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1. e n p Nf V Un VO PVT R 6 1 V us V PVT R P is the electric polarization due to e g piezoelectric effects and R is the net recombi nation rate ie recombination rate minus generation rate P and P are the electron and hole thermoelectric power respectively The models for the mobilities and the net recombination rates can be specified in the physical model sections as described in the following 6 2 Plot variables See tables 6 1 6 2 and 6 3 6 3 Models section The Models section looks as given in Listing 1 51 52CHAPTER 6 DRIFT DIFFUSION SIMULATION OF ELECTRONS AND HOLES model driftdiffusion 1 options simulation_name whatever_you_want physical_regions 2 3 4 physical_model recombination model model_to_be_used physical_model electron_mobility model model_to_be_used J physical_model hole_mobility model model_to_be_used J physical_model thermoelectric_power model model_to_be_used Listing 1 Models section for drift diffusion 6 3 MODELS SECTION Nodal quantities 53 Ec EcO Ev EvO Eg QFermi e QFermi h ElPotential eDensity hDensity eMob hMob Nd Na charge density Pn Pp NetRecombination Conduction band edge Conduction band edge Valence band edge without electric potential Valence band edge without electric potential Band gap Electro chemical potential of electrons Electro chem
2. If the spectral_shift is not defined then it will be calculated internally from the band edges For the iterative solvers the important parameters that may significantly change the performance are the Krylov subspace method type and the preconditioner type The Krylov method is defined as follows Esp type bcgsl gmres begs cg richardson preonly 8 3 PHYSICAL MODELS PARAMETERS 73 The preconditioner type is defined as follows pc_type cholesky jacobi ilu composite Other options e r periodicity true false e y periodicity true false e z periodicity true false e number_of_eigenstates number of eigenstates to be computed 8 2 2 Schr dinger equation parameters e particle el hl Y specifies a particle type according to each the eigenvalues are sorted e strain model name name of the simulation that can provide elastic strain e poisson model name name of the simulation that can provide electric and elec trochemical potential e heat model name of the simulation that can provide e relative density tolerance relative tolerance for charge density calculation e initial eigenstates number initial eigenstates number for charge density calcula tion e convergent density true false if true than number of eigenstates will be increased in oder to reach convergent density e cigen number increase factor factor to increase eigenvalues number for the nex
3. The generated Output files are 21 driftdiffusion materials vtk information about the material regions of the device driftdiffusion nodal vtk output for the nodal quantities which have been calcu lated e g conduction and valence bands quasi fermi levels electron and hole density and mobility driftdiffusion elemental vtk output for the elemental quantities e g electric field current density sweep 2 driftdiffusion Vg 0 000 Vd dat and similar for all the Vg steps drain current characteristics for each Vg bias 22 CHAPTER 3 GETTING STARTED 2D Chapter 4 Input for TiberCAD Input for TrBERCAD is composed by an input file e g input tib and a mesh file gen erated by a mesher software as for now mesh files from GMSH msh v 1 and v 2 0 and from ISE TCAD grd are supported Be sure that the material files are in the correct directory as specified in 4 7 To run the program type tibercad input file name 4 1 Description of Input file structure A valid input file for TIBERCAD is a text file with the structure described in the following In the whole input file everything following a Z is considered as a comment and is disregarded blank lines can be present anywhere and are disregarded too Input file is composed by several sections each section begins with a section name preceded by e g Physics A section is enclosed between 7 and brackets and is possibly composed de pendin
4. hl model kp k p for valence band Ep model 6x6 Definition of model indipendent parameters of the Simulation Simulation 1 searchpath materials mesh units 1e 9 dnm dimension 1 meshfile test msh temperature 300 solve strain driftdiffusion quantum electrons quantum holes 44 CHAPTER 4 INPUT FOR TIBERCAD resultpath output plot Ec Ev QFermi e QFermi h EField eDensity hDensity eCurrent hCurrent Current NetRecombination eMob hMob T strain polarization xEffPot xDensity xMob ExcitonRecombination EigenFunctions EigenEnergy EnergyLevels xCurrent output format grace Chapter 5 Simulation of strain 5 1 Theory The theoretical model of strain simulation can be found in Refs 1 2 The code can compute elastic deformations in a heterostructure and can calculate the deformed shape of the structure The heterostructure can be either grown on a substrate or not External pressure may be applied to a structure as well 5 2 Models section parameters The Models section looks like follows model macrostrain options 1 simulation name strain in transistor physical regions 2 3 4 There are three possible kinds of boundary conditions The mandatory keyword type substrate pressure extended material specifies the boundary condition type 5 2 1 Substrate boundary condition In this case the boundary condition region is the boundary betw
5. No AN T To A T To 6 10 The parameters are given in table 6 7 parameter electrons holes Amin mumin e mumin h Aq mud e mud h AN NO e NO h Aa a_e a_h Am am_e am_h aq ad e ad h QN an_e an_h Qa aa_e aa_h Table 6 7 Data file parameters for the mobility model by Arora Field dependent mobility model Currently one mobility model depending on the modulus of the electric field is imple mented identifier field dependent It is based on the Caughey Thomas model refined by Canali 6 Hlow field 1 B 1 s B By T To is the modulus of the electric field Wise Geld is the low field mobility For the latter one can specify the model to be used using the parameter lowfield model As default the doping dependent model is used There are two models for vsat identified with Vsat Formula 1 and 2 Formula 1 reads 6 11 with Usat Usato T To 7 6 3 MODELS SECTION 59 Formula 2 reads Vsat max Ausat Bussi T To aun The parameters for the field dependent mobility model are summarized in table 6 8 parameter electrons holes Bo beta0 e beta0 h b betaexp_e betaexp h Usat 0 vsatO e vsatO h y vsatexp_e vsatexp_h A vsat e A vsat h Basat B vsat e B vsat h Umnin vsat min e vsat min h Table 6 8 Data file parameters for the mobility model by Arora 6 3 4 Boundary conditions Boundary conditions are implement
6. H Tiber cluster to be used in Models section Cluster Quantum 1 1 mesh regions 3 4 5 Definition of the description scale only for not Continuous Media regions Syntax level scale cluster level Atomistic physical_regions list Tiber_region Tiber_cluster Scale section is optional Scale Atomistic TB 1 physical regions barrier 1 QWell barrier 2 38 Definition of Simulation Models Atomistic TB 2 physical regions Models d model driftdiffusion options 1 simulation name driftdiffusion physical regions all physical model recombination model srh physical_model recombination model direct CHAPTER 4 INPUT FOR TIBERCAD and associated Boundary Conditions 49 EXAMPLE OF INPUT FILE C 1 1e 8 BC Regions 1 BC Region cathode d BC reg numb 1 type ohmic voltage 0 0 BC Region anode 1 BC reg numb 2 type ohmic voltage 0 0 model macrostrain 1 options 1 simulation name strain physical regions all BC Regions 39 40 CHAPTER 4 INPUT FOR TIBERCAD 1 BC Region substr 1 BC reg numb 1 type substrate material GaN structure wz y growth direction 1 0 1 0 z growth direction 1 2 1 0 x growth direction 0 0 0 1 model efaschroedinger options d simulation name quantum electr
7. density over the contact surface lt rstf gt use the Ramo Shockley test functions gives better results Local scaling apply a local scaling scheme which leads to better scaled matrices true or false exact newton use exact or approximate without some parts in the jacobian Newton true or false the default is given in brackets Table 6 11 Parameters for the PETSc nonlinear solver the PETSc implementation petsc and the TIBERCAD implementation tiber of line search When using the TiBERCAD nonlinear solver one can additionally chose between the PETSc petsc or PARDISO pardiso linear solvers The possible combinations are nonlinear solver petsc Or nonlinear solver tiber linear solver petsc pardiso 6 5 1 Parameters for PETSc solvers Tables 6 12 and 6 13 list all solver parameters significant for the PETSc linear and nonlinear solvers more detailed description of the most important parameters follows The ksp type specifies the type of Krylov subspace method to be used The mostly used methods are 6 5 SOLVER SECTION 63 keyword description default nonlin rel tol relative tolerance for the residual 5 norm 10e 9 with respect to first nonlinear step nonlin abs tol absolute tolerance for the residual b norm 10e 15 nonlin step tol tolerance for the lo norm of the nonlinear 10e 3 step the maximum 5 norm for the line search 1 step in units of eV maximum numb
8. for each value of Vg in this way the IV drain characteristics for a series of gate biases are obtained in output sweep 1 simulation dd variable Vd start 0 0 stop 2 0 40 1 Steps 200 200 1 H plot data true p sweep 2 d variable Vg 20 CHAPTER 3 GETTING STARTED 2D start 0 1 stop 0 5 steps 6 simulation sweep 1 simulation driftdiffusion 5 Definition of Execution parameters In the Simulation section we decide the simulation dimension dimension 2 then which simulations to perform and in which order we set solve sweep_2 to execute the external gate voltage sweep sweep_2 which in its turn call the sweep sweep 1 where drain current is calculated for all the chosen drain voltage steps by running dd simulation Simulation meshfile mosfet msh dimension 2 temperature 300 solve sweep 2 resultpath output IV char output format vtk plot Ec Ev QFermi e QFermi h eDensity hDensity eCurrent hCurrent NetRecombination EField ElPotential ContactCurrents Output files with conduction and valence band profiles quasi fermi levels electron and hole density recombination electric field and potential plot Ec Ev will be generated together ContactCurrents with a file with all the calculated values of the drain current at the contacts for each gate bias step the IV characteristics Step 4 Run TiberCAD Now we can run TiberCAD tibercad mosfet tib
9. initial eigenstates and final eigenstates refer to the range of eigenstates to be taken in account for optical calculations By specifying in Solver section a range of energy values in this way Emin 3 0 Emax 5 0 dE 0 001 the emission optical spectrum for 0 is calculated The spectrum is calculated in the following way 1 we a P hw 2 3 mza Miel RE 5 0E d w wij w 2 dQ 9 1 where f and f are the Fermi distributions 75 76 CHAPTER 9 SIMULATION OPTICSKP 9 1 Output The output variables for optics calculations are e optical spectrum k 0 optical emission spectrum fork 0 calculated through opticskp model Chapter 10 Simulation opticalspectrum By defining the model opticalspectrum optical matrix elements are used to calculate the associated emission spectrum with a k space integration In Solver section opticalspectrum 1 k space dimension 2 k space basis true El 0 0 0 1 k2 0 0 1 0 refine fraction 0 30 relative accuracy 0 01 refine k space true number of nodes 2 2 wedge quarter optical matr elem model opticskp polarization 0 0 1 Emin 3 0 Emax 5 0 dE 0 001 The parameters TT 78 CHAPTER 10 SIMULATION OPTICALSPECTRUM k space dimension 1 for 2D simulations 2 for 1D simulations k space basis is true if the k space is defined by means of k vectors if false vectors are expressed in real
10. model associated to the sweep calculation plotvariable specify the integrated quantity to be calculated during the sweep and that will be shown in the output file sweep modelname sweepvariable dat eg sweep driftdiffusion Vb dat for a sweep of current calculation on the variable Vb typically a contact voltage plot data default is false if it is set to true output data will be written for each step of the sweep calculation otherwise just the results for the final step will be present in the output e selfconsistent block preceded by the keyword selfconsistent In this block it is possible to define a self consistent calculation based on two different simulation models e g driftdiffusion and excitontransport selfconsistent flavour relaxation simulations driftdiffusion excitons In simulations the list of simulations to be performed self consistently is specified Now it is possible to execute the specified simulations in self consistent way by using the selfconsistent keyword like a simulation name in the solve assignement e g solve selfconsistent or even in the sweep section with for example simulation selfconsistent 4 6 Physics section In this section several physical parameters can be entered in addition to or overwriting the material parameters present in the material files The section is organized in blocks 4 7 SIMULATION SECTION 33 each one preceded by a block name equal t
11. of the device usually related to the same material or doping In TiberCAD these regions are referred to as mesh regions Boundary regions are needed to specify boundary conditions b c for the solution of the PDEs of our simulation By default to all the external boundary of the device a Neumann b c is imposed meaning null derivative of electric field and zero flux of current normal to the boundary These are the usual b c applied in the simulation of electronic devices in particular these conditions are implicitly satisfied by using the finite element formulation Usually one needs to impose also specifical b c to the device relative most often to contacts of some kind ohmic schottky but also heat and temperature b c or reference substrates for strain calculations These regions constituted by surfaces 1 3 PHYSICAL AND BOUNDARY REGIONS IN TIBERCAD 3 lines or points respectively for 3D 2D and 1D simulations are referred to in TiberCAD with the keyword BC reg numb It is important to know that the information about the physical and boundary re gions must be present in the mesh file before it is read by TiberCAD and thus have to be produced by making use of the modeling mesher software As for now TiberCAD supports the mesh output of the following software tools GMSH v 2 and ISE TCAD v 9 5 By means of the utility DEVISE of ISE TCAD v 9 5 it is possible to design and mesh a device after the meshing has been successf
12. output values for these quantities are reported in the files modelname elemental ext In the case sweep calculation is performed and the plot data keyword is set to true the output files are of the kind modelname elemental sweepvariable step ext e g drifidiffusion elemental Vb 1 150 dat Integrated quantities are the quantities which are not associated to the mesh but are obtained by an integration on real or reciprocal space for example current at the contacts of a diode or quantized energy levels in quantum well These Integrated quantities are displayed in separated files with the format simname ext e g quantum electrons dat where simname is the name of the model simulation associated to the results If a sweep is performed the output file gets the format sweep simname varname ext where varname is the variable with respect to which the sweep is performed for example sweep driftdiffusion Vb dat Inside the file output values for all the steps of calculation are shown Finally a last class of output files is the Materials output These files contain the information about the physical regions of the device for each class of simulation a different material file is produced containing all and only the mesh regions associated to that simulation model The file has the format simulationname materials ert e g driftdiffusion materials dat 49 EXAMPLE OF INPUT FILE 35 4 9 Example of Input file Here is an exampl
13. structures are supported Atomistic Generator options to be put in the Atomistic section are described in the following reference region mandatory the Atomistic Generator can only build pseudomor phical heterostructures reference region must be defined to specify from which region TiberCAD Regions to get structure parameters such as lattice constants which depend on the material defined in the reference region passivation optional no is default option If set to no no passivation is performed If yes is specified a hydrogenation of the structure is performed taking into account the structure periodicity Up to now hydrogenation is supported fo Silicon structures preserve optional Default is none In some cases it is requested to build a structure in which the atom basis or the conventional cell has be preserved regardless to mesh geometry If none is specified no conservation is performed and only atoms strictly be longing to geometrical regions are put in the atomic structure If lattice is specified atom basis is preserved e g to preserve anion cation couples If conventional is specified conventional cell is preserved y_lenght optional Atomistic Generator builds the minimum periodical structure along y and z directions If y_lenght is specified the structure will be at least y_lenght sized along y_growth_direction Exact lenght is internally defined in order to keep struc ture p
14. to a group of physical regions described by Region blocks So for each Atomistic block defined in Input file an atomic structure description will be generated and used to solve a simulation problem with an atomistic approach The association to the physical macroscopic regions of the device allows the implementation of multi scale calculations Each Atomistic block must be preceded by the keyword Atomistic followed by the single word name of the atomistic region Atomistic TB 1 d physical regions barrier 1 qwell barrier 2 physical regions to be described with atomistic model Here are the description of the available keywords for an Atomistic block physical regions mandatory list of the physical regions TiberCAD Regions or Clusters of the device associated to an atomistic description all default is used to specify all the physical regions 4 4 MODELS SECTION 27 path optional path for importing an atomistic structure from an external file and gen formats are supported and are automatically recognized by file extension Each of the atom positions is imported as is so the atom coordinates must be consistent with the geometry of the device If no path is specified the TiberCAD Atomistic Generator builds the atomistic structure it is constructed as a bulk crystal structure covering with proper atomic species the physical regions and taking in account the dimension of the problem up to now 1D
15. 7 gt min eigenvalue number The rest of the parameters wedge k space dimension etc define the k space 79 80 dispersioniD el 11 quantum simulation quantum el min eigenvalue number 0 max eigenvalue number 5 wedge half k space dimension 1 0 0 1 0 number_of_nodes 10 2 Output CHAPTER 11 The output variable name is k space_dispersion QUANTUM DISPERSION Chapter 12 Quantum Density dens el 1 k space dimension 2 k space basis true El 0 0 0 1 k2 0 0 1 0 number of nodes wedge quarter refine fraction 0 20 relative accuracy 0 01 refine k space true uniform refinement false mesh order FIRST 4 4 quantum simulation quantum el degeneracy 2 initial eigenstates number 10 analitic false e quantum simulation name of the Schr dinger simulation e degeneracy degeneracy of the quantum state e initial eigenstates number initial number of eigenstates for the Schr dinger equation e analytic true false If true then the density is calculated analytically or numerically 8l 82 CHAPTER 12 QUANTUM DENSITY Analitcal calculation of density is done in the following way For each eigenstate we calculate the effective mass assuming quadratic dispersion Then the charge density is calculate as follows piole 9 1 exp Gee 72 12 1 kT E pap r dote For Fan Lie 12 2 where and are the 1D a
16. Density he Pi Bibliography 75 76 77 78 79 79 80 81 82 83 IV CONTENTS Installation instructions In the following VERSION denotes the version number of the TiBERCAD release you downloaded and INSTALLPATH denotes the directory where TIBERCAD gets installed Version 2 2 0 of GMSH http www geuz org gmsh will be installed together with TiperCAD For the Linux version of GMSH you need OpenGL libraries installed on your system Prerequisites Get the installer package for your OS architecture from http www tibercad org or by contacting support tibercad org Table 1 lists the packages available for download run TrBERCAD you will also need a license file that you will have to copy into the installation directory of TIBERCAD In the Windows version some graphical features such as graphical convergence mon itors are only available if an X Window server is installed and running Windows installation procedure To install TrBERCAD in Windows run the setup program tibercad setup exe During the installation you can choose the installation directory After finishing installation copy your license file tibercad lic into the license subdirectory of the TIBERCAD installation directory INSTALLPATH license without changing its filename installer package name Target architecture tibercad installer exe Windows 32 bit tibercad version i1386 deb Debian GNU Linux 4 0 etch
17. Intel x86 tibercad version tar gz Generic Linux package Table 1 Installer packages V VI CONTENTS Linux installation procedure The installation procedure for the Linux version of TIBERCAD depends on your distri bution Download the installer package that best fits your setup The standard method to launch TiBERCAD is by means of a shell script that is installed alongside the TiberCAD executable It takes care of setting all necessary envi ronment variables If for some reason you have to run the executable directly remem ber to set TIBERCADROOT to the TiberCAD installation directory INSTALLPATH and LD LIBRARY PATH to INSTALLPATH 1ib Debian If you are running Debian GNU Linux 4 0 etch on a 1386 architecture you can use the Debian package tibercad version 1386 deb Install it as root using dpkg or similar dpkg install tibercad VERSION i386 deb The package will be installed in usr share tibercad Next copy your license file tibercad lic into usr share tibercad license without changing the filename NOTE The debian version of TiberCAD depends on the following Debian packages e libboost regex1 33 1 e libboost filesystem1 33 1 e libblas so 3 provided e g by atlas3 base e liblapack so 3 provided e g by atlas3 base Other Linux distributions If you have a distribution other than Debian 4 0 etch or you want to install TIBERCAD into a different directory then use the tgz or tbz installati
18. Physical region s are the TiberCAD regions or clusters as defined in Device section Default value is all all physical regions of the device In a list the names must be separated by comma and enclosed between and parenthesis 4 4 2 physical model block physical model recombination 1 model SRH 30 CHAPTER 4 INPUT FOR TIBERCAD Currently available physical models and parameters recombination model SRH direct exciton generation exciton dissociation exciton simulation excitons electron mobility model doping dependent hole mobility model doping dependent 4 4 3 BC region block BC Region anode 1 BC reg numb 2 type ohmic voltage 0 0 voltage Vb 1 5 BC_region name of the present boundary region BC region ID s as specified in the meshing program GMSH type type of boundary condition ohmic schottky substrate for strain calcula tions voltage value of voltage V applied to the present BC region for ohmic and schottky BCs it can be the value of a sweep variable Vb indicated with Vb A possible default value can be indicated in parenthesis Vb 1 5 zero grad fermi h zero grad fermi e if true set Neumann b c to the fermi level in the b c region If type is substrate for strain calculations material name of material in the substrate region structure crystal structure wz wurtzite zb zincblend x growth direction y growth direct
19. Surface 2 Physical Surface 3 e Definition of the Physical surfaces each of them is composed by one or more geometrical Plane Surface For example Physical surface 2 comprises the two separated contact regions while Physical surface 3 corresponds to the oxide region The Physical surfaces are the 2D Physical regions of the mesh and will be as signed to the related TiBERCAD regions through the keyword mesh regions see Step Physical Line 1 Physical Line 2 Physical Line 3 13 source 139 38 gate 19 drain e Definition of the Phisical Lines In this 2D simulation 1D physical regions are used to carry information about boundary condition regions In other word each Phisical Line corresponds to a boundary condition a contact in the case of a driftdiffusion calculation thus Physical Line 1 refers to source contact P L 2 to gate contact P L 3 to drain contact The numerical identifications of these Phisi cal Lines will be asigned to TrBERCAD BC regions by means of the BC reg numb instruction In fig 3 1 the obtained geometrical model is shown Step 2 Meshing the device The geo script file with the geometrical description can be run in GMSH to display the modelled device and to mesh it through the GMSH graphical interface see fig 3 2 Alternatively a non interactive mode is also available in GMSH without graphical user interface For example to mesh this 2D tutorial in non interactive mode ju
20. TIBERCAD User Manual Fabio Sacconi Matthias Auf der Maur Michael Povolotskyi Giuseppe Romano Alessandro Pecchia Gabriele Penazzi Stefano Bellocchio Aldo Di Carlo May 7 2008 TIBERCAD User Manual TiberCAD authors F Sacconi M Auf der Maur M Povolotskyi G Romano A Pecchia G Penazzi S Bellocchio A Di Carlo 2008 Document revision 1 0 0 1004 Contents Contents Installation instructions 1 Overview Ll c x 53 3x RR weine Aw eG EG 1 2 Simulation environments LL LL LL LL 1 8 Physical and boundary regions in TiberCAD Getting started 1D Getting started 2D Input for TiberCAD 4 1 Description of Input file structure 12 OCI SEO x 52k A ho kw ae en GO eH rg 43 Scale section 44 Models section Ot Some Doek REL 442 physicaLmodel Block A nc ko kn E as 83 Dock Loss RRS MERE MOR RE T 15 Solver section e Lb S des 15 Phys BEN 94 quse ow Oa ee quels e qw AT seti an Sew da we eee Eade e 43 Output description 29 Exemple dE Input De 2 2 Seren Mei Neue y Rx arena Simulation of strain US luo oh UAE DE DE NEA SURGEN WIE ee E SE dE E 5 2 Models section parameters 5 2 1 Substrate b
21. d below The term between the brackets represents the thermal flux 7 2 Physical model By neglecting particle effects the thermal conductivity is only due to the lattice contri bution The lattice thermal conductivity is read from the database The thermal model is tagged as thermal In options subsection we indicate the simulation name simulation name whatever_you_want and the simulation domain physical_regions wherever_you_want model thermal d options 1 simulation name whatever you want 65 66 CHAPTER 7 HEAT BALANCE SIMULATION physical regions wherever you want 7 2 1 Electron and hole dissipations Electron and hole dissipations give the following heat source Hs V PaT ar F P T F Pp Jp 7 2 where P and P are the thermoelectric power of electrons and holes respectively o and are the electro chemical potentials The equation 7 2 represents severals heat source contributions Their estimates are reported in table 7 1 Expression Heat source Bal Electron Joule effect ek Hole Joule effect ass dp En T P Recombination effect TJa4 VB Electron Peltier Thomson effect TJ VP Hole Peltier Thomson effect Table 7 1 Drift diffusion heat sources The physical model heat source includes a specific source identified by its model name Concerning electron and hole dissipations the model is named drift diffusion dissipation as rep
22. data file parameters physical model recombination model direct Direct recombination is modeled as follows C np 6 5 The material data file and the input file use the same keyword C for the parameter C The database value can be overridden from the input file as described for SRH recombination tau tau n taup tau p E Et Table 6 5 SRH input file parameters 56CHAPTER 6 DRIFT DIFFUSION SIMULATION OF ELECTRONS AND HOLES 6 3 2 Thermoelectric power models The thermoelectric power models are the same for electrons and holes The keywords is thermoelectric_power i e physical_model thermoelectric_power S model The model keyword can be constant i e the thermoelectric powers are read from the database or diffusivity model where the thermoelectric powers are computed by En 5 en Es ep ky 5 E ep P The default is P P 0 6 3 3 Mobility models Mobility models have currently to be defined for electrons and holes independently The corresponding keywords are electron_mobility and hole_mobility i e physical_model electron_mobility d model physical model hole mobility d model The default model is the constant mobility model 6 3 MODELS SECTION 57 Constant mobility model The constant mobility model identifier constant assumes a mobility which depends only on temperature by means of the followin
23. e of the input file template Description of the device physical regions Device Syntax Region Tiber_region mesh_regions list gmsh reg ID list ISE_TCAD reg names Hif mesh regions is empty gt mesh regions Tiber region Region buffer mesh regions 1 structure 2 y growth direction 1 0 1 0 z growth direction 1 2 1 0 x growth direction 0 0 0 1 material GaN doping 1 15 doping_type donor doping_level 0 025 Region barrier 1 1 mesh regions 2 3 structure wz y growth direction 1 0 1 0 z growth direction 1 2 1 0 36 x growth direction 0 0 0 1 material AlInN 0 80 doping 1e15 doping_type donor doping_level 0 025 Region QWell mesh regions 4 structure wz y growth direction 1 0 1 0 z growth direction 1 2 1 0 x growth direction 0 0 0 1 material GaN doping 1e15 t doping type donor doping level 0 025 Region barrier 2 mesh regions 5 6 structure wz y growth direction 1 0 1 0 z growth direction 1 2 1 0 x growth direction 0 0 0 1 material AlInN x 0 80 t doping 1e15 t doping_type donor doping level 0 025 CHAPTER 4 INPUT FOR TIBERCAD 49 EXAMPLE OF INPUT FILE 37 Cluster group of mesh_regions with DIFFERENT material in general Syntax Cluster Tiber cluster mesh regions list gmsh reg ID list ISE TCAD reg names
24. e parameter Dirichlet_bc_everywhere true false in Solver section The default value for EFA problem is true 8 2 Solver parameters There are two groups of parameters The first group is related to the general eigensolver problem the second one is related to the Schr dinger equation 8 2 1 Eigenvalue problem parameters These parameters are common for all eigenvalue problems Their default values may be different for different eigenvalue problems for example for the Schroedinger equation and for the electromagnetic eigenvalue problem The eigenvalue problem can be solved by the solvers that are implemented into the SLEPc library The relative parameter is solver arnoldi lapack krylovshur The default value is krylovshur In the case of the lapack solver all the eigenvalues are computed In the case of arnoldi or krylovshur solver it is necessary to specify which and how many eigenvalues have to be computed The idea is that the iterative solver calculates several eigenvalues that a close to a specific number reffered to as the spectral_shift The relative parameters are max_iteration_number maximum number of iteration used as a stop condition eigen_solver_tolerance numerical eigensolver tolerance used as a convergence criteria spectral shift the closest eigenvalues to this value eV are found spectrum inversion tolerance tolerance used for linear solver Table 8 1 Iterative eigensolver parameters
25. ed for ohmic contacts Schottky contacts and free sur faces Contacts are boundary models that allow a nonzero normal electrical current For this type of boundaries one can define a contact resistance using the contact resistance option The contact resistance has units Rem2 The applied voltage is specified with the option voltage A variable can be assigned to this using the syntax For a finer control of the behaviour at electrical contacts the options zero field zero grad fermi e and zero grad fermi h can be used which when set to true will impose zero normal electric field and zero normal gradient of the electron and hole electro chemical potential respectively The ohmic contact identifier ohmic has no further parameters A Schottky contact identifier schottky has the additional parameter barrier which signifies the energy difference between the semiconductor band edge and the fermi energy in the metal As default the barrier is taken with respect to the conduction band By specifying band v the barrier can be imposed with respect to the valence band p type contact The type of boundary model is chosen by the parameter type e g type schottky The free surface or interface model identifier interface models surface charges Two modes are possible constant charge a constant charge can be assigned by specifying only the sheet carrier density Ns in cm The sheet charge density will then equal Ns multiplied by the eleme
26. een the device and the substrate The substrate does not belong to the device Therefore it is necessary to 45 46 CHAPTER 5 SIMULATION OF STRAIN define both the boundary region number and the substrate material Role of substrate Jn general the substrate is a material that defines the lattice matching conditions and not necessarily a real solid body om which the device is grown BC Region layer of Al 0 3 Ga 0 7 N BC reg numb 14 type substrate mat AlGaN x 0 3 structure wz y growth direction 1 0 1 0 z growth direction 1 2 1 0 x growth direction 0 0 0 1 5 2 2 External pressure boundary condition The parameter pressure specifies the value in GPa of the normal pressure applied to the boundary region BC reg numb BC Region tip upon a surface 1 BC reg numb 12 type pressure pressure 12 3 Sign of pressure The value of the pressure has a positive sign if the external force acts towards the surface which in general has to be the boundary of a simulation environment 5 2 3 Extended device boundary condition If device that is grown on a substrate is very large we may want to simulate a part of it only In this case the simulation domain boundary is not a free surface any more The boundary conditions are as follows Qu The syntax is as follows 5 8 SOLVER PARAMETERS 47 BC Region boundaryi d BC reg numb 12 type extended material 5 3 Solver parameters The c
27. efined 1 and 2 and associated to the first and to the last point of our 1D device These points are needed to impose some boundary conditions and in this way they are made available for TiberCAD and will be used to associate each of them to a boundary condition region through the keyword BC reg numb BC Regions 1 BC Region cathode BC_reg_numb 1 1 3 PHYSICAL AND BOUNDARY REGIONS IN TIBERCAD 5 BC Region anode d BC reg numb 2 In 2D case a set of Physical Surface will be defined to be used as mesh regions while Physical Line is used for boundary conditions Finally in 3D case Physical Volume is used to define mesh regions while Phys ical Surface is used to define boundary conditions CHAPTER 1 OVERVIEW Chapter 2 Getting started 1D In this section we will see step by step how to use TIBERCAD to simulate numerically a semiconductor device As a very simple example we will refer to the Tutorial O Si bulk that you can find in the Tutorials directory Step 1 Modeling the device As a first step we have to model the device To do so you can use DEVISE module of ISE TCAD 9 5 software package or GMSH program Here we ll see in details the procedure for GMSH There are two possible ways to use GMSH 1 Interactive using the graphical interface 2 Using a script file In the following we ll see how to write a basic GMSH script bulk geo for any details please refer to GMSH manual GMSH http geuz org gm
28. er of nonlinear iterations 20 ls max step nonlin max it Table 6 12 Parameters for the PETSc nonlinear solver keyword description default ksp type the linear solver type bcgsl pc type the preconditioner type ilu lin rel tol relative tolerance for the linear solver 1e 6 lin abs tol absolute tolerance for the linear solver 10e 50 lin max it maximum number of linear iterations 500 The linear tolerance gets automatically decreased after each nonlinear step Table 6 13 Parameters for the PETSc linear solver bcgs A stabilized version of the biconjugate gradient method This one works better in 1D than bcgs1 bcgsl default A modified version of bcgs gmres Generalized minimal residual method The pc type specifies the type of preconditioner to be used The most useful ones are ilu default Incomplete LU factorization Does not work for materials with high band Bap jacobi Jacobi preconditioning diagonal scaling composite Combination of ilu and jacobi The 1s max step parameter defines an upper bound of the lo norm of the nonlinear line search step It should be not too big to prevent the algorithm from diverging but 64CHAPTER 6 DRIFT DIFFUSION SIMULATION OF ELECTRONS AND HOLES also not too small to minimize the number of iterations Values between 1 and 10 should be a good choice The nonlin step tol defines at which line search step size in 5 norm the algorithm stops ie as
29. eriodicity z_lenght optional same as above for the z direction 4 4 Models section Models model driftdiffusion BC Regions i BC Region cathode 28 CHAPTER 4 INPUT FOR TIBERCAD In Models section one or more model blocks must be present each model block must be preceded by the keyword model followed by the single word model name This must be the name of one of the TrBERCAD simulation models Here are the simulation models implemented until now driftdiffusion Poisson driftdiffusion transport of electrons and holes thermal Heat balance simulation excitontransport Exciton transport model macrostrain Calculation of Elastic deformations in heterostructures efaschroedinger Envelop Function Approximation EFA solution of single particle Schr dinger equation for electrons and holes quantumdensity Calculation of quantum density of electrons and holes quantumdispersion Dispersion of quantized states in k space opticskp Optical properties optical kp matrix elements opticalspectrum Emission spectrum with k space integration For a complete description of these simulation models see the next chapters Each model block can contain some optional blocks to be written in the following order one options block preceded by the keyword options This block can contain general options for the present model 44 MODELS SECTION 29 e one or more physical model blocks each physical model block m
30. eter that controls shape calculation is number_shape_steps The value defines number of iterations The default value is zero that means no shape deformation calculation 50 CHAPTER 5 SIMULATION OF STRAIN 5 4 Physics section parameters There is a possibility to consider converse piezoelectric effect For this it is necessary to specify a name of another simulation that can provide electric field The parameter is poisson equation Example macrostrain 1 poisson equation DriftDiffusion Interaction with other simulations n order to take into account the converse piezzo effect the poisson equation has to recalculate the necessary parameters after the strain simulation To do so the following parameters has to be set in the Physics section of the drift diffusion equation for detailes see Sec 6 4 driftdiffusion 1 model strained strain simulation str recompute band parameters true 5 5 Output The output variables are e strain strain tensor 6 components in calculation system e polarization piezo polarization vector 3 components in calculation system Chapter 6 Drift diffusion simulation of electrons and holes 6 1 Theory The semi classical transport simulation of electrons and holes is based on the drift diffusion approximation see e g 31 Beside the electric potential the electro chemical potentials are used as variables such that the system of PDEs to be solved reads as follows V EVp
31. g formula Hconst Io T To 6 8 In the material data file ug and y have to be specified with the keywords mu max e mu max h and exponent e exponent h respectively ug can be ovverridden from the physical model section using the keyword mu or from the Region sections using the keywords mu e and mu h Doping dependent mobility model The doping dependent mobility model identifier doping dependent implements two models for mobility depending on the total doping density and the temperature The model that is used depends on the value of the mobility formula parameter Model by Masetti et al 4 The model by Masetti et al is identified by mobility formula formula 1 It uses the following P N Es Hconst Hmin 2 _ H TECN 6 9 H Umin where N is the total doping density and the mobility obtained from the constant mobility model The parameters are specified as given in table 6 6 Model by Arora 5 parameter electrons holes Hmin 1 mumini_e mumini_h Hmin 2 mumin2_e mumin2_h Hi mul e mul h P Pc_e Pc_h C Cr e Cr h C Cs e Cs h a alpha e alpha h B beta e beta h Table 6 6 Data file parameters for the mobility model by Masetti et al 58CHAPTER 6 DRIFT DIFFUSION SIMULATION OF ELECTRONS AND HOLES The model by Arora is identified by mobility formula 2 It reads Hd PT Ime LENIN with Hmin Amin T To uq Aq T To
32. g on the section by a variable number of blocks enclosed between 7 and V brackets Each block can be possibly composed by one or more blocks each preceded by a block name The elementary block parameters block is a block which contain zero or any number of parameter assignements in the form tagname tagvalue where e tagname is a string e tagvalue is a single numerical or string item or a list of items between and parenthesis and separated by commas e g cathode anode 23 24 CHAPTER 4 INPUT FOR TIBERCAD Format is free for the parameter assignements provided that they are separated by spaces Everything which follows a is considered as a comment and is disregarded dri d For example ftdiffusion coupling poisson nonlin max it 70 nonlin rel tol 1e 10 ls max step 2 Hls type none discretization fem integration order 2 pc type composite ksp type bcgs Hquasi equilibrium cathode anode Here and in the whole input file a string item can include a combination of characters special characters and numbers but not spaces if a space is found the string item is taken as terminated The input file is composed by the following sections Geometry Device Scale Models Physics Solver Simulation which will be described in the following 4 2 Device section Device d Region buffer 42 DEVICE SECTION 25 In Device
33. hoice of the necessary parameters to be put in the Solver section depends on the type of the strain boundary condition for the structure namely if it is considered as grown on a substrate or not 5 3 1 Structure with a substrate The only mandatory parameter is substrate to which a name of a substrate boundary condition region has to be assigned e g referring to the previous example strain in transistor 1 substrate layer of Al 0 3 Ga O 7 N 5 3 2 Structure without a substrate freestanding In this case the parameter substrate should not be present instead the following pa rameters should be defined e The reference lattice material is defined by the coordinates of a point belonging to this material using the parameter reference material point e As follows from Ref 1 additional geometrical points have to be specified accord ing to the device dimensionality The corresponding parameters are fired point fixed point2 and fixed point3 Since the elasticity energy is invariant with respect to translations and rotations of the structure then for the sake of uniqueness of solutions of the equations another set of constraints is required Hereafter we assume that a mesh is defined over the simulation domain and the displacement field u r is defined at the mesh nodes Let D be the dimensionality of the structure minus the number of directions along which the structure is periodic If D 0 then a Dirichlet boundary c
34. ical potential of holes Electric potential Electron density Hole density Electron mobility Hole mobility Ionized donor density Ionized acceptor density Total charge density Electron thermoelectric power Hole thermoelectric power The net recombination rate for each recom bination model and the total rate Table 6 1 Nodal quantities eV eV eV eV eV eV be edn eV cm Va cm V 1g cm cm cm Vk VK cm 3s The physical model sections can be omitted In this case default models are used namely no recombination generation for the recombination model and constant mobility for the mobility models There can be more than one recombination model 6 3 1 Recombination models This section describes the currently available generation recombination models Shockley Read Hall SRH recombination The SRH recombination model can be enabled in the input file as shown in Listing 2 SRH recombination is defined as follows Jann np n keT r p ne E ksT m 6 2 El Erap Ec E 2 is the trap level with respect to the midband energy n is the intrinsic carrier density T and 7 are the recombination times The parameters are taken 54CHAPTER 6 DRIFT DIFFUSION SIMULATION OF ELECTRONS AND HOLES Elemental quantities EField Electric Field Vom GradFermiE Gradient of the electron electro chemical potential GradFermiH Gradient of the hole elect
35. in Silicon and their empirical relation to electric field and temperature IEEE Trans on Electron Devices vol 22 pp 1045 1047 1975 Gerhard K Wachutka Rigorous thermodynamic treatment of heat generation and conduction in semiconductor device modeling IEEE Transaction on Computer aided Design vol 9 pp 11 1990 83
36. ion we decide which simulations to perform and in which order we set solve sweep to execute the sweep which run driftdiffusion_1 simulation for the specified loop Simulation 1 searchpath meshfile bulk msh dimension 1 temperature 300 solve sweep resultpath output output format grace plot Ec Ev ContactCurrents 12 CHAPTER 2 GETTING STARTED 1D Output files with conduction and valence band profiles plot Ec Ev and all the calculated values of the current at the contacts ContactCurrents the IV characteristic are generated Step 4 Run TiberCAD Now we can run TiberCAD tibercad bulk tib The generated Output files are driftdiffusion materials dat material mesh regions in this case just region 1 driftdiffusion nodal dat nodal quantities here conduction and valence band sweep driftdiffusion Vb dat integrated current at the two contacts for each sweep step Chapter 3 Getting started 2D In this second example we will refer to the Tutorial 4 Si n Mosfet that you can find in the Tutorials directory Step 1 Modeling the device Again as a first step we have to model the device We ll see in some details how to design and mesh a mosfet device with GMSH e In the GMSH script mosfet geo several variables are defined and given a value in this way lsub 0 03 lacc 0 002 1ct 0 0005 1g 0 0015 1h 0 01 1 0 0005 these variables are used the script to assign pro
37. ion z growth direction Bravais vectors with Miller indexes for wurtzite 4 5 Solver section Solver driftdiffusion 4 5 SOLVER SECTION 31 1 nonlinear solver tiber Esp type bcgsl nonlin rel tol 1e 12 nonlin abs tol 1e 15 nonlin step tol 1e 2 tnonlin rel tol 1e 12 lin rel tol 1e 6 nonlin max it 30 local density scaling true Hls type none discretization fem ls max step 1 pc type lu pc_type composite integration_order 2 relaxation_factor 0 5 In this section can define the setting parameters for the numerical solvers the section is organized in blocks each one preceded by a block name equal to one of the user defined simulation name Solver parameters defined in each block refer to that particular simulation Two extra blocks can be present e sweep block preceded by the keyword sweep This block contains the setting for a set of calculations applied to a boundary region e g to a drain contact for the calculation of a IV characteristic sweep Simulation driftdiffusion variable Vb start 0 0 stop 4 0 32 CHAPTER 4 INPUT FOR TIBERCAD steps 80 plot_data true plotvariable current variable name of the variable to which sweep is applied its value is assigned to a quantity e g voltage in a BC Region section start stop steps sweep starts from start value is repeated steps times and stops in stop simulation name of the simulation
38. le effect Recombination heat Electron Peltier Thomson effect Hole Peltier Thomson effect TotalHeat Table 7 4 Elemental scalar quantities Elemental vector quantities Wq Thermal flux Wem Wn Electron power flux Wem Wp Hole power flux Wem W Total power flux Wem Table 7 5 Elemental vector quantities Wem Wem Wem Wem Wem Wem 70 CHAPTER 7 HEAT BALANCE SIMULATION Chapter 8 Envelope Function Approximation The envelope function appriximation EFA simulation tool of TiBERCAD is developed in order to solve a single particle Schr dinger equation for electrons and holes in a semi conductor crystal This problem is an eigenvalue problem that is treated as a generalized complex eigenvalue problem Hy Sy 8 1 where H and S are the Hamiltonian and S matrix respectively 8 1 Models section parameters The Models section looks like follows model efaschroedinger options simulation name quantum welli physical regions 1 2 The default boundary conditions of the simulation domain are open that is zero flux for single band calculation It is possible to specify Dirichlet boundary conditions BC Region infinite barrierl d BC reg numb 12 71 72 CHAPTER 8 ENVELOPE FUNCTION APPROXIMATION type Dirichlet There is a way to impose automatically the Dirichlet boundary conditions over all the boundary of the simulation region This is done by th
39. m dos h valence band effective DOS mass me Table 6 10 Parameters for the simple semiconductor model 6 4 2 Default semiconductor model The default semiconductor model uses a bulk k p model to calculate the band parameters It can be chosen explicitly by model default The model reads all needed parameters from the material data file The band parameters are calculated considering locally strain and lattice temperature as obtained from the corresponding simulations specified using the strain simulation and thermal simulation keywords 6 5 Solver section Many of parameters for the numerical solver depend on the type of solver being used and on the device to be simulated Table 6 11 lists the options that are independent on the type of solver used The linear and nonlinear solvers to be used can be chosen using the keywords linear solver and nonlinear_solver respectively For the nonlinear solver one can chose between 62CHAPTER 6 DRIFT DIFFUSION SIMULATION OF ELECTRONS AND HOLES keyword description coupling defines which equations to couple together poisson solve only poisson eq electrons electrons and poisson holes holes and pois son current only electron and hole cur rents full the fully coupled system integration order order of the numerical gauss integration De fault is 2 current integration method method for the calculation of the contact cutrrents surfint integrate the local cur rent
40. mgr ascii data column type vtk for Paraview plot list of output variables which are calculated and available in output files See the corresponding chapters for the available output variables for each model 34 CHAPTER 4 INPUT FOR TIBERCAD 4 8 Output description At the end of the execution the program will write the results of the simulation in the directory specified by resultpath with the format specified by output format The output variables are specified in the list plot TiberCAD output is divided in three classes nodal elemental and integrated quantities Nodal quantities are all the quantities associated with the nodes of the mesh such as Fermi level electron and hole density conduction and valence band etc The output values for these quantities are reported in the files modelname nodal ert where model name is the simulation model used for the calculations and is the extension of the chosen file format In the case a sweep calculation is performed and the plot data keyword is set to true the output files are of the kind modelname nodal sweepvariable step ext where sweep variable is the variable with respect to which the sweep is performed e g gate voltage and step is the value of this variable at that step e g driftdiffusion nodal Vb 0 000 dat for the result at the step Vb 0 0 Elemental quantities are all the quantities associated with the elements of the mesh such as current density The
41. nd 2D charge densities m is the averaged mass the mass is different for each quantized state and is position independent g is the degeneracy of the states The sign is for electrons the sign is for holes Numerical calculation is done by the following formula 1 1 00 gt ope fOr gm 12 3 n The integration is performed on a mesh in the k space 12 1 Output The output parameter is quantum density Bibliography H Michael Povolotskyi and Aldo Di Carlo Elasticity theory of pseudomorphic het erostructures grown on substrates of arbitrary thickness Journal of Applied Physics vol 100 pp 063514 2006 Matthias Auf der Maur Michael Povolotskyi Fabio Sacconi and Aldo Di Carlo Simulation of piezoresistivity effect in FETs J Comp Electronics vol 5 pp 323 2006 Siegfried Selberherr Analysis and Simulation of Semiconductor Devices Springer Verlag Wien New York 1st edition 1984 G Masetti M Severi and S Solmi Modeling of carrier mobility against carrier concentration in Arsenic Phosphorus and Boron doped Silicon IEEE Trans on Electron Devices vol 30 pp 764 769 1983 N D Arora J R Hauser and D J Roulston Electron and Hole Mobilities in Silicon as a Function of Concentration and Temperature IEEE Trans on Electron Devices vol 29 pp 292 295 1982 C Canali Majni R Minder and Ottaviani Electron and hole drift velocity measurements
42. ntary charge e A positive Ns produces a positive surface charge 60CHAPTER 6 DRIFT DIFFUSION SIMULATION OF ELECTRONS AND HOLES electronic surface states in this case the surface charge is produced by electrons oc cupying a surface state with a density of states in form of a delta function The density of occupied states then reads Ns s 1 Ec A Es 1 TL The density of states N is specified by Ns the energy of the state with respect to the conduction band AE by Es o denotes the multiplicity of the state and defaults to 2 It can be changed by assigning a value to g 6 4 Physics section Options for controlling the drift diffusion semiconductor models can be specified in the Physics section The corresponding paramaters are given in table 6 9 When model is keyword possible val description ues model see following the model to use for the descrip subsections tion of the conduction and va lence band properties statistics B FD Boltzmann default or Fermi Dirac statistics strain simulation name the strain simulation to be used thermal simulation name the thermal simulation to be used electron quantum density name the quantum density simulation to be used for the electron den sity hole quantum density name the quantum density simulation to be used for the hole density Table 6 9 Common options for the drift diffusion semiconductor models not
43. o one of the user defined simulation name Physical parameters defined in each block refer to that particular simulation driftdiffusion 1 model unstrained For example in this case model specification of generical drift diffusion or exciton transport simulation Pos sible values simple strained effects of strain deformation potentials piezo and pyro polarization fields are taken in account unstrained effects of strain are NOT taken in account even if strain calculation is being performed 4 7 Simulation section In this section one can specify several general parameters and settings for the actual calculation to be run such as the mesh file to be used the dimension of simulation the process flow of simulation etc searchpath path for material files meshfile name of mesh file N B the extension is mandatory grd for ISE TCAD msh for GMSH mesh file v 1 and v 2 0 mesh units units of measurements used in the meshing relative to meters e g 1079 for um dimension dimension of simulation 1 2 3 temperature temperature of the system solve list of simulations to be executed in the order of execution if the list contains sweep a sweep is performed as specified in sweep block in the Solver section solve strain driftdiffusion quantum electrons quantum holes resultpath path for output directory output format format of the output data gmv for GMV ise for Tecplot grace for x
44. olver parameters which describes a physical problem to be solved by TIBERCAD A valid TIBERCAD simulation must belong to one of the predefined TIBERCAD simu lation models see section 4 4 To create a TIBERCAD simulation we first have to declare the TIBERCAD model class to which our simulation belongs Models 1 model driftdiffusion Here we declare that the simulation to be created will belong to the model class driftdiffusion model driftdiffusion In the next Options block we define the name of the TiBERCAD simulation simulationname and the TrBERCAD regions to which it will be applied e g physical regions all where all means the whole device In general several TIBERCAD simulations belonging to the same model can be created each of them must have a different name As we will see in the following see 4 5 4 6 it is possible to specify physical and solver parameters for a single TIBERCAD 1 2 CHAPTER 1 OVERVIEW simulation by referring to its name Anyway it is also possible to specify parameters common to all the TrBERCAD simulations belonging to the same model by referring to the name of the TiBERCAD model instead in this case driftdiffusion 1 2 Simulation environments TiBERCAD allows to compute different physical models in different parts of a device or nanostructure by coupling in a general way different simulation environments A simula tion environment is composed by all the physical region
45. ommand line using the command tibercad If not you probably have to add the bin subdirectory of the TIBERCAD installation directory to your PATH environment variable or start the TIBERCAD executable using the absolute path INSTALLPATH bin tibercad Copy the directory of the example you want to run e g bulk Si to your home directory or any place you have write permissions for Change to the newly created directory and run TIBERCAD by assuming Example 0 tibercad bulk tib directory containing the simulation results will be created with the name provided in the input file Bug reports Feedback Please send bug reports feedback or suggestions to support tibercad org When sub mitting bug reports please always include the full version number of TIBERCAD you are running The full version number appears in the first line of output when running the program tibercad TiberCAD version 1 0 0 961 Usage tibercad lt inputfile gt Chapter 1 Overview 1 1 Simulation models TiberCAD is a multiphysics software tool it includes several simulation models each describing a physical problem to be solved e g DriftDiffusion to solve Poisson and DriftDiffusion equations EFASchroedinger to solve Schroedinger equation in envelope function approximation Macrostrain to calculate macroscopical strain with an elastic model and others One simulation is particular set of equations boundary conditions physical pa rameters s
46. on packages Unpack the archive cd to the unpacked directory tibercad VERSION and run the install script After installation copy your license file tibercad lic into the license subdirectory of the TiBERCAD installation directory INSTALLPATH license without changing the file name Quick start guide In the examples subdirectory you can find several examples ready to run They are the same as the tutorials on http www tibercad org documentation tutorial list CONTENTS VII Windows Open Windows Explorer and go to the TIBERCAD installation directory If you have write permission in the installation directory you can browse to an examples directory and start the simulation by double clicking the input file e g bulk tib in Example 0 If not copy the whole directory to a location in your personal area and run the examples from there If you cannot run TrBERCAD by double clicking an input file tib then the input files are probably not correctly associated with the TIBERCAD executable In this case try to establish the association by right clicking the input file choosing open with Choose Program Browse browsing to the TIBERCAD installation directory and choosing the TIBERCAD executable tibercad exe A directory containing the simulation results will be created with the name provided in the input file Linux After the correct installation of TIBERCAD you should be able to run TiBERCAD from the c
47. ondition is applied at an arbitrarily chosen node 44 u r 0 5 2 48 CHAPTER 5 SIMULATION OF STRAIN in order to prevent the structure from undesirable translations In the case of D gt 1 another node 4 is chosen and a constraint u ri u r ri Kiz 0 5 3 is applied in order to keep the direction between the nodes 44 io unchanged If D 3 another node 23 is chosen and additional constraint is set ri Ne Tj Ti Tiz Uj 0 5 4 so the node iz has to belong to the r r ri plane Example for a 2D simulation Strain in transistor reference material point 0 100 0 fixed pointi 0 0 0 fixed point2 10 0 0 5 3 3 Additional parameters Numercal solver parameters tolerance relative tolerance of the iterative solver e g tolerance 1e 10 The default value is 1e 10 ksp type type of solver gmres bcgsl bcgs cg richardson Default is e gmres for 1D e bcgsl for 2D and 3D pc type of pre conditioner ilu composite jacobi lu cholesky eisenstat Default is e ilu for ID e jacobi for 2D and 3D iterations max number of iterations default 1000 monitor rmonitor if true textual or graphical monitor of convergence process is enabled default false 5 8 SOLVER PARAMETERS 49 Periodic boundary conditions It is possible to specify periodic boundary conditions along the coordinate axes The relative parameters are periodicity_
48. ons Syntax physical regions list Tiber region Tiber cluster physical regions Quantum 1 model efaschroedinger 1 options 4 9 EXAMPLE OF INPUT FILE 1 simulation name quantum holes physical regions Quantum 1 Definition of Model dependent Solver parameters Solver 1 driftdiffusion 1 coupling poisson Esp type bcgsl nonlin abs tol 1e 10 nonlin step tol 1e 2 tnonlin rel tol 1e 12 lin rel tol 1e 6 nonlin max it 30 Hlocal density scaling true Hls type none discretization fem ls max step 1 pc_type lu pc_type composite integration_order 2 relaxation_factor 0 5 macrostrain 41 42 CHAPTER 4 INPUT FOR TIBERCAD 1 substrate substr efaschroedinger x periodicity false Dirichlet_bc_everywhere true particle hl number_of_eigenstates 30 model conduction band eff mass cb poisson_model_name driftdiffusion potential from driftdiffusion strain_model_name macrostrain convergent_density true quantum_electrons particle el quantum_holes particle hl Definition of Model dependent physical parameters Physics t driftdiffusion t Statistics FD 49 EXAMPLE OF INPUT FILE 43 strain simulation macrostrain default driftdiffusion model including local strain obtained from macrostrain quantum electrons 1 particle el model conduction band eff mass cb quantum holes 1 particle
49. orted below physical model heat source d model drift diffusion dissipation drift diffusion simulation dd simul name In order to include such a heat source we have to use drift diffusion simulation The syntax drift diffusion simulation dd simul name allows this connection 7 2 PHYSICAL MODEL 67 7 2 2 Boundary conditions By default thermally insulating surfaces are considered i e Jq N 0 7 3 On the opposite side it is possible to include an ideal thermally conducting interface by fixing the temperature to the external one i e T Text 7 4 This condition can be imposed with the following notation BC_Regions BC Region name BC region 1 type heat reservoir BC reg numb 3 temperature 300 Once a BC Region is inserted in the thermal section heat reservoir is the default type T he default temperature is the one indicated in the solve section Between such extreme situations it is possible to take into account a thermally re sistive interface i e Ja NS DAT Tal 7 5 where G is the thermal surface conductance and Tert is the external temperature One can include this condition with the BC type thermal surface conductance BC Regions 1 BC Region name BC region type thermal_surface_conductance BC_reg_numb 3 g_surf 0 01 temperature 300 68 CHAPTER 7 HEAT BALANCE SIMULATION where g surf indicates and temperature stands for Tert Alternatively i
50. oundary condition I lt 13 23 23 24 26 Zr 29 29 30 30 32 33 34 35 II 5 2 2 External pressure boundary condition 5 2 8 Extended device boundary condition 5 3 Solver parameters Structure with a substrate 5 3 2 Structure without a substrate freestanding 5 3 3 Additional parameters 5 4 Physics section parameters 5 9 1 5 5 Output Drift diffusion simulation of electrons and holes 6 1 Theory 6 2 Plot variables 6 3 Models section Recombination models 6 3 2 Thermoelectric power models 6 3 3 Mobility models 6 3 4 Boundary conditions 6 4 Physics section Simple semiconductor model 6 4 2 Default semiconductor model 6 5 Solver section Parameters for PETSc solvers 6 5 2 Parameters for the TIBERCAD nonlinear solver 6 5 3 Parameters for the PARDISO linear solver 6 3 1 6 4 1 5 5 1 Heat Balance simulation 7 1 Heat equation 7 2 Physical model Electron and hole dissipations 7 2 2 Boundary conditions 7 3 Output data Tl Envelope Function Approximation 8 1 Models section parameters 8 2 Solver parameters Eigenvalue problem parameters 8 2 2 Schr dinger equation parameters 8 3 Physical Models parameters 8 2 1 8 4 Output CONTENTS CONTENTS 9 Simulation opticskp DA CONDES dup or uoa e eS ar GS e e 10 Simulation opticalspectrum ILI DNE e uox Des da RUE Su La E 11 Quantum dispersion 11 1 Olver options CN ae IS ONDE SEENEN 12 Quantum
51. ow field mobility see 6 3 3 physical model recombination 1 model srh physical model electron mobility d model field dependent low field model doping dependent 3 Definition of Boundary Conditions The source drain and gate contacts of the Mosfet device are defined as Boundary conditions regions BC Region source BC Region drain BC Region gate in the following way BC Region gate d BC reg numb 2 type schottk barrier height 3 0 voltage Vg 0 0 BC_Region source BC_reg_numb 1 type ohmic 19 voltage 0 0 BC Region drain BC_reg_numb 3 type ohmic voltage Vd 0 5 To each of the BC regions one BC reg numb is assigned that is one of the Physical Lines 1 2 3 defined in Step 1 which represent the contact regions Note that while source and drain are defined as type ohmic gate BC region is defined as type schottky barrier height 3 0 specifes the metal oxide interface barrier and depends on the contact metal workfunction Drain voltage is defined as Vd 0 5 and gate voltage as Vg 0 0 This specifies that the value of the voltage will be determined at each moment of the simulation by the value of the two variables Vd and Vg which will be assigned in the sweep definition 4 Definition of Simulation parameters Two sweeps are requested for this simulation that is an external loop on Vg the gate voltage and an internal loop on Vd the drain voltage
52. per values to mesh teristic lengh of the defined Points Lg 2 0 0375 d 0 01 Ls 0 1 h 0 25 b 0 0025 o 0 005 13 14 CHAPTER 3 GETTING STARTED 2D xd Lg 2 d xd2 Le 274 d 2 xmax xd Ls d These other convenient variables are used to parametrize the most relevant geometrical features such as channel length oxide thickness and so on Point 1 0 h 0 lsub Point 2 0 0 0 1c Point 3 xmax h 0 0 1sub Point 4 xmax h 0 0 1sub Point 5 xmax 0 0 0 1h Point 6 xmax 0 0 0 1h Line 1 4 1 Line 2 3 13 Line 6 4 14 Line 7 10 9 Line 8 12 2 Line 9 8 7 Line 10 11 8 Line 11 9 12 Line 13 7 6 e Geometrical Points and Lines are defined to design the device structure the fourth parameter in Point assignement is the characteristic length associated to that point this is an essential feature to control the mesh density and refine it where necessary usually n the channel region Line Loop 40 28 2 34 33 8 29 31 30 6 1 Plane Surface 41 40 e Definition of a surface first a line loop is composed listing all the lines con stituting the boundary of the surface then this line loop is assigned to a Plane Surface object this procedure can be alternatively performed throgh the graphical interface 15 41 n Si 44 47 n Si 46 8102 Physical Surface 1 Physical
53. ro chemical potential Current Total current density eCurrent Electron current density Acm 7 hCurrent Hole current density Acm 2 Polarization Electric Polarization Cm GradPn Gradient of electron ther VK cm moelectric power GradPp Gradient of hole thermo VR tem electric power Table 6 2 Elemental quantities Scalar quantities ContactCurrents Contact currents a depends on dimension and symmetry Table 6 3 Scalar quantities from the material database The recombination times are dependent on temperature and doping density e g TN Ta 6 3 Tmaz n Tmin n 2 2 6 4 OO en Tminn F where To is the reference temperature 300 K Table 7 2 shows the corresponding pa rameters for the material data files The recombination times and trap level can be overridden from the input file by using the keywords of table 6 5 in the appropriate physical model section or in the Region section the latter overrides the former Direct radiative recombination The direct recombination model can be enabled in the input file by specifying 6 3 MODELS SECTION 95 physical model recombination model Listing 2 Declaration of SRH recombination model parameter electrons holes Tin taumin_e taumin h Tar taumax_e taumax_h Nref e Nref h y gamma e gamma h Etrap a Talpha e Talpha h Table 6 4 SRH material
54. s inside the braces on the right hand side give the three X Y and Z coordinates of the point the last expression 0 5 or 0 002 in this example sets the characteristic mesh length at that point that is the size of a mesh element defined as the length of the segment 4 CHAPTER 1 OVERVIEW for a line segment the radius of the circumscribed circle for a triangle and the radius of the circumscribed sphere for a tetrahedron Thus the smaller is the value of the characteristic mesh length the greater is the mesh density close to that point The size of the mesh elements will then be computed in GMSH by linearly interpolating these characteristic lengths in the whole mesh In the definition of a geometrical Line the two expressions inside the braces on the right hand side give the identification numbers of the start and end Points of the line Then two physical regions are defined each associated to one of the two geometrical entities Physical Line 1 and Physical Line 2 The expression s inside the braces on the right hand side give in general the identification numbers of all the geometrical lines that need to be grouped inside the Physical Line In this way these physical regions are made available for TiberCAD and will be used to associate them to a TiberCAD region through the keyword mesh regions as follows Region reg 1 1 mesh regions 1 Region reg 2 mesh regions 2 Then in the GMSH script two Physical Point are d
55. s to which a particular model is assigned simulation environment is therefore defined by the mesh elements belonging to its physical regions and by the simulation model which has been associated to these regions This association is made possible by the definition of TrBERCAD Regions and Clusters Different simulation environments can have physical regions in common In this way each simulation is run on a subset of the device and can be possibly coupled even self consistently with a simulation run on a different subset of the device corre sponding to a simulation environment with a non void intersection with the first one The coupling of the two simulations is performed by means of appropriate Boundary Conditions e g Current Density Voltage In principle the two simulation environ ments can refer to two simulations at different scale e g atomistic tight binding and macroscopic drift diffusion This allows an effective multi scale simulation of the device to be studied 1 3 Physical and boundary regions in TiberCAD When TiberCAD is run it reads the mesh file which contains the finite element grid which meshes the geometrical description of the device or nanostructure and which will be the basis of PDE discretization To execute the proper simulations TiberCAD needs some information about the physical and boundary regions associated with the mesh a physical region associates all the elements corresponding to an homogeneous part
56. section two kinds of block can be present the Region blocks contain the description of the device in continuous media approach each of the Cluster blocks define a group of regions mesh regions even with different physical properties but to be treated together somewhere in the simulation e g quantum calculation In this way it is possible to refer to the set of these regions simply by the Cluster name Each Region block must be preceded by the keyword Region followed by the single word name of the TiberCAD Region For an ISE TCAD mesh it can be the name of an ISE TCAD mesh region as defined during the modeling of the device in this case if mesh regions is absent the TiberCAD Region will be associated to that ISE TCAD mesh region Region QWell 1 mesh regions 4 5 mesh regions 4 structure 2 y growth direction 1 0 1 0 z growth direction 1 2 1 0 x growth direction 0 0 0 1 material GaN doping 1e17 doping type donor doping level 0 025 Here are the description of the available keywords for a Region block material mandatory name of the material associated to the present region it can be an alloy in this case the keyword z must be present x alloy concentration e g in Al Ga _ As x is Al concentration mesh regions a list of region ID s for GMSH as specified in the meshing pro gram or ISE TCAD name s to be implemented If it is not present the TiberCAD Region name mu
57. sh In GMSH script several variables can be defined and given a value in this way Eom d 0 01 these are valid GMSH variables L is just the length of the Si sample d is the value of a characteristic mesh length see below e Definition of geometrical entities Points Point 1 Point 2 AA t o oo oo a Q Gei 8 CHAPTER 2 GETTING STARTED 1D In the definition of a geometrical point the three first expressions inside the braces on the right hand side give the three X Y and Z coordinates of the point the last expression d sets the characteristic mesh length at that point that is the size of a mesh element defined as the length of the segment for a line segment the radius of the circumscribed circle for a triangle and the radius of the circumscribed sphere for a tetrahedron Thus the smaller is the value of d the greater is the mesh density close to that point The size of the mesh elements will then be computed in GMSH by linearly interpolating these characteristic lengths in the whole mesh e Definition of geometrical entity Line Line 1 1 2 The two expressions inside the braces on the right hand side give the identification numbers of the start and end points of the line e Definition of the physical entity Physical Line 1 Physical Line 1 1 The expression s inside the braces on the right hand side give the identification numbers of all the geometrical lines that need to be gro
58. sh generation some command line options are 1 2 3 to perform 1D 2D or 3D mesh generation o mesh file msh to specify the name of the mesh file to be generated In this way a msh has been generated and is ready to be read in TrBERCAD Step 3 TiberCAD Input file Now we have to write down the TIBERCAD input file see bulk tib in the Tutorials 1 Definition of Device Regions First we have to list all the TIBERCAD Regions present in our Device a TiBERCAD Region is usually a section of the device featuring the same material and possibly the same doping Device Region bulk mesh_regions 1 material Si doping 1e16 doping_type donor The TiBERCAD Region bulk is made of Silicon and n doped with a concentration em Through the keyword mesh_regions one or more of the physical regions Physical Lines in 1D Physical Surfaces in 2D Physical Volumes in 3D previously defined in the GMSH mesh can be associated to the present TrBERCAD Region 10 CHAPTER 2 GETTING STARTED 1D With mesh regions 1 we associate the Physical Line 1 defined in the Step 1 to the TIBERCAD Region bulk 2 Definition of Simulation Now we define the Simulation driftdiffusion 1 it belongs to the class driftdiffusion Models 1 model driftdiffusion options simulation name driftdiffusion 1 physical regions all The TIBERCAD simulation driftdiffusion 1 belonging to the model driftdiffu
59. sion will be applied to the whole device structure physical regions all 3 Definition of Boundary Conditions The anode and cathode contacts of our 1D Si sample are defined as Boundary condi tions regions BC Region anode BC Region cathode in the following way BC Region anode 1 BC reg numb 1 type ohmic voltage Vb BC Region cathode BC_reg_numb 2 type ohmic voltage 0 0 Both contacts are defined as ohmic cathod is assigned a fixed voltage 0 0 while anode voltage is given by the value of the variable Vb voltage Vb 11 Through the keyword BC reg numb one or more of the n 1 D physical regions Physical Points in 1D Physical Lines in 2D Physical Surfaces in 3D previously defined in the GMSH mesh can be associated to the present TIBERCAD BC Region With BC reg numb 1 we associate the Physical Point 1 defined in the Step 1 to the TiBERCAD BC Region anode with BC reg 2 we associate the Physical Point 2 defined in the Step 1 to the TIBERCAD BC Region cathode 4 Definition of Simulation parameters The variable Vb is specified in the sweep block in the Solver section Sweep t simulation driftdiffusion 1 variable Vb start 0 0 stop 1 steps 10 In this way the simulation driftdiffusion_1 is performed for 10 steps 10 values of the anode voltage variable Vb between 0 and 1 5 Definition of Execution parameters In the Simulation sect
60. space If refine E space true that is adaptive k mesh refinement is enabled all the el ements whose error is greater than the value 1 refine fraction maximum error are going to be refined In this case Error is just the integrated quantity The refinement will end when the relative accuracy is obtained number of nodes numb of elememts in k mesh along each direction wedge half quarter to reduce calculation time by exploiting symmetry optical matr elem model name of the opticskp model associated polarization light polarization vector Emin Emaz dE energy range and step of spectrum calculation 10 1 Output The output variables for optics calculations are e optical spectrum k space integrated optical emission spectrum calculated by opticalspectrum model Chapter 11 Quantum dispersion There is a possibility to calculate the dependence of quantum eigenstates on k vector Such dependence is called dispersion The simulation name is quantumdispersion Example model quantumdispersion 1 options 1 simulation name dispersioniD el physical regions all 11 1 Solver options The dispersion of quantum states is calculate at k points that are nodes of the mesh in k space e quantum_simulation name of the Schr dinger equation simulation e min_eigenvalue_number max_eigenvalue_number the dispersion is calcu lated for the states number 7 where max eigenvalue number gt
61. specified the default semiconductor model based on bulk k p theory is used The electron quantum density and hole quantum density will use the parti cle densities calculated from the corresponding quantum density simulation In re gions where no quantum density is available the classical density will be used The electron quantum density and hole quantum quantum density keywords can be used also in the Region sections to be able to use different quantum density simulations in different regions 6 5 SOLVER SECTION 61 The strain simulation option is used to specify the simulation that provides strain in the case of strained systems If it is omitted an unstrained system is assumed for the drift diffusion calculation The thermal simulation option is used to specify the simulation that provides the lattice temperature for non isothermal simulations If it is omitted the simulation tem perature as provided in the Simulation section of the input file or if not provided the default value of 300 K is used 6 4 1 Simple semiconductor model When specifying model simple a very simple semiconductor model is used For this model one has to provide conduction and valence band edges and the effective density of states masses in the Region sections The corresponding keywords are given in table 6 10 keyword description Ec conduction band edge eV Ev valence band edge eV m dos e conduction band effective DOS mass me
62. st be a valid name of an ISE TCAD mesh region structure crystal structure wz wurtzite zb zincblend x growth direction y growth direction z growth direction Bravais vectors with Miller indexes for wurtzite crystal 4 element vectors or zincblende crystal 3 element vectors doping doping concentration doping type donor or acceptor doping level energy level of the dopant eV 26 CHAPTER 4 INPUT FOR TIBERCAD Each Cluster block must be preceded by the keyword Cluster followed by the single word name of the Cluster Cluster Quantum 1 mesh regions 3 4 5 mesh regions mandatory list of the physical regions region ID s for GMSH as specified in the meshing program or ISE TCAD name s to be grouped in the cluster Regions and Clusters represent the macroscopical description of the device or struc ture to be be simulated in TiberCAD In the rest of the input file the physical regions associated to Models or Atomistic descriptions will be indicated by means of the TiberCAD Region and Cluster names 4 3 Scale section The section Scale is dedicated to the optional definition of Non Continuous Media regions for the device these regions wiil be described and studied at a different scale e g atomistic circuit level lumped model etc As for now just the atomistic description is implemented Atomistic blocks if present specify a possible atomistic description associated to one or
63. st type gmsh mosfet geo 2 o mosfet msh Step 3 TiberCAD Input file Now we have to write down the TIBERCAD input file see mosfet tib in the Tutorials 16 CHAPTER 3 GETTING STARTED 2D 0 0025 0 0606 0 124 0 187 0 138 0 0688 0 0 0688 0 138 Figure 3 1 Geometrical structure as defined by GMSH modeller 0 0025 0 0606 0 124 0 187 0 138 0 0688 0 0 0688 0 138 Figure 3 2 2D Mesh for the mosfet device obtained with GMSH 17 1 Definition of Device Regions Three TrBERCAD regions are defined to each of them one mesh region is associated that is the Phisical Surfaces 1 2 and 3 defined in Step 1 However in general more than one mesh region can be associate to a single TIBERCAD region if this is convenient Region substrate 1 mesh regions 1 material Si doping 1e18 doping type acceptor Region contact mesh_regions 2 material Si doping 5e19 doping_type donor Region oxide mesh_regions 3 material 5102 2 Definition of Simulation Now we define the Simulation dd it belongs to the class driftdiffusion model driftdiffusion 1 options d simulation name dd physical regions all 18 CHAPTER 3 GETTING STARTED 2D We declare two driftdiffusion physical models the first defines a srh recom bination model see 6 3 1 the second defines a field dependent mobility model for electrons which implements a doping dependence for the l
64. sumes to have reached convergence nonlin step tol is measured in eV 6 5 2 Parameters for the Tisz amp CAD nonlinear solver Table 6 14 summarizes the parameters used for the TrBERCAD implementation of the line search algorithm keyword description default nonlin_rel_tol relative tolerance for the residual 5 norm 10e 9 with respect to first nonlinear step nonlin abs tol absolute tolerance for the residual 5 norm 10e 15 nonlin step tol tolerance for the maximum norm of the non 10e 3 linear step eV nonlin max it maximum number of nonlinear iterations 20 Table 6 14 Parameters for the TIBERCAD line search The stopping criterion based on the line search step uses the maximum norm of the nonlinear step i e convergence is controlled locally In addition to the parameters in table 6 14 one has to provide also parameters for the linear solver 6 5 3 Parameters for the PARDISO linear solver NOTE the PARDISO linear solver is currently not included in the distribution Currently the PARDISO interface has no adjustable parameters Chapter 7 Heat Balance simulation The theoretical model of the heat balance problem can be found in Ref 7 7 1 Heat equation The steady state heat equation with the continuity equation reads as where T is the temperature is the thermal conductivity tensor and Hg is the total heat source The latter term is the sum of the heat sources specified by the submodels describe
65. t charge density calculation 8 3 Physical Models parameters e particle el hl e model conduction band kp single conduction band point or k p e kp model 6x6 8x8 74 CHAPTER 8 ENVELOPE FUNCTION APPROXIMATION Here the particle name is the name of a particle type electron or hole model kp conduction band k p or single conduction band model If k p model is applied specify kp model 6x6 8x8 8 4 Output e EigenEnergy Eigen energy in eV e EigenFunctions v r function of the eigenstate Occupation probability to find the state occupied It is calculated assuming Fermi distribution and mean electrochemical potential and temperature ES hjal 8 2 T QT r v 8 3 EnergyLevels graphical output used for showing the energy level over the band diagram Chapter 9 Simulation opticskp By defining the opticskp model calculation of optical properties is enabled in particu lar the optical kp matrix elements are calculated from the quantum models specified in Solver section opticskp 1 initial state model Qui electrons quantum el final state model Wi holes quantum hl initial eigenstates 0 19 final eigenstates 0 19 Here initial state model and final state model are respectively the quantum models efaschroedinger model associated respectively to the initial state of optical transition e g electron and to the final state of optical transition e g hole
66. t is possible to indicate the R 1 G_s quantity i e the thermal surface resistance The notation is BC Regions 1 BC Region name BC region d type thermal surface resistance BC reg numb 3 r surf 100 temperature 300 Furthermore it is possibile to fix the normal thermal power density to a given value Le JaN dos 7 6 This condition is set with the BC type thermal flux BC Regions 1 BC Region name BC region 1 type thermal flux BC reg numb power density I wl 100 7 3 Output data The variable labels are listed in the tables 7 3 7 5 It is also possible to identify all heat sources with the keyword HeatSource and all power fluxes with PowerFlux Finally with the keyword thermal all quantities concern ing the thermal simulation will be stored 7 3 OUTPUT DATA 69 description type parameters units Ideal insulating interface Default No parameters Ideal conducting interface heat_reservoir temperature K Resistive interface thermal_surface_resistance temperature K r_surf cm KW Resistive interface thermal_surface_conductance temperature g_surf VR em Power density condition thermal flux power density Wem Table 7 2 Thermal boundary conditions Nodal scalar quantities LatticeTemp Temperature K Table 7 3 Nodal scalar quantities Elemental scalar quantities eJoule hJoule RecHeat ePelTh hPelTh TotalHeat Electron Joule effect Hole Jou
67. ully performed an output file is produced with the extension grd This file contains the description of the mesh and also the list of the user defined material regions and contact regions By reading this grd file in TiberCAD one can refer to the ISE TCAD material regions simply with the user defined name which is present in the grd file This name should be unique in the whole device In the same way ISE TCAD Boundary regions Contacts can be referred to in TiberCAD by means of their user defined name present in the grd output file too If GMSH program is used to model and mesh the device a bit more care has to be taken Please see the GMSH user manual http geuz org gmsh for further details In the context of GMSH it is possible to define several 1 2 and 3D Physical Entities These Physical Entities allow to associate one or more geometrical entities to a single numerical ID so that several mesh regions and BC reg numb can be defined and re ferred to by TiberCAD Here is a simple example of a script to generate a 1D geometrical model geo file in GMSH see also chapter 2 Point 1 25 0 0 0 5 Point 2 0 0 0 0 002 Point 3 25 0 0 0 5 Line i 1 2 Line 2 2 3 Physical Line 1 2 Physical Line 2 1 Physical Point 1 3 Physical Point 2 1 Here first the geometrical entities Points and Lines are defined In the definition of the geometrical Points the three first expression
68. uped inside the physical line In this way in general physical regions are created which associate together geomet rical regions and then the related mesh elements which share some common physical properties It s only these physical regions which can be referred to outside GMSH In TIBERCAD this is done by associating one or more physical regions to a TiberCAD region through the keyword mesh regions see in the following e Definition of two physical entities Physical Point Physical Point 1 Physical Point 2 1 2 N B In general in nD simulation n 1 D physical regions points in 1D lines in 2D surfaces in are used by TIBERCAD to impose the required boundary condi tions Each n 1 D physical region defined in this way in GMSH will be associated in TiBERCAD to a boundary condition region through the keyword BC reg numb Thus in this case Physical points 1 and 2 will be associated respectively to two BC regions see in the following Step 2 Meshing the device The geo script file with the geometrical description can be run in GMSH to display the modelled device and to mesh it through the GMSH graphical interface Alternatively a non interactive mode is also available in GMSH without graphical user interface For example to mesh this 1D tutorial in non interactive mode just type gmsh bulk geo 1 o bulk msh where bulk geo is the geometrical description of the device with GMSH syntax 1 means 1D me
69. ust be pre ceded by the keyword physical model followed by the single word name of the physical model Each physical model block can contain parameters relevant to a specifical model of a physical property or quantity related to the present model e one or more Boundary Condition regions blocks BC regions block The BC regions block must be preceded by the keyword BC Regions and it is com posed by one or more parameters blocks each preceded by the keyword BC Region followed by the single word name of the boundary condition region This parameters block can contain the possible description of the boundary region These optional blocks must be strictly in this order first the options then the physical model and finally the BC regions blocks A detailed description of the possible parameters for these blocks follows 4 4 1 options block options simulation_name driftdiffusion physical_regions all physical_regions channel_1 channel_2 simulation name user defined name of the particular instance of the simulation model defined for this block More than one simulation with different name and prop erties can be defined in separated model blocks which refer to a same TrBERCAD simu lation model If simulation name is not assigned by default the TIBERCAD model name is taken as current simulation name physical regions list of physical region s to which the present simulation model will be applied
70. x true false periodicity_y true false periodicity_z true false The default value is false Mesh refinement For the details about mesh refinement refer to the Libmesh library documentation The parameter refinement_steps defines the number of the refinement steps to be done with default value equal to zero The parameter uniform refinement true false is used to choose between uniform and adaptive refinement The default value is false i e adaptive refinement Example refinement_steps 4 refine_fraction 0 25 coarsen_fraction 0 max_refinement_level 10 Deformed shape calculation The displacement field and lattice matching parameters that are found from master equations can be used in order to define a new shape of the heterostructure This new shape is the first approximation to the equilibrium one The next approximations are obtained iteratively by the following steps at the n th iteration the master equations are solved using the lattice matching deformation which is defined as 1 out du a Let 5 5 LE 2 On Ox where the displacement field u has been taken from the iteration n 1 Then the new shape is defined by using the displacements from the last step solution and the iterative process is repeated until the displacement field vanishes and additional lattice parameters stabilise The iterative cycle usually converges after 3 4 iterations The only param

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