccccnncnnr Ihn n 3 1 II o PEE PE EIE ceo eee ha Pree ahh TEN 3 1 P oI550fi EN ees Pone AE te tui o E 3 1 Carer Conunuity EQUITON Sortie ars ata 3 1 The Transport Equations sisi a DER ROS ai is a CR IR 32 The Drift Diffusion Transport Model coste eere Eae o Fr ch pci 32 Energy Balance TransportModel 0 ccc ccc e cece ee eee mmm 3 4 Displaceme nt Current Equation a geste tee dece toe So abo c dat eR e Ele ates Joie DON seda 3 4 Basic Theory of Carrier Statistics coria cir nea merkt onis 3 5 Fermi Dirac and Boltzmann Statistics 5 uscsde lucis e ie Whee e hr HR ex gli Ya ha Rx 3 5 Effective Density of States suede cruip rai oct e hope to Doa be rr Eod di ee oe 3 5 Intrinsic Carrier Concentration 16 eor sacd bb C WOE VN Nip Oen a Oe ee daa 3 6 The Energy Bardgap uox abb orte dod wa ph NT it cde ot d 3 7 Bandgap NattoWIU 2 asa sse d tet vd aries GERI Oates ssa ted er a tac hunt arid seid aus rut s 3 7 Space Charge from Incomplete lonization Traps and Defects ssseeseeeeeeennnnnnnn 3 9 OVEIVIGW Sede dr Fes cta nek A AE Incomplete lonization of Impurities oo eect ccc eee mmm 3 9 Low Temperature Simulations on ODA 3 10 TANS ANG A E ELLA LE 3 11 MTM UE 3 11 Calculation of Trapped Charge in Poisson s Equation ccc cece cece eee eee n 3 12 Trap Implemen
199. cifiable Parameters for Equation 6 2 Statement Parameter Units MATERIAL TC A cmK w MATERIAL TC B cm w MATERIAL TELE cm wK Specifying Heat Capacity For transient calculations it is necessary to specify heat capacities for every region in the structure These are also functions of the lattice temperature and are modeled as 2 HC D C HC A HC BT gneve T 4 1 cm 6 3 E Default values of Hc A HC B Hc c and gc p are provided for common materials These values can be specified on the MATERIAL statement The following statements would be used to specify the temperature dependent heat capacities of the regions defined previously MATERIAL REGION 5 HC A lt n gt HC B lt n gt HC C lt n gt HC D lt n gt ATERIAL REGION 6 HC A lt gt gt HC B n HC C lt n gt HC D lt n gt Table 6 2 User Specifiable Parameters for Equation 6 3 Statement Parameter Units MATERIAL HC A J cm3 K MATERIAL HC B J cm K MATERIAL HC C J cm K MATERIAL HC D JK cm SILVACO International 6 3 UTMOST User s Manual Volume 1 Non Isothermal Models Effective Density Of States When lattice heating is specifed with the drift diffusion transport model the effective density of states for electrons and holes are modeled as functions of the local lattice temperature as defined by Equations 3 29 and 3 30 When lattice heating is specifed with the energy balance
200. cription Units Default Area TF Ideal forward transit time sec 0 XTF Coefficient for bias dependence of TF 0 voltage describing VBC ITF High current for effect on TF A 0 VIF Voltage describing TF dependence of V infinite VBC PTF Excess phase at f 1 0 2 m TF deg 0 TR Ideal reverse transit time sec 0 10 42 SILVACO International MIXEDMODE Table 10 11 Temperature Effect Parameters Parameters Description Units Default Area XTB Forward and reverse beta temperatur xponent ial Q Energy gap for temperature effect on IS eV Loli Silicon 0 69 Schottky Barrier Diode 0 67 Germanium 1 52 Gallium Arsenide XTI Temperatur xponent for effect on IS3 GAP1 First bandgap correction fac tor From Sze alpha term 7 02 10 4 Silicon old value 4 73 10 4 Silicon 4 56 10 4 Germanium 5 41 10 4 GaAs ev deg 7 02 10 4 GAP 2 First bandgap correction fac tor From Sze alpha term 1108 Silicon old value 636 Silicon 210 Germanium 204 GaAs deg MJC Base collector junction expo nent grading factor MJ Gl Base emitter junction expo nent grading factor MJS Substrate junction exponent grading factor TBF1 First order temp coefficient for BF 1 deg TBF2 Second order temp coeffi cient for BF 1 deg TBR1 First order temp coefficient for BR 1 deg TBR2
201. ct of surface channel mesh in MOSFETs is model dependent This result shows the current at Vds 3 0V and Vgs 0 1V versus the size of the first grid division into the silicon Results vary for each model but note that for all models a very fine grid is required in order to reduce the grid dependence to acceptable levels Wim r bermmba v3 reb rl AULAS HESH DEPEHDENCE OF HV SUPE ie lE Pt L 15 pala man 5 Clkkia plas P changes a gpreant ar draq do at leader ADO era il 128 Figure 4 1 Effect on MOS IV curve of progressive refinement of the vertical mesh spacing at the surface of the MOS channel 4 2 SILVACO International S PISCES Tomp Pin SEE Ph FI Th 4 Print D Props tas LICHE RACE Y MODEL vs GA DATA a E Dra Carrer Doi it E E m LL lu alsi ram LI L Ll siete lol E yr aar i E Briss Grd paci n A iy arm e PLAMI MOSFET examplk madri 1 kending Tiie Arad natnra rag ce cee reco mezb n dat 20 KC BD moesatkisal iust Figure 4 2 Effect of surface mesh spacing on simulated current for several MOS Mobility Models MOS Electrode Naming For MOS simulation S PISCES allows the use of standard electrode names to reduce confusion with the use of electrode indices These names include source drain gate and substrate Electrode names can be defined in ATHENA or DevEbiT Or in the EL ECTRODE statement in ATLAS
202. ction band edge Ey is the valence band edge Eg is the electron quasi F ermi level Eg is the hole quasi F ermi level and Ey is the energy of the trap level The electron and hole field enhancement factors then become E E Y Pap 2 mg exp E 3 67 where 2n 24 MASS TUNNEL m kT Er oe eg 3 68 and k is Boltzmann s constant and T is the lattice temperature and E is the electric field ee 2AE np At high values of electric field where lt p lt Km the enhancement terms becomes T S x b a erfd P 3 69 np 2KT ya P a Ja where 3 AE p 3 q AE p a gKn p 127 ZkT 7 4Kn and Pup 3 70 SILVACO International 3 15 ATLAS User s Manual Volume 1 Table 3 7 User Specifiable Parameters for Trap Assisted Tunneling Model Statement Parameter Default Units MODELS TRAP TUNNEL FALSE MATERIAL MASS TUNNEL 0 25 Transient Traps In the time domain the acceptor and donor traps do not reach equilibrium instantaneously but require time for electrons to be emitted or captured This is taken account of inside ATLAS by solving an additional differential rate equation whenever a transient simulation is performed The probability of occupation becomes linked to the time dependent emission of electrons through the rate equation S DENSITY En p R t Rp t 3 71 where Rp t and R t are the recombination rates of electrons and holes respectively The terms describing
203. ction band offset by modifying the electron affinity of the material for which the ALIGN parameter is specified 5 2 SILVACO International BLAZE In many applications Schottky barriers or more than two different semiconductor materials are present The user must keep the reference material bandgap and these assigned affinities in mind when defining offsets for multiple materials or Schottky barrier heights Examples for multiple materials and Schottky barriers are given in the examples section Manually Adjusting Material Affinity The AFFINITY parameter on the MATERIAL statement can be used in conjunction with the default affinity rule alignment method to manually adjust the conduction band offset In this case the electron affinity of the larger bandgap material is adjusted so that the difference between the two materials affinity equals the desired conduction band offset When more than two different materials are present each material affinity can be adjusted in this manner This is the easiest method for handling multiple materials and heterojunctions The following examples will describe the procedure for aligning heterojunctions using these three methods in BLAZE EXAMPLE 1 qvo L Material Material2 Figure 5 2 Band diagram of heterojunction with band offset Figure 5 2 diagrams a heterojunction consisting of two semiconductors with different bandgaps Eq and Eg and electron
204. ction that describes the dependence of the model parameters an AP BN and s asa function of the carrier temperatures These values will then be used within Toyabe s energy dependent impact onization model Concannon s Impact lonization Model The previous nonlocal impact ionisation model inherently assumes a Maxwellian shape to the distribution of hot carriers Recent work by Fiegna 129 using Monte Carlo simulations suggests a non M axwellian high energy tail to the energy distribution function To more accurately model these effects a non M axwellian based model from Concannon 112 has been implemented Based upon this energy distribution the model calculates the probability of a carrier having sufficient energy to cause impact ionisation The model results show good agreement with measured results for a 0 9um flash EPROM device 120 The Concannon substrate current is enabled for the electron and hole continuity equations by specifying the x coucaNNoN and P CONCANNON parameters of the Impact statement The generation rate is a function of the carrier temperature and concentration and is given by oo G X y CSUB NX n F T y de 3 262 ETH N Gp y CSUB Px p FET y pde 3 263 ETH P where n x y and p x y are the electron and hole carrier concentrations within the semiconductor e is energy T x y and Ty x y are the electron and hole carrier temperatures in the semiconductor CSUB N CSUB P ETH N and ET
205. ctor The formula calculates the injected gate current contribution from every node point within the semiconductor according to lini f PG y nox y lax dy Poo yl px yoldx dy 3 274 where J n p x y are the electron and hole current densities at a point x y within the semiconductor and P x y are the probabilities that a fraction of this current reaches the gate oxide and is injected across into the gate electrode The total probability Pj x y is defined by POS y Pg P P5 EG ELINR 3 275 P x y Pos pP1 P p IG HLINR 3 276 where E is the electric field parallel to the current flow 1G ELINR and 1G HLINR are the electron and hole mean free path lengths between redirecting collisions The three probability factors will now be described The probability Pop is the probability of a carrier gaining the energy og by moving in and parallel to an electric field E without suffering energy loss by optical phonon scattering and is given by E IG ELINF OB n Pos E oas E ett e SENF 3 277 nT E IG HLINF OB p PERT iugi 5 p Jee e iG HETNE i where IG ELINF and IG HLINF are the mean free path lengths of electrons and holes for scattering by optical phonons The barrier heights pg p are defined according to IG EBO IG EBETA E IG EETAE Ay x y 3 279 B n Y jj IG HBO IG HBETA E 1G HETAE Ay x y 3 280 B p L L where E is the electric field perpendicular to the semiconductor insulator int
206. d as a function of the refractive indices in the two media INCIDENT RAY REFLECTED R TRANSMITTED RAY Bi A Figure 8 3 Angles of incidence reflection and transmission The reflection and transmission coefficients of the light for parallel and perpendicular polarization are calculated as in Equations 8 1 to 8 6 n cos n cos 0 E E arallel polarization T n cos0 4n5cos0 p p 8 1 2n cos0 E E arallel polarization t n cos0 n cos0 p P 8 2 n cos06 n cos0 E _ _E erpendicular polarization r n cos0 4n5cos0 perp 8 3 SILVACO International 8 3 ATLAS User s Manual Volume 1 2n cos0 E i cos0 n cos0 i rpendicular polarization m t n cos0 n cos0 i perpendicular polarization E R 5 8 5 1 E n T 5 E 8 6 E ni where E is the incident intensity E is the reflected intensity E is the transmitted intensity R is the reflection coefficient T is the transmission coefficient ny is the refractive index on the incident side and nz is the refractive index on the transmission side The angles of reflection and transmission are given in Equations 8 7 and 8 8 0 6 8 7 r 1 n sin0 n sin0 8 8 where 6 is the angle of incidence 6 is the angle of transmission and 0 is the angle of reflection Specifying Reflections By default no reflections are considered during the ray trace The parameter REFLEC
207. d structure files The solutions are used as the initial guess or initial conditions for subsequent MIXEDMODE simulation To usethis feature the user must 1 Calculate a solution for each ATLAS device and save each solution in a separate standard structure format file using SAVE Or SOLVE MASTER 2 For each ATLAS device usethe A statement in the MIXEDMODE command file to specify the associated standard structure format file 3 Set node voltages to appropriate values with the vopeseT statement Specify LOADSOLUTIONS in the options statement Note If using this feature you must specify solutions for all ATLAS devices The NODESET statement must always be used when LOADSOLUTIONS is used The NODESET statement is used to make the initial circuit voltages match those for which device solutions were obtained It may also be necessary to specify the NOSHIFT parameter of the OPTIONS statement By default MIXEDMODE shifts device terminal voltages with respect to the voltage on the first terminal that is specified in the A statement You must either prepare initial solutions with this terminal grounded or specify NosHIFT in the options statement Z PARAM specifies that the Z parameters should be written to the LOG file This is used in conjunction with the NET statement Y PARAM specifies that the Y parameters should be written to the LOG file This is used in conjunction with the NET statem
208. d then the current is scaled by this factor and is in Amperes Similar rules apply for the capacitance and conductance produced by AC simulations These are usually in 1 ohms microns and Farads micron respectively Parameter Extraction In DeckBuild The EXTRACT command is provided within the DEckBuiLD environment It allows you to extract device parameters The command has a flexible syntax that allows you to construct very specific extract routines EXTRACT operates on the previous solved curve or structure file By default EXTRACT uses the currently open log file To override this default the name of a file to be used by extract can be supplied before the extraction routine in the following way EXTRACT INIT INF lt filename gt A typical example of the use of extract is the extraction of the threshold voltage of an MOS transistor In the following example the threshold voltage is extracted by calculating the maximum slope of the y Mg curve finding the intercept with the x axis and then subtracting half of the applied drain bias EXTRACT NAME nvt XINTERCEPT MAXSLOPE CURVE V GATE I DRAIN AVE V DRAIN 2 0 2 40 SILVACO International Getting Started with ATLAS Theresults of the extraction will be displayed in the run time output and will by default also be stored in the file results final You can store the results in a different
209. d to the contact instead CONTACT NAME drain RESIST 1e20 Note that extremely large resistance values must be used to keep the current through the contact insignificant bearing in mind the tolerance on potential will allow the contact voltage to move slightly above zero For example if the tolerance is 10 V and the defined resistance was only 10M o um then a current of 1012 A um may flow through the contact which is probably significant in breakdown simulations Shorting two contacts together It is possible in ATLAS to tie two or more contact together so that voltages on both contacts are equal This is useful for many technologies for example dual base bipolar transistors There are several methods for achieving this depending on how the structure was initial defined If the structure is defined using ATLAS syntax it is possible to have multiple ELECTRODE statements with the same NAME parameter defining separate locations within the device structure In this case the areas defined to be electrodes will be considered as having the same applied voltage A single current will appear combining the current through both ELECTRODE areas Similarly if two separate metal regions in ATHENA are defined using the ATHENA ELECTRODE statement to have the same name then in ATLAS these two electrodes will be considered as shorted together If the electrodes are defined with different names the following
210. de DECKBUILD TONYPLOT DEVE DIT MASKVIEWS and OPTIMIZER are documented in the VWF INTERACTIVE TOOLS MANUAL The complete ATLAS documentation consists ofthe ATLAS User s Manual this document and the VWF INTERACTIVE TOOLS MANUAL SILVACO International 1 1 ATLAS User s Manual Volume 1 How To Use This Manual All users should read this Chapter and the Getting Started Chapter in order to obtain an overview of ATLAS Users of earlier versions of ATLAS will find it helpful to review the updated version history provided in Appendix D The remaining chapters can then be referred to for a more detailed understanding of the capabilities of each ATLAS product If you are a new user you should read the tutorial in the VWF INTERACTIVE TooLs MANUAL to get a basic idea of the mechanics of using the user interface ATLAS is supplied with numerous examples that may be accessed conveniently through DeckBuild The examples demonstrate most of the capabilities of ATLAS The input files provided as part of these examples can provide an excellent starting point for developing your own input files 12 SILVACO International Introduction Organization Of This Manual The organization of this manual is as follows Technical Support Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Appendix A Appendix B Append
211. ded though the fn parameter esi T DELTA fn a Theterm fs expresses the effect of the short channel and is given by XJ led fs die Sca Ly o 23172 LD scaled WE Hg LD scaled XJ scaled scaled 10 169 10 170 10 171 10 172 10 173 10 174 10 175 10 176 10 177 10 64 SILVACO International MIXEDMODE xd PHI vsb wp 2 pap aD xd ceen were We S XJ scaled wp wp Y 0 0831353 0 08013929 gt 2_ 0 0111077 XJ scaled XJ scaled Effective Channel Length and Width lett Lscaled XL scated 2 LDscaled Wert 7 Wscateg XWscaled 2 WDscaled Threshold Voltage 22 8 14e x 10 7 ETA vth vbi v4 GAMMA fs COX ls PHI v fn PHI vcb where vbi vgb PHI or vbi VTO GAMMA PHI 2 Saturation Voltage 10 178 10 179 10 180 10 181 10 182 10 183 10 184 10 185 10 186 10 187 MIXEDMODE calculates the saturation voltage due to channel pinch off at the drain side vmax is used to include the reduction of the saturation voltage due to carrier velocity saturation effects Vos Vth m 10 1 vsat 137b 0 188 2 2 172 vdsat vsat vc vsat t vc 10 189 where VMAX I ea 10 190 us SILVACO International 10 65 ATLAS User s Manual Volume 1 The parameter us is surface mobility see Effective Mobility vdst vsat 10 191 Effective Mobility The car
212. degrees Kelvin MUMINN KLA and MUMINP KLA are user defined parameters shown in Table 3 23 and the other parameters are as described in Table 3 21 and Table 3 22 SILVACO International 3 39 ATLAS User s Manual Volume 1 Table 3 23 User Specifiable Parameters for Equations 3 137 and 3 138 Statement Parameter Default Units MOBILITY MUMINN KLA 5252 cm V s MOBILITY MUMINP KLA 44 9 cm V s The carrier carrier scattering components Hnc and upe are given by MUMINN KLA x ag s idu nc MUMAXN KLA MUMINN KLA T _ MUMINP KLA x MUMAXP KL A 300 ae pc MUMAXP KLA MUMINP KLA T The parameters of equations 3 135 and 3 136 N psc and N ps are given by N psc Np NA n 3 142 3 where Np is the donor concentration in cm3 Na is the acceptor concentration in cm n is the electron concentration in cm and p is the hole concentration in cm The parameters of equations 3 135 and 3 136 N sc er and N psc err are given by p N asc eff Np GP Fp 3 143 n N psc eff Na GO Np 5 3 144 where Np is the donor concentration in cm N 4 is the acceptor concentration in cm and n is the hole electron concentration in cm and p is the hole concentration in cm The two functions G P and F P are functions of the screening factors P and Pp for electrons and holes The function G P in Equations 3 143 amd 3 145 are given by G P 2 1 SLKLA S5 KLA n m TL SA KLA S3 KLA m 30
213. del 3 56 3 34 User Specifiable Parameters for Equations 3 197 3 207 0 c cece eee eee eens 3 58 3 35 User Specifiable Parameters for Equation 3 211 ccc eee eee eee e eee nena 3 60 3 36 User Specifiable Parameters for Equations 3 212 to 3 214 1 cece eect eee eee eee 3 61 3 37 User Specifiable Parameters for Equations 3 215 to 3 216 ccc cece eee e eee eens 3 62 3 38 User Specifiable Parameters for Equations 3 218 and 3 222 0c cee cece eee eee eens 3 63 3 39 User Specifiable Parameters for Equation 3 225 cc cece cece teen eee ee eeeaee 3 64 3 40 User Specifiable Parameters for Equation 3 227 and 3 228 cece cece eee eens 3 65 3 41 User Specifiable Parameters for Equations 3 232 to 3 234 1 ccc eee e eee eee eee 3 66 3 42 User Definable Parameters in the Selberherr Impact lonization Model 3 67 3 43 Temperature Coefficient Parameters of the Selberherr Impact lonization Model for Silicon in Equations 3 238 to 3 241 cece eee ees 3 68 3 44 Crowell Sze Impact lonization Model Parameters ccceeeee cece eee eee ee eeneeee 3 70 3 45 User Specifiable Parameters for Equations 3 258 3 261 2 0 0 cece ee cece eee eee eens 3 71 3 46 User Specifiable Parameters for Equations 3 262 and 3 263 cece cece eee eee eee 3 73 3 47 User Definable Parameters for the Energy Distribution Functions 3 73 3 48 User De
214. dels for MOSFET and bipolar devices while PROGRAM and ERASE enable the models for programming and erasing programmable devices F or example the statement MODELS MOS PRINT enables the CVT SRH and FERMIDIRAC models while the statement MODELS BIPOLAR PRINT enables the CONMOB FLDMOB CONSRH AUGER and BGN Note The PRINT parameter lists to the run time output the models and parameters which will be used during the simulation This allows the user to verify models and material parameters It is highly recommend to include the PRINT parameter on the MopEL statement Physical models can be enabled on a material by material basis This is useful for heterojunction device simulation and other simulations where multiple semiconductor regions are defined and may have different characteristics For example the statements ODEL MATERIAL GaAs FLDMOB EVSATMOD 1 ECRITN 6 0e3 CONMOB ODEL MATERIAL InGaAs SRH FLDMOB EVSATMOD 1 ECRITN 3 0e3 change both the mobility models and critical electric field used in each material For devices based on advanced materials these model parameters should be investigated carefully Energy Balance Models The conventional drift diffusion model of charge transport neglects non local effects such as velocity overshoot and reduced energy dependent impact ionization ATLAS can model these effects through the use of an energy balance m
215. description of the available models is given in the mobility section of this chapter 3 22 SILVACO International Physics Boundary Physics Overview ATLAS supports several boundary conditions ohmic contacts Schottky contacts insulated contacts and Neumann reflective boundaries Voltage boundary conditions are normally specified at contacts but current boundary conditions can also be specified Additional boundary conditions have been implemented to address the needs of specific applications Lumped elements can be connected between applied biases and semiconductor device contacts A true distributed contact resistance is included to account for the finite resistivity of semiconductor contacts Ohmic Contacts Ohmic contacts are implemented as simple Dirichlet boundary conditions where surface potential electron concentration and hole concentrations ys Ns Ps are fixed Minority and majority carrier quasi F ermi potentials are equal to the applied bias of the electrode i e 0n79p7Vappli ed The potential Vs is fixed at a value that is consistent with space charge neutrality i e nj NA p No 3 103 Equation 3 103 can be solved for ys Ns and Ds since and 0 are known If Boltzmann statistics are used substitution of Equations 3 34 and 3 35 into Equation 3 103 yields 2 1 Ns 53 N m MB Nz T 3 104 2 p _le 3 105 S ns KT n KT Vs Ont ging g Im 3 106 Note Contacts are assumed to be ohmic if
216. e this peak is slightly different within the semiconductor Surface recombination is implemented on a triangle by triangle basis That is using the surface recombination velocity and geometrical data a recombination component is calculated for each triangle so that an element of interest is connected Using the electric field for each triangle an adjusted recombination term can be computed if barrier lowering is incorporated This is in contrast to where a single field value for the electrode node is used to compute total recombination value Also unlike 32 barrier lowering can be used with any of the basic numerical solution procedures i e Gummel or Newton Floating Contacts A contact that is not connected to a either a current or voltage source and is totally insulated by dielectric is called a floating contact arras accounts for floating contacts such as floating gates in EPROM devices by using a distributed charge boundary condition which is applied to all nodes of the floating electrode p dS Qe 3 115 S where Distheelectric displacement vector Srepresents the external surface of the floating gate e Qraisthe injected charge ATLAS performs an integration over the entire surface of the electrode and forces the potential on the floating nodes to produce the correct total charge on the electrode The total charge when performing a simulation is by default zero but can be defined using the soLvz statement The total char
217. e ER ER Oe UNE Aut PEOR Alen 10 13 CAC a oa ib acti bete a A ee PL eke 10 13 PE a E TA E 10 13 E Linear voltage controlled Source ci PE CRT ORA et rnrn a Ed eee Ed 10 14 F Linear current controlled current Source cc cece cece eee me 10 14 G Linear voltage controlled Current Source oi a e a e OC oe C a 10 15 H Linear current controlled voltage source isssssssssse mmm 10 15 Independent current Source nia II nn 10 15 K Coupling between two inductors cisco o TR tea Piper Reo Gade iets 10 16 ES snis irr PER M TERRE IR NA 10 16 SILVACO International XV ATLAS User s Manual Volume 1 M MOSFET ee Rao A ARA RR oda vos RD 10 17 oed c re teens 10 17 Q Bipolar junction transistor ssa ces Od IE duds ER eR db Ra exe She aaa 10 18 A s dh Deed i e Cb sce adorada 10 18 T Lossless transmission line sida 10 19 V Independent voltage source cesser RERO ER ci eb CD Cen 10 19 BEGIN ita geo deb a CUL e hcc adria 10 20 END v 10 20 ii nat iaa docs 10 20 DE NA UR PT p AS 10 20 jare 10 21 TRAN eee Le um ord tot teat iad il voc EE SEL AR AN VS o he UE 10 23 EOAD odo oe dd 10 23 SAVE HET 10 24 E ROA 10 24 LA A E TENET 10 25 NODE GE T 3 042253 ste nokia Say A a AS Gade pre and ESTAS 10 25 NUMERO 10 26 fors cR 10 28 MODE nd 10 28 Transient Parameters iisselerei e her eren A AA 10 29 DUSINIBNS LI vahe hate Foot clos dst Lo rusa ood orla SEE nca i s dd 10 29 PESE a
218. e MODELS statement The parameter defaults for the Klaassen model are as follows BB A 4 00e14 V cm BB B 1 97e7 BB GAMMA 2 5 The third alternative allows these model parameters to be calculated from first principles by specifying the parameter auTOBBT on the MODELS statement In this case the parameters are calculated according to q 2x MASS TUNNEL mj BB AG SOS I no 3 269 3 2 5 IMASS TUNNEL Mo x EG300 5 BB B xx_E 3 270 BB GAMMA 2 3 271 where q is the electronic charge h is Planck s constant Eg is the energy bandgap mo is the rest mass of an electron and mass TUNNEL is the effective mass The parameter vass ruwwEL may be set on the MODELS Statement and the bandgap at 300K E G300 is defined on the maTERIAL statement 3 74 SILVACO International Physics Table 3 48 User Definable Parameters in the Band toBand Tunneling Model Statement Parameter Default Units MODEL BB A 9 66e18 vs lom MODEL BB B 3e17 V cm MODEL BB GAMMA 2 0 Gate Current Models Overview In devices that have a metal insulator semiconductor MIS formation the conductance of the insulating film would ideally be considered as zero However for the sub 0 5um generation of MOS devices there is now considerable conductance being measured on the gate contacts This gate current has resulted in two major consequences one negative a
219. e Parameters for Equations 6 14 and 6 15 2 0 cece eee eee 6 7 6 5 User Specifiable Parameters for Equations 6 16 and 6 17 2 0 cece cece eee eee eens 6 8 xxii SILVACO International List of Tables Figure Page No Table Title No 7 1 User Specifiable Parameters for Equations 7 2 to 7 5 10 cc cece eect e eee eene 7 2 7 2 User Specifiable Parameters for Equations 7 8 to 7 10 oooooooccoccconrcnrc ene 7 4 7 3 Additional Parameters for the DEFECTS Statement oooococcocccccnrr nn 7 6 8 1 User Specifiable Parameters for Equation 9 2 10 cece eee eee eee eee etna 9 2 8 2 User Specifiable Parameters for Equation 9 3 ccc cece e eee eee eee e 9 3 8 3 User Specifiable Parameters for Equation 9 6 cc cece cece ete eee e 9 3 8 4 User Specifiable Parameters for Equation 9 7 cece cece teen teen enna 9 4 8 5 User Specifiable Parameters for Equation 9 8 ccc cece cece e 9 5 8 6 User Specifiable Parameters for LASER Loss Models 0 cceeeeeeeeeee teen eeeeee ane 9 5 0 7 LASER Parameters 0 e Tx wr ae ex dar Vut unite Da epa x RN Mop iat 9 8 10 1 Diode DC Parameters 1 ioseph RR Rn ek 10 33 10 2 Diode Capacitance Parameters ssssssesseeeen eee teens 10 34 10 3 A complete Gummel Poon parameter list 0 cece cece eee eee eee eee ene tenes 10 39 10 4 Basic DC Model Parameters ccc cece e eee eet Inn 10 40 10 5 Low Current Beta Degradation Parameters
220. e bands has a large impact on the charge transport in these heterodevices There are three methods for defining the conduction band alignment for a heterointerface the affinity rule the ALIGN parameter on the MaTteRTAL statement and by manually adjusting the material affinities using the AFFINITY parameter on the MATERIAL statement The Affinity Rule The default method in BLAZE for assigning how much of the bandgap difference appears as the conduction band discontinuity makes use of the affinity rule The affinity rule assigns the conduction band discontinuity equal to the difference between the two materials electron affinities AFFINITY on the MATERIAL statement The affinity rule method is used by default for all materials where the aLicn parameter has not been defined on the MATERIAL statement The ALIGN parameter on the MATERIAL statement Experimental measurements of the actual band discontinuities can differ from what is assigned using the affinity rule with the standard material electron affinities Therefore BLAZE allows AE to be calculated by specifying the A rcu parameter on the MATERIAL Statement ALIGN specifies the fraction of the bandgap difference which will appear as the conduction band discontinuity This bandgap difference is between the material for which the arrcw parameter is specified and the smallest bandgap material in the overall structure the reference material Internally BLaze creates the desired condu
221. e entered on energies EGA and EGD respectively 1 8 SILVACO International Chapter 8 Luminous Introduction Before continuing to the sections that follow you should be familiar with ATLAS and either S PISCES or BLAZE If not read Chapter 2 and either Chapter 4 or Chapter 5 of this manual before proceeding with this chapter LUMINOUS is a general purpose ray trace and light absorption program integrated into the ATLAS framework to run with device simulation products When used with the S PISCES or BLAZE device simulators LUMINOUS calculates optical intensity profiles within the semiconductor device and converts these profiles into photogeneration rates in the device simulators This unique coupling of tools allows the user to simulate electronic responses to optical signals for a broad range of optical detectors These devices include but are not limited to pn and pin photodiodes avalanche photodiodes Schottky photodetectors MSMs photoconductors optical FETs optical transistors solar cells and CCDs The following sections address various types of optoelectronic devices You can proceed to the sections most relevant to your application but we strongly recommend you read the other sections as well Thereis little overlap in the sections Simulation Method Optoelectronic device si mulation is split into two distinct models that are calculated simultaneously at each DC bias point or transient timestep 1 Opti
222. e optimum operating bias of devices such as avalanche detectors and photo transistors Obtaining Transient Response to Optical Sources It is sometimes desirable to examine the time domain response of a detector to time dependent e g ramped or pulsed optical sources LUMINOUS provides this capability with the RAMP LIT parameter When the RAMP LIT parameter is specified in a SOLVE statement the optical intensity is changed linearly from the most recently set intensity to the intensity set in the B parameter If a particular source intensity is not set using the corresponding B parameter its intensity is not varied during the transient The period of the linear ramp is specified by the RAMPTIME parameter Thetransient simulation stops after the time specified by the TsTOP parameter If the time given by TSTOP is greater than that given by RAMPTIME the source intensities remain constant until the time given by TSTOP For transient ramps the TSTEP parameter should also be set TSTEP is typically set to allow several samples within the RAMPTIME After the first time step subsequent time step sizes will be chosen automatically based on estimates of truncation error The following is an example of the specification of an optical impulse transient SOLVE B1 1 0 RAMPTIME 1E 9 TSTOP 1E 9 TSTEP 1E 11 SOLVE B1 0 0 RAMPTIME 1E 9 TSTOP 20E 9 TSTEP 1E 11 In this example a triang
223. e start of the circuit part of a mIxeDMODE command file END END indicates the end of the circuit part of a MIxEDMODE command file AC AC performs an AC linear small signal analysis on the circuit MIxEDMODE first creates a linearized small signal model at the operating point of the circuit and the computes the frequency response over a user specified range of frequencies SILVACO International 10 19 ATLAS User s Manual Volume 1 Syntax AC DEC OCT LIN nump fstart fstop Description DEC specifies that the frequency sweep is by decades OCT specifies that the frequency sweep is by octaves LIN specifies that the frequency sweep is linear This is default nump is the total number of points per decade or per octave or the total number of points of the linear sweep fstart is the starting frequency Hz fstop is the final frequency Hz Several AC statements can be specified in the same command file In this case they will be executed sequentially Before the execution of the first AC statement the program will execute all DC statements if any regardless of the order of the AC and DC statements in the command file Examples AC DEC 3 1 63 1 012 AC LIN 20 1 e5 2 e6 DC DC causes a DC transfer curve to be computed for the circuit with all capacitors opened and all inductors shorted Syntax DE DEC OCT LIN source_name start stop numbers_steps
224. e width of the device The effect of the resistance R is to add an extra equation to be satisfied to node i This equation is given by 1 kT R V applied vita Nnw lp Ip Igisp 0 3 118 where Vapplied is the external applied voltage Vj is the surface potential N is the net doping nj is the intrinsic electron concentration and In Ip I gis are the electron hole and displacement currents at node i This equation simply balances the current in and out of the resistor added to each node i As with the case for lumped elements ATLAS can print out a value of contact resistance for each contact in the run time output Since the actual value depends on the length of each surface segment for distributed contacts ATLAS prints out the value of CON RESIST wIDTH Which is the same for all contact surface segments This runtime output is enabled by adding the print option on the mopELs statement SILVACO International 3 29 ATLAS User s Manual Volume 1 Table 3 15 User Specifiable Parameters for Equation 3 117 Statement Parameter Units CONTACT CON RESIST Q cn MESH WIDTH um Note AC small signal analysis can not be performed when any distributed contact resistance has been specified Also only the NEWTON numerical scheme should be chosen on the METHOD statement Energy Balance Boundary Conditions When the energy balance model is applied special boundary conditions are applied for ca
225. ecombination dnd Generation Models iso cerei rt ORE EE E REPRE R CHEER REALE Rd Fas 5 17 Material Dependent Physical Models 0 0 cece eee eee eee me 5 18 SA ts cust aba Atv etta a eas Ranta 5 18 Bandgap Narrowing A AS 5 18 Low Field Mobily So 268 e eta lO tae ei 5 19 bv andi V NMS S IE EE 5 20 Al x Ga 1 xX As System ii a tada 5 20 Mrs Dc rada 5 20 Electron AM a c toas 5 21 Density of States and Effective MASS ip o ERO EA a e OA E bU 5 21 DICE POTETE ouch aes a eee ovata ta Ere San hn acd Lerobafesof ates abba 5 22 Low Field MODI sessi hacc t ERR is is da AR RIA oleaje 5 22 e A aser entia tu Ede AN 5 22 Bandgap ccsiok tele ue e A 5 23 Electron MINDY accen een adc are de Dose ao ou a fiip a Dal adn dA SD aco a ctt 5 23 Density of States and Effective MaSS cece cece eee nn 5 23 Dielectric ESTI vet sco esa AA chs bbe AA Do ec Nd n f 5 24 LOW FIERE Mob lease iaa alg ds ia o Red er dad di 5 24 The SI 1 x G e X System sos eio a URL HORS RATER APR A UT TERR 5 24 A otav b Rate cda E pitt dub tete caduto seb quet niea dS 5 25 Xii SILVACO International Table of Contents Electron i ti AA Ae Ad 5 26 Density ofS ES rre do os Ao Me a Macs 5 26 Diel ctri FUNCOM a A A AA 5 26 SO Mop dmt ER 5 26 Velocity Saturation cute di 5 26 Silicon CAMI SIC MR 5 27 Band Parameters TORSO alar a a lid 5 27 SIC Mobility Paramet asua A A a LAA ries 5 2 OEM A t inp a p cv testi unde ide Perey A 5 27 ANSIA a 24 Ties 5 28 D
226. ed current source is characterized by the equation n n trcon v nc nc Example G245675 H Linear current controlled voltage source Syntax Hxxx n n vcontrolname trres Description Hxxx specifies the name of the linear current controlled voltage source Must begin from an H n n are the positive and negative terminal node numbers A positive current flows from the node n through the source to the node n vcontrolname is the name of voltage source through which the controlling current flows The direction of positive controlling current flow is from the positive node through the source to the negative node of vcontrolname trres is thetransresistance in Ohms Thelinear current controlled voltage source is characterized by the equation v n n trres i vcontrol name Example H1245V10 1K Independent current source Syntax Ixxx n n value ac parameters transient parameters Description Ixxx specifies the name of the independent current source It must begin with an 3472 lt al48 gt SILVACO International 10 15 ATLAS User s Manual Volume 1 n n arethe positive and negative terminal node numbers ac parameters are described on page 10 23 value is the DC value of the source ampers transient parameters are described on page 10 24 Example 11280 PULSE 0 200 0 20ns 20ns 100ns 10 100 K Coupling between two inductors Syntax Kxxx Lyyy Lzzz kval Descri
227. ed to give an overview to the basic use of ATLAS without regard to the details required for a given technology Requirements for ATLAS simulation vary considerably The needs of the sub micron MOS device engineer the 1000V power device engineer and the III V RF device engineer differ cannot all be covered in one chapter Silvaco provides many references to individual technology problems using ATLAS These are e alibrary of over 500 examples that can be accessed on line from DEckBuiLp Users should look at these examples not only for their technology but also related ones For example different aspects of high frequency analysis is covered in the MESFET and silicon bipolar example sections e the chapters on each individual ATLAS product in this manual For example the S PISCES chapter contains hints for EEPROM devices the LUMINOUS chapter hints on photodetectors e the Simulation Standard newsletter distributed by Silvaco To make sure you are on the mailing list contact your local Silvaco office e the Silvaco World Wide Web Page www silvaco com This web site contains on line versions of the artides in our newletter on line searchable index of the examples links to other TCAD web sites and a section on solutions to known problems with all Silvaco programs for more information about suggested technology specific strategies contact your local Silvaco support engineer 2 44 SILVACO International Chapter 3 Physics Basic Semiconduct
228. een carriers and between the carriers and the lattice See the section on MOS simulation for more information An example of a set of typical models for a partially depleted SOI MOSFET could be MODEL KLA SHI FLDMOB SRH AUGER BGN LAT TEMP INTERFACE QF 1e10 Y MAX 0 05 T INTERFACE QF 1el11 Y MIN 0 05 THERMCONTACT NUM 1 ELEC NUM 4 EXT TEMP 300 IMPACT SELB Numerical Methods for SOI One important issue with SOI device simulation is the choice of numerical methods In SOI technology the potential in the channel or body region is commonly referred to as floating This occurs because there exists no direct contact to it by any electrode As a result when a bias is applied or increased on a contact there may be some convergence problem This occurs because the guess used in the numerical solution scheme for w n p may be poor particularly in the floating region This is particularly true if impact ionization is used To overcome the problem of poor initial guess the following numerical methods syntax should be used in isothermal drift diffusion simulations METHOD GUMMEL NEWTON This method initially performs a Gummel iteration to obtain an improved initial guess for the Newton solution scheme Although this method is more robust the penalty is that it has proved slower than using the Newton scheme alone For more information on the numerical schemes available please refer tothe N
229. efining Anisotropic Mobility in ATLAS issues hem RORIS Re xn 5 28 Impact lonization and Thermal Parameters 0 ccc cece eee e eee Hm 5 29 Simulating Heterojunction Devices with Blaze 6 0 ccc ccc cece corr teeennes 5 29 Defining Material Regions with Positionaly Dependent Band Structure 0 cece cece eee 5 29 STD UDEHORS cles ts is Leod E Cue east cae Ne Als E Dd coc A ach hed Foto beet o 5 29 ETC UCI As idad D 5 29 Defining Materials and Models 4 vss cats cos dels anao ds dera cv 5 30 pur T A et A EA A 5 30 Models ro aldeas 5 30 Parser FUNCHONS 220 A rt wr AU GATTO a EVO soe IDEE edd 5 30 Chapter 6 GIGA ar wien ce Guten Hinks 60k Ob ke eae oman eoadied 6 1 OUEN cies os xxi exc PO eas Orn nd XR OO RUE RA EXE wed Aa cn EORR EUER ARAS 6 1 AIN cis rosae to der ah kway RS KR EG eae PA Eur MU dean aad QUU a 6 1 NUTS S cra ee eio d cid esce o Id 6 1 Physical Models 5 1325 aa Vara kac nari afi ara ac a Line aca On Ea Y S Qc ERA E ox E Gd Rare a ele 6 2 The Lattice Heat Flow Equation xiii derer ud exe eee da a Rare ehe ED eS ees 6 2 Specifying Heat Sink Layers For Thermal Solutions esses 6 2 Specifying Thermal Conductivity 5 ue doo ora TRE YER Re e EC tod darse AN Lato 6 2 Mon IsomeirmialMOgBlS s sh a5 stan setae am de s a OD ae 6 4 Effective Density OP Stale G arar d ttd ecol p Edw cl OE ar Dicti efe Op d rd sema pa 6 4 Nonisothermal Current Densities cuicos o a td EAR GOL ORT S 6 4 A amati uec artes Reate bubus eA oo
230. ement can also be used for this purpose When enabled the mIx surr parameter will ensure that the Watt model will only apply to minority regions The logical parameters EXP WATT N and EXP wATT P Of the moBILITY statement can also be used to enable a additional modification to the Watt model When these parameters are enabled the effective normal electric field becomes a function of the depth beneath the silicon oxide interface according to Be Se SO ine 3 193 in y XP YCHARN WATT AY Yint E me 3 194 Lp 7 Ey SPYCHARP WATT where E is the perpendicular electric field E is the perpendicular electric field at the interface y is the local y coordinate and Yint is the y coordinate of the silicon oxide interface The equation parameters YCHARN WATT and YCHARP WATT are user definable on the moBILITY statement SILVACO International 3 53 ATLAS User s Manual Volume 1 Shirahata s Mobility Model The Shirahata mobility model 111 is general purpose MOS mobility model that takes into account screening effects in the inversion layer as well as improved perpendicular field dependence for thin gate oxides In the original paper the authors present the model as a combination of portions of Klaassen s model for low field mobility contributions and an empirically fit expression for the perpendicular field dependent mobility in the inversion layer In our implementation we simply fit our more complete implementation of Kla
231. ent Floating Field Plates You should use the ELECTRODE statement to specify the field plate regions as electrodes If these plates do not contact any semiconductor then these electrodes can be set to float in the same manner as EEPROM floating gates The following statement line specifies that the field plate region PLATE1 is a floating field plate CONTACT NAME PLATE1 FLOATING If the plates do contact the semiconductor this syntax must not be used Instead current boundary conditions are used at the electrode with zero current See the Getting Started Chapter for more about floating electrodes SILVACO International GIGA External Inductors Inductors are commonly used in the external circuits of power devices The CONTACT statement can be used to set an inductor on any electrode The following statement sets an inductance on the drain electrode of 3 uH um CONTACT NAME DRAIN L 3E 3 The next statement is used to specify a non ideal inductor with a resistance of 100 ohms micron CONTACT NAME DRAIN L 3E 3 R 100 More Information Many examples using GIGA have been installed on your distribution tape or CD These indude power device examples but also SOI and III V technologies More information about the use of GIGA can be found by reading the text associated with each example SILVACO International 6 9 UTMOST User s Manual Volume 1 This page intentionally
232. ent H PARAM specifies that the H parameters should be written to the LOG file This is used in conjunction with the NET statement ABCD PARAM Specifies that the AB CD parameters should be written to the LOG file This is used in conjunction with the NET statement GAIN specifies that the stability factor K unilateral power gain GU maximum unilateral transducer power gain GTUmax and H21 2 are written to the LOG file This is used in conjunction with the NET statement Example OPTIONS TNOM 2293 FULLN MODEL MODEL specifies the circuit element model to be used for diodes BJ Ts or MOSFETs and the numerical values of parameters associated with the model 10 28 SILVACO International MIXEDMODE Syntax MODEL name lt lt type gt gt lt lt parameters gt gt Description name specifies the name of the model Circuit element definition statements refer to this name to link elements to models type specifies the type of the model This type must be consistent with the type of the circuit elements that uses the model Thetype can be one of the following D Diode model NMOS n channel MOSFET model This corresponds to the SmartSpice Level 3 model PMOS p channel MOSFET model This corresponds to the SmartSpice Level 3 model NPN npn BJ T model PNP pnp BJ T model Sets of model parameters exist for each model type These sets of parameters are described in detail in the model descript
233. ent of the ramped electrode equals or exceeds END VAL Either voLT CONT or CURR CONT is used to specify whether END vat is a voltage or current value When plotting the log file created by the curve trace statement in TonyPLor it is necessary to select the internal bias labelled int bias for the ramped electrode instead of the plotting the applied bias which is labelled Voltage SILVACO International 2 31 ATLAS User s Manual Volume 1 Using DeckBuild To Specify SOLVE Statements The DEckBuiLD Solve menu can be used generate SOLVE statements The menu has a spreadsheet style entry The Solve menu may be accessed by selecting the Command Solutions Solve button in DEckBuiLD To define a test the right mouse button is depressed in the worksheet and the first option in the menu Add new row should be selected This will add a new row tothe worksheet This procedure should be repeated once per electrode in your device structure The entry for each cell may then be edited to construct a SOLVE statement Some cells require the selection using a pop menu or the entry of numerical values The electrode name is specified in the first cell It is edited using a popup menu that is accessed by pressing the right menu on the cell The second cell specifies whether the electrode will be a voltage V current I or charge Q controlled The third cell specifies whether the solve statement is to be a single DC solve CON
234. er high power high frequency circuit simulation SOI IGBT GTO TFT and optoelectronic devices Advantages of MIXEDMODE Simulation The limitations of compact models can be overcome by using physically based device simulation to predict the behavior of some of the devices contained in a circuit The rest of the circuit is modeled using conventional circuit simulation techniques This approach is referred to as mixed mode simulation since some circuit elements are described by compact models and some by physically based numerical models MIXEDMODE simulation provides several worthwhile advantages No compact model need be specified for a numerical physically based device The approximation errors introduced by compact models can be avoided particularly for large signal transient performance In addition the user can examine the internal device conditions within a numerical physically based device at any point during the circuit simulation The cost is increased CPU time over SPICE however CPU time is comparable to a device simulation excluding the external circuit nodes Mixed mode simulation normally uses numerical simulated devices typically only for critical devices Non critical devices are modeled using compact models Using MIXEDMODE Syntax Overview Input file specification for MIXEDMODE is different in many respects to the rest of ATLAS However users familiar with SPICE and ATLAS syntax should have little difficulty understanding
235. er than to a single LOG file LOG files are described later in this chapter The Importance Of The Initial Guess To obtain convergence for the equations used it is necessary to supply a good initial guess for the variables to be evaluated at each bias point The ATLAS solver uses this initial guess and iterates to a converged solution For isothermal drift diffusion simulations the variables are the potential and the two carrier concentrations Provided a reasonable grid is used almost all convergence problems in ATLAS are caused by a poor initial guess to the solution During a bias ramp the initial guess for any bias point is provided by a projection of the two previous results Problems tend to appear near the beginning of the ramp when two previous results are not available If one previous bias is available it is used alone This explains why although the following two examples eventually produce the same result the first will likely have far more convergence problems than the second 1 SOLVE VGATE 1 0 VDRAIN 1 0 VSUBSTRATE 1 0 2 SOLVE VGATE 1 0 SOLVE VSUBSTRATE 1 0 SOLVE VDRAIN 1 0 In the first case one solution is obtained with all specified electrodes at 1 0V In the second case the solution with only the gate voltage at 1 0V is performed first All other electrodes are at zero bias Next with the gate at 1 0V the substrate potential is raised to 1 0V and another solution is obtained Fin
236. erface The traditional barrier heights 1G EB0 and Ic HBO are reduced to take account of three effects The first is due to Schottky barrier lowering which depends on the perpendicular electric field at the semiconductor insulator interface The second takes account of tunneling through the gate oxide by reducing the barrier height The third takes into account that a potential difference exists between the semiconductor insulator interface and the starting position of the hot carrier By default this last effect SILVACO International 3 77 ATLAS User s Manual Volume 1 is disabled but may be enabled with the parameters e BENDING and H BENDING for electrons and holes respectively The second probability P4 is the probability that no energy is lost by optical phonon scattering as the hot carrier travels towards the semiconductor insulator interface after being redirected and is given by P LES 3 281 in amp XP TG ELINF f Pip mane ver where r is the distance from point of redirection to the semiconductor insulator interface The final probability P5 accounts for the probability of scattering in the image force potential well in the gate oxide and is given by SM S l6neE ox Pon exp PATH N for 0 THETA N 3 283 P n 0 foro 2THETA N 3 284 NM DNE P SE for 9 gt THETA P 2 2 p 7 exp PATH P or 8 gt al 3 285 Pr 0 foro lt THETA P 3 286 where PATH N and PATH P are the electon and
237. es 6 EPROM Application Examples LATCHUP CMOS Latchup Application Examples 8 ESD ESD Application Examples 9 POWER Power Device Application Examples 10 ISOLATION ISOLATION Applications Examples 11 MESFET Application Examples 12 HBT HBT Application Examples 13 HEMT HEMT Application Examples 14 QUANTUM Device Simulation with Quantum Mechanics 15 FASTATLAS FastATLAS MESFET and HEMT Application Examples Figure 2 2 Examples Index in DeckBuild The examples are divided by technology or technology group The most common technologies are dear e g MOS BJ T while others are grouped with similar devices e g IGBT and LDMOS are under POWER and solar cell and photodiode are under OPTOELECTRONICS 2 4 SILVACO International Getting Started with ATLAS 4 Choosethe technology you are interested in by double clicking the left mouse button over that item in the examples index 5 A list of examples for that technology will appear These examples typically illustrate different devices applications or types of simulation An examples search feature also exists by pressing the right hand mouse button over the button Index Wildcards can be used in the search 6 Choose a particular example by double dicking the left mouse button over that item in the list 7 A text description of the example will appear in the window This text describes the important physical mechanisms in the simulation as well as details
238. es the WAVELENGTH parameter can be used to assign the optical wavelength WAVELENGTH uses the units microns to be more consistent with the rest of ATLAS Users used to the optoelectronic engineering preference for nanometers should note this For multispectral sources spectral intensity is described in am external ASCII file specified by the POWER FILE parameter This is a text file that contains a list of pairs defining wavelength and spectral intensity The first line of the file gives the integer number of wavelength intensity pairs in the file An example of the contents of such a fileis shown below ooo0oo0 u hero PPNOW JO OSB This example specifies that there are four samples and that at a wavelength of 0 4 um the intensity is 0 5 Watts per square cm per um of wavelength and so on With multispectral sources the user must specify a discretization of the interpolated information Values must be specified for the WAVEL START WAVEL END and WAVEL NUM parameters These specify the starting and ending wavelengths and the number of wavelengths to sample LUMINOUS will use wavelengths at equal intervals over the specified range of wavelengths The program performs an independent ray trace at each of the sample wavelengths F or example WAVEL START 0 4 WAVEL END 0 6 WAVEL NUM 2 will cause ray traces at wavelengths of 0 45 and 0 55 LUMINOUS obtains the intensity associated with each sample by in
239. espondds to KT D q n 3 17 KT D q p 3 18 SILVACO International 3 3 ATLAS User s Manual Volume 1 If Fermi Dirac statistics are assumed for electrons these become KT 1 n a erc tern ecl 1 ERA a ell where F is the Fermi Dirac integral of order and eg is given by q0p Note The effects resulting from bandgap narrowing and their implementation into ATLAS are described in detail in a later section of this chapter Energy Balance Transport Model A higher order solution to the general Boltzmann Transport Equation consists of an additional coupling of the current density to the carrier temperature or energy The current density expressions from the drift diffusion model are modified to include this additional physical relationship The electron current and energy flux densities are then expressed as me T J aD V ua4nVy qnD4 VT 3 20 k hn gt Sn K VT a nTa 3 21 d T J p qD V HpPVY qpD VT 3 22 gt KS Sp KYT pT 3 23 Where T and T represent the electron and hole carrier temperatures and Sp and Sp are the flux of enery or heat from the carrier to the lattice The energy balance transport model indudes a number of very complex relationships and therefore a later section of this chapter has been devoted to this model Displacement Current Equation For time domain simulation the displacement current is calculated and included in the structure log fileand t
240. evice simulation This rectangular mesh and the region mesh in which the Helmholtz equation is solved is specified using the rx wEesg and Ly mesH statements The specified region must lie completely inside the ATLAS simulation domain and should completely cover the actively lasing region e Specify a gain model The optical gain model is specified using the carnmop parameter in the MODELS Statement GAINMop 1 specifies the use of the physically based model and carnmop 2 specifies the use of the simple empirical model For single frequency calculations you can select different gain models for different regions materials using the REGION Or MATERIAL parameters of the MopELs statement Note If multiple longitudinal modes are to be accounted for then carnmoD 1 must be specified for the active lasing region e Specify laser physical parameters and models Specify CAVITY LENGTH MODELS statement the length of the laser cavity in the z direction Specify PHOTON ENERGY Or LAS OMEGA to specify initial photon energy or laser frequency wopgrs statement Specify laser loss mechanisms LAS MIRROR LAS FCARRIER LAS ABSORPTION ON the moDeLs statement and any associated constants FCN FCP ALPHAA On the MATERIAL Statement 9 6 SILVACO International LASER Specify any additional laser losses LAs LOSSES MODELS statement e fcalculation
241. expression in equation 3 320 AEs B DORT p er ENS 3 320 9 kgT 1 SILVACO International 3 89 ATLAS User s Manual Volume 1 Here B port is a user definable adjustment parameter on the mopEL statement P is equal to 6 1x108 eV cm E is the perpendicular electric field and g y is a function to restrict the application of the model to the channel region given by equatioin 3 321 Y D DORT g y z 3 321 DX c CET 14 a DORT The Van Dort model for N channel devices is enabled by specifying x ponr on the MopELs statement 3 90 SILVACO International Chapter 4 S PISCES Introduction Note Before reading this chapter you should be familiar with ATLAS If you are not familiar with basic operation of ATLAS read the Getting Started chapter S PISCES is a powerful and accurate two dimensional device modeling program that simulates the electrical characteristics of silicon based semiconductor devices including MOS bipolar SOI EEPROM and power device technologies S PISCES calculates the internal distributions of physical parameters and predicts the electrical behavior of devices under either steady state transient or small signal AC conditions This is performed by solving Poisson s equation and the electron and hole carrier continuity equations in two di mensions S PISCES solves basic semiconductor equations on non uniform triangular grids The structure of the simulated device can be
242. extra lumped capacitor from the floating gate to the control gate or one of the other device terminals This is often required since S PISCES is performing a 2D simulation whereas the coupling of the gates is often determined by their 3D geometry Parameters on the CONTACT statement are used to apply these extra lumped capacitances For example to add a capacitor of 1fF um between the control and floating gates the syntax is CONTACT NAME fgate FLOATING FG1 CAP 1 0e 15 EL1 CAP cgate Gate Current Models The gate currents for the floating gate structure can be supplied by one of three sources hot electron injection HEI Or N CONCAN hot hole injection HHI or P CONCAN and Fowler Nordheim tunneling current FNORD These currents are of importance depending on whether electrons are being moved onto the gate or off the floating gate In the case of placing electrons on the floating gate hot electron injection and Fowler Nordheim tunneling should be used In the case of removal of electrons from the floating gate hot hole injection and F owler Nordheim tunneling should be set In drift diffusion simulations hot electron injection is simulated by setting the HEI parameter of the MODELS statement Hot hole injection is simulated using the HHI parameter of the MODELS statement Fowler Nordheim tunneling is enabled by setting the rNoRD parameter of the MODELS statement The following example demonstrated the proper setting for Flash EPROM pr
243. f varying composition fraction a parser function can be used To define the parser function for composition fraction writea C function describing the composition fraction as a function of position A template for the function named composition is provided with this release of ATLAS Once the function composition is defined it should be stored in a file In order to use the function for composition the parameter F compos1IT should be set to the file name of the function 5 30 SILVACO International Chapter 6 GIGA Overview GIGA extends ATLAS to account for lattice heat flow and general thermal environments GIGA implements Wachutka s thermodynamically rigorous model of lattice heating which accounts for J oule heating heating and cooling due to carrier generation and recombination and the Peltier and Thomson effects GIGA accounts for the dependence of material and transport parameters on the lattice temperature and supports the specification of general thermal environments using a combination of realistic heatsink structures thermal impedances and specified ambient temperatures GIGA works with both S PISCES and BLAZE and with both the drift diffusion and energy balance transport models Before continuing with this chapter you should be familiar with ATLAS as described in Chapter 2 and with either S PISCES Chapter 4 or BLAZE Chapter 5 Applications A major application of GIGA is the simulation of high power structures
244. f yen SA thom L nom Vnom Yun q t t t VISCA VIS eas 3 in ae tnom tnom Vi tnom Vict TEMPLEVC 2 CJE t CJE 1 CTE Dt CJC t CJC 1 CTC Dt CJS t CJS 1 CTS Dt and contact potentials are determined as VJE t VJE 1 TVJE Dt VJC t VIC 1 TVJC Dt VJS t VJS LAE TVJIS DE TEMPLEVC 3 VJE MJE CJE t CJE mew VJC MJC CJC t CJC Cant VJS MJS CJS t cis F 10 137 10 138 10 139 10 140 10 141 10 142 10 143 10 144 10 145 10 146 10 147 10 148 10 149 10 150 10 151 10 58 SILVACO International MIXEDMODE where VJE t VJE TVJE Dt 10 152 VJC t VIC TVJC Dt 10 153 VJS t VJS TVJS Dt 10 154 TEMLEVC24 CJE t CJE 1 0 5 dvjedt 10 155 B vjedt TTE CJC t CJC 1 0 5 dvjcdt au 10 156 x E OO i CJS t CJS 1 0 5 dvjsdt Al 10 157 VJS VJE t VJE dvjedt At 10 158 VJC t VIC dvjcdt A 10 159 VJS t VJS dvjsdt A 10 160 where for TEMPLEV 1 or 2 dvjedt egnom 3 Vi tnom 1 16 egnom tnom thom 1108 WE Hus tnom dvjcdt 2 egnom 3 Vt tnom t 1 16 egnom tnom TT e Tode tnom dvjsdt egnom 3 Vittnom 1 16 egnom tnom ow IIS 59 ges tnom and for TEMPLEV 3 dvjedt egnom 3 Ve tnom EG egnom tnom ENTES E basa tnom SILVACO International 10 59 ATLAS User s Manual Volume 1 dvjcdt egn
245. facility will detect the problems in the 0 8V solution and cut the bias step in half to 0 7V and try again This will probably converge The solution for 0 8V will then be performed and the bias ramp will continue with 0 2V steps Small Signal AC Solutions Specifying AC simulations is a simple extension of the DC solution syntax AC small signal analysis is performed as a post processing operation to a DC solution Two common types of AC simulation in ATLAS are outlined here The results of AC simulations are the conductance and capacitance between each pair of electrodes Pointers on interpreting these results are given later in this chapter Single Frequency AC Solution During A DC Ramp The minimum syntax to set an AC signal on an existing DC ramp is just the AC flag and the setting of the small signal frequency SOLVE VBASE 0 0 VSTEP 0 05 VFINAL 1 0 NAME base AC FREQ 1 0e6 Other AC syntax for setting the signal magnitude and other parameters are generally not needed as the defaults suffice One exception is in 1D MOS capacitor simulations To obtain convergence in the inversion deep depletion region the parameter DIRECT should be added to access a more robust solution method Ramped Frequency At A Single Bias For some applications such as determining bipolar gain versus frequency it is necessary to ramp the frequency of the simulation This is done using the following syntax 1 SOLVE VBASE 0 7 AC FREQ 1e9 FSTEP 1e9 N
246. fies the number of squares for source resistance PD specifies the periphery length of the drain PS specifies the periphery length of the source Example M12345moslL luW 30u O Optical source Syntax Oxxx beam value transient parameters Description Oxxx spedifies the name of an independent optical source It must begin with an O beam specifies the beam number The beam with this number should be described in the ATLAS section of the command file See the LUMINOUS chapter for a complete description of optoelectronic simulation value is the DC optical intensity value W cm2 transient parameters are described later in this chapter Note The treatment of optical sources is fully similar to the treatment of independent voltage current sources i e DC statements can be used to simulated DC light responses of the circuit and transient parameters can be used to describe the transient behavior of the optical sources Example O1 1 0 001 pulse 0 001 0 002 0 2ns 2ns 100ns 10 100 SILVACO International 10 17 ATLAS User s Manual Volume 1 Q Bipolar junction transistor Syntax Oxxx nc nb ne ns mname area Description Qxxx specifies the name of a bipolar junction transistor It must begin with a Q nc nb ne ns arethe collector base emitter and substrate node numbers mname is the model name It must refer to a BJ T model area is the area factor The default valueis 1 0 This parameter is optional
247. file by using the the following option at the end of extract command EXTRACT DATAFILE lt filename gt Cut off frequency and forward current gain are of particular use as output parameters These functions can be defined as follows MAXIMUM CUTOFF FREQUENCY EXTRACT NAME FT MAX MAX G COLLECTOR BASE 6 28 C BASE BASE FORWARD CURRENT GAIN EXTRACT NAME PEAK GAIN MAX I COLLECTOR I BASE Note Over 300 examples are supplied with ATLAS to provide many practical examples of the use of the EXTRACT statment EXTRACT has two additional important functions 1 It provides data for the VWF database i e to store device parameters to the VWF database they must be evaluated using EXTRACT 2 When using the DEckBuiLD Optimizer to tune parameters EXTRACT statements must be used as the optimization targets Functions In TonyPlot The Functions Menu in TonyPLot allows you to specify and plot functions of the terminal characteristics in the Graph Function text fields For example transconductance can be calculated using the following function dydx drain current gate voltage Current gain can be evaluated as collector current base current When creating functions the key to correct syntax is that the name for any variable in a function is the same as that in the Y Quantities list on the Display menu SILVACO International
248. finable Parameters in the Band toBand Tunneling Model 3 75 3 49 User Specifiable Parameters for Equation 0 0 e cece e eee eee eee e 3 76 3 50 User Definable Parameters in Concannon s Gate Current Model lt lt lt lt 3 79 3 51 User Definable Parameters for Equations 3 305 and 3 306 ooooocoooococcrorcrr o 3 83 3 52 User Specifiable Parameters for Equations 3 307 to 3 308 oooocoococccocrrrr 3 05 3 53 Interpretations of FIXED FERMI and CALC FERMI Parameters during Post Processed Schrodinger solution seen 3 87 5 1 User Specifiable Parameters for Equations 5 45 and 5 46 cece eect e eee eee eee 5 15 5 2 User Specifiable Parameters for Equation 5 47 and 5 48 o oooooocoocccccnn o 5 16 5 3 User Specifiable Parameters for Equation 5 49 and 5 50 ccc cece eee eee 5 17 5 4 Default Bandgap Narrowing Values sese 5 18 5 5 Default Concentration Dependent Mobility for GaAs sseeeeennnnnnnRI 5 19 5 6 6H SIC Low Fle ld Mobllily exe oer EE TIN eaters sees eee ewe 5 27 5 7 4H SiC Low Field Mobility llle HH 5 27 6 1 User Specifiable Parameters for Equation 6 2 0 ccc eee eee eee eens 6 3 6 2 User Specifiable Parameters for Equation 6 3 0 cece eect e eee eee eee nee 6 3 6 3 User Specifiable Parameters for Equations 6 6 and 6 7 1 0 cece cece eee eee eens 6 4 6 4 User Specifiabl
249. fined in five different ways e using the parameters mun and mu to set constant constant values for electron and hole mobilities e using a look up table model conmos to relate the low field mobility at 300K to the impurity concentration e choice of analytic low field mobility models awarvrric and arora to relate the low field carrier mobility to impurity concentration and temperature choice of a carrier carrier scattering model ccswos that relates the low field mobility to the carrier concentrations and temperature e aunified low field mobility model kLaassen that relates the low field mobility to donor acceptor lattice carrier carrier scattering and temperature SILVACO International 3 31 ATLAS User s Manual Volume 1 Constant Mobility In ATLAS the choice of mobility model is specified on the mopELs statement The parameters associated with mobility models are specified on a separate mosrLITY statement One or more mobility models should always be specified explicitly The default is to use constant low field mobilities within each region of a device This default model is independent of doping concentration carrier densities and electric field It does account for lattice scattering due to temperature according to T TMUN Hno MUN 355 3 119 T TMUP MUP 305 3 120 where T is the lattice temperature and the low field mobility parameters MUN MUP TMUN and TMUP may be specified on the moBILITY statement wit
250. finite Table 10 7 High Current Beta Degradation Effect Parameters Parameters Description Units Default Area IKF Corner for forward beta high cur A infinite rent roll off IKR Corner for reverse beta high cur A infinite rent roll off Table 10 8 Parasitic Resistor Parameters Parameters Description Units Default Area RC Collector resistance ohm 0 5 RB Zero bias base resistance ohm 0 m RBM Minimum base resistance at high cur ohm RB x rents IRB Current where base resistance falls A infinite E halfway to its min value RE Emitter resistance Ohm 0 SILVACO International 10 41 ATLAS User s Manual Volume 1 Table 10 9 Junction Capacitor Parameters Parameter Description Units Default Area CAPMOD Capacitance model selector 1 CJE B E zero bias depletion capacitance F 0 2 VJE B E built in potential V 0 75 MJE B E junction exponential factor 0 33 FC Coefficient for forward bias deple 0 5 tion capacitance formula CJC B C zero bias depletion capacitance F 0 VJC B C built in potential V TAS MJC B C junction exponential factor 0 33 CJS Zero bias collector substrate capaci F 0 m tance VJS Substrate junction built in potential V 0 75 MJS Substrate junction exponential factor 035 XCJC Fraction of B C depletionl capaci 1 tance connected to internal base node Table 10 10 Transit Time Parameters Parameters Des
251. frequency sweep is by decades SILVACO International 10 21 ATLAS User s Manual Volume 1 OCT specifies that the frequency sweep is by octaves LIN specifies that the frequency sweep is linear This is default nump is the total number of points per decade or per octave or the total number of points of the linear sweep fstart is the starting frequency Hz fstop is the final frequency Hz Additional optional parameters may also be specified on the NET statement ZO specifies the matching I mpedance default 250 Ohms INDIN specifies the inductance through which the DC voltage source is connected to the input source only if INPORT is given as Vxxxx RSIN specifies the series resistance of INDIN INDOUT specifies the inductance through which the DC voltage source is connected to the output source only if OUTPORT is given as Vxxxx RSOUT specifies the series resistance of INDOUT CIN specifies the capacitance through which the S parameter test circuit is connected to the input port COUT specifies the capacitance through which the S parameter test circuit is connected to the output port Note The S parameters will be automatically saved to the LOG file The Z Y H ABCD and gain small signal parameters can also be written to the LOG file These are selected via the OPTIONS statement Also the default values can be viewed if PRINT is specified on the OPTIONS statement Examples NET V1V2 DEC 10 1e6 1e10
252. ge may change if a charge injection model has been turned on These models are defined in a later section underneath Gate Current Models To define a contact as a floating contact use CONTACT NAME fgate FLOATING Note When specifying a floating contact it is necessary to use the Newton scheme as the numerical technique Current Boundary Conditions In some devices the terminal current is a multi valued function of the applied voltage This means that for some voltage boundary conditions the solution that is obtained depends on the initial guess An example of this is the CMOS latch up trigger point At thetrigger point thel V curve changes from being flat to vertical and may exhibit a negative slope The solution will then have three different solutions of current for one applied bias The particular solution which the model finishes in will depend upon the initial conditions 3 26 SILVACO International Physics This trigger point is difficult to determine using a simple voltage boundary condition In addition it is almost impossible to compute any solutions in the negative resistance regime when using voltage boundary conditions Some of these problems can be overcome using current boundary conditions Calculation of current boundary conditions is activated by the CURRENT parameter in the CONTACT statement The voltage boundary condition should be used in regions where dl dV is small The current boundary condition may
253. gt KT E p v w q In nie 3 40 The variation in the energy bandgap is also applied partially to the electron affinity X The effective electron affinity X efg given as follows Xett X AEgx A 3 41 where As is a user specifiable asymmetry factor The user can specify the value of the asymmetry factor using the asymMETRY parameter of the MATERIAL statement Note In addition to this in built model for bandgap narrowing ATLAS allows the use of it s C interpreter module A user is allowed to write an external file within which an equation for bandgap narrowing may be specified through a C function The filename is specified with the parameter r BcN on the MODEL statement Further details for the C interpreter may be found in Appendix A 3 8 SILVACO International Physics Space Charge from Incomplete lonization Traps and Defects Overview Poisson s equation Equation 3 1 induding the carrier concentrations the ionized donor and acceptor impurity concentrations N D and NA charge due totraps and defects Q1 has the form In ATLAS the default is to assume full impurity ionization i e N D N D total and NA Na total and to set Qy equal to zero ATLAS also provides the options of accounting for incomplete ionization of impurities and accounting for additional charge associated with traps and defects Incomplete lonization of Impurities ATLAS can account for impurity freeze out 18 by using Fer
254. gy Ey is the valence band energy and the subscripts T G A D stand for tail Gaussian deep level acceptor and donor states respectively E E gp4 E NTA exp E 7 2 E grp E NTD exp Wap 7 3 E EG A7 8Ga E NGA epl wa 7 4 E EGD For an exponential tail distribution the pos is described by its conduction and valence band edge intercept densities ra and wtp and by its characteristic decay energy wra and wTD For Gaussian distributions the DOS is described by its total density of states ca and nep its characteristic decay energy wca and wep and its peak energy peak distribution ca and Ecp The user specifiable parameters for the density of defect states are shown in Table 7 1 Table 7 1 User Specifiable Parameters for Equations 7 2 to 7 5 Statement Parameter Default Units DEFEC NTA 1 12 10 1 cm DEFEC NTD 4 0 107 cm DEFEC NGA 5 0 1017 cm DEPRE GD BELGA cm DEFEC EGA 0 4 eV DEFEC EGD 0 4 eV DEFEC WTA 0 025 eV 1 2 SILVACO International TFT Table 7 1 User Specifiable Parameters for Equations 7 2 to 7 5 Statement Parameter Default Units DEFECT WTD 0 05 eV DEFECT WGA Out eV DEFECT WGD 0 1 eV Trapped Carrier Density The electron and hole concentrations due to trapped states ny and pr respectively are given by E
255. h Mode With DeckBuild To use DECKBUILD in a non interactive or batch mode you add the run parameter to the command that invokes DeckBuILD A pre prepared command fileis required for running in batch mode It is advisable to savethe run time output to a file since error messages in the run time output would otherwise be lost when the batch job completes deckbuild run as lt input filename outfile output filename Using this command requires a local X Windows system to be running The job runs inside a DECKBUILD icon on the terminal and quits automatically when the ATLAS simulation is complete You can also run DECKBUILD using a remote display deckbuild run as input file outfile output file display lt hostname gt 0 0 2 2 SILVACO International Getting Started with ATLAS No Windows Batch Mode With DeckBuild For completely non X Windows operation of DEckBuiLDb the ascii parameter is required deckbuild run ascii as input filename outfile output filename This command directs DEckBuiLD to run the ATLAS simulation without any display of the DECKBuILD window or icon This is useful for remote execution without an X windows emulator or for replacing Unix based ATLAS runs within framework programs When using batch mode use the UNIX command suffix amp to detach the job from the current command shell To run a remote ATLAS simulation under DeckBuiLD without display and then logout from the
256. h can be set in each SOLVE statement successive solutions can be obtained as a function of wavelength Each time the LAMBDA parameter is specified a new ray trace is run for that new wavelength and the electrical solution recalculated The following statements could be used to extract terminal currents at a series of discrete wavelengths SOLVE Bl 1 LAMBDA 0 2 SOLVE B1 1 LAMBDA 0 3 SOLVE Bl 1 LAMBDA 0 4 SOLVE B1 1 LAMBDA 0 5 SOLVE B1 1 LAMBDA 0 6 SOLVE Bl 1 LAMBDA 0 7 SOLVE Bl 1 LAMBDA 0 8 In this example the spectral response is obtained for wavelengths from 0 2 microns to 0 8 microns When using LAMBDA the WAVELENGTH parameter of the BEAM statement is overridden However users should be sure to use a monochromatic beam and not a multi spectral beam for this simulation Note The units of LAMBDA and WAVELENGTH in the BEAM statement are in um Simulating Solar Cells Obtaining Open Circuit Voltage and Short Circuit Current To obtain Voc and Iss for a solar cell first the illumination conditions should be defined This should be done as discussed above in describing multi spectral sources The short circuit current is obtained by defining the contacts as voltage dependent contacts default and obtaining a solution with the device under zero bias with illumination This can typically be done as a first step by the following input statement for example
257. h small signal frequency This is a useful strategy for analyzing the frequency response of the device as a function of bias voltage 8 14 SILVACO International Luminous Obtaining Spatial Response Toobtain spatial response an optical spot is moved along a line segment perpendicular to the direction of propagation of the source Each incremental step is equal to the width of the spot The total distance over which the source is scanned is defined by the MIN WINDOW and MAX WINDOW parameters of the BEAM statement The number of steps is defined by the RAvs parameter of the BEAM statement The spot width is defined by the ratio MAX WINDOW MIN WINDOW RAYS The spot scan is started by the SCAN SPOT parameter of the SOLVE statement This parameter is set to the beam index of the optical source to be scanned i e the beam defined by the BEAM statement whose NUMBER parameter is set to the beam index During the spot scan ATLAS obtains solutions and outputs terminal currents etc as well asthe relative beam location at each incremental spot location This information can be used by TonyPlot to produce plots of photresponse as a function of position Obtaining Spectral Response The spectral response defined as device current as a function of the wavelength of the optical source wavelength can be obtained The LAMBDA parameter of the SOLVE statement sets the source wavelength of the beam in microns Since the wavelengt
258. h the defaults as shown in Table 3 16 Table 3 16 User Specifiable Parameters for the Constant Low Field Mobility Model Statement Parameter Default Units MOBILITY MUN 1000 cm V s MOBILITY MUP 500 cm V s MOBILITY TMUN ES MOBILITY TMUP 1 5 Note This particular default leads to unrealistically high carrier velocities at intermediate and high electric fields Concentration Dependent Low Field Mobility Tables ATLAS provides empirical data for the doping dependent low field mobilities of electrons and holes in silicon at T 300K only This data is used if the conmoB parameter is specified in the MODELS statement The data that is used is shown in Table 3 17 Table 3 17 Mobility of Electrtons and Holes in Silicon at T 300K Concentration cm Mobility cm v s Electrons Holes 1 0 10 4 1350 0 495 0 2 0 1014 1345 0 495 0 4 0404 1335 0 495 0 3 32 SILVACO International Physics Table 3 17 Mobility of Electrtons and Holes in Silicon at T 300K Continued Concentration cm Mobility cm2 v s Electrons Holes 6 01014 1320 0 495 0 8 0104 1310 0 495 0 1 0 x1015 1300 0 491 1 2 041015 1248 0 487 3 4 0 1015 1200 0 480 1 6 0x1015 1156 0 413 3 8 0x1015 1115 0 466 9 1 0 1016 1076 0 460 9 2 01016 960 0 434 8 4 01016 845 0 396 5 6 0 1016 760 0 369 2 8 041016 720
259. he bi polar current gain when the SOI MOSFET behaves like a bipolar transistor The parameters for this model are specified on the MODELS statement Carrier Generation mpad ionization significantly modifies the operation of SOI MOSFETs To account for this phenomena the impact ionization model IMPACT should be switched on and calibrated for SOI technology The calibration parameters are set on the IMPACT statement 4 8 SILVACO International S PISCES Lattice Heating When a device is switched on there can be significant current density within the silicon This could generate a significant amount of heat In bulk MOS devices the silicon substrates behaves like a good heat conductor and this generated heat is quickly removed However this is not the case with SOI substrates as the buried oxide layer allows this generated heat to be retained For SOI MOSFETS this can be a significant amount and can drastically affect the operation of the device In such cases it would be necessary to take account for this by using the GIGA module Note when lattice heating is switched on by using the parameters LAT TEMP on the wopgrs statement it is also necessary to specify a thermal boundary condition with the THERMCONTACT statement seethe GIGA section for more details Carrier Heating In deep submicron designs it may also be important to switch on the additional energy balance equations These take into account the exchange of energy betw
260. he following statements specify two layers of a heatsink for inclusion in the thermal calculation REGION NUM 5 Y MIN 0 5 Y MAX 2 0 INSULATOR REGION NUM 6 Y MIN 2 0 Y MAX 3 0 INSULATOR Specifying Thermal Conductivity For steady state calculations the thermal conductivity is the only parameter of Equation 6 1 that must be specified for each material region in the structure Thermal conductivity varies as a function of the lattice temperature The temperature dependence of is modeled in GIGA as K T 6 2 TC A TC B Tj TCC TT where rc A rc B and TC C are constants for a particular material There are reasonable default values of the parameters rc a rc B and rc c for common semiconductor device materials such as silicon and silicon dioxide For silicon the default values are 6 2 SILVACO International GIGA those given by Selberherr3 If the default values are not used for all materials the thermal conductivity parameters must be explicitly specified for all materials in the structure The values of TC A TC B and TC C are specified using the MATERIAL statement The following statements would be used to specify the temperature dependent thermal conductivity of the regions defined previously MATERIAL REGION 5 TC A n TC B lt n gt TC C lt n gt MATERIAL REGION 6 TC A n TC B lt n gt TC C lt n gt Table 6 1 User Spe
261. he run time output The expression for displacement current is given as AE J dis 3 3 24 3 4 SILVACO International Physics Basic Theory of Carrier Statistics Fermi Dirac and Boltzmann Statistics Electrons in thermal equilibrium at temperature T with a semiconductor lattice obey Fermi Dirac statistics That is the probability f e that an available electron state with energy e is occupied by an electron is 3 25 where Ef is a spatially independent reference energy known as the Fermi level and k is Boltzmann s constant In the limit that e Ep gt gt kT Equation 3 25 can be approximated as Ef e f e epr 3 26 Statistics based on the use of 3 26 are referred to as Boltzmann statistics The use of Boltzmann statistics instead of Fermi Dirac statistics makes subsequent calculations much simpler The use of Boltzmann statistics is normally justified in semiconductor device theory but Fermi Dirac statistics are necessary to account for certain properties of very highly doped degenerate materials The remainder of this section outlines derivations and results for the simpler case of Boltzmann statistics which arethe default in ATLAS Users can specify that ATLAS is to use Fermi Dirac statistics by specifying the parameter FERMIDIRAC on the MODEL statement Effective Density of States Integrating the F ermi Dirac statistics over a parabolic density of states in the conduction and valence bands whose ene
262. here E is the perpendicular electric field and the equation parameters AsN vawa and AsP vaMA are user definable on the moBILITY statement and have the defaults shown in Table 3 29 The final calculation of mobility takes into acount the parallel electric field dependence which takes the form 1 Me E 2 GN YAMA u E 1 Were 4272 lct erwxuwxll nrzz leu WAkuwx 3 168 Hn hs Urn Yama ULN YAMA VSN YAMA 1 Me E 2 GP YAMA u E 1 u E 27 i rec ee E E 3 169 Hp sp ULP YAMA ULP YAMA VSP YAMA where E is the parallel electric field and the equation parameters ULN YAMA ULP YAMA VSN YAMA VSP YAMA GN YAMA and cP vaMa are user definable on the moBIL1TY statement and have the defaults shown in Table 3 29 Table 3 29 User Specifiable Parameters for Equations 3 164 to 3 169 Statement Parameter Default Units OBILITY SN YAMA 350 0 OBILITY SP YAMA 81 0 OBILITY REFP YAMA 3 0 1016 nies OBILITY REFP YAMA 4 0 101 en OBILITY ULN YAMA 1400 0 cm V s OBILITY ULP YAMA 480 0 cm V s OBILITY ASN YAMA 1 54 10 cm V OBILITY ASP YAMA 5 35 10 cm V OBILITY VSN YAMA 1 036 107 cm s OBILITY VSP YAMA 1 200 107 cm s OBILITY ULN YAMA 4 9 10 cm s OBILITY ULP YAMA 2 92 109 cm s OBILITY GN YAMA 8 8 cm s OBILITY GP YAMA 1 6 cm s SILVACO International 3 47 ATLAS User s Manual Volume 1 The Tasch Model S PISCES inc
263. hese materials See Example 4 for more details on Schottky barrier considerations Manually Adjusting Material Affinity Assigning the conduction band offsets for each heterojunction is accomplished by setting the electron affinities for Material 1 and Material 3 using the arrinity parameter on the MATERIAL statement The electron affinity for Material 1 and Material 3 are adjusted relative to Material 2 by the amount of the desired conduction band offset for each heterojunction Since Material 2 affinity is larger than that for Material 1 and Material 3 the affinities for Material 1 and Material 3 are reduced relative to Material 2 to provide the desired conduction band offset Let s assume an electron affinity for Material 2 of 4eV that of GaAs Let s decide that between Material 1 and Material 2 the conduction band offset is 0 3eV and that between Material 3 and Material 2 the conduction band offset is 0 2eV Then for Material 1 MATERIAL NAME Materiall AFFINITY 3 7 and for Material 3 MATERIAL NAME Material3 AFFINITY 3 8 This is the easiest method to define the conduction band offsets for multiple materials This value of electron affinity will override any electron affinity specification This has an impact on any calculation where this materials electron affinity is used and must be considered when specifying Schottky barriers contacted to this materials See Example 4 for more details on Schottky b
264. hole mean free path lengths within the oxide j is the oxide permittivity and E ox is the electric field in the oxide The angle introduces an angle dependence which is based upon the work of Wada 131 His experiments indicate a critical rejection angle THETA N and THETA P between the angle 0 formed between the semiconductor insulator interface and the electric field in the oxide If the angle 0 is less than the rejection angle then the electrons are repelled back to the substrate Table 3 50 lists the user definable model parameters which can be set on the mopeL statement their default values and their units 3 78 SILVACO International Physics Table 3 50 User Definable Parameters in Concannon s Gate Current Model Statement Parameter Default Units ODELS IG ELINR 6 16X10 cm ODELS IG HLINR 6 16X10 cm ODELS IG ELINF 9 2x1077 cm ODELS IG HLINF 9 2x1077 cm ODELS IG EBETA 2 59x10 4 Vem 1 2 ODELS IG HBETA 2 59x10 4 Vom 1 2 ODELS IG EETA 2x1075 vi 3 3 ODELS IG HETA 2x107 vi 3eg2 3 ODELS PATH N 3 4x1077 cm ODELS PATH P 2 38x1077 cm ODELS THETA N 60 degrees ODELS THETA P 60 degrees ODELS IG EBO 92 eV ODELS IG HBO 4 0 eV The implementation of this model is similiar to that for F owler Nordheim tunneling Each electrode insulator and insulator semiconductor interface is divided into
265. hould begin with go atlas Line 2 The BEGIN and END statements indicate the beginning and end of the circuit simulation syntax These commands are similar to those used in SPICE Lines 3 7 Circuit components topology and analysis are defined within In general the circuit component definition consists of three parts the type of component the lead or terminal mode assignments and the component value or model name For example the first component definition in this simulation is a DC voltage source V1 defines the component as voltage source number one 1 and O are the two circuit modes for this component and 1000 indicates that the voltage source value is 1000 volts The remaining circuit components are resistors R1 R2 inductor L1 and independent current source IL Thereverse recovery of the diode is simulated by dropping the value of output resistor R2 over a small increment of time The R2 statement contains additional syntax to perform this task Here the resistor is treated as a source whose resistance decreases exponentially from 1 M Ohm to 1 mOhm over the specified time step This action essentially shorts out the parallel current source i1 which is also connected to the base of the diode Line 8 The ADIODE statement specifies a device to be analyzed by ATLAS The A part of the ADIODE command specifies that this is a device statement The DIODE portion simply defines the device name The option rNFILE indicates which device
266. hrough the MOSFET is assumed to be in accordance with the following diagram Figure 10 9 shows the current convention for an n channel MOSFET For a p channel MOSFET polarities of the terminal voltages gate junction directions and the direction of the nonlinear current source are reversed Drain E M2SK780 ig M2SK780 a ib M2SK780 gt Gate CP 25K780 lis M2SK780 lll A Substrate Source Figure 10 8 Channel MOSFET Current Convention p channel currents are opposite MOSFET Equivalent Circuits MIXEDMODE uses two equivalent circuits in MOSFET analysis DC and transient The components of these circuits form the foundation for all element and model equations The DC equivalent circuit is the same as that of transient analysis except that capacitances are not included The basic component in the equivalent circuit is the drain to source current ids The ids equation accounts for all DC currents of the MOSFET model The gate capacitance and source and drain diodes are considered separately from the ids equation A MOS transistor is described using both the element and the mopeL statements The element statement defines the connectivity of the transistor as well as referencing the mopEL statement The MODEL statement specifies either an n or p channel device the level of the model and a number of user specified model parameters SILVACO International 10 61 ATL
267. ide layer buried below the surface of the silicon at some predefined depth The existence of this buried oxide layer has resulted in a change not only in the fabrication process used to manufacture a device in the surface silicon but also in the challenges facing device simulation All of the issues raised previously about MOS device simulation should also be considered with some extra SOI specific problems The most common device technology that uses these SOI substrates is the SOI MOSFET This section shall try to summarise the simulation requirements for SOI using this particular technology as a reference Meshing in SOI devices The mesh requirements for SOI MOSFETs is very similiar to that described in the previous section for bulk MOS transistors In addition to these four requirements there are some additional points 1 Two channel regions may exist one underneath the top front gate oxide and one above the bur ied back gate oxide 2 Inside the buried oxide layer the mesh constraints may be relaxed considerably compared with the top gate oxi de 3 Theactive silicon underneath the top gate may act as the base region of a bipolar transistor and as such may require a finer mesh when compared to bulk MOS transistors Physical Models for SOI Simulation of SOI MOSFETs is based upon the physical operation of the device which exhibits both MOS and bipolar phenomena As a result a more complex set of physical models will be required
268. ified ramp from zero to 1 5V in 0 2V steps would finish at 1 4V or 1 6V SILVACO International 2 31 ATLAS User s Manual Volume 1 Generating Families Of Curves Many applications such as MOSFET Id Vds and bipolar Ic Vce simulations require that a family of curves is produced This is done by obtaining solutions at each of the stepped bias points first and then solving over the swept bias variable at each stepped point For example in MOSFET Id Vds curves solutions for each Vgs value are obtained with Vds 0 0V The output from these solutions are saved in ATLAS solution files Then in turn for each gate bias the solution file is loaded and the ramp of drain voltage performed The family of curves for three 1V gate steps and a 3 3V drain sweep would be implemented in ATLAS as follows SOLVE VGATE 1 0 OUTF solve vgatel SOLVE VGATE 2 0 OUTF solve vgate2 SOLVE VGATE 3 0 OUTF solve vgate3 LOAD INFILE solve vgatel LOG OUTFILE mos drain sweepl SOLVE NAME drain VDRAIN 0 VFINAL 3 3 VSTEP 0 3 LOAD INFILE solve vgate2 LOG OUTFILE mos drain sweep2 SOLVE NAME drain VDRAIN 0 VFINAL 3 3 VSTEP 0 3 LOAD INFILE solve vgate3 LOG OUTFILE mos drain sweep3 SOLVE NAME drain VDRAIN 0 VFINAL 3 3 VSTEP 0 3 The LOG statements are used to save the I d Vds curve from each gate voltage to separate files It is recommended to save the data in this manner rath
269. ift diffusion equations has been made a tensor property As a result the mobility has become u 0 0 u 0 p 0 5 94 0 0 n where i4 represents the mobility defined in one plane and p the mobility defined in a second plane In the case of SiC uy represents the mobility of plane 1100 whilst up represents the mobility of plane 1000 These mobilities are defined for both holes and electrons Defining Anisotropic Mobility in ATLAS To define a material with anisotropic mobility it is necessary to specify two MOBILITY statements n each statement the parameters N ANGLE and P ANGLE are used to specify the direction in which that particular mobility is to apply The following is an example of how this is done FIRST DEFINE MOBILITY IN PLANE 1100 MOBILITY MATERIAL B SIC VSATN 2E7 VSATP 2E7 BETAN 2 BETAP 2 MU1N CAUG 10 MU2N CAUG 410 NCRITN CAUG 13E17 DELTAN CAUG 0 6 GAMMAN CAUG 0 0 ALPHAN CAUG 3 BETAN CAUG 3 MUIP CAUG 20 MU2P CAUG 95 NCRITP CAUG 1E19 A DELTAP CAUG 0 5 GAMMAP CAUG 0 0 A ALPHAP CAUG 3 BETAP CAUG 3 NOW DEFINE MOBILITY IN PLANE 1000 MOBILITY MATERIAL B SIC N ANGLE 90 0 VSATN 2E7 VSATP 2E7 BETAN 2 BETAP 2 MU1N CAUG 5 MU2N CAUG 80 NCRITN CAUG 13E17 A DELTAN CAUG 0 6 GAMMAN CAUG 0 0 A ALPHAN CAUG 3 BETAN CAUG 3 MU1P CAUG 2 5 MU2P CAUG 20 NCRITP CAUG 1E19 DELTAP CAUG 0 5 GAMMAP CAUG 0 0 A ALPH
270. ime Model The constant carrier lifetimes that are used in the SRH recombination mode above may be made a function of impurity concentratrion after Roulston 11 using the equations 2 R pn Mie 3 212 SRH ETRAP ETRAP Tp M Nieexp T afp a Tt o 3 213 n 1 N NSRHN i TAUPO no p TXN 7 NSRHP where N is the local total impurity concentration The parameters TAUNO TAUPO NSRHN and NSRHP may be user defined on the MATERIAL Statement and have the default values shown in Table 3 36 This model is activated with the consrx parameter of the mopELs statement Table 3 36 User Specifiable Parameters for Equations 3 212 to 3 214 Statement Parameter Default Units MATERIAL TAUNO le 7 S MATERIAL NSRHN 5el6 cm MATERIAL TAUPO le 7 S MATERIAL NSRHP 5el6 cm Klaassen s Concentration Dependent Lifetime Model The Klaassen concentration and temperature dependent SRH lifetime model 115 is enabled by setting the kLasrH logical parameter on the vopgrs statement The lifetimes for electrons and holes in this model are given by the equations 1 1 300 KSRHGN TAUNO KSRHTN KSRHCN x T7 3 215 L E 1 300 KSRHGP TAUPO KSRHTP KSRHCP x mr 3 216 L SILVACO International 3 61 ATLAS User s Manual Volume 1 where N is the local total impurity concentration The default values for the user definable parameters KSRHTN KSRHTP KSRHCN
271. increase by one each time The spectrum data can be stored in a single file for the transient simulation only if LAS MULTISAVE MODELS statement is set tO FALSE Saving near and far field patterns The user may optionally save near and far field patterns by specifying a value for the PATTERNS parameter on the save statement The value of the PATTERNS parameter is a character string representing the root name of a file for saving the near and far field patterns The near field pattern is saved to a file with the string nfp appended tothe root and the far field pattern is saved to a file with the string ffp appended to the root name These files can be examined using TonyPLoT Optionally specify numeric parameters The numeric parameters are LAS TOLER LAS ITMAX LAS SIN LAS TAUSS LAS MAXCH The default values of these parameters have been selected to give a good trade off between accuracy efficiency and robustness for most applications Users can fine tune the calculation by specifying different values These parameters are discussed below Numerical Parameters The following numerical parameters control the way LASER simulation is performed All of these parameters have reasonable default values but the user can specify the values LAS TOLER Sets the desired relativetolerance of the photon density calculation The default value is 0 01 Setting this parameter to a lower value may slow down the
272. ined by applying approximations and simplifications to the Boltzmann Transport Equation These assumptions can result in a number of different transport models such as the drift diffusion model the energy balance model or the hydrodynamic model The choice of the charge transport model will then have a major influence on the choice of generation and recombination models The simplest model of charge transport that is useful is the drift diffusion model This model has the attractive feature that it does not introduce any independent variables in addition to w n and p Until recently the drift diffusion model was adequate for nearly all devices that were technologically feasible However the drift diffusion approximation becomes less accurate for smaller feature sizes More advanced energy balance and hydrodynamic models are therefore becoming popular for simulating deep submicron devices ATLAS supplies both drift diffusion and advanced transport models The charge transport models and the models for generation and recombination in ATLAS make use of some concepts associated with carrier statistics These concepts are summarized in a further section of this chapter that deals with the carrier statistics The Drift Diffusion Transport Model Derivations based upon the Boltzmann transport theory have shown that the current densities in the continuity equations may be approximated by a drift diffusion mode 3 In this case the current densities
273. ing equations model the depletion capacitance For the reverse biased junction defined as vy lt FC VJ is A e irc a nsu st 10 7 p 1 epo nM VJ For the forward biased junction defined as v4 2 FC VJ va MI Cdep AFCA gre CJO 1 77 10 8 BJT Model To model bipolar junction transistors MIXEDMODE provides a modified Ebers Moll model and the integral charge control model of Gummel and Poon The E bers Moll model is a physical model and its parameters can be easily measured and extracted However the simplicity of the Ebers M oll model limits its applications to simple digital circuits The MIXEDMODE model extends the original E bers Moll model to indude several effects at high bias levels The Gummel Poon model is accurate and complex with approximately 40 parameters The model parameters all have physical meaning This makes the model attractive for complicated circuit designs and process characterization In cases where some parameters are not specified the model automatically limits itself to a simpler E bers M oll model The parameter names used in the modified Gummel P oon model are more easil y understood by circuit designers and better reflect physical processing and circuit design thinking The circuit designer does not necessarily always need to use the entire model but specifying a complete model is highly recommended Model Application The Ebers Moll model is specified by the parameters IS BF and BR This model i
274. ing the reference material Once calculated this value for the ALIGN parameter can be used on the MaTERIAL statement for Material3 FRACTION and ALIGN Will only be equal when the reference material is one of the two materials in the heterojunction For this example lets assume that and AE 3 0 4 5 17 g3 then for a desired conduction band offset fraction of 0 70 ALIGN AE 45 AE a1 FRACTION 0 2 0 4 x 0 70 0 35 5 18 5 8 SILVACO International BLAZE The proper value of the aLtcn parameter reflecting the desired conduction band offset can be assigned as MATERIAL NAME Material3 ALIGN 0 35 This assigns 7096 of the bandgap difference between Material3 and Material2 as the conduction band offset Internally the affinity of Material 3 is adjusted so that AE 3 equals this value Note Calculating AL IGN in this manner is only necessary when the reference material is not in contact with the material for which the ALIGN parameter will be specified These new values of electron affinity for Material2 from the first heterojunction band offset calculation and Material 3 from the second heterojunction band offset calculation will override any electron affinity specification for these materials This has an impact on any calculation where these materials electron affinity is used and must be considered when specifying Schottky barriers contacted tothese materials See Example 4 for more details on Schottky b
275. interface recombination in a similiar manner as the bulk gerneration recombi nation rate SILVACO International 3 65 ATLAS User s Manual Volume 1 2 pn nie Rourt 3 232 eff ETRAP eff ETRAP Tp n nieexp Far ee P nee er 1 1 d Tt ASN 3 233 Th Th 1 1 di tA SP 3 234 Tp Sg where d is the bulk lifetime calculated at node i along the interface and which may be a function of the impurity concentration as well The parameters d and A are the length and area of the interface for node i The two parameters s n and s are the recombination velocities for electrons and holes respectively which are user definable on the INTERFACE statement The parameters x MIN X MAX Y MIN and Y Max can also be set on the INTERFACE statement to define the region in which the specified values of the surface recombination velocities apply This model is activated by the presence of the recombination velocities on the INTERFACE statement Table 3 41 User Specifiable Parameters for Equations 3 232 to 3 234 Statement Parameter Default Units INTERFACE S N 0 cm s INTERFACE S P 0 cm s Impact lonization Models Overview In any space charge region with a sufficiently high revere bias the electric field will be high enough to accelerate free carriers up to a point where they will have acquired sufficient energy to generate more free carriers when in collision
276. ion of the ferroelectric model from Miller 113 has been inmplemented The ferroelectric model is enabled by setting the FERRO parameter of the mopELs statement In this model the permitivity used in Poisson s equation Eq 3 1 is given the following functional form E FERRO EC e E FERRO EPSF FERRO PS 20 sech e a 3 307 where FERRO EPSF is the permitivity E is the electric field and 6 is given as follows 3 FERRO EC o FERRO PR FERRO PS oe E logs FERRO PR FERRO PS The user definable parameters rERRO EPSF FERRO PS FERRO PR and FERRO EC Can be modified on the MATERIAL Statement as shown Table 3 52 The derivative of the dipole polarization with respect to electric field is given by de dE SS where Pg is the position dependent dipole polarization A numeric integration of this function is carried out in ATLAS to determine the position dependent di pole polarization 3 04 SILVACO International Physics For saturated loop polarization the function r is equal to unity which corresponds to the default model If the user specifies the parameter uNSAT FERRO on the moDELs statement the function T can take on a more general form suitable for simulation of unsaturated loops In this case the function T is given by Pa Psat H kos 1 tanh zp p2 3 310 where amp 1 for increasing fields and amp 1 for decreasing fields
277. ional to energy according to V 3 294 The function F e Ty p x y is determined by the density of states and the energy distribution function according to amp Tu y MEINE 3 295 IP greyf e de The density of states g e follows the analysis of Cassi 141 where 0 25 g e 3 296 Finally the energy distribution functions for electrons and holes are defined by 3 3 fule exp Eta COexp E 3 297 Te i Th CHI A e fh exp 3 SEND Ty l where ETH N ETH P CHI A and co are user definable constants found from fitting to measured data The terms T and T are the mean carrier temperatures for electrons and holes which are calculated from the energy balance model Normalization in all of the above equations is accounted for in the combined constants of proportionality ccATE N and CGATE P The second probability P4 is the probability that no energy is lost by optical phonon scattering as the hot carrier travels towards the semiconductor insulator interface after being redirected and is given by P T 3 299 in 7S9XPI TG ELINF Pip exp re HALIN F See where r is the distance from point of redirection to the semiconductor insulator interface The final probability P5 accounts for the probability of scattering in the image force potential well in the gate oxide and is given by SILVACO International 3 81 ATLAS User s Manual Volume 1 E E l 6neE ox
278. ions and have a profound impact on the values of the collector and base currents The collector resistance affects the performance of transistors at higher frequencies and also limits their current handling capability The base resistance affects the switching speed The emitter resistance normally affects the small signal current gain An additional contribution of the Gummel P oon model is the inclusion of accurate models for junction capacitances These capacitances are represented in the model by corresponding changes in the 10 38 SILVACO International MIXEDMODE emitter base and collector junctions Their junction voltage dependence is modeled by three parameters cox MJX and vox Base collector capacitance is modeled with cac mgc and voc parameters Base emitter capacitance is modeled with parameters cog MJE and vue Collector substrate capacitance is modeled with parameters CJ S MJ S and VJ S An additional non physical parameter FC improves the modeling of all junction capacitances under conditions of moderate to large forward bias It also prevents computing excessive values for capacitances under large forward bias For very small values of vse secondary order effects such as surface leakage currents and finite resistances makethe collector and base currents vary non linearly with VBE For large values of VBE high current injection effects make the collector and base currents non linear functions of VBE
279. ions presented later in this chapter Example MODEL MODBJ T NPN IS 1 E 17 BF 100 CJ E 1F TF 5PS CJ C 0 3F RB 100 RBM 20 Transient Parameters Overview MIXEDMODE allows the user to specify transient parameters for voltage sources Vxxx current sources I xxx and resistors Rxxx These parameters describe the time development behavior of the source PULSE PULSE is used to define a pulse waveform The waveform is specified as follows PULSE 1 2 td tr tf pw per where ilis the initial value i2 is the pulsed value td is the delay time before the pulse is started tr is the rise time of the pulse tf is the fall time of the pulse pw is the pulse length per period per is the period SILVACO International 10 29 ATLAS User s Manual Volume 1 The transient behavior is described by the following table Intermediate points are found by linear interpolation Time Value 0 11 td ld Ed br i2 td EL pw 12 td EL pw tf 11 td per il td per tr i2 second period EXP EXP is used to define an exponential waveform The waveform is specified as follows EXP 112 td1 taul td2 tau2 where ilistheinitial value i2 is the pulsed value td1 is the rise delay time td2 is the fall delay time tau is the rise time constant tau2 is the fall time constant The transient behavior will be Time Value 0 lt t lt tdi il tdl t td2 il i2 il 1 exp t td1 taul td2 lt t i1 12
280. is activated with the parameter crant on the moDEL statement The model parameters an AP BN and Bp are NOT user definable Instead the three electric field regions have in built values as follows 1 Low Electric Field E lt 2 4e5 V cm 3 244 AN 2 6e6 AP 2 0e6 BN 1 43e6 BN 1 97e6 2 Intermediate Electric Field 2 4e5 gt E gt 5 3e5 V cm 3 245 AN 6 2e5 AP 2 0e6 BN 1 08e6 BP 1 97e6 3 High Electric Field E gt 5 3e5 V cm 3 246 AN 5 0e5 AP 5 6e5 BN 9 9e5 BP 1 32e6 Crowell Sze Impact lonization Model Crowell and Sze 1 have proposed a more physical but complicated relationship between the electric field and the ionization rates This model represents ionization coefficients as follows da ro PIC ol C r x C r x 3 247 A E 2753 3 248 C r 1275x10 7 11 9r 46r 3 249 C r 3 9x10 1 17r 11 5r 3 250 SILVACO International 3 69 ATLAS User s Manual Volume 1 where r X 3 251 E qa E 0 063 eV 3 252 for electrons i 3 253 1 8eV for holes tanh QE 2KT 5 tanh qE 2kT The Crowell Sze model for impact ionization is selected by setting the croweLL parameter of the IMPACT Statement Table 3 44 Crowell Sze Impact lonization Model Parameters Statement Parameter Default IMPACT AMDAE 6 2 10 7cm IMPACT LAMDAH 3 8 10 7 cm Non Local Energy Dependent Models All local electric field based models will normally overes
281. is the mirror loss These are defined as a JacpHaa E x y l dx dy is Qr ffen n FCP p EG y dx dy s 7 1 l l 9 14 Omir ZCAVITY LENGTH e l Table 9 6 User Specifiable Parameters for LASER Loss Models Statement Parameter Default Units MODELS MIRROR LOSS 90 0 MODELS CAVITY LENGTH 100 0 um The user specifiable parameters for the loss models are given in Tables 9 6 and 9 7 MIRROR LOss is the percentage reflectivity for the facet cavity mirrors cCavITY LENGTH is the length of the laser cavity aig is calculated as follows when the physically based model is used for local optical gain ho E ho E Esp y o XT s Efn GAMMA 9 15 1 GAMMA ho E For the steady state case the time dependent terms in the photon rate equation Equation 9 8 are set to zero SILVACO International 9 5 ATLAS User s Manual Volume 1 Solution Techniques LASER solves the electrical and optical equations self consistently Two models are available The first is a single frequency model that does not take into account the existence of multiple longitudinal modes It is in this sense similar to the work described in 94 95 96 The second model accounts for multiple longitudinal modes and is in this sense similar to the work described in 96 LASER solves the Helmholtz equation in a rectangular region that is a subdomain of the general ATLAS simulati
282. is the temperature in degrees Kelvin Alternatively the saturation velocities can be set to constant values using the vsarw and vsarP parameters of the MATERIAL statement Velocity Saturation with Energy Balance When the energy balance transport model is activated the mobility can be made a function of carrier energy In Chapter 3 physical models for the dependence of carrier mobility on carrier energy were introduced The same models are applicable for use within BLAZE with one additional model which applies when the negative differential moibility model is used The carrier temperature dependence is activated when the paramter gvsarwop 1 on the MODEL statement This model can be derived in a similar fashion as in the case of evsarmoD 0 described in Chapter 3 These expressions however require several piecewise approximations which are too complex to reproduce in this manual Sufice it to say that these piece wise expressions provide a continuous velocity saturation model for mobility versus carrier temperature completely analogous to the expressions for drift diffusion given in Equations 3 202 and 3 203 of Chapter Three Recombination and Generation Models The recombination and generation models for compound semiconductors are the same as the models previously described in Chapter 3 Default parameters for different materials are automatically used unless new values are specified by the user The default parameter values are listed in
283. is value of electron affinity can be used to assign the proper value of wonkruw on the CONTACT statement to provide for a Schottky barrier height of 0 2eV bm 3 84402 4 04 5 25 This value can now be assigned to the wonkruN parameter on the contact statement as CONTACT NUMBER 1 WORKFUN 4 04 producing a Schottky barrier height of 0 2eV between the metal and Material 2 SILVACO International 5 11 ATLAS User s Manual Volume 1 Manually Adjusting Material Affinity Let s assign a conduction band offset between Material 1 and Material 2 of 0 15eV an electron affinity for Material 1 of 4eV and the desired Schottky barrier height of 0 2eV The affinity for Material 2 is calculated from the affinity of Material 1 and the desired conduction band offset as X X1 0 15 4 0 15 3 85 5 26 This is then used to assign the value of AFFINITY using MATERIAL NAME Material2 AFFINITY 3 85 This value of electron affinity can now be used to calculate the metal workfunction necessary to produce a Schottky barrier height of 0 2eV as Q4 3 85 0 2 4 05 5 27 This value can now be assigned to the workFUN parameter on the contact statement as CONTACT NUMBER 1 WORKFUN 4 05 This produces a Schottky barrier height of 0 2eV between the metal and Material2 The Drift Diffusion Transport Model Drift Diffusion with Position Dependent Band Structure The current continuity equations for electrons and holes and the
284. ith lumped elements it is important to distinguish between the applied voltage Vapp and the internal bias p in the log file produced by ATLAS Note AC small signal analysis can not be performed when any lumped elements have been specified AC small signal analysis can be performed with the resistance specified on the Loc statement Also when lumped elements have been defined the NEWTON numerical scheme should be chosen on the METHOD Statement Distributed Contact Resistance Because contact materials have finite resistivities the electrostatic potential is not always uniform along the metal semiconductor surface To account for this effect a distributed contact resistance can be associated with any electrode This is in contrast to the lumped contact resistance described in the previous section ATLAS implements this distributed contact resistance by assigning a resistance value to each surface element associated with the contact If each surface element is a different length a different value for the contact resistance will be assigned ATLAS calculates a resistance value Rj for each surface element from the value of cox RESIST as specified on the contact statement The units of con RESIST are Qcm and R calculated as CON RESIST i dis WIDTH Ld where R is the resistance at node i P is specified by the cow nEsrsT parameter d is the length of the contact surface segment associated with node i and wrptu is th
285. its VMIN Real 5 x107 V VCHANGE Real 5x107 V DTMIN Real 1 10712 S Description IMAXDC specifies the maximum number of mixed circuit device iterations to be performed during steady state analysis IMAXTR specifies the maximum number of mixed circuit device iterations to be performed during transient analysis TOLDC specifies the relative accuracy to be achieved during steady state analysis for the calculation of voltages in circuit nodes TOLTR specifies the relative accuracy to be achieved during transient analysis for the calculation of voltages in circuit nodes LTE specifies the local truncation error for transient analysis VMAX specifies the maximum value for circuit node voltages VMIN specifies the minimum value for circuit node voltages VCHANGE specifies the maximum allowable change in circuit node voltages between two mixed circuit device iterations This parameter can be useful for reaching steady state convergence with a bad initial guess DTMIN specifies the minimum time step value for transient analysis Example NUMERIC LTE 0 05 TOLDC 1 10 8 DTMIN 1ns OPTIONS OPTIONS specifies various circuit simulation options Syntax OPTIONS TNOM lt value gt FULLN M2LN PRINT RV value RELPOT NOSHIFT WRITE value CYLINDR LOADSOLUTIONS CNODE value Parameter Type Default Units TNOM Real 300 K FULLN iogica True M2LN Logical False PRINT iogical False 10 26 SIL
286. ix C Appendix D provides a brief overview of ATLAS helps all users to get an overivew of typical use presents the base set of physical models available in ATLAS documents the additional models and simulation capabilities of S PISCES documents the additional models and simulation capabilities of BLAZE documents the models and simulation capabilities of GIGA documents the models and simulation capabilities of TFT documents the models and simulation capabilities of LUMINOUS documents the models and simulation capabilities of LASER documents the models and simulation capabilities of MIXEDMODE documents the differences between the 3D capabilites in ATLAS as compared tothe 2D products documents the models and simulation capabilities of INTERCONNECT3D documents the models and simulation capabilities of THERMAL3D describes the numerical methods and options available documents the input syntax explains how to usethe C interpreter to specify models summarizes the default numerical values of model coefficients used gives information on error messages provides a version history If you have difficulties or questions relating to the use of any Silvaco product you can communicate with SILVACO support personnel by sending electronic mail to support silvaco com When you send us an email message please 1 2 3 4 Explain the problem or question as fully as possible Include any input files that you have created
287. kfunction for each case Using the affinity rule for the heterojunction and AE AE AE 5 21 5 10 SILVACO International BLAZE AE is the amount of the conduction band discontinuity at the heterointerface and AE is is the amount of the valence band discontinuity Note Remember the Affinity Rule is invoked for a material as long as the ALIGN parameter is NOT specified on the MATERIAL statement for that material Let s use an electron affinity for Material1 of 4eV and for Material2 of 3 5eV Since the affinity of the material on which the Schottky barrier is formed was not modified with this method of alignment the metal work function needed to provide for a Schottky barrier height of 0 2eV is bm 35402 37 5 22 This value can now be assigned to the workFUN parameter on the contact statement as CONTACT NUMBER 1 WORKFUN 3 7 This produces a Schottky barrier height of 0 2eV between the metal and Material 2 Using the ALIGN parameter on the MATERIAL statement Let s assign 80 of the bandgap difference between Materiall and Material2 to the conduction band offset an electron affinity for Material 1 of 4eV and AE of 0 2eV Defining the aL1cN parameter on the MATERIAL Statement for Material 2 using MATERIAL NAME Material2 ALIGN 0 80 Then AE Ej5 E 0 80 0 2 0 80 0 16 5 23 Internally the affinity of Material2 is reduced by 0 16eV so X AE 4 0 16 3 84 5 24 Th
288. l Solution Techniques aii i 2 ere a RR vx Ret Chee SAS rk Oe eh ewes da 2 21 Basic Drift Diffusion Calculations 3 5 oia li ewes de E Mast al eher Rc 2 21 Drift Diffusion Calculations with Lattice Heating cc cece eect eee een eens 2 27 Energy Balance Calculations s wee tet uo pe CN ee oe iba t b emeret 2 28 Energy Balance Calculations with Lattice Heating cc cece cece cece e 2 28 Seting The Number Or CAMS rers 5 aie eresi eni dba hd age dece dace wild Ota dne eet 2 28 Important Parameters Of the METHOD Statement 2 29 Restrictions on the Choice of METHOD sooner rex Feet eer perte e e Eur RA VA 2 29 Pisces ll Compatibilty escort is CENE ERE E Pu CE P Rr facea 2 30 Obtaining SOMOS 3 iS aiia ueniet iat 2 31 DC Solutions ieina dtrexere D laa he GAS VE Era qd Eie dide Midi rat 2 31 Sweeping Me Bis da id 2 31 Generating Families Of Curves a re OR AR A e eee era AA 2 32 The Importance Of The ACUSA SS oe eC A Dee ue sts 2 32 The initial SOL MDIDTT ns hate IO EAS 2 33 The First And Second Non Zero Bias Solutions ccc cece eee eee rr 2 33 The Trap Paralelas 2 33 Smells ond AG SOIMMONS o erp e E EORR br EVER fend dE baies ah dab RR 2 34 Single Frequency AC Solution During A DC R amp i ur cate a Re o eee td 2 34 Ramped Frequency AtA Single Bldg 435a ot TY ot a een 2 34 Transient Solutions o ac bit o SOR n Dom tc tp am ol dU DERI NE ub 2 35 Advanced Solution Fechiniques roscas lesbians ERE UA EA RE CR RYEYE Lettre nba 36 Ob
289. l Sources Identifying an Optical Beam Up to ten optical sources are allowed Optical sources are described using the BEAM statement All BEAM statements must appear somewhere after the MESH REGION DOPING and ELECTRODE statements and before any SOLVE statement The parameters of the BEAM statement describe a single optical source The NUM parameter is used to uniquely identify one optical source Values between 1 and 10 are valid for the NUM parameter Optical sources are subsequently referred to by the value of their NUM parameter The power of the optical beam is set using the B lt n gt parameter of the SOLVE statement where nisthe beam number defined by NUM Origin Plane of the Beam The origin of the optical source is specified using the X ORIGIN and Y ORIGIN parameters These parameters describe the origin of the optical beam relative to the device coordinate system Currently it is required that the origin lie outside any device region The ANGLE parameter specifies the angle of the direction of propogation of the beam with respect to the device coordinate system ANGLE 90 specifies vertical normal illumination from above The width of the optical beam is specified using the MIN WINDOW and MAX WINDOW parameters These parameters specify the limits of the source beam relative to the beam origin If either of the limits are omitted that limit will be clipped to the edge of the device domain
290. l model has been introduced that better matches experimental results This model is set by the 10N1Z parameter of the vopELs statement In this model the activation energies of the dopants in Equations 3 43 and 3 44 have been modified for doping dependence as given in the following equations E DB meV 244 0 3 6109 Np Np lt 1018 3 48 E AB meV 43 8 3 037x10 Na Np 1018 3 49 At doping concentrations above 3x1019 cm the model predicts complete ionization At doping concentrations between 1018 cm and 3x1018 cm3 the model predicts a linearly interpolated value between the above expressions and complete ionization Low Temperature Simulations In conjunction with Fermi Dirac statistics and impurity freeze out ATLAS simulates device behavior under low operating temperatures In general simulations can be peformed at temperatures as low as 50K without loss of quadratic convergence Below this temperature carrier and ionization statistics develop sharp transitions which cause slower convergence Since many more iterations will probably be required if temperatures below 50K are specified the 1TLIMIT parameter of the METHOD statement should be increased Due to the limited exponent range on some machines ATLAS can have trouble calculating the quasi Fermi level of minority carriers As the temperature decreases the intrinsic carrier concentration also decreases In quasi neutral regions the minority carrier concentration can
291. lated automatically by ATLAS For example the statement SOLVE VGATE 1 0 RAMPTIME 1E 9 TSTOP 10e 9 TSTEP 1e 11 specifies that the voltage on the gate electrode will be ramped in the time domain from its present value to 1 0V over a period of 1 nanoseconds Time domain solutions are obtained for an additional 9 nanoseconds An initial time step of 10 picoseconds is specified It is important to remember that if subsequent transient solutions are specified the time is not reset to zero Vg RAMP TIME TSTOP TSTEP 1 2 3 4 5 6 7 8 9 10 time ns Figure 2 7 Diagram showing syntax of Transient Voltage Ramp in ATLAS SILVACO International 2 35 ATLAS User s Manual Volume 1 Advanced Solution Techniques Obtaining Solutions Around The Breakdown Voltage Obtaining solutions around the breakdown voltage can be difficult using the standard ATLAS approach It requires special care in the choice of voltage steps and also in interpreting the results The curvetracer described later is the most effective method in many cases A MOSFET breakdown simulation might be performed using this standard syntax for ramping the drain bias Note the setting of cLIMIT as required for breakdown simulations when the pre breakdown leakage is low IMPACT SELB METHOD CLIMIT 1e 4 SOLVE VDRAIN 1 0 VSTEP 1 0 VFINAL 20 0 NAME drain If the breakdown were 11 5V then convergence problems will be expec
292. lectrically connected Some shortcuts may be used when defining the location of an electrode If no y coordinate parameters are specified the electrode is assumed to be located on the top of the structure In addition you may usethe parameters RIGHT LEFT TOP and BOTTOM For example ELECTRODE NAME SOURCE LEFT LENGTH 0 5 specifies the source electrode starts at the top left corner of the structure and extends to the right for the distance LENGTH Specifying Doping You can specify analytical doping distributions or have ATLAS read in profiles that come from either process simulation or experiment You specify the doping using the DOPING statement DOPING distribution type dopant type position parameters SILVACO International 2 11 ATLAS User s Manual Volume 1 Analytical Doping Profiles Analytical doping profiles can have uniform or Gaussian forms The parameters defining the analytical distribution are specified on the DOPING statement Two examples are shown below and their combined effect is shown in Figure 2 5 The first DOPING statement specifies a uniform n type doping density of 1016 cm in the region that was previously labelled as region 1 DOPING UNIFORM CONCENTRATION 1E16 N TYPE REGION 1 TonyPlot Y2 2 1 Parameters of the DOPING statement for Gaussian Doping Profiles LATERAL SPREADING X RIGHT pe BY RATIOLAT J
293. left blank 6 10 SILVACO International Chapter 7 TFT Polycrystalline and Amorphous Semiconductor Models Introduction Before continuing with this chapter you should be familiar with ATLAS If not read Chapter 2 before proceeding further TFT is an ATLAS based product that enables the simulation of disordered material systems Since TFT contains no material models it is necessary to combine the use of TFT with either S PISCES or BLAZE under the ATLAS framework TFT enables the user to define an energy distribution of defect states in the bandgap of semi conductor materials This is necessary for the accurate treatment of the electrical properties of such materials as polysilicon and amorphous silicon The syntax used by TFT is part of the ATLAS syntax There is no need for users to learn a completely new simulator to run TFT simulations Simulating TFT Devices This section is intended to illustrate the basic building blocks for a thin film transistor simulation To use TFT you should specify the addition of defect states into the bandgap of a previously defined crystalline material Throughout this section the example of polysilicon is used However amorphous silicon and other disordered materials are handled in a similar manner Defining The Materials Defining a simple polysilicon thin film transistor structure can be done using the command syntax of ATLAS ThemesH X MESH and Y MESH statements can be used to construct
294. ll current through that electrode Each of these methods are feasible but if in doing so a floating region is created within the structure then numerical convergence may be affected As a result it is normally recommended that the second method that of a lumped resistance be used as it ensures better convergence Specifying Material Properties Semiconductor Insulator or Conductor All materials are split into three classes semiconductors insulators and conductors Each class requires a different set of parameters to be specified For semiconductors these properties include electron affinity band gap density of states and saturation velocities There are default parameters for material properties used in device simulation for many materials Appendix B lists default material parameters and includes a discussion on the differences between specifying parameters for semiconductors insulators and conductors Setting Parameters The MATERIAL statement allows you to specify your own values for these basic parameters Your values can apply to a specified material or a specified region The statement MATERIAL MATERIAL Silicon EG300 1 12 MUN 1100 sets the band gap and low field electron mobility in all silicon regions in the device If the material properties are defined by region the region is specified using the REGION or NAME parameter on the MATERIAL Statement For example the statement MATERIAL REGION 2 TA
295. ludes an improved local field dependent mobility model This model which was originally derived and published by Tasch et al has been designed explicitly for MOSFETs 7 9 It defines the mobility as a function of the perpendicular and parallel electric fields the interface charge the lattice temperature and the doping concentration This model is activated by the parameter rascu on the MODELS Statement This mobility model is given by the following expressions 3 170 T E E an dk Hn n perp 0 dE per Hp IS E 3 171 dU perp E VE per where Eperp is the transverse electric field and Eg is the transverse electric field at the edge of the inversion layer The functions T y are defined as T Meff n 3 172 1g Hoff nE ll BETAN 1 BETAN Uwe A A 3 173 p o E y BETAP BETAP eff p _ 1 VSATP The carrier mobilities uar and perc are defined by three components Lips Hsr and pic which are combined by Mathiessen s rule according to u gt 3 174 i Moh Hsr He The term upn takes account of the degradation in mobility due to acoustic phonon scattering through the expressions T TMUBN TAS 1 T 421 gt Hohn muen TAS 355 2 DN TAS Y 555 3 175 TMUBP TAS 1 T 14241 T Hph p muse TAS spp 2 DP TAS Y 395 3 176 where the functions Z y and Y y y are defined as 4 1 m Z Z11N TAS 395 Ee eff n Z22N TAS E 3 177 eft n 2 N II T Z1P TA
296. lume 1 Note If the cvr YAMAGUCHI Or TASCH mobility models are chosen in the moDEL statement then no energy dependence is applied No energy dependence is included in any perpendicular electric field model such as SHIRAHATA Of SURFMOB Table 3 34 User Specifiable Parameters for Equations 3 197 3 207 Statement Parameter Units MOBILITY MUN cm Vs MOBILITY MUP cm Vs MATERIAL VSATN cm s MATERIAL VSATP cm s Mobility Model Summary Model Syntax Notes Concentration Dependent CONMOB Lookup table valid at 300K for Si and GaAs only Uses simple power law temperature dependence Concentration and ANALYTIC Caughey Thomas formula Tuned for 77 450K Temperature Dependent Arora s Model ARORA Alternative to ANALYTIC for Si Carrier Carrier Scattering CCSMOB Dorkel Leturq Model Includes n N and T dependence Important when carrier concentration is high e g forward bias power devices Parallel Electric Field Dependence FLDMOB Si and GaAs models Required to model any type of velocity satuation effect Tasch Model TASCH Includes transverse field dependence Only for planar devices Needs very fine grid Watt Model WATT Transverse field model applied to surface nodes only Klaassen Model KLA Includes N T and n dependence Applies separate mobility to majority and minority carriers Recommended for bipolar devices Shirahata Model SHI Includes N E An
297. lways refer to a model A set of elements can refer to the same model For some elements such as resistors and capacitors model referencing is optional Each element type has its own set of parameters For example a resistor statement can specify a resistance value after the optional model name The bipolar transistor Q statement can specify an area parameter All parameters have corresponding default values see chapter 8 Compact and User Defined Model Reference Independent voltage and current sources have different specifications for transient DC and AC phases of simulation Transient specifications use the keywords EXP PULSE GAUSS SFFM SIN and TABLE AC parameters start with the key word AC Elements to be simulated numerically are defined as A devices ATLAS devices At least one ATLAS device in a circuit is mandatory SILVACO International 10 3 ATLAS User s Manual Volume 1 MIXEDMODE supports the use of the following circuit elements e Resistors R devices may be time dependent Capacitors C devices Inductors L devices Independent voltage sources V devices may be time dependent e Independent current sources I devices may be time dependent Dependent voltage and current sources E F G H devices Coupled mutual inductors K devices Lossless transmission lines T devices Diodes D devices Bipolar junction transistors Q devices Gum
298. m case This is specified by the SOLVE INIT statement However if this syntax is not specified ATLAS will automatically evaluate an initial solution before the first SOLVE statement In order to aid convergence of this initial guess it is performed in the zero carrier mode solving only for potential The First And Second Non Zero Bias Solutions From experience with ATLAS it is found that the first and second non zero bias solutions are the most difficult in which to obtain good convergence The reason is clear Once these two solutions are obtained the projection algorithm for the initial guess is available and solutions should all have a good initial guess However these first two solutions must usethe result of the initial solution as the basis of their initial guess Sincethe initial solution is at zero bias it provides a very poor initial guess The practical result of this is that the first and second non zero bias solutions should have very small voltage steps In the following example the first case will likely converge whereas the second case may not 1 SOLVE INIT SOLVE VDRAIN 0 1 SOLVE VDRAIN 0 2 SOLVE VDRAIN 2 0 2 SOLVE INIT SOLVE VDRAIN 2 0 The Trap Parameter Although ATLAS provides several features to overcome a poor initial guess and other convergence problems it is important to understand the role of the initial guess in obtaining each solution The simplest and most effective is the s
299. magnitude in current may need to be covered Important points to remember about current boundary conditions are that the problems of initial guess are more acute when very small noise level currents are used Often it is best to ramp the voltage until the current is above 1pA um and then switch to current forcing When interpreting the results it is important to remember the calculated voltage on the electrode with current boundary conditions is stored as the internal bias eg base int bias in TonYPLoT or vint base in DECKBUILD s extract syntax The Compliance Parameter Compliance is a parameter used to limit the current or voltage through or on an electrode during a simulation An electrode compliance can be set and after it is reached the bias sweep will stop This is analogous to parametric device testing when we stop a device from being over stressed or destroyed The compliance refers to the maximum resultant current or voltage present after a solution is obtained If an electrode voltage is set then the compliance refers to the electrode current If current boundary conditions are used then a voltage compliance can be set The statements SOLVE VGATE 1 0 SOLVE NAME drain VDRAIN 0 VFINAL 2 VSTEP 0 2 COMPL 1E 6 CNAME drain first solves for 1V on the gate and then ramps the drain voltage towards 2V in 0 2V steps If 1u A U m of drain current is reached before Vd 2V the simulation will
300. mel Poon SPICE model MOSFETSs M devices Level 3 SPICE models User defined two terminal elements B devices Optical sources O devices Numerically simulated ATLAS devices A devices The physical models for linear elements resistors capacitors sources etc are very simple The models for diodes BJ Ts and MOSFETS are described in this chapter More extensive descriptions of the diode BJ T and MOSFET electrical models can be found in SPICE manuals such as SmartSPI CE A node is a point in the circuit where two or more elements are connected The node numbering is arbitrary with the exception of 0 Node O is grounded i e all voltages at nodes are calculated with respect to the voltage at node 0 As an example the netlist for the circuit shown in Figure 10 1 is represented by the following MIXEDMODE input deck fragment VO 1 R1 1 ATLAS device ADIO 2 anode lkOhm resistor current scaled by 5e7 independent voltage source 0 2 connected to node 2 O cathode 0 1V connected to node 0 GND and 1 Or 1 1K WIDTH 5e7 anode and O ca connected to node 1 and 2 mesh from file dio str thode INFILE dio st us 10 4 SILVACO International MIXEDMODE H1 r1K V vdc 100 0m Figure 10 1 Schematic of Primitive Example Circuit Control Statements Control Statements are used to specify the analysis to be performed
301. meter of junction perimeter MJSW Bulk junction sidewall grading coefficient 0 33 FC Coefficient for forward bias depletion capaci 0 5 tance formula CBD Zero bias B D junction capacitance F 0 CBS Zero bias B S junction capacitance F 0 JS Bulk junction saturation current per sq A m 1 0 1078 meter of junction area Is Bulk junction saturation current A 1 0 10714 NSS Surface state density 1 cm 0 NFS Fast surface state density 1 cm 0 TPG Type of gate material 1 0 1 opposite to substrate 1 same as substrate O AI gate LD Lateral diffusion m 0 UO Surface mobility eh d weg 500 TNOM Parameter measurement temperature oc 27 VMAX Maximum drift velocity of carriers m s 0 XD Depletion layer width m 0 XJ Metallurgical junction depth m 0 SILVACO International 10 63 ATLAS User s Manual Volume 1 DC Current Equations The DC current equations describe how the model calculates the drain current ids In these equations vos is the gate intrinsic source voltage vgd is the gate intrinsic drain voltage vds is theintrinsic drain intrinsic source voltage vbs is the bulk intrinsic source voltage vbd is the bulk intrinsic drain voltage vth is the thermal potential Cutoff Region ids 0 for vds lt vth On Region 1 fb ids BETA v cv 2 vde vde for Vgs gt vth where Ww x BETA KP z eff w ug COX 72 eff vde min vds vdsat and GAMMA fs fb fn Ga See TL 4 PHI vsb The narrow width effect is inclu
302. meters of the INTERFACE statement The syntax INTERFACE AR INDEX 2 05 AR THICK 0 07 P1 X 0 0 P1 Y 0 0 P2 X 10 0 P2 Y 0 0 defines a 70nm layer of real refractive index 2 05 at Y 20 0um in a structure The AR layer is assumed to be non absorbing that is the imaginary refractive index is zero For the case of non normal incidence absorbing AR coatings or multi layer AR coatings the user must use the C interpreter function F REFLECT specified on the BEAM statement Using this function SILVACO International 8 5 ATLAS User s Manual Volume 1 the user can specify the reflection coefficient angle of transmission and transmitted polarization as a function of position wavelength angle of incidence and incident polarization SOURCE 1 AR INDEX AR THICK A 79 Di Do ES No PHOTODETECTOR Figure 8 4 Single Layer AR Coating Under Normal Incidence Light Absorption and Photogeneration The cumulative effects of the reflection coefficients transmission coefficients and the integrated loss due to absorption over the ray path are saved for each ray The generation associated with each grid point can be calculated by integration of the generation rate formula Equation 8 11 over the area of intersection between the ray and the polygon associated with the grid point P A G Noke ae i where P contains the cumulative effects of reflections transmissions and loss due
303. mi Dirac statistics with appropriate degeneracy factors for conduction and valence bands ccs and cvs The ionized donor and acceptor impurity concentrations are then given by TCU Drm p EDB 3 43 1 GeBexp C L NA MAL BABES d 1 evBexp Ae L where eos is the donor energy level gas is the acceptor energy level and Np and Na are net compensated n type and p type doping respectively N et compensated doping is defined as follows If Ntotal Np total NA totai 70 3 45 then Np Ntota and NA 0 3 46 Otherwise Np 0andNA Ntotal 3 47 The INCOMPLETE parameter of the MopELs statement is used to select incomplete ionization and the parameters SILVACO International 3 9 ATLAS User s Manual Volume 1 Table 3 4 User Specifiable Parameters for Equations 3 43 and 3 44 Statement Parameter Units MATERIAL GCB MATERIAL EDB ev MATERIAL GVB MATERIAL EAB ev To properly handle incomplete ionization in silicon for high doping levels a new incomplete ionization model has been added The models that form incomplete ionization of impurities given by Equations 3 43 and 3 44 give good physical results for low to moderately doped semiconductors For heavily greater than 3x10 8 cm doped semiconductors these models fail to predict experimental results of complete ionization For silicon an optiona
304. mm On the right hand plot note how specifying the parameter SPACE MULT to have a value of 0 5 has doubled the density of the mesh in both the x and y directions SILVACO International 2 9 ATLAS User s Manual Volume 1 TonyPlot v2 2 1 File v View 7 Plot 7 Tools v Print v Properties 7 Help 7 ATLAS ATLAS Ngn uniform Mesh Creation using ATLAS syntax _ PAC Parameter Effect on Mesh Creation J 0 SPAC 1 0 3 NESH SPAC 0 5 ad N LOC 50 SPAC 05 ad THEN SANE SYNTAX AS MESH ON LEFT 1 YN LOC 10 SPAC 1 0 1 a Figure 2 4 Non uniform Mesh Creation using ATLAS Syntax SILVACO International 1994 j After an initial mesh has been defined you can remove grid lines in specified regions This is typically done in regions of the device for which a coarse grid is expected to be sufficient such as the substrate The removal of grid lines is accomplished using the ELIMINATE statement The ELIMINATE statement removes every second mesh line in the specified direction from within a specified rectangle The statement ELIMINATE COLUMNS X MIN 0 X MAX 4 Y MIN 0 0 Y MAX 3 removes every second vertical grid line within the rectangle bounded by x 0 x 4 y 0 and y 3 microns Specifying Regions And Materials After
305. model the effective densities of states are modeled as functions of the local carrier temperatures T and Tp as defined by Equations 3 92 and 3 93 Nonisothermal Current Densities When GIGA is used the electron and hole current densities are modified to account for spatially varying lattice temperatures Jn qu n VO P VT gt Jp qu P Y O P VT where P and P are the absolute thermoelectric powers for electrons and holes Pn and P are modeled as follows k n 3 P In 5 sw V k p 5 P ing G xsr v The default values forare given in Table 6 3 6 4 6 5 6 6 6 7 Table 6 3 User Specifiable Parameters for Equations 6 6 and 6 7 Statement Parameter Default Units MODELS KSN None MODELS KSP None 6 4 SILVACO International GIGA Heat Generation When carrier transport is handled in the drift diffusion approximation the heat generation term H used in Equation 6 1 has the form 60 2 2 H Ja IA T VP T VP 6 8 quan qu p Hr mo Lop p E 00 IE 90 2 Tr E P div p 5 E P ivi In the steady state case the last two terms are equal to zero and Equation 6 8 simplifies to i3 H NM R G T P P T X VP IVP 6 9 qun qup q R G 0 6 Tj P P Tj J VP J VP The components of Equation 6 9 can be identified as follows
306. mulation is not a familiar concept for all engineers A brief overview is provided here to serve as a high level orientation for new users Physically based device simulators predict the electrical characteristics that are associated with specified physical structures and bias conditions This is achieved by approximating the operation of a device onto a two or three dimensional grid consisting of a number of grid points called nodes By applying a set of differential equations derived from Maxwells laws onto this grid it is possible to simulate the transport of carriers through a structure This means that the electrical performance of a device can now be modelled in DC AC or transient modes of operation Physically based simulation provides three major advantages it is predictive it provides insight and it captures theoretical knowledge in a way that makes this knowledge available to non experts Physically based simulation is different from empirical modeling The goal of empirical modeling is to obtain analytic formulae that approximate existing data with good accuracy and minimum complexity Empirical models provide efficient approximation and interpolation They do not provide insight or predictive capabilities or encapsulation of theoretical knowledge Physically based simulation is an alternative to experiments as a source of data Physically based simulation has become very important for two reasons First it is almost always much q
307. multiple simulators ATLAS is very often used in conjunction with the ATHENA process simulator ATHENA predicts the physical structures that result from processing steps The resulting physical structures are used as input by ATLAS which then predicts the electrical characteristics associated with specified bias conditions The combination of ATHENA and ATLAS makes it possible to determine the impact of process parameters on device characteristics The electrical characteristics predicted by ATLAS can be used as input by the UTMOST device characterization and SPICE modeling software Compact models based on simulated device characteristics can then be supplied to circuit designers for preliminary circuit design The use of ATHENA ATLAS UTMOST and SMARTSPICE in combination makes it possible to predict the impact of process parameters on circuit characteristics ATLAS can be used as one of the simulators within the VWF AUTOMATION TooLs VWF makes it convenient to perform highly automated simulation based experimentation VWF is used in a way that dosely mirrors experimental research and development procedures using split lots It therefore links simulation very dosely to technology development resulting in significantly increased benefits from the use of simulation SILVACO International 1 5 ATLAS User s Manual Volume 1 The Nature Of Physically Based Simulation ATLAS is a physically based device simulator Physically based device si
308. n ATLAS For example to regrid on potential and re solve at the original bias the following statements are used REGRID POTENTIAL RATIO 0 2 MAX LEVEL 1 SMOOTH K 4 DOPFILE lt filenamel gt SOLVE PREV Note The REGRID statement may be used any number of times on a structure However it often advisable to quit and restart ATLAS between regrids on electrical quantities The go atlas statement can be used to do this This should be followed by a MESH statement loading the output file of the REGRID command and a re setting of all material and model parameters 2 14 SILVACO International Getting Started with ATLAS Specifying 3D Structures The syntax for forming 3D device structures is an extension of the 2D syntax described in the previous section The MESH statement should appear as MESH THREE D The parameter THREE D tells ATLAs that a three dimensional grid will be specified The other statements used to specify 3 D structures and grids are the same as for 2 D with the addition of z direction specifications The statements MESH THREE D X MESH LOCATION 0 SPACING 0 15 X MESH LOCATION 3 SPACING 0 15 Y MESH LOCATION 0 SPACING 0 01 Y MESH LOCATION 0 4 SPACING 0 01 Y MESH LOCATION 3 SPACING 0 5 Z MESH LOCATION 0 SPACING 0 1 Z MESH LOCATION 3 SPACING 0 1 define a 3D mesh that is uniform in the x and z directions and v
309. n gap of the semiconductor This is essentially a two step process the theory of which was first derived by Shockley and Read 133 and then by Hall 132 Shockley Read Hall recombination is modeled as follows 2 pn Die RR 3 211 ETRAP ETRAP TAU Pon Nj e amp Xp Fa TAU No p meo L L where Errar is the difference between the trap energy level and the intrinsic Fermi level T is the lattice temperature in degrees Kelvin and tauno and tauro are the electron and hole lifetimes This model is activated with the sau parameter of the mopeLs statement The electron and hole lifetime parameters TAUNO and TAUPO are user definable on the MATERIAL Statement The default values for carrier lifetimes are shown in Table 3 35 Materials other than silicon will have different defaults and a full description of these are given in Appendix B Table 3 35 User Specifiable Parameters for Equation 3 211 Statement Parameter Default Units MATERIAL ETRAP 0 ev MATERIAL TAUNO le 7 S MATERIAL TAUPO le 7 S 3 60 SILVACO International Physics Note This model only presumes one trap level which by default is ETRAP 0 and corresponds to the most efficient recombination centre If the TRAP statement is used to define specific trap physics then separate SRH statistics are implemented as described earlier in trap description earlier in this chapter SRH Concentration Dependent Lifet
310. n the MEASURE statement should be used to obtain the integrated total recombination rate using the U TOTAL parameter A ratio of radiative recombination rate with total rateis an estimate of luminous efficiency The following illusates this procedure MEASURE U RADIATIVE MEASURE U TOTAL In order to extract luminous intensity a luminous wavelength must be specified by the user This is done by setting the L WAVE parameter of the SOLVE statement When the luminous wavelength is set the program automatically calculates the luminous intensity of the device and stores this data in the log file The following SOLVE statement illustrates this process SOLVE L WAVE 0 8 The equation for luminous intensity P is hc P e Roos dA 8 20 8 16 SILVACO International Chapter 9 Laser Introduction LASER is an ATLAS product that performs coupled electrical and optical simulation of semiconductor lasers LASER works in conjunction with BLAZE and allows you to Solve the Helmholtz equation in order to calculate the optical field and photon densities e Calculate the carrier recombination due to light emission i e stimulated emission e Calculate optical gain which may depend on the photon energy and the quasi F ermi level e Calculate laser light output power e Calculate the light intensity profile corresponding to the fundamental transverse mode e Calculate light output
311. n using the command language to define a structure the information described in the following four sub sections must be specified in the order listed Specifying The Initial Mesh Thefirst statement must be MESH SPACE MULT lt VALUE gt This is followed by a series of x MESH and Y MESH statements X MESH LOCATION VALUE SPACING lt VALUE gt Y MESH LOCATION VALUE SPACING lt VALUE gt ThesPACE MULT parameter value is used as a scaling factor for the mesh created by the X MESH and Y MESH statements The default value is 1 Values greater than 1 will create a globally coarser mesh for fast simulation Values less than 1 will create a globally finer mesh for increased accuracy The X MESH and Y MESH statements are used to specify the locations in microns of vertical and horizontal lines respectively together with the vertical or horizontal spacing associated with that line At least two mesh lines must be specified for each direction ATLAS automatically inserts any new lines required to allow for gradual transitions in the spacing values between any adjacent lines The X MESH and Y MESH statements must be listed in the order of increasing x and y Both negative and positive values of x and y are allowed Figure 2 4 illustrates how these statements work On the left hand plot note how the spacing of the vertical lines varies from 1 mm at x20 and x 10 mm to 0 5 mm micron at x 5
312. nd 3 124 cece eee eee eee eens 3 36 3 20 User Specifiable Parameters for Equations 3 127 and 3 128 cc cece eee eee eee eens 3 37 3 21 User Specifiable Parameters for Equations 3 133 and 3 134 ccc eee eee eee eee eens 3 38 3 22 User Specifiable Parameters for Equation2 3 135 and 3 136 cece cece eens 3 39 3 23 User Specifiable Parameters for Equations 3 137 and 3 138 ccc cece cence eee eens 3 40 3 24 User Specifiable Parameters for Equations 3 145 and 3 146 ccc cece eee eee eee ees 3 41 3 25 User Specifiable Parameters for Equations 3 147 and 3 148 0 cece eee eee eee ees 3 41 3 26 User Specifiable Parameters for Equations 3 149 and 3 150 cece eee eee eee eens 3 42 3 27 User Specifiable Parameters for Equation 3 155 and 3 156 cece eee eee eee ees 3 43 3 28 User Specifiable Parameters for Equations 3 158 to 3 163 cece cece eee eee eens 3 45 3 29 User Specifiable Parameters for Equations 3 164 to 3 169 00sec cece eee eee eens 3 47 SILVACO International xxi ATLAS User s Manual Volume 1 Figure Page No able Title No 3 30 Parameters for Equations 3 172 through 3 188 eect eee ne 3 50 3 31 User Specifiable Parameters for Equations 3 189 3 192 0oooococcococccncnro 3 52 3 32 User Specifiable Parameters for Equations 3 195 and 3 196 oooooococoocrnnnr oro 3 54 3 33 User Definable Parameters in the Field Dependent Mobility Mo
313. nd one positive On the negative side the gate current is responsible for the degradation in device operating characteristics with time This reliability issue is of considerable importance as the lifetime of electronic parts has to be guaranteed Reliability may be simulated within the Silvaco suite of tools for device level reliability which are described in a later chapter On the positive side the existence of this gate current has caused the proliferation of the non volatile memory market These devices use the existence of gate current to program and erase the charge on a floating contact This concept has resulted in a variety of different devices such as FLASH FLOTOX EEPROM etc All such devices rely on the physics of the gate current process for their existence There are a variety of different conduction mechanisms within an insulating layer 13 but for the case of nonvolatile memory only two mechanism are relevent Fowler Nordheim tunneling and hot carrier injection Models for these two injection processes are described in the following sections In the case of hot electron injection two models are available the lucky electron model and the Concannon gate current model Fowler Nordheim Tunneling If the electric field across an insulator is sufficiently high then it may cause tunneling of electrons from the semiconductor or metal Fermi level into the insulator conduction band This process is strongly depende
314. nergies Kmax Cer 2 T n Nc y 64 Zu E 3 315 k 1 where Nc n is also a constant for a given effective mass and temperature given by the Equation 27 Make T No 3 316 2D h The self consistent Schrodinger P oisson model is enabled by setting the scHro parameter of the MODEL statement With this parameter set ATLAS solves the one dimensional Schrodinger s equation along a series of slices in the y direction relative to the device Each slice is taken along an existing set of v nodes in the ATLAS device mesh Note This feature can only be used with rectangular grids in ATLAS After the Schrodinger equation solution is taken carrier concentrations calculated from equation 3 315 are substituted into the charge part of Poisson s equation The potential drived from solution of Poisson s equation is substituted back into Schrodinger s equation This solution process alternating between Schrodinger s and Poisson s equation is continued until convergence is reached and a self consistent solution of Schrodinger s and Poisson s equation is obtained The solutions of the self consistent system can be written to a structure file using the save statement or using the ouTFILE parameter of the soLve statement These structure files will contain the self consistent potential and electron concentrations The Eigen energies and Eigen functions can also be written to the structure file by specifying the zrcexs parameter of the output statemen
315. ngth of 0 55 microns C Interpreter Function The dependence of complex index on wavelength can also be specified using the C Interpreter function The syntax is MATERIAL NAME Silicon F INDEX myindex c Thefile myindex c is an external file conforming to the template supplied with the program It returns wavelength dependent real and imaginary indices Instructions for using the C Interpreter and finding the template functions are described in Appendix A SILVACO International 8 11 ATLAS User s Manual Volume 1 Extracting Dark Characteristics One of the first tasks in analyzing a new detector design is to examine dark current device capacitance and possibly other un illuminated characteristics This can normally be done without the use of LUMINOUS Extraction of the characteristics is adequately covered in the chapters on s PISCES or BLAZE The extraction of reverse bias leakage currents for diodes presents some difficult numerical problems for device simulators These problems save associated with limitations on numerical precision ATLAS as well as most other available device simulators uses double precision arithmetic to evaluate terminal currents Double precision arithmetic provides roughtly 16 decimal digits of precision With the scaling performed internally this allows the measurement of currents down to a level of between about 101 A micron to 1016 A micron Unfortunately photodiode leakage cur
316. ns for betas and the saturation currents are t XTB BF t sr 10 72 tnom t XTB BR t R os 10 73 ISE facln NE ISE t 7 5 REB e 10 74 os ISC facln NC ISC t 7 g NER e 10 75 o ISS facin NS ISS t 7 WTB e 10 76 o IS t IS e 10 77 facln IBE t IBE e 10 78 10 54 SILVACO International MIXEDMODE facin IBC t IBC e P 10 79 where E E t facln ae pe tXTI s 10 80 Vri tnom VO inom IKF t IKF 1 TIKF1 At TIKF2 At 10 81 IKR t IKR 1 TIKR1 At TIKR2 At 10 82 IRB t IRB 1 TIRB1 At TIRB2 At 10 83 TEMPLEV 2 Thefollowing equations model the energy gap with temperature moni egnom 1 16 7 02e 4 n 11080 10 84 P eg t 1 16 7 02e 4 H089 10 85 The basic BJ T temperature compensation equations for betas and the saturation currents are BF t BF 1 XTB At 10 86 BR t BR 1 XTB At 10 87 ISE facin NE ISE t I4 XTB At e 10 88 ISC facin NC ISC t TEXTB At e 10 89 ISA facin NE ISS t TEXTB At e 10 90 S t IS f 10 91 facln IBE t IBE e 10 92 facin IBC t IBC e Y 10 93 SILVACO International 10 55 ATLAS User s Manual Volume 1 where EG EG facln 22 eXTI Inf 10 94 Vritnom Vi r inom IK F t IKF 1 TIKF1 At TIKFZ2 At 10 95 IKR t 2IKR 1 TIKR1 At TIKR2 At 10 96 IRB t IRB 1 c TIRBI1 At TIRB2 At 10 97 TEMPLEV 3 The following
317. nt energy to surmount the insulator semiconductor barrier of height op is now defined as a function of energy The probability now has the form e j v e F e T x y d 3 290 ONES i v e F e T x y d 3 291 B p where v e is the perpendicular velocity of a hot carrier and defines the probability of a hot carrier with an energy e travelling in the direction of the insulator semiconductor The barrier heights gn p are defined according to PEFF N IG EBETA E IG EETA ESP Ay x y 3 292 B n E L PEFF P IG HBETA E IG HETA E Ay x y 3 293 B p il y where E is the electric field perpendicular to the semiconductor insulator interface The traditional barrier heights rc EBo and 1G HB0 are reduced to take account of three effects The first is due to Schottky barrier lowering which depends on the perpendicular electric field at the semiconductor insulator interface The second takes account of tunneling through the gate oxide by reducing the barrier height The third takes into account that a potential difference exists between the semi conductor insulator interface and the starting position of the hot carrier By default this last effect 3 80 SILVACO International Physics is disabled but may be enabled with the parameters e BENDING and H BENDING for electrons and holes respectively wW The carrier velocity model follows the approach of Fiegna 129 where velocity is proport
318. nt on the applied electric field but is independent of the ambient temperature The Fowler N ordheim equation 69 expresses tunnel current density through the oxide as F BE Jen F AE E oxp 5 3 272 2 F BH Jep F AH E exp E 3 273 where E specifies the magnitude of the electric field in the oxide The model parameters F AE F AH F BE and F BH may be defined on the mopEts statement but have the default values obtained from Keeney Piccini and Morelli 69 shown in Table 3 49 SILVACO International 3 15 ATLAS User s Manual Volume 1 Table 3 49 User Specifiable Parameters for Equation Symbol Statement Parameter Default Values Ros ODELS F AE 1 82 10 BiN ODELS F BE 1 90 108 Res ODELS F AH 1 82 1077 Bpg ODELS F BH 1 90 108 The Fowler N ordheim model in ATLAS has been implemented as either a post processing function or as a self consistent scheme with the other equations The post processing option may be chosen by specifying the paramter rner on the mopeL statement The self consistent scheme is activated by specifying the parameter rNonp on the MopEL statement For either model the implementation scheme is the same Each electrode insulator and insulator semiconductor interface is divided into discrete segments which are based upon the mesh For each insulator semiconductor segment the F owler N ordheim current is calculated as de
319. o 428 Rob actam adde TCR aoa Rf Fons 3 75 Fowler Nordheim TU Misas a td RC RR RR 3 75 Lucky Electron Hot Carrier Injection Model 4o e AAA a 3 76 Concannon s Injection Model codo eie etu iuc eto rri PRA ete AA d P Yr itp 3 80 Device Level Reliability Modeling lt o o0oooococcocccarccnar HHee 3 83 Hansch MOS Reliability MOI oss os Pott testatore aaa Scr tutto eta SANA ae 3 83 ORCHID ia 3 84 The Ferroelectric P ermittivity Model 2s ie ac ead doni o RS Lact e tr de dd 3 84 Quantum Mechanical Models daa 3 85 Self Consistent Schrodinger Poisson Model cde ct e E a ao er t ottiene 3 85 Dana Moments Model s ve ael ra aid tci Pete d air tere tero or Re bruto Eo PRI CIR genes 3 87 Quantum Correction Models src Feo Che E Ehe eR ERR RENTE RE RR XA PR 3 89 PANS CIS MOUS ous ees ic Grecos tob aE oxi quisa etatem ce dur EY dee qv tare cba duc f DUAE 3 89 Vali DOTS MOGE reri de Vp we nied RE uhr aie RATE Per eH Eee uds nei eden 3 89 Chapter 4 S PISGES A dE pA DD d cR Da ead p 4 1 Introduction s issver n re A KU XR 4 1 Simulating Silicon Devices Using S PISCES 0 cece cece eee eee eee een eee eeeee 4 1 simulating MOS Technologies 55 bx REOR PER bss 4 1 Physical Models Tor MOSFETS deus itte tete Pade can e fal ttn trt eda tie ta un Cala 4 1 Meshing for MOS DaVIC8S das 4 1 MOS El amp ctrage Naming saab dete oc ead Co Sala dla e does fe dia 4 3 rate WEOTETUDIGIQIT rte opt bot dae LORI Ld AD AK ds he D ls 4 3 nterface
320. o an exception similar to sET Since MIXEDMODE input files are parsed completely before execution see also Things to know Recommendations extractions can only be done after completion of the simulation To extract results from a MIXEDMODE simulation EXTRACT should be specified after re initialization of ATLAS go atlas Circuit and Analysis Specification The SPICE like MIXEDMODE statements can be divided into three categories element statements defining the circuit netlist simulation control statements specifying the analysis to be performed spedial statements typically related to numerics and output first character being a dot The specification of the circuit and analysis part has to be bracketed by a BEGIN and an END statements i e all MIXEDMODE statements before BEGIN or after END will be ignored or regarded as an error Between BEGIN and END the order is arbitrary Netlist Statements Each device in the circuit is described by an element statement The element statement contains the element name the circuit nodes to which the element is connected and the values of the element parameters The first letter of an element name specifies the type of element to be simulated For example a resistor name must begin with the letter R and can contain one or more characters This means that R R1 RSE ROUT and R3AC2ZY are all valid resistor names Some elements such as diodes and transistors must a
321. o atlas log outfile hallo dc 2 10g append log outfile hallo tr log append Initial Settings Initial convergence is critically dependent on the initial settings of the node voltages IC NODESET There should not be any problem starting from the zero bias case Similarly starting from a preceding MIXEDMODE solution is simple since the complete solution of the circuit and the ATLAS devices is directly available LOAD SAVE However when loading solutions for the numerical devices from ATLAS using OPTIONS LOADSOLUTIONS sometimes precise matching of the initial circuit condition is required In this case it is practical to extrac the relevant properties in the preceding ATLAS run and use them to parameterize the MIXEDMODE input In the following example the voltages and current of an ATLAS solution is extracted and the results are used for the initial definition of the circuit SILVACO International 10 9 ATLAS User s Manual Volume 1 End of the first part the stand alone ATLAS simulation extract the final voltage drop on the anode extract name Von max vint anode extract the gate current extract name I gate y val from curve vint anode i gate where x val Von extract name V gate y val from curve vint anode vint gate where x val Von now the MIXEDMODE part go atlas BEGIN define the gate current source use extracted value as p
322. o the probed location while taking into account the direction for vector quantities See the earlier section on Interpreting Contour Plots Note Specifying the probe location exactly at a material or region interface will often lead to erroneous results It is best to very slightly offset the location of the probe inside the material or region of interest Re initializing ATLAS at a Given Bias Point Each solve statement will begin with the device biased at the previous value solved If you wish to begin a solution at a previously solved bias point you can re load the structure file saved at that point This is accomplished in the following manner LOAD INFILE lt filename gt MASTER Information about that solution point will be displayed in the output window This command is useful for solving a set of IAM curves For example to solve a family of Id Vd at various V9 the gate can be ramped with zero drain bias and a structure file saved at each desired value of Vg These structure files can then be reloaded in turn while a Vd sweep is performed Note An ATLAS input file cannot start with a LOAD statement Prior to loading the structure file the user needs to ensure that the device mesh for the same structure has been loaded using the MESH statement Also the same MODELS MATERIAL and CONTACT settings are required as when the files was saved by ATLAS Technology Specific Issues in ATLAS This chapter was design
323. ocities for electrons and holes Table 3 45 User Specifiable Parameters for Equations 3 258 3 261 Statement Parameter Units IMPACT REL EL um IMPACT IREL HO pm MATERIAL VSAT cm s MATERIAL VSATN cm s SILVACO International 3 71 ATLAS User s Manual Volume 1 Table 3 45 User Specifiable Parameters for Equations 3 258 3 261 Statement Parameter Units MATERIAL VSATP cm s IMPACT TAUSN S IMPACT TAUSP S Note As an added level of flexibility the relaxation times used for the energy balance equation and those used in the impact ionization model have been separated into two user definable parameters In contrast to TAUREL EL and TAUREL HO Which are used in different formulae the parameters TAUSN and TAUSP are only applicable in the impact ionization expression 3 260 and 3 261 By default TAUREL EL TAUSN and AUREL HO TAUSFE H H It can also be argued that the parameters an AP BN and Bp should also be a function of the carrier temperature However no dear theoretical basis for this has been proposed and accepted Instead the C Interpreter within ATLAS has been extended to include two C interpreter functions These functions are specified via the F EDIIN and F EDIIP parameters of the impact statement These parameters specify the filename of a text file containing a C interpreter fun
324. odel which uses a higher order approximation of the Boltzmann transport equation In this formalism transport parameters such as mobility and impact ionization are functions of the local carrier temperature rather than the local electric field To enable the energy balance transport model the HCTE HCTE EL and HCTE HO parameters on the moDELs statement are used These parameters enable the energy transport model for both carriers electrons only or holes only respectively The statement MODELS MOS HCTE enables the energy balance transport model for both electrons and holes in addition to the default MOSFET models 2 22 SILVACO International Getting Started with ATLAS Summary Of Physical Models Table 2 1 Carrier Statistics Models Model Syntax Notes Boltzmann BOLTZMANN Default model Fermi Dirac FERMI Reduced carrier concentrations in heavily doped regions sta tistical approach Incomplete Ionization INCOMPLETE Accounts for dopant freeze out Typically used at low tempera tures Silicon Ionization Model IONIZ Accounts for full ionization for heavily doped Si Use with INCOMPLETE Bandgap Narrowing BGN Inportant in heavily doped regions Critical for bipolar gain Use Klaassen Model Table 2 2 Mobility Models Model Syntax Notes Concentration Dependent CONMOB Lookup table valid at 300K for Si and GaAs only Uses simple
325. of tun trons neling through insulators Used in EEPROMs Fowler Nordheim holes FNHOLES As FNORD for holes Not usually required Band to Band standard BBT STD For direct transitions Required with very high fields Klaassen Band to Band BBT KL Includes direct and indirect transi tions Hot Electron Injection HEI Models energetic carriers tunneling throug insulators Used for gate current and Flash EEPROM program ming Hot Hole Injection HHI As HEI for holes For ULSI PMOS devices Concannon Gate Current N CONCAN Non local gate model consistent with Model P CONCAN Concannon substrate current model Table 2 6 Model Compatibility Chart CONMOB BLDMOB TFLDMB2 YAMAGUCHI CVT ARORA ANALYTIC CCSMOB SURFACE LATTICE H E BALANCE CONMOB CM OK OK YA CV AR AN CC OK OK OK SILVACO International 2 25 ATLAS User s Manual Volume 1 Table 2 6 Model Compatibility Chart Continued CONMOB BLDMOB TFLDMB2 YAMAGUCHI CVT ARORA ANALYTIC CCSMOB SURFACE LATTICE H E BALANCE FLDMOB FM OK Tr YA CV OK OK OK OK OK OK TFLDMB2 TF OK TF YA cv OK OK TF TF OK OK YAMAGUCHI YA YA YA YA CV YA YA YA YA NO NO CVT CV CV CV CV CV CV CV CV CV OK O ARORA AR AR O OK YA CV 2 AR cc O O O ANALYTIC AN AN O OK YA CV ES O OK O CCSMOB CC CC O TF YA CV CC CC O O O SURFMOB SF OK O TF YA CV OK OK OK OK O LATTICE H LH OK O OK NO OK OK OK OK O
326. ogramming MODELS MOS HEI PRINT The next example would be appropriate for EEPROM erasure MODELS MOS HHI FNORD PRINT With energy balance simulations the Concannon Models should be used for EPROM programming and erasing Note Writing and erasure of floating gate devices should be done using transient simulation Gate Current Assignment NEARFLG The actual calculation of floating gate current magnitude is done at the silicon oxide interface The question of distribution of oxide currents to the various electrodes near the interface is resolved using one of two models The actual flow of carriers in oxides is not well known Accepted physical models of carrier flow in oxides are still under research As such S PISCES provides two heuristic models to choose from The default is distribute currents calculated at points along the interface to the electrode in the direction of highest contributing field This model is somewhat analogous to a purely drift model of oxide carrier transport Thealternativeisto set the NEARFLG parameter of the MODEL statement In this case the currents calculated at points along the interface are distributed to the geometrically dosest electrode This model is analogous to a purely diffusion model of carrier transport in oxide SILVACO International 4 7 ATLAS User s Manual Volume 1 Simulating SOI Technologies Silicon substrates are now being produced that contain a thin ox
327. om 3 Vittnom t EG egnom tnom GAP2 thom VJC tnom dvjsdt egnom 3 Ve tnom EG egnom e tnom 1108GAP2 tnom VJS tnom Parasitic Resistor Temperature Equations 10 165 10 166 Thefollowing parameters are also modified when corresponding temperature coefficients are specified RE T RE 1 REl t tnom TRE2 t tnom 2 10 167 RB t RB 1 RE1 t tnom 10 168 MOSFET Model MIXEDMODE supports the popular LEVEL 3 model which is widely used in SPICE circuit analysis programs MOSFETs The equations inside MIXEDMODE are the same for both n and p channel devices and MIXEDMODE evaluates the current equations for n and p channel devices in the same way For p channel devices the polarities of the threshold voltage and the node voltages VGS VDS and VBS arereversed and the transistor is handled internally as an n channel device The final p channel drain current is then obtained by reversing the sign of the computed drain current Scaling Scaling of currents resistances or capacitances is controlled by a number of parameters see the description of the mxxx statement These parameters are AD Area of drain AS Area of source NRD Number of squares for drain resistance NRS Number of squares for source resistance PD Sidewall of drain PS Sidewall of source 10 60 SILVACO International MIXEDMODE MOSFET Current Convention Current flow t
328. ombardi 108 is selected by setting cvt on the mopeEL statement This model overrides any other mobility models which may be specified on the mopELs statement In the cvt model the transverse field doping dependent and temperature dependent parts of the mobility are given by three components that are combined using Mathiessen s rule These components are Lac Hsr and up and are combined using Mathiessen s rule as follows 1 1 1 1 HT HAC Hp tHe 3 157 The first component Hac is the surface mobility limited by scattering with acoustic phonons _ BN CVT CN CVT qj AU CVT 3 158 AC n E 1 3 2 L TLE TAUP CVT i BP CVT CP CVT N TR AC p E 1 3 P l TLE where T is the temperature E is the perpendicular electric field N is the total doping concentration The equation parameters BN CVT BP CVT CN CVT CP CVT TAUN CVT and TAUP cvT May be user defined on the moB11 1TY statement and have the defaults shown in Table 3 28 The second component Usr is the surface roughness factor and is given by _ DELN CVT E 3 160 Sr 2 Er DELP CVT Le E 3 161 E The equation parameters DELN CVT and DELP cvT may be user defined on the moBILITY statement and havethe defaults shown in Table 3 28 The third mobility component up is the mobility limited by scattering with optical intervalley phonons This component is given by T GAMN CVT MUMAXN CVT 355 MUON CVT gt j lS 300
329. on If the final ATHENA mesh is not appropriate for ATLAS DEVEDIT may be used to re mesh the structure or the REGRID command may be used 2 8 SILVACO International Getting Started with ATLAS Interface From DevEdit A 2D or 3D structure created by DEvEpiT can be read into ATLAS using the command MESH INF lt structure filename This single statement loads in the mesh geometry electrode positions and doping of the structure ATLAS will automatically determine whether the mesh is 2D for S PISCES or BLAZE or 3D for DEVICE3D or BLAZE3D If the structure coming from DeEvEpiT was originally created by ATHENA the electrodes should be defined in ATHENA as described in the previous section If the structure is created in DevEbiT the electrode regions should be defined on the Region Add menu in DevEDIT Using The Command Language To Define A Structure To define a device through the ATLAS command language you must first define a mesh This mesh or grid covers the physical simulation domain The mesh is defined by a series of horizontal and vertical lines and the spacing between them Next regions within this mesh are allocated to different materials as required to construct the device For example the specification of a MOS device requires the specification of silicon and silicon dioxide regions After the regions are defined the location of electrodes is specified The final step is to specify the doping in each region Whe
330. on affinity x of SiGeis taken to be constant with respect to composition Density of States The density of states for SiGe is defined differently compared to the previous materials by not being a function of the effective masses Instead the density of states have been made to depend upon the Ge mole fraction x composition according to N 2 8x10P t x composition 1 04x10P 2 8x10 5 89 Cc N 1 04x10 x composition 6 0x10 1 04x10P 5 90 Dielectric Function The compositional dependence of the static dielectric constant of SiGe is given by 11 8 42 x composition 5 91 Low Field Mobility No specific SiGe low field mobility models have been implemented into BLAZE Velocity Saturation In SiGe the temperature dependent velocity saturation used in the field dependent mobility model is defined by the following equations VSATN 138 10 tan 5 92 TL VSATP 9 05 10 tanh 5 93 L Note All other defaults used for SiGe are taken from Silicon Silicon Carbide SiC Recently there has been a great deal of interest in silicon carbide materials for high power high temperature applications The main characteristics of silicon carbide are that they have a very wide bandgap high thermal conductivity high saturation velocity and high breakdown strength Silicon carbide is commercially available in two polytypes called 6H SiC and 4H SiC The ATLAS framework supports both of these polytypes whi
331. on region An eigenvalue solver provides a set of eigenfunctions and corresponding eigenvectors and LASER selects the fundamental transverse mode solution LASER uses boundary conditions of the form E x y 0 on the boundaries of the solution region This region should therefore be large enough to cover the entire active region of the laser diode with some inclusion of the passive regions When the single frequency model is used for simulation the lasing frequency used in Equation 9 1 is an external parameter that is fixed during the calculation and either model for optical gain can be used The multiplelongitudinal mode model requires the use of the physically based optical gain model The user specifies an initial estimate of the lasing frequency and this is adjusted during calculations The user also spedifies a frequency range or photon energy range within which LASER will calculate multiple longitudinal modes Specifying Laser Simulation Problems Thestructure of the laser diode and the mesh used to simulate it are specified in the normal way using the capabilities provided by ATLAS and BLAZE To enable LASER simulation the user must do the following using the parameters as shown in Table 9 7 Activate LASER Specifies the LASER parameter of the mopELs statement Defineamesh for solution of the Helmholtz equation The Helmholtz equation is sol ved on a uniform rectangular mesh that is independent of the triangular mesh used for d
332. one or more electrodes The NAME parameter is used to identify which electrode will haveits properties modified The WORKFUNCTION parameter sets the workfunction of the electrode The statement CONTACT NAME gate WORKFUNCTION 4 8 sets the workfunction of the electrode named gate to 4 8eV The workfunctions of several commonly used contact materials may be specified using the name of the material Workfunctions for ALUMINUM N POLYSILICON P POLYSILICON TUNGSTEN and TU DISILICIDE may be specified in this way The following statementsets the workfunction for a n type polysilicon gate contact CONTACT NAME gate N POLYSILICON Aluminum contacts on heavily doped silicon is usually ohmic and you should not specify a workfunction for this situation For example for MOS devices you should not specify CONTACT NAME drain ALUMINUM wrong The CONTACT statement may also be used to specify barrier and dipole lowering of the Schottky barrier height Barrier lowering is enabled by specifying the BARRIER parameter while dipole lowering is specified using the ALPHA parameter The statement CONTACT NAME anode WORKFUNCTION 4 9 BARRIER ALPHA 1 0e 7 sets the work function of the Schottky contact named anode to 4 9eV enables barrier lowering and sets the dipole lowering coefficient to 1 nm Note When a Schottky barrier is defined at a contact it is recommended that a fine y mesh is present just beneath the contact inside
333. ong similar lines the overlapping of regions can be used to an advantage in forming graded heterojunctions between two materials in the same system with different non zero composition fractions For example REGION Y MIN 0 1 MATERIAL Al1GaAs X COMPOSITION 0 3 GRAD 1 0 02 REGION Y MAX 0 11 MATERIAL A1GaAs X COMPOSITION 0 1 specifies a graded heterojunction with a composition of 0 3 at y 0 1 falling to 0 1 at y 0 11 SILVACO International 5 29 ATLAS User s Manual Volume 1 By default heterojunctionsin BLAZE are simulated using a drift diffusion approximation To simulate thermionic emission at an abrupt heterojunction the eEmIss parameter must be set The following illustrates specification of a thermionic heterojunction REGION Y MIN 0 1 MATERIAL GaAs REGION Y MAX 0 1 MATERIAL A1GaAs X COMPOSITION 0 3 EMISS 3 This is similar to the first example of the previous section The only difference is that in the second REGION Statement the EmIss 3 parameter is set This envokes the thermionic emission model The EMISS n parameter is indexed in the same way as the GRaD n paramter Defining Materials and Models Materials For example to set the bandgap for the material InP the following syntax should be used MATERIAL MATERIAL InP EG300 21 35 Models BLAZE has two ways of simulating the physical effects of variations in semiconductor composition For relatively gradu
334. ons the relationship between mole fraction and material parameters for the AlGaAs material system will be described Note Users should not use this material system to form GaAs by setting x 0 but instead specify GaAs as the material Bandgap There are three primary conduction bands in the AlGaAs system that depending on mole fraction determine the bandgap These are named Gamma L and X The default bandgaps for each of these conduction band valleys are as follows E r EG300 x composition 0 574 0 055 x composition 5 53 Egy 1 734 x composition 0 574 0 055 x composition 5 54 5 20 SILVACO International BLAZE E x 1 911 x composition 0 005 0 245 x composition 5 55 The bandgap used for any given Al concentration is the minimum as calculated from these equations EG300 is the bandgap at 300K and specified on the material statement x composition is the Aluminum mole fraction and may be user defined on the REGION statement Thetemperature dependence of the bandgap is calculated iaccording to 300 T E TL E 300 EGALPHA 5 56 300 EGBETA T EGBETA The value of Eg 300 is taken as the minimum of E gr Egx and Eg The default temperature dependent bandgap parameters for AlGaAs are listed in Table 5 1 Statement Parameter Default Units MATERIAL EG300 T1259 eV MATERIAL EGALPHA 5 405 1074 eV K MATERIAL EGBETA 20
335. or Equations Overview Many years of research into device physics has resulted in a mathematical model of the operation of any semiconductor device This model consists of a set of fundamental equations which link together the electrostatic potential and the carrier densities within some simulation domain These equations which are solved inside any general purpose device simulator have been derived from Maxwell s laws and consist of Poisson s equation the continuity equations and the transport equations Poisson s equation relates variations in electrostatic potential tolocal charge densities The continuity equations describe the way that the electron and hole densities evolve as a result of transport processes generation processes and recombination processes This chapter shall describe the mathematical model implemented into ATLAS H owever it is important to note that a discretization of the equations is also performed so that they may be applied to the finite element grid used to represent the simulation domain Poisson s Equation Poisson s equation relates the electrostatic potential to the space charge density divieVy p 3 1 where y is the electrostatic potential e is the local permittivity and p is the local space charge density The reference potential can be defined in various ways For ATLAS this is always the intrinsic Fermi potential w which is defined in the next section The local space charge density is the sum of
336. or defaulted the entire base collector capacitance is connected to the internal base node CAPMOD 1 Assuming FC 0 bex CIC AXIO a EC 10 62 cbcx et VJC or vbcx lt J vbcx cbcx CIC e 1 XCJC 10 63 eff Garo o for vocx gt FC VJC CAPMOD 2 RT ER o a Oe eR EU 10 64 cbcx gt VIC or vbcx lt J i vbcx cbcx CIC oy 1 XCJC 1 MJC ve for vbcx gt 0 10 65 where vbcx is the voltage between the external base node and the internal collector node Substrate Capacitance For Lateral Substrate Capacitance For reverse bias vbs y MIS cbs CIS orp 1 ws for Vp lt 0 10 66 For forward bias ba CIS WS Fares 10 67 For Vertical Substrate Capacitance For reverse bias ve MIS csc CJS 5 1 75 for Ve lt 0 10 68 For forward bias OI EMI 10 69 CSC eff VIS T SILVACO International 10 53 ATLAS User s Manual Volume 1 Temperature Effects Equations Analysis at Different Temperatures All model input data for MIXEDMODE are assumed to have been extracted at a nominal temperature of 27 C The circuit simulation will also be performed at a temperature of 27 C unless overridden by a TEMP parameter on the moDE1 control statement TEMPLEV 1 The following equations model the energy gap with temperature 2 tnom egnom 1 16 7 02e 4 n4 1089 10 70 K eg t 1 16 7 02e 4 T080 10 71 The basic But temperature compensation equatio
337. orm 9T CF V kVT H 6 1 where C is the heat capacitance per unit volume is the thermal conductivity H is the heat generation T is the local lattice temperature The heat capacitance can be expressed as C pCp where C is the specific heat and p is the density of the material Specifying the parameter LAT TEMP on the moDzLs statement includes the lattice heat flow equation in ATLAS simulations GIGA supports different combinations of models For example if the parameters HCTE and Lat TEMP are specified in the mopeL statement and both particle continuity equations are solved all six equations are solved If hcTE EL is specified instead of HcTE only five equations are solved and the hole temperature Ty is set equal to lattice temperature T Specifying Heat Sink Layers For Thermal Solutions Regions may be defined for inclusion only in thermal calculations These regions will typically consist of layers associated with heat sinks They are defined using the REGION statement Even though in reality the heat sink materials are typically metal conductors it is more convienient to specify these layers with the material type INSULATOR This is because as insulators the program will only solve heat flow and not attempt to solve current continuity in these layers The region number is subsequently used as an identifier when thermal conductivities and heat capacities are assigned to these regions T
338. orresponding eigenfunctions E xy LASER takes into account only the fundamental transverse mode solution so the index k will be dropped from subsequent equations In principle equation 9 1 should be solved for each longitudinal mode that is taken into account Since very few longitudinal modes are actually lasing LASER equation 9 1 only once for the longitudinal SILVACO International 9 1 ATLAS User s Manual Volume 1 mode with the greatest power and subsequently assumes E x y E 9 x y where E x y is the optical field corresponding to the most powerful longitudinal mode This assumption is reasonable since the shape of the solution is almost independent of frequency within the range of interest For dielectric permittivity Laser uses the following model 135 ngg X y ng ALPHAA FCN n FCP p CAELI Rc A 0 e x y ng CALPHAR j where Ng is the bulk refractive index ALPHAR S a line width broadening factor ja ko oc and g x y is the local optical gain e ALPHAA is the bulk absorption loss and is specified on the varERrArL statement LAS ABSORPTION Must be specified on the mopELs statement to include absorption loss e FCN and rc are the coefficients of the free carrier loss and are set via the MATERIAL statement LAS FCARRIER must be specified on the vopgrs to include this loss mechanism
339. orresponding to neutrality At this condition those traps above the Fermi level are defined as acceptor like and those below the F ermi level are donor like Figure 3 1 shows the terminology used within ATLAS to define the type of trap The position of the trap is defined relative to the conduction or valence bands using E LEVEL so for instance an acceptor trap at 0 4eV would be 0 4eV below the conduction band SILVACO International 3 11 ATLAS User s Manual Volume 1 E level for acceptor trap E level for donor trap Figure 3 1 Definition of the trap energy level for acceptor and donor traps in reference to the conduction and valence band edges Calculation of Trapped Charge in Poisson s Equation The total charge caused by the presence of traps is added into the right hand side of Poisson s equation The total charge valueis defined by Q q p ni 3 50 where n and p are the densities of trapped charge for donor like and acceptor like traps respectively The trapped charge depends upon the trap density Density and its probability of occupation F p p For donor like and acceptor like traps respectively the trapped charge is calculated by the equations D DENSITYXF 3 51 p DENSITYXF 3 52 In the case where multiple traps at multiple trap energy levels are defined the total charge becomes k m a p m ni P Pr 3 53 a 1 B 1 where k is the number of acceptor like tra
340. ouble charge user supplied code here return 0 Input Parameters Four input parameters are supplied to the function and can be used in the user defined code The input parameters are V the voltage across the element V temp the temperature K ktq the thermal voltage kT q V time transient time sec a value of 0 is supplied during DC calculations Output Parameters The four output parameters that must be returned by the function are curr the value of F1 Amps didv the value of dFl v time dU A V cap the value of F2 v time charge the value of the charge Q SILVACO International 10 69 ATLAS User s Manual Volume 1 Example Consider an element that consists of a resistor R and a capacitor C connected in parallel The equation for the total current through this combination is I U t pte The quantities that must be defined by the user are U FI U 1 F2 U t 2C dF U t 1 dU R Q C U When R 2kQ and C 100pF a user defined function could have the following form intrc v temp ktq ti me curr didv cap charge double v double temp double ktq double time double curr double didv double cap double charge curr v 2000 0 didv 1 0 2000 0 cap 1 0e 10 charge 1 0e 10 v return 0 Kf 10 227 10 228 10 229 10 230 10 231 10 70 SILVACO International
341. p Ap RsrH Eg G5 Rp 3 96 where i are defined by expressions 3 80 and 3 83 and are equal to 1 for Boltzmann statistics TAUREL EL and TAUREL HO are the electron and hole energy relaxation times Ey is the bandgap energy of the semiconductor The relaxation parameters are user definable on the mopELs statements and havethe default parameters shown in Table 3 8 The relaxation times are extremely important as they determine the time constant for the rate of energy exchange and therefore precise values are required if the model is to be accurate However this is not a measurable parameter and Monte Carlo analysis is the only method through which values may be extracted for the relaxation time Itis alsoimportant totake into consideration that different materials will have different values for the energy relaxation time but within ATLAS the relaxation time will always default tothe valuefor silcon 3 20 SILVACO International Physics Table 3 8 User Specifiable Parameters for Equations 3 95 and 3 96 Statement Parameter Default Units MODELS AUREL EL 0 4e 12 S MODELS AUREL HO 0 4e 12 S Temperature Dependence of Relaxation Times ATLAS does not provide an explicit default model for the temperature dependence of energy relaxation times However two methods exist to make the relaxation time a function of carrier energy First the user can use an in buil
342. p during transient analysis Different variants of the N ewton algorithm are used depending on the circumstances The full Newton method oerroNs FULLN and a modified two level Newton method oPTIONS M2LN are available for steady state simulation The full Newton method provides rapid convergence when a good initial guess is available The modified two level Newton algorithm is less sensitive to the initial guess For transient simulation a good initial guess always exists The full Newton method therefore works very well and is therefore always used for transient simulation When using MIXEDMODE3D it is recommended that either the DIRECT or GMRES solver be specified These are specified in the ATLAS part of the MIXEDMODE 3D input deck on the METHop statement Multi Device Structure Representation If more than one ATLAS device is defined in a MIXEDMODE simulation the structures are merged together internally The output solution file is a single file which contains both structures The first structure referenced will be on top all other structures will be attached below Example A diode and a bipolar transistor are specified as numerical devices with the following element statements ABJT 1 BASE 2 EMITTER 4 COLLECTOR WIDTH 1E4 INFILE bjt str ADIO 3 ANODE 4 CATHODE WIDTH 1 5E5 INFILE dio str After outputting the solution with SAVE MASTER mas The solution file for the first DC point ma
343. pact or circuit models are analytic formulae that approximate measured terminal characteristics Advanced compact models provide high accuracy with minimum computational complexity Device modeling device characterization and parameter extraction are concerned with the development and use of accurate and efficient compact models Physically based device simulation solves systems of equations that describe the physics of device operation This approach provides predictive capabilities and information about the conditions inside a device but it can require significant amounts of CPU time Information is usually transferred from device simulation to circuit simulation as follows Electrical characteristics are calculated using a physically based device simulator These calculated electrical characteristics are then used as input by a device modeling and parameter extraction package such as UTMOST The extracted parameters are used to characterize a compact model used by the circuit simulator This approach is adequate for many purposes but has limitations It requires that satisfactory compact models already exist The use of compact models always introduces some error and models SILVACO International 10 1 ATLAS User s Manual Volume 1 that are adequate for digital circuit simulation may be inadequate for other applications Applications and devices for which compact modeling is not always satisfactory include precision low pow
344. pendix B of this manual For the AlGaAs region a composition fraction of 0 3 is specified Graded Junctions A grading can be applied tothis heterojunction with a simple modification For example REGION Y MIN 0 1 MATERIAL GaAs REGION Y MAX 0 1 MATERIAL AlGaAs N X COMPOSITION 0 3 GRAD 3 0 01 specifies that the composition fraction of the AlGaAs region decreases from 0 3 at y 0 1 microns to 0 0 at y 0 11 microns The crap parameter specifies the distance over which the mole fraction reduces to zero The crap parameter is indexed such that crap 1 corresponds to the v wrw side of the region GRAD 2 Corresponds to the x wax side of the region cnap 3 corresponds to the v max side of the region and cnap 4 corresponds to the x mIwN side of the region In most cases the GRAD n parameter acts to increase the size of the region By default the GRAD n parameters are set to zero and all heterojunctions are abrupt It should also be noted that the crap parameter acts just like the other region geometry parameters in that later defined regions overlapping the graded part of the region will overlap the grading If in the previous example the grading had been applied tothe GaAs region it would be over lapped by the AlGaAs region This would have produced an abrupt interface A solution would be to limit y max in the AlGaAs region to 0 09 Care should always be taken to specify regions in the proper order to avoid such problems Al
345. point The accessing and running of examples for ATLAS are documented in the DeckBuiLp chapter of the VWF Interactive Tools manual It is recommended for all users to run at least one MIXEDMODE example provided on the distribution tape before trying their own simulations 10 2 SILVACO International MIXEDMODE General Syntax Rules The SPICE like part of any MIXEDMODE input file starts with the parameter Bgcrw The SPICE like part of the input file ends with END All parameters related to the device simulation models appear after the END statement The first non comment statement after initializing ATLAS go atlas has to be BEGIN The order of the following netlist and control statements is arbitrary but the last SPICE like statement has to be END Unlike the rest of ATLAS for the SPICE like statements the exact command has to be used unique abbreviations are not accepted Statements are not case sensitive There has to beat least one numerical ATLAS device A device within the netlist Comment characters are and but not All ATLAS statements specifying the parameters for the numerical device simulation have to be specified after END After all ATLAS statements the simulation has to be explicitly terminated quit go lt simulator gt These rules do not apply to the SET statement for parameterization of the input file since it is interpreted by DEckBuiLD only EXTRACT statements are als
346. pper limit of SILVACO International 3 13 ATLAS User s Manual Volume 1 the integration and specifies ratio of the increment added to the integral divided by the current value of the integral The default value of the INFINITY parameter is 0 001 Note To maintain self consistent results it is important that this model is implemented if the Concannon model is being used for the simulation of gate current Band to Band Tunneling If a sufficiently high electric field exists within a device local band bending may be sufficient to allow electrons to tunnel by internal field emission from the valence band into the conduction band An additional electron is therefore generated in the conduction band and a hole in the valence band This generation mechanism is implemented into the right hand side of the continuity equations The tunneling generation rateis 69 70 as 3 268 BB GAMMA BB B Gggr BB A E ex E E where E is the magnitude of an electric field and BB A BB B and BB GAMMA are user definable parameters In ATLAS there are three different sets of values that may be applied to the model parameters The model parmaeters can be set to the standard mode 69 by specifying BBr srp on the MODELS statement The parameter defaults for the standard model are as follows BB A 9 66e18 V cm BB B 3 0e BB GAMMA 2 0 The model parameters may also be set to the Klaassen model 70 by specifying BaT k1 on th
347. ps and m is the number of donor like traps The probability of occupation assumes that the capture cross sections are constant for all energies in a given band and follows the analysis developed by Simmons and Taylor 126 The probability of occupation is defined by the following equations for donor and acceptor like traps respectively 3 12 SILVACO International Physics V SIGN N 6 VA SIGN N SIGP p e VpSIGP p e P V SIGN N SIGP p e where sien and src arethe carrier capture cross sections for electrons and holes respectively v and Vp are the thermal velocities for electrons and holes and the electron and hole emission rates en and ep are defined by E LEVEL E DEGEN FAC V SIGN Njexp py 3 56 1 E E LEVEL p DEGEN FAC Vp SIGP eS ee 3 57 where E is the intrinsic Fermi level position E LeveL is the energy level in the bandgap of each discrete trap center and DEGEN Fac is the degeneracy factor of the trap center The latter term takes into account that spin degeneracy will exist that is the empty and full conditions of a flaw will normally have different spin and orbital degeneracy choices Table 3 5 User Specifiable Parameters for Equations 3 51 to 3 57 Statement Parameter Units TRAP E LEVEL ev TRAP DENSITY em TRAP DEGEN FAC TRAP SIGN cm TRAP SIGP cm
348. pter 3 a comprehensive set of physical models has already been described for silicon However it is known that for 111 V I VI and terniary compounds that special consideration are required such as for mole fraction dependence material properties etc Thefollowing sections will describe the material dependent physical models that have been implemented into BLAZE to account for these effects First a description of the common mobility model equations is given which are applicable to all materials unless otherwise stated in following material sections Following this are sections describing the physical models on a material per material basis For each material there are descriptions of the models for bandgap narrowing electron affinity density of states dielectric permittivity and low field mobility 5 14 SILVACO International BLAZE Common Physical Models Low Field Mobility Models The default low field mobility models used for most materials in BLAZE are given by the following ro TL Ho TL Ti TMUN wow sos Ti TMUP moe 556 5 45 5 46 Where T is the temperature in degrees Kelvin and the parameters MUN MUP TMUN and TMUP are user definable as shown in Table 5 1 Note All the mobility models described in Chapter 3 may also be used within BLAZE except for the TASCH model However all default coefficients exist only for Silicon and therefore are not suitable for compound materials
349. ption This is not a real circuit element This statement defines only the coupling between two inductors Kxxx specifies a name This parameter is not important and is used only to distinguish the statement It must begin with a K Lyyy specifies the first inductor element name It must begin with an L and match one of the inductor names from the circuit Lzzz specifies the second inductor element name It must begin with an L and match one of the inductor names from the circuit kval is the coefficient of mutual coupling which must be in the range O kval 1 The mutual inductance M will be determined from the relation M kval L1 L2 Example K1L22LLOAD 0 99 L Inductor Syntax Lxxx n n value Description L xxx specifies the inductor name It must begin with an L n n arethe positive and negative terminal node numbers value is the inductance in Henrys Example L2 2 3 2 5nH 10 16 SILVACO International MIXEDMODE M MOSFET Syntax Mxxx nd ng ns nb mname L al W val AD val AS val PD val PSzval NRD val NRS val Description Mxxx specifies the MOSFET element name It must begin with an M nd ng ns nb arethe drain gate source and bulk terminal nodes numbers respectivel y mname is the model name It must refer toa MOSFET model AD specifies the area of the drain AS specifies the area of the source NRD specifies the number of squares for drain resistance NRS speci
350. ption coefficient in the material that the ray is traversing The available photo current can be thought of as a measure of the rate of photo absorption in the device expressed as a current density This should be similar but somewhat less than the source photo current The losses are due to reflection and transmission of light out of the device structure Nr B Xi E I ic y wi P Qe dy 8 14 i21 Depending how the user wants to define it quantum efficiency can be readily calculated by dividing the current from one of the device electrodes by either the source photo current or the available photo current The definitions for source photo current and available photo current for multi spectral sources are given in Equations 8 15 and 8 16 Here the symbols have the same definitions as in Equations 8 13 and 8 14 but the first summation is taken over the number of descrete wavelengths N P is the relative intensity at the wavelength lambda N Bol 0E I q V PA 8 15 i 1 B Ny Ng PA I a Y PA de Wal P 0 e dy 8 16 O i l i l 8 8 SILVACO International Luminous Simulating Photodetectors Overview This section describes techniques to simulate photodetectors This section applies to the simulation of any of the following devices p n and p i n photodiodes avalanche photodiodes Schottky photodetectors CCDs MSMs photoconductors optical FETs and optically triggered power devices Defining Optica
351. r ad ye Da todo ad pde teh Meas 8 12 Integrated Recombination a ll O el e es AO e la Lea 8 12 Extrapolation from High Temperatures seein a dei 8 12 Numerical Solution Parameters isssssssssssse memes 0 13 Extracting Detection Efficiency inso eaim ce RT Deko ete A VUE fes aoa pde d 8 13 Obtaining Quantum Efficiency versus Bias 1 cece cece rr 8 14 Obtaining Transient Response to Optical Sources isses 8 14 Obtaining Frequency Response to Optical Sources 00ooccooocoocoor mnn 8 14 Obtaining Spatial Response alert o ie eol Leal la 8 15 Obtaining Spectral Response 0 cece ccc eI 8 15 Sim lating Solar Cells gt gt A en eae Bana ets eG Rees 8 16 Obtaining Open Circuit Voltage and Short Circuit Current isses 8 16 Simulating LEDS sirrini eco tr e a per ex LE A A AAA AAA 8 16 Xiv SILVACO International Table of Contents Chapter 9 Laser Gaine ca il Loop PEE OPE TI E ORE UE Er tad RO RR 9 1 hier mE 9 1 Physica Models 1c p e Abd 9 1 kcal OpticalG aNs caste deni ote dpt eee bI EEbRDUR Ob ME Retire robert tees ara fte Ea 9 2 SUUNMUATCC EMISSION ose 00 a oio ctos os usd pU Dos Fol a TM sie 9 4 Photon ate Equations A S Mate e S cas SNPRA CO ias 9 4 Solution Techniques lt lt seis ona uere A OH EIE AER RT TELA 9 6 Specifying Laser Simulation Problems ski ee ete ERE RR RE RR s 9 6 Numerical Parameters vasi os reu bot casted tied aa 9 7 Semiconductor Laser Simulation Techniques 0 0 cece ce
352. rameter list Junction Capacitor CJE VJE MJE FC CJC VJC MJC CJS VIS MJS XCJC Transition Time TF XTF ITF VTF PTF TR Temperature Effects XTB EG XTB BJT Model Parameters Table 10 4 Basic DC Model Parameters Parameter Description Units Default Area GEOM Substrate connection selector Sub SUBS strate connection selector vertical geometry lateral geometry Default 1 for NPN Default 2 for PNP IBC Reverse saturation current between A AO base and collector If IBC and IBE are both specified they are used instead of IS IBE Reverse saturation current between A AO base and emitter If IBC and IBE are both specified they are used instead of IS Is Transport saturation current A 1 0 10 18 BF Ideal maximum forward beta 100 NF Forward current emission coefficient 1 50 BR Ideal maximum reverse beta 1 0 NR Reverse current emission coefficient 1 0 Table 10 5 Low Current Beta Degradation Parameters Parameter Description Units Default Area ISE B E leakage saturation current A 0 NE B E leakage emission coefficient T4975 ISC B C leakage saturation current A 0 x NC B C leakage emission coefficient TRD 10 40 SILVACO International MIXEDMODE Table 10 6 Base Width Modulation Parameters Parameter Description Units Default Area VA F Forward early voltage V infinite VAR Reverse early voltage V in
353. rents are often around or below this level This means that the currents printed are subject to significant numerical noise and do not provide an accurate estimate of the device leakage currents Two ways of estimating reverse leakage current are available to the user Integrated Recombination From a theoretical standpoint the reverse behavior of diodes can be dominated by one of two effects diffusion currents in the neutral regions or recombination currents inside the depletion region ATLAS can provide insight into both of these contributing mechanisms To estimate recombination current use the MEASURE statement to calculate the integrated recombination rate The following statement can be used MEASURE U TOTAL When this statement is executed it prints out the total integrated recombination rate The user needs to multiply this value by the electron charge 1 0623 101 coulombs to obtain an estimate of the recombination current contribution to the reverse diode leakage current Extrapolation from High Temperatures The diffusion current contribution can be estimated by taking advantage of the non linear relationship between the diffusion current and temperature Referring to the expression for the Ideal Diode current given by Equation 8 17 the dominant temperature dependency arises from the variation of the intrinsic concentration qD Pno qD npo qV po ee PY N 1 En where npo and Pro are thermal equilib
354. rgy minimum is located at energies Ec and Ey respectively yields the following expressions for the electron and hole concentrations E E n Ncep 7 3 27 E E p Nyexp r 3 28 Nc and Ny are referred to as the effective density of states for electrons and holes and are given by 3 3 NAT 22 2m mekT Y TL X 2 NC 3 29 or n 506 3 3 2nmf kT Y T 2 SILVACO International 3 5 ATLAS User s Manual Volume 1 where NC300 and NV300 are user definable on the MATERIAL statement as shown in Table 3 1 Table 3 1 User Definable Parameters for the Density of States Statement Parameter Default Units MATERIAL NC300 2 8e19 cm MATERIAL NV300 2 8e19 cm Intrinsic Carrier Concentration Multiplying Equation 3 27 and 3 28 yields np n 3 31 where nieis the intrinsic carrier concentration and is given by E Die INcNvexp ser 3 32 and Eg E Ey is the band gap energy For intrinsic undoped material p n Equating 3 27 and 3 28 and solving for Ep yields E E kT N C V L V Er E QVi PEU mea infa 3 33 C where Ej is the Fermi level for intrinsic doped silicon and y is the intrinsic potential Equation 3 33 defines the intrinsic potential under non equilibrium conditions also As indicated previously for ATLAS the y used in Equation 3 1 is the intrinsic potential The electron and hole concentrations can be expressed
355. rier mobility reduction dueto the normal field is modeled as us the effective surface mobility us es ee for Vgs gt Vth 10 192 THETA v vth If VMAX is specified the degradation of mobility due to the lateral field and carrier velocity saturation is determine as us Uoff e for VMAX gt 0 10 193 ve else Ueff US 10 194 Channel Length Modulation For vds gt vdsat the channel length modulation factor is calculated The channel length reduction Al is determined depending on the value of vmax Al xd KAPPA vds vdsat 10 195 2 exp xd jet Ay lt P se a KAPPA xd vds vdsat 10 196 For VMAX gt 0 ep is the electric field at the pinch off point Its value is approximated by Spee vc vc vdsat 10s lg vdsat The current ids in saturation region is computed as ids ids Al 10 198 ES eff To prevent the denominator from going to zero the value of AI is limited by 2 Al d AT for A1 gt o5f 2 10 199 Subthreshold Current The subthreshold current region of operation is characterized by the fast surface state parameter urs The modified threshold voltage von is determined by 10 66 SILVACO International MIXEDMODE von vth fastfor NFS gt 0 where 1 2 x o os q NFS P GAMMA fs PHI vsb fn PHI vsb 10 200 COX 2 PHI vsb The current ids is given by ids Aids Von Vde Vsp SUR ENOTES for vos Ve 10 201 ids ids Vos Vde Vs
356. ristics being saved to this file is to use another LOG statement with either a different log filename or the parameter OFF Typically a separate log file should be used for each bias sweep For example separate log files are used for each gate bias in a MOS Id Vds simulation or each base current in a bipolar c Vce simulation These files are then overlaid in ToNYPLOr Log files contain only the terminal characteristics They are typically viewed in TonyPLot Parameter extraction on data in log files can be done in DEckBuiLD Log files cannot be loaded into ATLAS to re initialize the simulation Units Of Currents In Log files In general the units of current written into the log file and hence seen in TonyPLot is Amperes per micron This is because ATLAS is a two dimensional simulator It sets the third dimension or z direction to be one micron Thus if you compare ATLAS 2D simulation results for a MOSFET versus the measured data from a MOSFET of width 20 micron you need to multiply the current in the log file by 20 There are four exceptions nthe 3D modules of ATLAS thewidth is defined in the 3D structure and sothe units of the current are Amperes n MIXEDMODE the width of devices is set by the user so again the current is in Amperes When cylindrical coordinates are used the current written to the log file is integrated through the cylinder and is alsoin Amperes e When the WIDTH parameter on the MESH statement is use
357. rium minority carrier densities on either side of the junction This gives an exponential variation of the diffusion current with temperature as given in Equation 8 18 E V gy LM NN Je expert a i 8 18 This relation can be used to estimate the diffusion current contribution at the operating temperature The basic idea is to calculate the current at a high temperature where the problem of numerical precision does not arise and then scale the current to the operating temperature using Equation 8 12 For example if the device is to operate at 300K the temperature may be set to 450K using the TEMPERATURE parameter of the MODEL statement Any temperature dependence of the energy gap should be disabled by explicitly specifying the band gap using the EG300 parameter and setting 8 12 SILVACO International Luminous EGALPHA and EGBETA parameters to zero all on the MATERIAL statement The following statement illustrates this approach as it might apply to a silicon diode MODEL TEMPERATURE 450 MATERIAL EG300 1 12 EGALPHA 0 0 EGBETA 0 0 ATLAS can then be used to obtain the reverse bias current at the elevated temperature The following equation can be applied to obtain the depletion current contribution at the operating temperature qV E E exper l J J exp pot prt CIA 8 19 exper where J is the current measured at the elevated temper
358. rrier temperatures At the contacts Dirichlet boundary conditions are used for carrier temperatures Ta Tp T Elsewhere on the boundary the normal components of the energy fluxes vanish The boundary conditions for y n p are the same as for the drift diffusion model 3 30 SILVACO International Physics Physical Models Mobility Modeling Overview Electrons and holes are accelerated by electric fields but lose momentum as a result of various scattering processes These scattering mechanisms indude lattice vibrations phonons impurity ions other carriers surfaces and other material imperfections Since the effects of all of these microscopic phenomena are lumped into the macroscopic mobilities introduced by the transport equations these mobilities are therefore functions of the local electric field lattice temperature doping concentration and so on Mobility modeling is normally divided into i low field behaviour ii high field behavior iii bulk semiconductor regions and iv inversion layers The low elecric field behaviour has carriers almost in equilibrium with the lattice and the mobility has a characteristic low field value that is commonly denoted by the symbol uno po The value of this mobility is dependent upon phonon and impurity scattering Both of which act to decrease the low field mobility The high electric field behaviour shows that the carrier mobility declines with electric field because the
359. s ssssssssssss Hmmm 7 7 Chapter 8 Bill avc aa a A 8 1 Introd ction i sc ovre A 8 1 Simulation Method cose acts iacu os me aea EEEE 8 1 Ray TRACING y iori ads ide d baba St o cue 1d M eae ELLE frt D dot MM EAT 8 1 D amp fining the Incident BEAM osse a AAA a oda CV Kc E EO ERE ped 8 1 Ray Splitting at Imelda a ex E end EX d RR e ios 82 Reflection and Transmission peor va dista ofa aL es Otto bats E4ob ean poU ued Re pot 8 3 Anti Reflective Coatings a A da ASA 8 5 Light Absorption and Photogeneration ooooccccoccoccnnc Hn 8 6 Photogeneration on a Non uniform Mesh ssssssssss mn 8 7 Photogerieratiori dt Contacts viciosa ear RE RERO ORAT ac KORR oia 8 7 User Defined Arbitrary Photogeneration iisssssssssse mn 8 7 Photocurrent and Quantum Efficiency 0 isses 8 7 Simulating PIO D ASCO nt ts atc scd td a eai Sr sod dab i sot 8 9 OIM a ld e lA ed anal AC a des A A E 8 9 Defining Optical Sources iia do bd 8 9 Identifying an Optical Beam oi aoa brat soc Hoaiedonut ard qr bou p da ali drca ade t dat ted Berend 8 9 Origin P lane of the Beam 2 5 uu o os td ERA Ren 8 9 Reflections AA A E RS 8 9 Monochromatic or Multispectral Sources 8 10 Defining Optical Properties of Materials A a 8 10 Setting Single Values For The Refractive Index sssssssssss rarnana 8 11 Setting A Wavelength Dependent Refractive Index issssssssss tenet etter eens 8 11 Extracting Dark Ciaractensucs esses dd rper dre x oed ri
360. s Note The band offsets are always defined with reference to the conduction band Therefore if a specific valence band offset is required the appropriate conduction band offset should be calculated from the desired valence band offset and the materials bandgap SILVACO International 5 9 ATLAS User s Manual Volume 1 EXAMPLE 4 UMS scs A Metal Figure 5 5 Figure 5 5 details a heterostructure device consisting of two semiconductors with different bandgaps Ey and E and electron affinities x and x and a Schottky barrier For this example E lt E 2 and x2 es This example will first define the heterojunction band offsets and then the Schottky barrier height Schottky contact barrier heights are calculated by BLAZE using the metal work function and the semiconductor electron affinity as Dp On Xs 5 19 where op is the Schottky barrier height m is the work function of the metal and xs is the semiconductor electron affinity m is set using using the wonkruN parameter on the CONTACT statement Therefore the semiconductor electron affinity as modified or defined during the heterojunction alignment process plays an important role in determining the value of the metal workfunction needed to provide the desired barrier height Let s assume for this example that a Schottky barrier height of 0 2eV is desired and calculate the appropriate metal wor
361. s dc 1 will contain both structures the second one diode shifted downwards see Figure 10 2 This coordinate shift has to be accounted for eventually when extracting position dependent solution quantities or when defining spatially dependent properties with the c Interpreter SILVACO International 10 7 ATLAS User s Manual Volume 1 ATLAS Data from mas dc 1 ollector 3 Microns Figure 10 2 Display of a MIXEDMODE solution with two Numerical Devices Extraction of Results By default EXTRACT reads it s data from the currently opened log file when executed along with ATLAS Since the extraction of MIXEDMODE log files require a re initialization of ATLAS see Input Parsing EXTRACT has to be initialized explicitly with the correct name of the MIXEDMODE log file To extract voltages at specific nodes the syntax vcct node circuit node gt has to be used for extraction of circuit elements icct node circuit element gt Example specify log file LOG OUTFILE hallo Subsequent extraction from the transient log file is done with go atlas extract init inf hallo_tr log extract name t0 x val from curve time icct node Adio anode where y val 0 10 8 SILVACO International MIXEDMODE It extracts the time tO when the transient of the current from the anode electrode of the device adio in the circuit crosses zero For more details for the EXTRACT syntax refer to the Inter
362. s are evaluated locally at each point in the device When lattice heating is not solved for the models provide only global temperature dependence i e all points in the device are assumed to be at the specified temperature The non isothermal energy balance model uses the same carrier temperature dependencies of the mobility and impact ionization models as in the pure energy balance case but with coefficients that depend on the local lattice temperature mpact ionization coefficients depend on lattice temperature Almost all other models and coefficients depend on lattice temperature When lattice heating is used there is no point in specifying models that do not include temperature dependence For mobilities you should not specify conmoB instead you also specify ANALYTIC Or ARORA For impact ionization coefficients you should specify the seLBERHERR model GIGA can account for the temperature dependence of the minority carrier lifetimes for electrons and or holes The rr Taun electrons and 1 T TAUP holes parameters of the mMaTERIAL statement are used to select this model The model is turned on whenever the value of 1 T TAUN Or LT TAUP iS greater than O which is the default The temperature dependence of electron and hole lifetimes in the SRH recombination model has the form T LT TAUN Un ravno 355 6 16 T MLT TAUP Tp TAUPO 355 6 17 SILVACO International 6 7 UTMOST
363. s simple fast and easy to use for basic applications Its main application is to quickly provide initial solutions for complex models and circuits For large circuits a complete model should be used and all parameters should be specified to achieve maximum accuracy Depending on how many parameters are not specified the Gummel Poon model will decompose itself into a simpler variant of the Ebers M oll model Convergence SILVACO International 10 35 ATLAS User s Manual Volume 1 To achieve a stable convergence the model needs to be complete and accurate To improve the convergence accuracy and speed of the simulation non zero collector base and emitter resistances should be induded in the model When these resistances are not specified the junction currents are exponentially dependent on the collector base and emitter bias voltages When the bias voltages have no limiting factors an overflow of current is likely to occur Scaling Scaling of currents resistances or capacitances is controlled by the area control option This dimensionless parameter multiplies all currents and capacitors and divides all resistors The default value for area is 1 0 The DC model parameters rBC IBE IS ISE ISC IKF IKR and IRB for both vertical and lateral Bat transistors are scaled according to the following equations IBCeff area IBC 10 9 IBE sf area IBE 10 10 ISeff area IS 10 11 ISE off area ISE 10 12 ISCag are
364. s specified on the mopELs statement The default model parameters are tuned to describe the measured mobilities in silicon at 300K Users may modify model parameters using the moBILITY statement 1 The Watt model takes into consideration the following primary scattering mechanisms in the inversion layer 2 Phonon scattering which results primarily from the interaction between two dimensional inversion layer carriers and bulk phonons 3 Surface roughness scattering caused by the interaction between inversion layer carriers and deviations from ideal planarity at the interface Charged impurity scattering caused by the interaction between inversion layer carriers and ions located in the oxide at the interface or in the bulk The phonon and surface roughness components are functions of effective electric field The charged impurity component is a function of the channel doping density The effective mobilities for electrons and holes are given by Equations 3 189 and 3 190 1 MREFINWATT ETT MREF2N WATT E eff 5 1 MREF3NWATT 1 Ng 1 1 Mor n MREFIN WATTLE eff n ic 2N WATT 1 Ni ju 3N WATT y 1N WATT 3 189 SILVACO International ATLAS User s Manual Volume 1 3 190 1 1 1 a 1P WATT Hoff p MREFIP WATTE fc 1 1 AL2P WATT werd MREF2P WATT E rr p 1 1 1 1 AL3N WATT ns mj MREF3P WATT Ng Where Ng is the surface trapped charge density N is the inversion layer ch
365. s to be written to a file called name The ATLAS model solutions will be written to the file name and the circuit solution will be written to the file name cir These files can be used later for loading solutions to be used as an initial guess see LOAD statement master specifies that the internal states of all ATLAS models should be written during the simulation in standard structure format for future visualization using TonYPLoT These files with the base name mname will be written after the calculation of each bias point during DC simulation and after of each time step during transient simulation SILVACO International 10 23 ATLAS User s Manual Volume 1 The program will automatically add the following suffixes to mname During DC simulation dc number where number is the number of the DC point During transient simulation tr number where number is the number of the time step Example SAVE OUTFILE 2pdsave MASTER pd LOG LOG specifies the filename in which circuit voltages and currents will be saved Syntax LOG outfile lt filename gt Description outfile specifies the filename in which circuit voltages and currents are to be saved in standard structure format files These files will have the following names For steady state analysis filename dco 1 log filename dc 2 1og filename dc 3 log new file will be created for each DC statement For AC analysis filename ac 1 log For ne
366. scribed above This current will then be added to a segment on the electrode insulator boundary Two schemes have been implemented to find out to which segment this current should be added The default model that calculates which electrode segment receives the Fowler Nordheim current follows the path of the electric field vector at the semiconductor insulator interface The first electrode insulator segment that is found along this trajectory provided no other semiconductors or metals are found along the trajectory will receive the Fowler Nordheim current A second model may be chosen using the NEARFLG parameter of the MopEL statement In this case the electrode insulator segment found dosest to the semiconductor insulator segment will receive the Fowler Nordheim current The total current on the gate electrode is then the sum of the currents from all the individual segements around the electrode boundary Note Since Fowler Nordheim tunneling current is responsible for EPROM and EEPROM cell erasure this model should always be specified when performing erasure simulation It is also recommended that the band to band tunneling model is included if Fowler Norheim tunneling is being modelled Note When simulating EPROM erasure in a transient analysis with this model the floating contact charge becomes a function of the gate current In this case the total current flowing into the floating electrode is multiplied by the time step to calculate
367. see 4 3 5 1 Band Diagram of p n heterojunction sess 5 1 5 2 Band diagram of heterojunction with band offset ccc e eee e eee eee eee ene 5 3 5 3 Band diagram of three material system lowest Eg in center 00s c cece eee e eee eee 5 5 5 4 Band diagram of three material system lowest Eg notin center o oooooooommommmoo 5 7 5 5 Band diagram of heterojunction with Schottky contact ccseee eect eee eee eee eens 5 10 7 1 Syntax Guide to Define Two Tail States and Two Gaussian Distributions NGA and NDG are the integrated values of the Gaussian distributions Gaussians are entered on energies EGA and EGD respectively 0cceeee cece cece teen eee e eee eeeenee 7 8 9 1 Optical Beam Geometry cioe n me yeh nth n yes 9 2 9 2 Reflected and Transmitted Rays seseseeeeeeseeenenennnnnnnK ee 9 2 9 3 Angles of incidence reflection and transmission ccc eee eee eee eee eee eee 9 3 9 4 Single Layer AR Coating Under Normal Incidence 0 ccceee eee eee eee eee eee eeaee 9 6 10 1 Schematic of Primitive Example Circuit 10 5 10 2 Display of a MIXEDMODE solution with two Numerical Devices eese 10 8 10 3 Diode Equivalent Circuit ccc cece teen eee eee eee Hn 10 34 SILVACO International xix ATHENA User s Manual Volume 1 Figure e Page No Caption Title No 10 4 NPN BJT Current Convention PNP are opposite ccc eee
368. sic concentration Nije defined according to hi nvexo see 3 37 Bandgap narrowing effects in arras are enabled by specifying the scn parameter of the MODELS statement These effects may be described by an analytic expression relating the variation in bandgap AE q to the doping concentration N The expression used in ATLAS is from Slotboom 14 N 2 AE BGN E Ingeu N Mm BGN C 3 38 SILVACO International 3 7 ATLAS User s Manual Volume 1 Table 3 3 User Definable Parameters of Slotbooms Bandgap Narrowing Model Statement Parameter Defaults Units MATERIAL BGN E 6 92e 3 V MATERIAL BGN N 1 3e17 m MATERIAL BGN C 0 5 z The parameters BGN E BGN N and BGN c may be user defined on the MATERIAL statement and have the defaults shown in Table 3 3 Note The default values used in Table 3 3 have been modified from those used in the original Slotboom paper to values suggested by Klaassen 114 To return to the original Slotboom coefficients BGN E 9e 3 BGN N 1e17 and BGN C 0 5 the parameter BGN SLOTBOOM must be set on the MODELS statement in place of BGN The variation in bandgap is introduced to the other physical models by subtracting the result of Eq 3 38 from the bandgap Eg In addition an adjustment is also made to the electric field terms in the transport models as described earlier The adjustment takes the form gt KT E n v y q In Nie 3 39
369. source_name2 DEC OCT LIN start2 stop2 number_steps2 Description source name is the name of the independent voltage or current source to be swept source name2 is the name of the secondary sweep source start is the starting value of the sweep argument start2 is the start value of the secondary sweep source stop is the final value of the sweep argument stop2 is the final value of the secondary sweep source number steps is the number of steps of theinner sweep number steps2 is the number of steps of the secondary sweep DEC is the DC bias voltage or current sweep by decades OCT is the DC bias sweep by octaves LIN isa linear DC bias sweep This is the default 10 20 SILVACO International MIXEDMODE Several pc statements can be specified in a command file In this case they will be executed sequentially Before executing the first DC statement the program will simulate the circuit with the independent source values given in the description of those sources The DC statement is also often used to increment the values of independent voltage and current sources in a circuit to avoid convergence problems Examples DC VIN 0 5 0 25 DC IE 50 500 50 NET NET specifies that a network parameter extraction is to be performed Syntax NET inport outport DEC OCT LIN nump fstart fstop 20 INDIN RSIN INDOUT RSOUT CIN COUT Description inport is the input port description It should be in one of the
370. stem of equations is strongly coupled and has quadratic convergence The Newton method may however spend extra time solving for quantities which are essentially constant or weakly coupled N ewton also requires a more accurate initial guess to the problem to obtain convergence Thus a block method can provide for faster simulations times in these cases over Newton Gummel can often provide better initial guesses to problems It can be useful to start a solution with a few Gummel iterations to generate a better guess and then switch to Newton to complete the solution Specification of the solution method is carried out as follows METHOD GUMMEL BLOCK NEWTON The exact meaning of the statement depends upon the particular models it is applied to This will be discussed in the following sections Basic Drift Diffusion Calculations The isothermal drift diffusion model requires the solution of three equations for potential electron concentration and hole concentration Specifying GUMMEL or NEWTON alone will produce simple Gummel or Newton solutions as detailed above For almost all cases the Newton method is preferred and it is the default Specifying METHOD GUMMEL NEWTON will cause the solver to start with Gummel iterations and then switch to Newton if convergence is not achieved This is a very robust although more time consuming way of obtaining solutions for any device However this method is highly recommended
371. steps that you go through to run the program If you have used earlier versions of ATLAS you will find this chapter to be a useful overview of the new version and a source of useful hints and advice Note This chapter concentrates on the core functionality of ATLAS If you are primarily interested in the specialized capabilities of particular ATLAS products you should read this chapter first and then read the chapters that describe the ATLAS products you wish to use ATLAS Inputs and Outputs Figure 2 1 shows the types of information that flow in and out of ATLAS Most ATLAS simulations use two inputs a text file that contains commands for ATLAS to execute and a structure file that defines the structure that will be simulated ATLAS produces three types of output The run time output provides a guide to the progress of simulations running and is where error messages and warning messages appear Log files store all terminal voltages and currents from the device analysis and solution files store two and three dimensional data relating to the values of solution variables within the device for a single bias point Structure and Mesh Editor Runtime Output Structure Files ATHENA 5 Process Simulator ATLAS Device Simulator Command File Solution Files DeckBuild Run Time Environment Log Files Visualization Figure 2 1 ATLAS Inputs and Outputs SILVACO International 2 1 ATLAS User s Manual
372. stop Thus as in parametric testing a particular level can be defined and the simulation can be set to solve up to that point and no further Once the compliance limit is reached ATLAS simulates the next statement line in the command file The Curvetrace Capability The automatic curve tracing algorithm can be invoked to enable ATLAS to trace out complex IV curves Thealgorithm can automatically switch from voltage to current boundary conditions and vice versa A single SOLVE statement may be used to trace out complex IV curves such as breakdown curves and CMOS latch up including the snapback region and second breakdown The algorithm is based upon a dynamic load line approach For example typical curvetrace and solve statements to trace out an IV curve for the breakdown of a diode would look like CURVETRACE CONTR NAME cathode STEP INIT 0 5 NEXT RATIO 1 2 MINCUR 1e 12 END VAL 1e 3 CURR CONT SOLVE CURVETRACE The name of the electrode which is to be ramped is specified using CONTR NAME STEP INIT specifies the initial voltage step NExT RATIO Specifies the factor used to increase the voltage step in areas on the IV curve away from turning points wzxcun may be used to set a small current value above which the dynamic load line algorithm is activated Below the mincur level the srEP INIT and NEXT RATIO are used to determine the next solution bias END VAL is used to stop the tracing if the voltage or curr
373. structure file is to be used Lines 9 10 These set numerical options for the circuit simulation WRITE 10 specifies that every tenth timestep will be saved into the solution file specified on the SAVE statement Line 12 specifies a file generated by a previous MIXEDMODE simulation to be used as an initial guess to the voltage Line 13 14 specifies the output log and solution filenames These names are root names and extensions will be added automatically by the program Line 16 indicates the type of analysis required In this case it is a transient simulation lasting 2 microseconds with an initial timestep of 0 1 nanoseconds Line 18 indicates the end of the circuit description All following statements will be related to the ATLAS device Lines 20 22 To completely specify the simulation the physical models used by ATLAS must be identified Note that pevrcE AapropE must be specified for each line The vopEr statement is used to turn on the appropriate transport models This set includes conmob the concentration dependent mobility mode f1dmob the lateral electric field dependent mobility model consrh Shockley Read H all recombination using concentration dependent lifetimes auger recombination accounting for high level injection effects bgn band gap narrowing SILVACO International 10 11 ATLAS User s Manual Volume 1 The MATERIAL statement is used to o
374. surface hole concentrations The terms Neg and Peg are the equilibrium electron and hole concentrations assuming infinite surface recombination velocity y 6p Vapplied If Vsn and Vsp are not specified their values are calculated from Equations 3 110 and 3 111 ARICHN T Man AN 3 110 sn q Nc 2 ARICHP T Nep me 3 111 sp q Ny 3 24 SILVACO International Physics Table 3 12 User Specifiable Parameters for Equations 3 110 to 3 111 Statement Parameter Default Units MATERIAL ARICHN 110 A cm K MATERIAL ARICHP 30 A cm K where ARICHN and arIcHP are the effective Richardson constants for electrons and holes account of quantum mechanical reflections and tunneling Nc and Ny are the conduction and valence band density of states The parameters ARICHN and ARICHP are user definable as shown in Table 3 12 and Ncand Ny are functions of the lattice temperature T according to equations 3 29 and 3 30 The Schottky model also accounts for field dependent barrier lowering mechanisms These mechanisms are caused by image forces and possible static dipole layers at the metal semiconductor interface 13 If the barrier height is defined as Opn WORKFUN AFFINITY 3 112 E AFFINITY 2 WORKFUN 3 113 bp q the amount by which these barriers are lowered becomes 1 2 AQp le E ALPHA E 3 114 Table 3 13 User Specifiable Parameters for Equation 3 114 Statemen
375. system use the UNI X nohup command before the DeckBuild command line nohup deckbuild run ascii as input filename outfile output filename amp Running ATLAS inside Deckbuild Each ATLAS run inside DEcKBUILD should start with the line go atlas A single input file may contain several ATLAS runs each separated with a go atlas line Input files within DEckBuiLD can also contain runs from other programs such as ATHENA or DEvEpiT along with the ATLAS runs Running a given version number of ATLAS The go statement can be modified to provide parameters for the ATLAS run To run version 4 3 0 R the syntax is go atlas simflags V 4 3 0 R Starting Parallel ATLAS The P option is used to set the number of processors to use in a parallel ATLAS run If the number set by P is greater than the number of processors available or than the number of parallel thread licenses the number is automatically reduced to this cap number To run on 4 processors go atlas simflags V 4 3 2 C P 4 Batch Mode Without DeckBuild It is possible to run ATLAS outside the DEckBuiLD environment However this is not recommended by Silvaco Users who do not want the overhead of the DEckBuiLb window can use the No Windows Mode described above M any important features such as variable substitution automatic interfacing to process simulation and parameter extraction are not available outside the DEckBuiLp environment Torun ATLAS directly under U
376. t This parameter specifies the number of Eigen energies wavefunctions to be written Note The number of Eigen values solved is limited to a number of 2 less than the total number of grid points in the Y direction It should be noted that the self consistent solution of Schrodinger s equation with Poisson s equation does not allow for solutions of the electron and hole continuity equations in the current ATLAS version However non self consistent solutions can be obtained by setting the post scHRo parameter of the moDeLs statement These non self consistent solutions are obtained by solving Schrodinger s equation only after convergence is obtained In this manner Schrodinger soltuions can be obtained with the electron and hole continuity equations Similar results are saved to the structure file and the meaning of the EIGENS parameter of the output statement are the same In obtaining post processed PosT SCHRO solutions to Schrodinger s equation some assumption is made about the location of the electron quasi fermi level Two flags can be set on the mopeLs statement to vary the interpretation of the results These parameters are FIXED FERMI and CALC FERMI and have interpretations as outlined in Table 3 53 3 86 SILVACO International Physics Table 3 53 Interpretations of FIXED FERMI and CALC FERMI Parameters during Post Processed Schrodinger solution FALSE FALSE Quasi
377. t Parameter Units CONTACT ALPHA cm where E is the magnitude of the electric field at the interface and arpa is the linear dipole barrier lowering coefficient This barrier lowering coefficient is specified by the arrua parameter in the contact statement Typical values of amp may be seen in Note that the term with the square root dependence on electric field corresponds to the image force while the linear term corresponds to the dipole effect 13 Barrier lowering had been previously implemented in an earlier version of s Prsces 32 It has been reincorporated into ATLAS in a slightly different manner In ATLAS the Poisson equations are normally solved using the boundary condition Ys Wsy see Equation 3 107 If electric field is consistent with solved potentials effective surface potentials are computed as Vsett VsotAOp where is used for electrons and is used for holes SILVACO International 3 25 ATLAS User s Manual Volume 1 Continuity equations are then solved using Equations 3 108 and 3 109 as boundary conditions The variables ns and Neg see Equation 3 108 are replaced by Nee and negar Which are computed using Vseff The physical interpretation of this approach is that the Poisson equation is solved consistent with the charge but that electrons and holes use combined Poisson and image force potential Although the full barrier lowering term has been applied directly at the surfac
378. t always necessary to simulate using two carriers This is dueto the importance of minority carriers to device operation n certain cases non local carrier heating may be of importance for the accurate simulation of bipolar devices n these cases the energy balance model should be used To model non local carrier heating for electrons holes the HCTE EL HCTE HO parameters should be set on the MODEL statement For example the statement MODEL HCTE EL invokes the carrier heating equation for electrons Simulating Non Volatile Memory Technologies EEPROMs FLASH Memories As might be expected users wishing to simulate non volatile memory devices should first become familiar with the basics of MOSFET simulation described earlier in this chapter Defining Floating Gates To simulate non volatile memory technologies such as EEPROMs or FLASH EEPROMs it is necessary to specify one or more electrodes as floating gates This is done by setting the FLOATING parameter of the CONTACT statement For example CONTACT NAME fgate FLOATING This specifies that the electrode named fgate is simulated as a floating gate This means that the charge on the floating gate is calculated as the integral of the gate current at that gate during a transient simulation 4 6 SILVACO International S PISCES Modeling the correct coupling capacitance ratio between the floating gate and control gate often requires adding an
379. t may be used if the coordinates of a thermal contact coincide with the coordinates of an electrical contact In this case it is permissible to specify the location of the thermal contact by referring to the electrode number of the electrical contact For example the statement THERMCONTACT NUM 1 ELEC NUM 3 TEMP 400 6 6 SILVACO International GIGA specifies that thermal contact number 1 is located in the same position as electrode number 3 and that the contact temperature is 400K Table 6 4 User Specifiable Parameters for Equations 6 14 and 6 15 Statement Parameter Units HERMCONTAC TEMPER K HERMCONTAC ALPHA W cm K Representing a thermal environment in terms of thermal impedances leads to efficient solutions However thermal impedance representations are typically only approximations Detailed thermal modeling e g of the effect of heatsink design changes typically requires the use of detailed modeling of thermal regions with specified external ambient temperatures Note It is not possible to alter the value of a thermal resistor within a sequence of SOLVE statements Users should rerun the input file whenever a thermal resistor is changed Temperature Dependent Material Parameters GIGA automatically uses the built in temperature dependence of the physical models that are specified When lattice heating is specifed temperature dependent value
380. t model where the parameters Ta Tez Te3 Wer Wez and Waz in the MATERIAL Statement and activate the electron temperature electron energy dependent energy relaxation time using TAUR van in the vopErs statement Electron energy relaxation time will then be TRE T1 W lt W Te 4 TRE T2 W W TRE T3 W gt W where 3 W 5kT n For Wa WW the energy relaxation time varies quadratically between rRE T1 and TRI 3 98 E T2 For We2 lt W lt We3 energy relaxation time varies quadratically between TrRE T2 and TRE T3 The corresponding parameter for hole energy relaxation time in the mopELs statement is H TAUR VAR other parameters are listed in Table 3 9 The default values are TRE T1 TRE T2 TRE T3 TAUREL EL 3 99 TRH T1 TRH T2 TRH T3 TAUREL HO 3 100 Table 3 9 User Specifiable Parameters for Variable Energy Relaxation Time Statement Parameter Units MATERIAL RE T1 s MATERIAL RE T2 s MATERIAL RE T3 s SILVACO International 3 21 ATLAS User s Manual Volume 1 Table 3 9 User Specifiable Parameters for Variable Energy Relaxation Time Statement Parameter Units ATERIAL RE W1 eV ATERIAL TRE W2 eV ATERIAL RE W3 eV ATERIAL RH T1 S ATERIAL RH T2 S ATERIAL RH T3 S ATERIAL TRH W1 eV ATERIAL TRH W2 eV ATERIAL TRH W
381. t using the parameters vsatn and vsat n this case no temperature dependence is implemented Specifying the rLDmoB parameter on the vopELs statement invokes the field dependent mobility FLDMop should always be specified unless one of the inverson layer mobility models which incorporate their own dependence on the parallel field are specified It is possible to invoke a C interpreter function for the saturation velocities The parameter r vsATN and r vsarP of the MATERIAL statement may be set to provide the filenames of two text files containing the particular functions These functions allow the temperature dependence to be induded See Appendix A for more details SILVACO International 3 55 ATLAS User s Manual Volume 1 Table 3 33 User Definable Parameters in the Field Dependent Mobility Model Statement Parameter Default Units MOBILITY BETAN 2 0 MOBILITY BETAP 1 0 MOBILITY VSATN cm s MOBILITY VSATP cm s Note The above model which was derived for the drift diffusion approximation ensures that velocity overshoot can not occur To model velocity overshoot in silicon the energy balance model must be applied This model follows the above implementation but with the electric field term replaced by a new effective field calculated from the carrier temperature see the following section for more details Note BLAZE includes a different field dependent mobility model that does simul
382. taining Solutions Around The Breakdown Voltage 000ooocooocococc een ene ees 2 36 Using Current Boundary Conditions 6x bina chicas tin ot ure i eria oa 2 36 The Compliance Parameter i2 stes eek reno EXER CUR AY an XE RO SERE MER HER e s 2 37 ThesCur trace C AAD IY queer etur aac on eae otii tcu chen ale ont mu ed ee eats 2 37 viii SILVACO International Table of Contents Using DeckBuild To Specify SOLVE Statements 0 e eet e eee a 2 38 Interpreting The Resulls oia aane cac ned rini ox e OC anda ac de a c dax a Ea eee 2 38 Done MME MU cas eee Ser serrer err 6 a eae egre vertus ue pua aan as 2 38 log Files aspis Pao idein cete Med Mg d tcs p ee Ae SACR aa e Ae a ce eM PALA yn ir ra Id 2 40 Units Of Currents In Log files A sts ea A A sta acto Ma s dede che 2 40 Parameter Extraction In DeckBulld ini eR Cede a X Rc idv Rl o EROS Reda 2 40 Functions Hr TONY PIO una e mess ars at dos 2 41 AC Parameter EXITaCUOH anoano doe pac oa RO A AAA A Ra 2 42 UTMOST Interface a a OE ER btc ERU Poco da Sent diced 2 42 Solunom SA dieto x Sade a CR RA 2 42 interpreting Contour Plots siers Po eese oun a Roda di dat ER etie ne e ente acer de renta eu 2 43 Customizing Solution Files OUTPUT Statement 0 cc ccc cece e 2 43 Saving Quantities from the Structure ateach Bias Point PROBE statement oo o 2 43 Re initializing ATLAS ata Given Bias Point 2 44 Technology Specific Issues in ATLAS s 21d pisos des
383. tatement This is almost never done in practice Single Carrier Solutions Frequently for MOS simulation the user may choose to simulate only the majority carrier This will significantly speed up simulations where minority carrier effects can be neglected This can be done by turning off the minority carrier This is done using the ATLAS negation character and one of the carrier parameters ELECTRONS Or HOLES on the METHOD statement For example if the the user wanted to simulate electrons only you could specify METHOD CARRIERS 1 ELECTRONS or METHOD HOLES Single carrier solutions should not be performed where impact ionization any recombination mechanism lumped element boundaries or small signal AC analysis are involved Energy Balance Solutions As MOS devices become smaller and smaller non local carrier heating effects become important Accurate simulation of non local carrier heating effects can be simulated using the energy balance model EBM As a general rule the gate length can be used as a gauge to predict when non local effects are important Generally for drain currents energy balance should be applied for gate lengths less than 0 5 microns for substrate currents energy balance should be applied for gate lengths less than 1 0 micron To enable energy balance for electrons holes the HCTE EL or HCTE HO parameters should be set on the MODEL statement
384. tation into Recombination Models cc ccc cee cece eee e tent e 3 13 TPAD Assisted Tunneling ari eoo er be toc RO e HAC e vite ahead ane de 3 14 MANS Pocos sspe v baec detras a Dd 3 16 The Energy Balance Transport Model ooooocoooccocooccccnc or 3 17 OVEIVIGW lt x os arre ml Ex when tcu E E A a 3 17 The Energy Balance Equations 51 oppose xiv I4 sea aie Sete inne eee 3 17 Density ofS Late Sa decedit e uar io 3 20 Energy Density Loss Rates ds oio s Ion Inch cs e ola al eds a pls AE es tq LN 3 20 Temperature Dependence of Relaxation Times ssssssssssssse I 3 21 SILVACO International ix ATLAS User s Manual Volume 1 Energy Dependent Mobilities nre c ese hc o Ie e haec c eo Ro 3 22 Boundary PAYSICS sois taa Dri RR a Dr a ala E nci acd alada ps 3 23 ANI CR P EM M EE 3 23 OKMICC ONAC ee PUEDE m barbudo dating dal dos 3 23 Seno CODICIS oes eso AL eL ds od ae os oae LIU togae ld Fo ath 0 ha ace 3 24 Floating COMES d xod edis vos doi as 3 26 C rr nt Boundary CONGIDONS erar qu eate ne title died p I ER ut E Dita ERCCUR Ux dte te ata bre 3 26 INSUlAIAO CONOS Lp 3 27 Neumann Boundaries casos inet ud o a M rte ei EA M Eee 3 21 Lumped R L and C EJemeris z ss sod cerea aad wed oyu i p e A 3 28 Disttbuteg Cofitact Resistance a sie c obe aei a adas 3 29 Energy Balance Boundary Conditions urna sus scott afe er of ctr A Ote IDA ETE aet 3 30 lE hpc T 3 31 Mobility Modeling lt lt lt ative sted c
385. ted for biases higher than 11 0V using this syntax Although technology dependent it is common for the breakdown curve to be flat up to a voltage very dose to breakdown and then almost vertical The current changes by orders of magnitude for very small bias increments This produces some problems for ATLAS using the syntax described above First if the breakdown occurs at 11 5V there are no solutions for voltages greater than this value ATLAS is trying to ramp to 20 0V soit is likely that ATLAS will fail to converge at some point This is usually not a problem since by that point the breakdown voltage and curve have been obtained Above 11V bias step reduction will take place duetothe trap parameter ATLAS will continually try to increase the drain voltage above 11 5V and those points will fail to converge However it will solve points asymptotically approaching Vds 11 5V until the limit set by the waxrRAPs parameter is reached If the default of 4 traps is used it is clear that the minimum allowed voltage step is 1 0x 0 5 4 or 0 004V This is normally enough accuracy for determining the breakdown point However the simulation might not allow the current to reach a sufficiently high level before MAXTRAPS is needed Typically in device simulation the breakdown point is determined once the current is seen to increase above the flat pre breakdown leakage value by two orders of magnitude in a small voltage increment If users do wish to trace the full
386. tegrating the values of the spectral intensity file using a piece wise linear approximation Each integral is performed over the range between succesive midpoints In the preceeding example the integration for the sample at 0 45 would be performed over therange of 0 4 to 0 5 For either the monochromatic or multispectral sources the wavelength s and intensities can be uniformly scaled using the WAVEL SCALE parameter and the POWER SCALE parameter respectively These parameters are useful if the intensities or wavelengths are specified in units other than the default units Note The units of spectral intensity in the POWER FILE are W cm per um of wavelength The per micron of wavelength is important to remember when integrating the total power across the spectrum Defining Optical Properties of Materials For ray tracing the complex index of refraction of the various material regions in the structure must be spedified For many of the more common semiconductors and insulators there are built in tables of index versus wavelength For those materials lacking reasonable default complex index of refraction the user can specify the index 8 10 SILVACO International Luminous Note The parameter TNDEX CHECK can be added to any SOLVE statement to print out the refractive indices being used for that bias step Setting Single Values For The Refractive Index The parameters REAL INDEX and IMAG INDEX of the MATERIAL statement
387. tement STRUCTURE OUTFILE output filename at the end of the SSUPREM3 run In ATLAS the MASTER parameter of the doping statement specifies that a SSUPREM3 file will be read by ATLAS Since this file will usually contain all the dopants from the SSUPREM3 simulation the desired dopant type must also be specified The statement DOPING MASTER INFILE mydata dat BORON REGION 1 specifies that the boron profile from the file mydata dat should be imported and used in region 1 SSUPREM3 profiles are imported into ATLAS one at a timei e one doping statement is used for each profile or dopant The statements DOPING MASTER INFILE mydata dat BORON OUTFILE doping dat DOPING MASTER INFILE mydata dat ARSENIC X RIGHT 0 8 RATIO 0 75 DOPING MASTER INFILE mydata dat ARSENIC X LEFT 2 2 RATIO 0 75 offset the arsenic doping from boron to create a 2D doping profile from a single SSUPREM3 result It is advisable to include the OUTFILE parameter on the first doping statement to create a 2D doping file This file will be used in the next section to interpolate doping on a refined mesh after a REGRID It cannot be plotted in ToNvPLor The position parameters and RATIO LATERAL are used in the same manner as for analytical doping profiles to set the extent of the 1 D profile Remeshing Using The Command Language When specifying a structure using the command language it can be difficult to define a suitable grid
388. than for either MOS or bipolar technologies Mobility Klaassens model KLA is recommended to account for lattice scattering impurity scattering carrier carrier scattering and impurity dustering effects at high concentration The Shirahata mobility model SHI is needed to take into account surface scattering effects at the silicon oxide interface which is a function of the transverse electric field High electric field velocity saturation is modelled through the field dependent mobility model FLDMoB Model parameters may be tuned using the MOBILTY statement syntax Interface Charge n SOI transistors there exist two active silicon to oxide interfaces on the wafer The top interface under the top gate is similiar to MOS technology The bottom interface is quite different and typically contains significantly more charge Different interface charges may be set in SPISCES using the INTERFACE statement with region specific parameters Recombi nation To take account of recombination effects we recommend the use of the Shockley Read Hall sRH model This will simulate the leakage currents that exist due to thermal generation It may also be necessary to simulate the presence of interface traps at the silicon oxide interface Finally the direct recombination model AUGER should be turned on The parameters for both models may be tuned on the MOBILITY Statement Bandgap Narrowing This model BGN is necessary to correctl y model t
389. the MODELS statement The parameters of this model are specified in the moBILITY statement The default parameters are for silicon at T 300K Table 3 18 User Specifiable Parameters for Equations 3 121 and 3 122 Statement Parameter Default Units OBILITY U1N CAUG 55 24 cm2 V S OBILITY U1P CAUG 49 7 cm2 V S OBILITY U2N CAUG 1429 23 cm V S OBILITY U2P CAUG 479 37 cm V S OBILITY ALPHAN CAUG 0 0 unitless OBILITY ALPHAP CAUG 0 0 unitless OBILITY BETAN CAUG 2 3 unitless OBILITY BETAP CAUG 2 2 unitless OBILITY GAMMAN CAUG 3 8 unitless OBILITY GAMMAP CAUG 1337 unitless OBILITY DELTAN CAUG 0 73 unitless OBILITY DELTAP CAUG 0 70 unitless OBILITY NCRITN CAUG 1 072x10 7 em OBILITY NCRITP CAUG 1 606x10 7 em The Arora Model for Low Field Mobility Another analytic model for the doping and temperature dependence of the low field mobility is available in ATLAS This model which is dueto Arora et al 119 has the following form T BBETAN ARORA T ALPHAN ARORA MU2N ARORA 555 L 300 Hno MUIN ARORA 355 E e 3 123 F T GAMMAN ARORA NCRITN ARORA 505 T BETAP ARORA T ALPHAP ARORA MU2P ARORA s u MU1P ARORA sx 3 124 pO 300 v N T GAMMAP ARORA NCRITP ARORAP 505 This model is used if conmos and arora are specified on the mopELs statement The parameters of the model
390. the circuit element name in each device simulation statement even if there is only one A device in the circuit All statements specifying the device properties and models are just supplemented by the parameter DEVICE name where name is the circuit element in the netlist lt name gt will always begin with the letter A This makes it possible to define different material properties and model settings for different devices within the circuit It is also recommended to specify the REGION parameter referring to only one region in IMPACT MATERIAL and MODELS statements If the device consists of more than one region several statements with the same device parameters and different region parameters are recommended For example to specify the bipolar set of models to a device the syntax used might be MODEL DEVICE AGTO REGION 2 BIPOLAR PRINT Recommendations Input Parsing In regular ATLAS non MIXEDMODE simulations the input is interpreted line by line and each statement is executed immediately This is very useful and nicely supported by DeckBuild for the interactive development of the input Circuit simulations however require the complete input before any simulation can be performed As a consequence a the complete input is read and parsed before any simulation is initiated b an explicit termination of a simulation is required quit C all post processing extraction and plotting has
391. the emission and capture processes Ry and Ry take form E LEVEL EF R DENSITY v SIGN n 1 F F DEGEN FAC mer 5 3 72 L Rp 1 E E LEVEL A transient trap simulation using this model is more time consuming than using the static model but gives a much more accurate description of the device physics It may sometimes be acceptable to perform transient calculations using the static trap distribution and assume that traps reach equilibrium instantaneously If this is the case a flag rast on the TRap statement will neglect the trap rate equation from the simulation 3 16 SILVACO International Physics The Energy Balance Transport Model Overview The conventional drift diffusion model of charge transport neglects nonlocal transport effects such as velocity overshoot diffusion associated with the carrier temperature and the dependence of impact ionisation rates on carrier energy distributions These phenomena can have a significant effect on the terminal properties of submicron devices As a result ATLAS offers two nonlocal models of charge transport the energy balance and hydrodynamic models The energy balance model follows the derivation by Stratton 48 which is derived starting from the Boltzmann Transport Equation By applying certain assumptions this model decomposes into the hydrodynamic model The energy balance transport model adds continuity equations for the carrier temperatures and treats mobilities and
392. the hashed line in each column are the tolerances used When the symbol appears as the least significant digit in the number it means this error measure has met its tolerance After convergence is achieved ATLAS lists the results by electrode The column Va lists the voltage at the contact surface This will differ from the applied voltage if external resistors or the curvetracer are used All relevant current components are listed Here only electron hole conduction and total currents are given n other modes of simulation these columns may differ The output of AC analysis MixEpMope and 3D simulations differ from this standard ATLAS may produce a very large amount of run time output for complex simulations Run Time output may be saved to a file as shown in the Modes of Operation section of this chapter SILVACO International 2 39 ATLAS User s Manual Volume 1 Log Files Log files store the terminal characteristics calculated by ATLAS These are current and voltages for each electrode in DC simulations In transient simulations the time is stored and in AC simulations the small signal frequency and the conductances and capacitances are saved The statement LOG OUTF lt FILENAME gt is used to open a log file Terminal characteristics from all soLvE statements after the LOG statement are then saved to this file along with any results from the prope statement The only way to stop the terminal characte
393. the integral The default value of the INFINITY parameter is 0 001 The implementation of this model is similiar to that for Fowler Nordheim tunneling Each electrode insulator and insulator semiconductor interface is divided into discrete segments which are based upon the mesh For each insulator semiconductor segment the Fowler Nordheim current is calculated as described above This current will then be added to a segment on the electrode insulator boundary Two schemes have been implemented to find out to which segment this current should be added The default model that calculates which electrode segment receives the hot carrier injected current follows the path of the electric field vector at the semiconductor insulator interface The first electrode insulator segment that is found along this trajectory provided no other semiconductors or metals are found along the trajectory will receive the current A second model may be chosen using the NEARFLG parameter of the moDzLs statement In this case the electrode insulator segment found closest to the semiconductor insulator segment will receive the hot carrier injected current The total current on the gate electrode is then the sum of the currents from all the individual segements around the electrode boundary 3 82 SILVACO International Physics Note To maintain self consistent results it is important that this model is implemented if the Concannon model is
394. the mesh is specified every part of the mesh must be assigned to be a particular material type This is done with REGION statements REGION number lt integer gt lt material_type gt lt position parameters gt Region numbers must start at 1 and are increased for each subsequent region statement Up to 55 different regions are allowed in ATLAS A large number of materials is available If a composition dependent material type is defined the x and y composition fractions can also be specified on the REGION statement The position parameters are specified in microns using the X MIN X MAX Y MIN and Y MAX parameters If the position parameters of a new statement overlap those of a previous region statement the overlapped area is assigned as the material type of the new region Care must be taken to ensure that materials are assigned to all mesh points in the structure If this is not done error messages will appear and ATLAS will fail to run You can use the MATERIAL Statement to specify the material properties of the defined regions However the complete mesh and doping definition must be completed before any MATERIAL statements can be used The specification of material properties is described in the later section Specifying Material Properties 2 10 SILVACO International Getting Started with ATLAS Cylindrical Coordinates Cylindrical coordinates are often used when simulating discrete power devices In this
395. the semiconductor This allows the Schottky depletion region to be accurately simulated SILVACO International 2 17 ATLAS User s Manual Volume 1 Setting Current Boundary Conditions The CONTACT statement is also used to change an electrode from voltage control to current control Current controlled electrodes are useful when simulating devices where the current is highly sensitive to voltage or is a multivalued function of voltage e g post breakdown and when there is snap back The statement CONTACT NAME drain CURRENT changes the drain electrode to current control The BLOCK or NEWTON solution methods arequired for all simulations using a current boundary condition Defining External Resistors Capacitors or Inductors Lumped resistance capacitance and inductance connected to an electrode can be specified using the RESISTANCE CAPACITANCE and INDUCTANCE parameters on the contact statement The statement CONTACT NAME drain RESISTANCE 50 0 CAPACITANCE 20e 12 INDUCTANCE 1e 6 specifies a parallel resistor and capacitor of 50 ohms and 20 pF respectively in series with a 1 uH inductor Notethat in 2D simulations these passive element values are scaled by the width in thethird dimension Sincein 2D ATLAS assumes a lum width the resistance becomes 50 Q um Distributed contact resistance for an electrode can be specified using the CON RESIST parameter The statement CONTAC
396. til convergence is obtained or the maximum number of trap steps is exceeded The following is a typical fragment from an input file that ramps the oractor parameter from O to 1 model numcarr 1 output con band sol sol sol sol sol sol sol ve ve ve ve ve ve log out SO ve init factor 0 factor 0 factor 0 factor 0 factor 0 factor 1 quantum fldmob conmob srh print val band band param t quantum 0001 001 01 1 0 f test log lve vdrain 0 01 3 88 SILVACO International Physics Note A t quantum Switch on the output statement includes the quantum temperature across the semiconductor as discussed in the previous section Examples An example of the application of this model would be the quantization of the electrons in an AlGaAs GaAs HEMT structure The figures below illustrates such a structure as well as an outline through the channel for both a classical type structure and a quantum structure illustrating the concentration of electrons throughout the device Note The smoothing out of the sharp carrier peaks predicted by the quantum model which is characteristic of a quantized channel device Quantum Correction Models Hansch s Model The quantum mechanical correction as given by H ansch et al 124 is suitable for accurate simulation of the effects of quantum mechanical confinement near the gate oxide interface in MOSFETs This correction factor is
397. timate the rate of impact ionization This occurs because lucky electron theory inherently assumes that a carrier is traveling through a constant electric field E As a result it will predict a distance Ax qE over which the carrier will gain the ionization energy E However in real devices the electric field is never constant but is normally sharply peaked at metallurgical junctions Therefore as a carrier passes through the peaked electric field the lucky electron model will predict the ionization distance Ax to be too small As a result the ionization rate is overestimated The effect of this is that all the simulated breakdown voltages will be underestimated and substrate currents overestimated The energy balance model can be used to improve the simulation of impact ionization by implementing ionization models based upon the carrier temperature instead of the electric field The carrier temperature is a more meaningful basis as the velocity field relationship is more closely modeled This allows a nonlocal dependence on the electric field within the impact ionization model Energy balance models will therefore result in more accurate simulations of breakdown voltage and substrate current Two different impact ionization models have been implemented into ATLAS the first is based upon the classical Chynoweth relationship modified to include carrier temperature but the second is a more advanced non M axwellian approach based upon carrier temperat
398. tion below these values might be seen due to virtual memory constraints on your hardware For each simulation ATLAS dynamically allocates the virtual memory See the Silvaco Installation Guide for information about virtual memory requirements The virtual memory used by the program depends not only on the number of nodes but also on such items as the models used and the number of equations that are solved SILVACO International Getting Started with ATLAS Defining Material Parameters And Models After the mesh geometry and doping profiles are defined you can modify the characteristics of electrodes change the default material parameters and choose which physical models ATLAS will use during the device simulation These actions are accomplished using the CONTACT MATERIAL and MODELS statements respectively Impact ionization models can be enabled using the IMPACT statement and interface properties are set by the INTERFACE statement Many parameters are accessible through the Silvaco C Interpreter which is described in more detail in Appendix A This allows you to define customized equations for some models Specifying Contact Characteristics Workfunction for Gates or Schottky Contacts An electrode in contact with semiconductor material is assumed by default to be ohmic If a work function is defined the electrode is treated as a Schottky contact The CONTACT statement is used to specify the metal workfunction of
399. tional 10 37 ATLAS User s Manual Volume 1 wee 10 24 8H Svbc Vp 7 const BUBBTRATE RE EMITTER i CEXTERNAL Figure 10 5 BJT Equivalent Circuit for DC and Transient Analysis Bipolar models are selected by use of both the element and model statements The element statement references the model statement by the reference model name Where the region of operation is narrow the Ebers Moll models are sufficiently accurate The simplicity of the models makes computation efficient The model parameters are easy to understand and trace back to the process parameters The simplicity of the E bers Moll models comes at a price of many approximations Wide application ranges for example can create significant errors The Gummel P oon model extends over the boundaries of the E bers Moll model Many incorporated second order effects make the model more accurate over all four operating regions active reverse cutoff and saturated The Gummel Poon model is more difficult to understand because it is derived from a physical model If second order parameters are not specified by the user the model defaults to a simpler E bers M oll model The first contribution of the Gummel Poon model is the inclusion of the finite base collector and emitter resistances These resistances represent the ohmic resistance between the bonding wire or contact and the semiconductor material itself These resistances change the bias across the internal junct
400. tions describe the functional relationship between Ge mole fraction x and the SiGe material characteristics necessary for device simulation Bandgap Bandgap is one of the most fundamental parameters for any material For SiGe the dependence of the bandgap on the Ge mole fraction x composition is divided into ranges as follows Eg 1 08 x composition 0 945 1 08 0 245 5 79 for x lt 0 245 E g 0 945 x composition 0 245 0 87 0 945 0 35 0 245 5 80 or 0 245 lt x lt 0 35 Eg 0 87 x composition 0 35 0 78 0 87 0 5 0 35 5 81 for 0 35 lt x lt 0 5 Eg 0 78 x composition 0 5 0 72 0 78 0 6 0 5 5 82 for 0 5 lt x lt 0 6 Ey 0 72 x composition 0 6 0 69 0 72 0 675 0 6 5 83 for 0 6 lt x lt 0 675 Ey 0 69 x composition 0 675 0 67 0 69 0 735 0 675 5 84 for 0 675 lt x lt 0 735 E 0 67 5 85 g for 0 735 xx 1 The temperature dependence of the bandgap of SiGe is calculated the same as for Silicon using except that EGALPHA and EGBETA are a function of Ge mole fraction x as follows 2 2 T 300 L Eg TU E EGALPHA 307 aga 7 T EGBETA zum EGALPHA 4 73 x composition 4 77 4 73 x10 5 87 EGBETA 626 x composition 235 636 5 88 where Ey is dependent upon the mole fraction as above SILVACO International 5 25 ATLAS User s Manual Volume 1 Electron Affinity The elecr
401. tive One important exception is that commands described in this manual as being executed by DeckBuiLD rather than ATLAS are case sensitive This includes EXTRACT SET GO and SYSTEM n addition filenames for input and output under UNIX are case sensitive For any STATEMENT ATLAS may have four different types for the VALUE parameter real integer character and logical An example of a statement lineis DOPING UNIFORM N TYPE CONCENTRATION 1 0e16 REGION 1 OUTFILE my dop The statement is popinc All other items are parameters of the popinc statement uNIFORM and N TYPE are logical parameters Their presence on the line sets their values to true otherwise they take their default values usually false CONCENTRATION is a real parameter and takes floating point numbers as input values REGION is an integer parameter taking only integer numbers as input and OUTFILE is a character parameter type taking strings as input SILVACO International 2 5 ATLAS User s Manual Volume 1 B The statement keyword must come first but after this the order of parameters within a statement is not important It is only necessary to use enough letters of any parameter to distinguish it from any other parameter on the same statement Thus CONCENTRATION can be shortened to conc However REGION cannot be shortened to R since there is also a parameter RATIO associated with the DOPING statement
402. to apply different models to electrons and holes Meshing for MOS Devices In device simulation of MOS devices the key areas for a tight mesh are l very small vertical mesh spacing in the channel under the gate The exact size of mesh required depends on the transverse field or surface mobility model chosen See figure 4 1 for an example of the effect of mesh size on drain current 2 lateral mesh spacing along the length of the channel for deep sub micron devices This is required to get the correct source drain resistance and to resolve the channel pinch off point SILVACO International 4 1 ATLAS User s Manual Volume 1 3 lateral mesh at the drain channel junction for breakdown simulations This is required to resolve the peak of electric field carrier temperature and impact ionization 4 several vertical grid spacings inside the gate oxide when simulating gate field effects such as gate induced drain leakage GI DL or using any hot electron or tunneling gate current models The figures 4 1 and 4 2 show the effect of mesh size in the MOS channel on IV curves In Figure 4 1 the mesh density in the vertical direction is increased As the mesh density increases the resolution of the electric field and carrier concentration is improved This example uses the cvr mobility model Improvements in transverse electric field resolution lead to a reduced mobility in the channel and a stronger IV rolloff However Figure 4 2 shows the effe
403. to be done after re initializing ATLAS again No simulation is started until either a QUIT statement or a co statement is seen in the input file Post processing can be done by re starting ATLAS Scale and Suffixes In the MIXEDMODE part of the input numerical values of parameters are represented in standard floating point notation The scale suffix may be followed by a unit suffix e g A for Ampere V for Volt etc Use of a unit suffix can increase the clarity of a command file The unit suffix is ignored by the program The scale suffixes are Factor Name Suffix 10715 femto F 10712 pico P 1072 nano N 10 6 SILVACO International MIXEDMODE Factor Name Suffix 107 micro U 1073 milli M 10 kilo K 10 mega MG 10 giga G 1012 tera T Numerics MIXEDMODE solves circuit and device equations simultaneously using fully coupled algorithms This provides better convergence and requires less CPU time than alternative approaches The number of circuit variables is often small in comparison with the number of device variables In this case the CPU time required for simulation performed using MIXEDMODE does not increase drastically compared to the sum of the simulation times required for the individual numerical physically based devices MIXEDMODE uses the Newton algorithm for each bias point during steady state analysis and for each time ste
404. to the neighboring node inside the semiconductor This means for a uniform mesh and photogeneration rate if the photogeneration rate is 1 0x10 7 pairs cm s then the nodes at the contacts will have zero photogeneration and the next node into the semiconductor will have 2 0x10 7 pairs cm s User Defined Arbitrary Photogeneration An option exists for the user to define the photogeneration rate A C Interpreter function written into a text file can be supplied to the program using the F RADIATE parameter of the BEAM statement For example if a file myoptics c was developed using the template C interpreter functions supplied it can be referenced using BEAM NUM 1 F RADIATE myoptics c SOLVE B1 1 0 SOLVE B1 2 0 The file myoptics c returns a time and position dependent photogeneration rate to the program This returned value is mutiplied at every node point by the value of B1 With this option all other parameters of the BEAM statement and all the material refractive indices are overridden Photocurrent and Quantum Efficiency One of the important figures of merit of a photodetector is quantum efficiency Here quantum efficiency is defined as the ratio of the number of carriers detected at a given photodetector electrode SILVACO International 8 7 ATLAS User s Manual Volume 1 divided by the number of incident photons on the detector Ideally this ratio should 1 0 in detectors without any positive feed
405. twork parameter extraction filename net 1l log For transient analysis filename tr log To plot results of and entire steady state analysis simultaneously load all files related to steady state analysis into TONYPLOT Example LOG OUTFILE d 10 24 SILVACO International MIXEDMODE JC 1C sets specified node voltages during steady state simulation Syntax IC V I sVAL I Description This statement forces the specified node voltages to be set to specified values during steady state simulation These voltages are released when transient simulation begins Example JC V 1 10 NODESET NODESET sets initial values for circuit node voltages Syntax NODESET V I 2VAL 1 Description This statement specifies the initial values for circuit node voltages If a node voltage is not specified the program will try to find a solution using O as an initial guess for this node This statement can significantly reduce the CPU time needed to calculatethe initial condition Example NODESET V 1 50 V 2 249 4 V 3 210 V 5 1 NUMERIC NUMERIC specifies special numeric parameters for the circuit analysis Syntax NUMERIC lt lt parameters gt gt Parameter Type Default Units IMAXDC Integer 25 IMAXTR Integer 15 TOLDC Real 1 1074 TOLTR Real 1 1074 LTE Real Oral VMAX Real 5 10 V SILVACO International 10 25 ATLAS User s Manual Volume 1 Parameter Type Default Un
406. uations 3 147 and 3 148 Statement Parameter Default Units MOBILITY RA KLA 2 3670 MOBILITY R5 KLA 0 8552 MOBILITY R6 KLA 0 6478 The screening parameters P and Py used in the previous equations are given by FCW KLA FBH KLAT P _ gt 3 149 Pcw n PBH n FCW KLA FBH KLAT P 5 3 150 CW p BH p where the parameters fcyy and fgy are user specifiable model parameters as shown in Table 3 26 Table 3 26 User Specifiable Parameters for Equations 3 149 and 3 150 Statement Parameter Default Units MOBILITY FCW KLA 2 459 MOBILITY FBH KLA 3 828 Thefunction PgH n and Ppgp p are given by the following equations 136x079 me TL 2 BH n n mg 300 p 136x10Mpy TL v Ses BH p p Mo 500 where T is the temperature in degrees Kelvin Me Mp and my mo are the normalized carrier effective masses and n and p are the electron and hole concentrations in cm The functions Pcw n and Pew p of Eqs 3 149 and 3 150 are given by 4 3 97 x TE 3 153 ZaNp Pcw n 13 1 Ty s 3 97 x 10 oco 3 154 300 Z N Pcw p A 3 42 SILVACO International Physics where N p and NA arethe donor and acceptor concentrations in am T is the temperature in degrees Kelvin and Z and Z are clustering functions given by 1 quee NREFD KLA sm CD KLA mw D pct SRE FA KLA 2 a CA KLA a A where Np and Na are the donor and acceptor concentrations in cm and cp KLA
407. uicker and cheaper than performing experiments Second it provides information that is difficult or impossible to measure The drawbacks of simulation are that all the relevant physics must be incorporated into a simulator and numerical procedures must be implemented to solve the associated equations These tasks have been taken care of for users of ATLAS Users of physically based device simulation tools must specify the problem to be simulated Users of ATLAS specify device simulation problems by defining 1 The physical structure to be simulated 2 The physical models to be used 3 The bias conditions for which electrical characteristics are to be simulated The subsequent chapters of this manual describe how to perform these steps 1 6 SILVACO International Chapter 2 Getting Started with ATLAS Overview ATLAS is a physically based two and three dimensional device simulator It predicts the electrical behavior of specified semiconductor structures and provides insight into the internal physical mechanisms associated with device operation ATLAS can be used standalone or as a coretool in Silvaco s VIRTUAL WAFER FAB simulation environment In the sequence of predicting the impact of process variables on circuit performance device simulation fits between process simulation and SPICE model extraction If you are a new user this chapter will help you to start using ATLAS effectively The organization of topics parallels the
408. ular impulse in the intensity of the optical source is simulated The peak intensity is 1 0 and the impulse width is 2 ns The response of the device is simulated for an additional 18ns An initial time step of 10 ps is chosen for both parts of the impulse Obtaining Frequency Response to Optical Sources Small signal response to optical sources can also be simulated To obtain a solution for small signal response the SS PHOT parameter should be set in the SOLVE statement The BEAM parameter must also be asigned to the specific optical source index for small signal response of that source A single source small signal frequency can be specified using the FREQUENCY parameter The frequency can be varied within a single SOLVE statement using the NFSTEP and FSTEP parameters The NFSTEP indicates how many frequency steps are to be simulated while the rsTEP indicates the step size If the MULT F parameter is specified the start frequency is multiplied by the step size for the specified number of steps Otherwize the step size is added to the start frequency for the specified number of steps For example SOLVE SS PHOT BEAM 1 FREQUENCY 1e6 NFSTEP 5 FSTEP 10 MULT F will invoke solutions as optical frequencies at every decade from 1M Hz to 100 GHz If the small signal parameters are specified in the same SOLVE statement as a DC bias ramp the small signal response is extracted for each bias voltage for eac
409. ulated as in Equation 9 5 1 2 No 5 1 V GAMMA 9 5 where Ne and N are the material specific densities of states in the conduction band and the valence band respectively The second model is a simple empirical model that is defined by the following equation g x y GAIN00 GAININ n GAINIP p GAIN2NP np 9 6 GAINIMIN min n p Table 9 3 User Specifiable Parameters for Equation 9 6 Statement Parameter Default Units MATERIAL GAINOO 200 0 cm MATERIAL GAININ 0 cm SILVACO International 9 3 ATLAS User s Manual Volume 1 Table 9 3 User Specifiable Parameters for Equation 9 6 Statement Parameter Default Units MATERIAL GAIN2N 0 nd MATERIAL GAININP 0 en MATERIAL GAIN1MIN 3 0e 16 cm This model does not take into account frequency dependence and is valid only for the lasing frequency It can not be used for calculations that involve multiple longitudinal modes Stimulated Emission Carrier recombination due to stimulated light emission is modeled as follows C 2 Ruy A pas nere EG Y Sm ds m where Ra is the recombination rate due to stimulated light emission LAs NEFF is the group effective refractive index and S is the photon density This subscript m in this and all subsequent equations refers to a modal quantity for example Sm in Equation 9 7 is the photon density for mode
410. umerical Analysis section SOI Physical Phenomena The physical models and the numerical schemes described above should allow S PISCES to study all the important SOI phenomena These include full or partial depletion effects threshold voltage subthreshold slopes front to back gate coupling effects leakage current analysis high frequency analysis device breakdown snapback effects the kink effect in the output I ds Vds characteristics negative differential resistance SILVACO International 4 9 ATLAS User s Manual Volume 1 This page intentionally left blank 4 10 SILVACO International Chapter 5 BLAZE Introduction Before continuing to the sections that follow you should be familiar with ATLAS If not read Chapter 2 of this manual before proceeding with this chapter BLAZE is a general purpose 2 D device simulator for III V II VI materials and devices with position dependent band structure i e heterojunctions BLAZE accounts for the effects of positionally dependent band structure by modifications to the charge transport equations BLAZE is applicable to a broad range of devices including HBTs HEMTs LEDs heterojunction photodetectors APDs solar cells etc and heterojunction diodes This chapter is composed of several sections The Basic H eterojuction Definitions section diagrams the basic heterojunction band parameters and indudes a section on heterojunction alignment
411. ures 3 70 SILVACO International Physics When the energy balance transport model is applied only two impact ionization models are available the Toyabe model and the Concannon model Toyabe Impact lonization Model Thetemperature dependent impact ionization model is founded on the Sel berherr model and is similar to that suggested by Toyabe 5 The carrier temperature is used to calculate an effective electric field based upon the homogeneous temperature field relation To maintain self consistency within the energy balance model this is the same relationship used for the effective electric field within the carrier temperature dependent mobility This model is the default model for impact ionization and is activated with the TOYABE or SELB parameters on the impact statement The ionization rates now have the form an aN ep e 3 256 eff n BP ap APexp p 3 257 eff p where the model parameters an AP BN and sr are user definable on the impact statement and have the default values shown in Table 3 42 The effective electric field is calculated according to 3 KT E eff n 2QLREL EL 3 258 3 KT Eett p 2qLREL HO 3 259 where the energy relaxation lengths LREL L and LREL HO may be explicitly defined on the Impact statement or may be calculated according to p LREL EL VSATN X TAUSN 3 260 LREL HO VSATP X TAUSP 3 261 where vsarN and vsatp are the saturation vel
412. ut file separated by theline go atlas Similarly there is no need to separate process and device simulation runs of Silvaco products into separate input files A single file containing ATHENA and ATLAS syntax is permitted in DECKBUILD e the interface from process to device simulation is handled though a single file format compatible with other programs The file read by ATLAS is the default output file format of ATHENA No special file format for the interface is required when defining a grid structure within ATLAS the NODE and LOCATION syntax to define exact grid line numbers in X and Y is not recommended A more reliable and easier to use syntax using LOCATION and SPACING is available e use of the REGRID command is not recommended due to the creation of obtuse triangles A standalone program DevEbiT can be used as a grid pre processor for ATLAS all numerical method selection commands and parameters are on the METHOD statement The SYMBOLIC statement is not used Typically SYMBOLIC and METHOD Were used as a coupled pair of statements and it is more convienient to use a single statement Most of the old parameters of the SYMBOLIC statement have the same meaning and names despite this move to a single statement One notable change in ATLAS is that numerical methods can be combined together There is a separate section later in this chapter concerning translation of PISCES II numerics statements e various general purpose commands are actually
413. ve and negative controlling node numbers gain is the voltage gain Thelinear voltage controlled voltage source is characterized by the equation v v n gain v nc nc Example ER456755 F Linear current controlled current source Syntax Fxxx n n vcontrolname gain Description F xxx specifies the name of the linear current controlled current source It must begin with an F n n arethe positive and negative terminal node numbers A positive current flows from the node n through the source to the node n vcontrolname specifies the name of the voltage source through which the controlling current flows The direction of positive controlling current flow is from the positive node through the source to the negative node of vcontrolname gain specifies the current gain The linear current controlled current source is characterized by the equation i n n gain i vcontrolname Example F1245VIN 0 1 10 14 SILVACO International MIXEDMODE G Linear voltage controlled current source Syntax GXXX mt n Net nc trcon Description Gxxx specifies the name of the linear voltage controlled current source It must begin with a G n n arethe positive and negative terminal node numbers A positive current flows from the node n through the source to the node n nc nc arethe positive and negative controlling node numbers trcon is the transconductance in 1 Ohms Thelinear voltage controll
414. verride default material parameters In this case the carrier recombi nation fixed lifetimes are set Finally the Selberherr impact ionization model is enabled using the IMPACT statement with the SELB option Line 24 The METHOD statement specifies numerical options for the device simulation The METHOD statement must come after all other device simulation statements Line 26 The command GO ATLAS or a QUIT statement is needed to initiate simulation Since a plot of the final log file is desired the Go ATLAS option is used to restart ATLAS after the end of the MIXEDMODE simulation Line 27 The TONYPLOT command is used to plot the resulting log file MIXEDMODE Syntax This section is split into two parts circuit element statements to describe the netlist control and analysis statements Circuit Element Statements A ATLAS device to be simulated using device simulation Syntax Axxx nl namel n2 name2 n3 name3 infile filename width val Description This statement defines a device to be represented by a numerical ATLAS model The device description with all necessary information geometry mesh doping models electrode names etc must be available in a standard structure file prior to starting a MIXEDMODE simulation Axxx specifies the name of the element It must begin with an A n1 namel specifies the circuit node number to which the ATLAS device electrode with the name namel is connected The A
415. version linear region For vgs gt von and vds vdsat 10 225 E vdsat vds 7 cgd 2 3 cap bs User Defined Two Terminal Elements Overview MIXEDMODE users who have acquired the C interpreter can define their own two terminal elements using the B statement and a function written in C that defines the behavior of the element User Defined Model A user defined model is specified by defining The dependencies of the device terminal current on the terminal voltages 10 68 SILVACO International MIXEDMODE The derivatives of the terminal current with respect to the terminal voltages The device current I is described by the following equation FIU F200 77 10 226 where U is the device voltage t is time and F1 and F2 are functions that determine the behavior of the device The first term on the right hand side describes the DC current and the second term describes capacitive current Thefollowing four functions are specified by the user 1 F1 U t the DC current 2 F2 U t the capacitance 3 dF 1 U t dU the DC differential conductance 4 Q the charge associated with F 2 U t To define the element the user prepares a text filethat contains an appropriate function written in C A template for this user defined function is shown below int udef v temp ktq time curr didv cap charge double v double ktq double time double curr double didv double cap d
416. w field mobility has been user defined then it is important to also define this value inside the Shirahata model with the parametes MUON sHI and MUOP sHI On the MOBILITY statement Parallel Electric Field Dependent Mobility As carriers are accelerated in an electric field their velocity will begin to saturate at high enough electric fields This effect has to be accounted for by a reduction of the effective mobility since the magnitude of the drift velocity is the product of the mobility and the electric field component in the direction of the current flow The following Caughey and Thomas expression 22 is used to implement a field dependent mobility that provides a smooth transition between low field and high field behavior 1 BETAN u E Hno Ano E BETAN 3 197 1 vsarn LI 1 BETAP Hp E Hpo oy E BETAP 3 198 1 vdATP where E is the parallel electric field and uno and upo are the low field electron and hole mobilities respectively The low field mobilities are either set explicitly on the moB111TY statement or calculated by one of the low field mobility models The model parameters BETAN and BETAP are user definable on the MoprLity statement and have the default values shown in Table 3 35 The saturation velocities are calculated by default from the temperature dependent model 13 2 4x 10 VSATN VSATP 3 199 T 4 0 8 exp s but can be set to constant values on themoB111TY statemen
417. ween two different materials the difference between the normal components of the respective electric displacements must be equal to any surface charge accordi ng to A e Vy e Vy pg 3 116 where n is the unit normal vector e and e are the permittivities of the materials on either side of the interface and ps is the sheet charge at the interface SILVACO International 3 27 ATLAS User s Manual Volume 1 Lumped R L and C Elements ATLAS supports some simple configurations of lumped elements These are indicated in Figure 3 2 Vapp ATLAS Device Figure 3 2 The lumped elements supported by ATLAS Lumped elements can be extremely useful when simulating CMOS or MOSFET structures For example the p tub contact in the CMOS cross section might betens or hundreds of microns away from the active area of an embedded vertical npn bipolar transistor which may only be 10 20 um on a side If the whole structure were simulated a tremendous number of grid points probably more than half are essentially wasted in accounting for a purely resistive region of the device In the case of a MOSFET substrate you would not want to include grid points all the way to the back side of a wafer In either of these cases a simple lumped resistance can be substituted Table 3 14 User Specifiable Parameters for Figure 3 1 Symbol Statement Parameter Units E CONTAC CAPACITANCE F pm R CONTAC RESISTANCE Oum L C
418. with the atoms of the crystal In order to acquire sufficient energy two principle conditions must be met e the electric field must be sufficiently high the distance between the collisions of the free carrier must be enough to allow acceleration to a sufficiently high velocity In other words the carrier must gain the ionisation energy E between collisions If the generation rate of these free carriers is sufficiently high this process may eventually lead to avalanche breakdown The general impact ionisation process can be described by the equation G O p OJ p 9 299 where G is the total generation rate of electron hole pairs n are the ionisation coefficient for electrons and holes and J pp are their current densities The ionisation coefficient represents the 3 66 SILVACO International Physics number of electron hole pairs generated by a carrier per unit distance travelled The accurate calculation of this parameter has been the subject of much research work as it is vital if the effects related to impact ionization such as substrate current and device breakdown are to be simulated These models may be classified into two main types local and nonlocal models The former assume that ionization at any particular point within the device is a function only of the electric field at that position Nonlocal models on the other hand perform a more rigorous approach by taking into account the energy that the carrier gains Loc
419. y the normal components of the energy fluxes vanish EL electron Hot carrier transport equations are activated by the mopELs statement parameters HCTE temperature HCTE Ho hole temperature and HcTE both carrier temperatures SILVACO International 3 19 ATLAS User s Manual Volume 1 Density of States The calculation of the effective density of states is modified for the energy balance model The electron and hole temperatures replace the lattice temperature in Equations 3 29 and 3 30 i e 3 x a 3 21me kT 2 Ts 2 No or 505 N 300 3 92 i 3 21M KT 2 To Y Ny me c i 503 N 300 3 93 Energy Density Loss Rates The energy density loss rates define physical mechanisms by which carriers exchange energy with the surrounding lattice environment These mechanisms include carrier heating with increasing lattice temperature as well as energy exchange through recombination processes SRH and Auger and generation processes impact ionization If the net generation recombination rate is written in the form A A U Ren Rp RB Gn Gp 3 94 where Rar is the SRH recombination rate R are RC Auger recombination rates related to electrons and holes Gn and Gy are impact ionization rates then the energy density loss rates in equations 3 74 and 3 77 can be written in the following form Wn 5 exuREL EL 2K n n RsrH Eg G5 Ro 8 95 3 K Tg Ti 3 A Wo 5 P zaUREL Ho 2K T
420. yntax METHOD TRAP This is enabled by default Its effect is to reduce the bias step if convergence problems are detected Consider the example from the previous section SOLVE INIT SOLVE VDRAIN 2 0 SILVACO International 2 33 ATLAS User s Manual Volume 1 f the second SOLVE statement does not converge TRAP will automatically cut the bias step in half and try to obtain a solution for Vd 1 0V If this solution does not converge the bias stepwill be halved again to solve for Vd 0 5V This procedure is repeated up to a maximum number of tries set by the METHOD parameter MAXTRAPS Once convergence is obtained the bias steps are increased again to solve up to 2 0V The default for MAXTRAPS is four and it is not recommended to increase it since changing the syntax to use smaller bias steps is generally much faster This trap facility is very useful during bias ramps in overcoming convergence difficulties around transition points such as the threshold voltage Consider the following syntax used to extract a MOSFET Id Vgs curve SOLVE VGATE 0 0 VSTEP 0 2 VFINAL 5 0 NAME gate Assume the threshold voltage for the device being simulated is 0 7V and that ATLAS has solved for the gate voltages up to 0 6V The next solution at 0 8V might not converge at first This is because the initial guess was formed from the two sub threshold results at Vgs 0 4V and 0 6V and the solution has now become non linear The trap

ATLAS User's Manual

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