TRIDYN - FZR User Manual
Contents
1. 0 16 In analogy to 3 3 6 the combination of eqs 9 12 15 yields for the stoichiometric compound n m Zum SBV SBV Z AH ZiM AH ze AH 17 n In summary the matrix formulation for the surface binding energies eg 2 allows a large 12 variety of different models for the surface binding as discussed in 3 3 1 3 3 7 Similar formalisms can be derived for more than two components Other models might be appropriate for specific problems 3 4 Relocation Threshold Energy Subthreshold Recoils The relocation of recoils is steered by the recoil index IRCO and the relocation threshold energies ED I The relocation threshold critically determines the amount of ion mixing but also the shape of compositional profiles resulting from low energy implantation and or preferential sputtering The width of collisional mixing profiles scales as ED The conventional model assumes that a Frenkel pair can only be formed if the interstitial atom is relocated far enough from its original lattice site corresponding to a minimum energy transfer when it is created This minimum energy transfer is denoted as the displacement threshold energy which is in the order of several 10 eV This model can be implemented by identifying the relocation threshold energies with the displacement threshold energies and setting subthreshold recoils bound with IRCO gt 0 In the simulation this causes all recoil atoms to be2. part name is used for the characters creation of all output files Decides whether plots with intermediate results of the simulation appear in a separate window after each 20 progress of the calculation Plots appear y Plots do not appear n Integer 0 lt IFOUT lt NH Default IFOUT NH 20 the number of pseudoprojectile histories after which the status messages appear on the screen UT the number of pseudoprojectile Integer 0 lt IDOUT lt NH histories after which integral data Default IDOUT NH 5 files nameSRFC DAT see below are written the number of pseudoprojectile histories after which the profile output files namePRxx DAT are created NCP total number of components Integer 2SNCPS5 IDREL index of suppression of dynamic Integer Default 0 gt 0 suppression of relaxation dynamic relaxation lt 0 suppression of dynamic relaxation and cascades index of structure type Integer 0 1 0 homogeneous target 1 inhomogeneous target l index for treatment of recoil atoms Integer Default 1 lt 0 subthreshold in cascade recoils free 20 subthreshold recoils bound initial random number for the Integer IRAND gt 0 Default 147483647 random number generator l JCP1 JCP2 suppression of recoils of Integer O lt ICP1 lt ICP2 1sJCP24 components with number between Default JCP1 0 JCP2 1 i
3. WISSENSCHAFTLICH TECHNISCHE BERICHTE FZR 317 April 2001 ISSN 1437 322X ai a Wolfhard Moller and Matthias Posselt TRIDYN_FZR User Manual Forschungszentrum Rossendorf e V Mitglied der Wissenschaftsgemeinschaft Gottfried Wilhelm Leibniz Herausgeber FORSCHUNGSZENTRUM ROSSENDORF Postfach 51 01 19 D 01314 Dresden Telefon 49 351 26 00 Telefax 49 351 2 69 04 61 http Awww fz rossendorf de Als Manuskript gedruckt Alle Rechte beim Herausgeber FORSCHUNGSZENTRUM ROSSENDORF 774 WISSENSCHAFTLICH TECHNISCHE BERICHTE FZR 317 April 2001 _ TRIDYN_FZR User Manual Wolfhard M ller and Matthias Posselt Institute of Ion Beam Physics and Materials Research Forschungzentrum Rossendorf 01314 Dresden Germany The present report contains the User Manual of the FZR version of the dynamic binary collision computer simulation code TRIDYN The present version of the code is based on TRIDYN Vs 4 0 by W M ller and W Eckstein Department of Surface Physics Max Planck Institute of Plasma Physics Boltzmannstra e 2 85748 Garching Germany 1989 Modifications in particular for PC implementation quasi dynamic display and the input dialog have been performed at the Institute of Ion Beam Physics and Materials Research by V Kharlamov T Schwieger M Posselt and W M ller 1995 2001 General remarks TRIDYN simulates the dynamic change of t
4. SBV tac SBV ratte 8 1 eV and SBEc SBV cra SBV cc SBV cue 8 95 eV and for the projectile component SBEy SBVuera SBV ec SBVusne EFy 9 eV see 3 3 1 and eq 1 3 3 5 Solid Gas Compounds Constant Surface Binding Energy If one of the constituents of the target A Bm e g B is from a diatomic gas its enthalpy of dissociation AH has to be taken into account Then in analogy to eq 7 l n SBE m SBE n AH AH AH 9 As the gaseous component will normally not be enriched significantly a proper choice is SBE SBV 4 SBV 4 AHS 1 1 10 SBE SBV 4 SBV ps AH AH Example During the ion beam synthesis of SiN by nitrogen bombardment of silicon the surface stoichiometry remains between pure Si and the stoichiometric Si N4 compound With AH 4 7 eV AH 9 85 eV and AH Tyan 7 8 eV one obtains SBEs SBV sis SBV 4 7 eV and SBEy SBVys SBV yy 6 95 eV In some cases an atomization enthalpy AH per atom of the gaseous component can be found in the literature see e g ref 5 Then SBE SBV SBV AH 11 This is strictly valid only if the deviation of the surface composition from stoichiometry is small For a diatomic compound A B eq 2 reads 12 SBE SBV z Cy SBV 5 Cp il Physically the matrix elements SBV denote the interaction energies between atoms i and j Therefore SBV SB
5. energies can be chosen independently with corresponding results in the static output file see below Note With the free subthreshold recoil option RCO lt 0 make sure that sputtering is not influenced by the choice of excessively high cutoff energies 4 Maximum Concentration Reemission Simplified Diffusion Model For each component a maximum atomic fraction can be defined by QUMAX This is of particular interest if gaseous species are involved 13 4 1 Nonreactive Gas Implantation An implantation of nonreactive gaseous atoms is often limited by a saturation in the implanted region which often depends on the implantation temperature Physically sizeable amounts of gas reside in gas filled voids If the saturation concentration is known from experiment it can be inserted into the TRIDYN simulation If it is not known it is preferred to fully ignore the implanted species such as for ion mixing preferential sputtering and nonreactive ion assisted deposition using QUMAX 0 The opposite case of an unlimited implantation QUMAX 1 is problematic for several reasons In addition to an unrealistically high gas incorporation a large fraction of the collisional energy will be transferred to the gaseous component thus reducing e g the sputtering yields of the other components 4 2 Solid Gas Compound In a solid gas compound the atomic fraction of the gaseous component is often limited to a value close to
6. followed down to their cutoff energy but to be restored at their original sites after cutoff provided their initial energy had been below the relocation threshold energy In this way in the subthreshold regime only mass transport is suppressed whereas cascade evolution and momentum transport are maintained Thus e g sputtering is not influenced by the choice of the relocation threshold It should be noted that the concept of a displacement threshold is strictly valid only for a perfect and nondamaged crystal In an amorphous substance or in a solid being subjected to high fluence ion bombardment which is the standard application of a TRIDYN simulation relocation thresholds might be significantly lower Well based data cannot be given However according to experience with ion mixing and preferential sputtering simulations and their comparison to experimental findings a relocation threshold energy of 8 eV has turned out to be successful in a number of different systems such as metallic compounds at low temperature and oxides so that this value is recommended For each element the relocation threshold energy given in the file elements dat is taken as the default value The free subthreshold recoil option IRCO lt O gives additional flexibility In this case all recoils remain at the position where the cutoff energy is reached Thus the cutoff energies see 3 1 serve as efficient relocation thresholds Then the displacement threshold
7. immediate dissociation of the incident molecule Then the incident energy F0 of the molecule is distributed according to the atomic masses MM and Mg resulting in E 0 M 9 Bm nM mM 23 E0 a BB _ 50 nM mM Anim Example For the plasma etching of silicon CF ions may represent a major species For a substrate bias of 500 V corresponding to an incident ion energy of EOcr 500 eV eq 23 yields with Mo 12 g mole and M 19 g mole E0c 87 eV and E0 138 eV 6 2 Thermal Neutrals and Low Energy Ions Often the incident flux consists of ions and neutral particles at thermal energies such as in ion assisted deposition or plasma enhanced chemical vapor deposition Such species can be treated in TRIDYN by setting E0 0 24 neutr 16 As stated above the treatment of the collisional processes in TRIDYN is problematic for very low ion energies about 30 eV and below Nevertheless the low energy incident particles will be correctly deposited at the surface The user should be aware of the fact that each incident pseudoparticle is accelerated by the surface binding energy SBE I before entering the solid 17 Output TRIDYN provides the following output files Depth profiles of the components for given namePRxx DAT AINSPRO4 DAT values of the incident fluence nameSRFC DAT AINSSRFC DAT nameARDN DAT AINSARDN DAT nameSPYL DAT AINSSPYL DAT nameREEM DAT AINSREEM DAT nameS
8. parameters Therefore the input file namexxxx IN should preferably be edited directly once it is available Step 2 Running the Simulation The following input files are necessary for starting the simulation see above a in the case of a homogeneous target namexxxx IN e g AIN5xxxx IN b in the case of a inhomogeneous target namexxxx IN e g AIN5xxxx IN and namexxxx LAY e g AIN5xxxx LAY Run of the simulation code tridynfzr exe Command tridynfzr exe lt namexxxx IN Example tridynfzr exe lt AIN5xxxx IN During the run information about the status of the calculation appears on the screen Input Data The input file namexxxx IN contains the following variables Line 1 namexxxx IN Line 2 PPLOT Line 3 IFOUT Line 4 NH IDOUT IQOUT NCP IDREL IQ0 IRCO IRAND JCP1 JCP2 JFRP INRM Line 5 FLC INEL IWC IDIFF Line 6 TT TTDYN NQX DSF IOXN IOXX IMCP Line 7 ZZ 1 M 1 BE 1 ED 1 EF 1 QU 1 DNSO 1 CK 1 Line 8 E0 1 ALPHA0 1 QUBEAM 1 QUMAX 1 SBV 1 1 SBV 1 NCP Line 9 ZZ 2 M 2 BE 2 ED 2 EF 2 QU 2 DNS0 2 CK 2 Line 10 E0 2 ALPHA0 2 QUBEAM 2 QUMAX 2 SBV 2 1 SBV 2 NCP Line 11 The names used above are the same as in the TRIDYN_FZR source code Name of Description Parameter range or meaning variable Default settings namexxxx IN the name of input file The first Part name consist of A ASCI
9. simulation as e g for high energy or low fluence implantations or inert gas bombardment where the gas concentration is neglected see 4 In such cases the choice of the surface binding energy of the projectile species is not critical A reasonable choice is SBE pro EF proj 3 proj T 3 3 2 Enthalpy of Sublimation For the prediction of the sputtering yield of monoatomic substances by TRIM the choice of the sublimation enthalpies AH for the surface binding energies has proven to be successful For each element the sublimation enthalpy given in the file elements dat is taken as the default value For multicomponent solids one might also choose as the most simple approximation SBE AH 4 This simple model is also a good approximation for multiatomic targets with low heats of fusion such as metallic alloys SBV AH for all j 5 3 3 3 Nonreactive Gaseous Components It is often difficult to define the surface binding energy of a nonreactive gaseous component due to the very low and often unknown enthalpy of physisorption Ideally on would tend to set AH gt 0 6 However this choice would require consistently low cutoff energies see 3 1 and result in long computing times A general recipe cannot be given The stability of the results against the choice of the surface binding energy should be checked 3 3 4 Solid Solid Compounds Constant Surface Binding Energy The following recipes shall be restricted t
10. MCP lt 5 Default O if calculation of the moments of the IMCP 0 no moment calculation depth distribution no output in present version ZZ i atomic number of component Integer value in real format 1 lt ZZ D lt 92 number I MQ mass in amu of component Real M D gt 0 number I BEM bulk binding energy of component Real BE gt 0 number I eV x g relocation threshold energy of Real ED D gt 0 component number I eV EF cut off energy eV atom with Real EF gt 0 Default 0 1 energy falling below this value is considered to be stopped Real 0 lt QU lt 1 For beam component default 0 fraction of component number I in the target substrate atomic density of component Real DNSO gt 0 number I 10 cm DNSO 1 V where V is the volume occupied by atom of component number I CK D electronic stopping correction Real CK D gt 0 Default 1 factor EOD incident energy of component Real EO I gt 0 number I eV angle of incidence of component Real OSALPHA lt 90 number I with respect to the surface normal QUBEAM fraction of component number Iin Real OsQUBEAM lt I For target the beam component QUBEAM D 0 QUMAX UD maximum fraction of component Real OSQUMAX lt QU D number I in the target SBVAN surface binding e
11. RRS DAT AINSSRRS DAT nameOUT DAT AINSOUT6 DAT In the output listing 7 the lines given below the lines denoted by areal densities and fluences should in general be ignored for a dynamic TRIDYN run They contain information on depth and energy deposition profiles as well radiation damage in a simple Kinchin Pease model integrated over the whole run However in static mode IDREL lt O the simulation corresponds to a standard TRIM simulation with this output Default xx 00 01 02 03 04 05 i e an output file is created at the beginning of the simulation and after each fluence increment of 20 of the total fluence Surface composition within the averaging depth DSF as function of incident fluence Default cf 1 Integrated areal densities of the components within TTDYN as function of the incident fluence Default cf 1 Sputtering yields of the components as function of the incident fluence Default cf 1 Accumulated reemitted fluence as function of the incident fluence Default cf 1 Surface recession as function of incident fluence A negative surface recession corresponds to a thin film deposition Default cf 1 Output listing Gnput data statistics particle balances static projectile component 1 only and energy deposition profiles see remark given below 18 Test of the statistical quality and precision of the results
12. V has been assumed For a solid solid compound they are related to the enthalpies of formation and sublimation AH and AH respectively For ca J and cs 0 and vice versa the pure components A or B are given so that SBV AH SBV AHS 13 The combination of eqs 7 12 13 yields for the stoichiometric compound with c n n m and cs m n m SBV SBV x gt aH AH 27 ant 14 nm Compared to eq 8 eqs 13 14 are of better symmetry and thus more rigorous but still only valid if the deviation from the stoichiometric compound is not too strong Alternatively by setting c 0 and cg 1 in eq 12 top or vice versa in eq 12 bottom the non diagonal matrix elements may be identified with the sorption energy of A on the elemental B surface and vice versa which are not symmetric in general Then SBV AH 2 SBV AH 2 a5 where AH denotes the sorption enthalpy of atom i on the elemental surface j Unfortunately the sorption enthalpies are not readily available in literature so one will generally prefer the approach of eq 14 except when treating specific problems of surface physics 3 3 7 Solid Gas Compounds Variable Surface Binding Energy If in a diatomic compound A B one of the components is from a diatomic gas e g B one may neglect any interaction of B atoms in the surface Otherwise they would react and form a volatile molecule Therefore SBV AH SBV
13. a given total fluence However the statistical quality and the precision of the results is deteriorated simultaneously A fluence increment of 10 cm per pseudoprojectile e g 10000 pseudoprojectiles at a total fluence of 10 cm is normally a reasonable initial choice The statistical quality can be checked after the termination of the run by means of the output quantity MAXCHA see below The stability of the results against a variation of NQX should be checked 3 Energy Parameters TRIM and correspondingly TRIDYN are BCA simulations with only a repulsive interaction potential Therefore in contrast to classical dynamics simulations solid state energy parameters have to be defined additionally As a general remark the energy parameters should not be misused as fitting parameters e g in order to reproduce experimental values They should rather be chosen according to the best knowledge and according to TRIM and TRIDYN conventions as described in the following 3 1 Cutoff Energy The cutoff energies EF determine the energy at which any pseudoparticle projectile or atom in a collision cascade is stopped Obviously very long computation times result from very low cutoff energies so that these should be chosen as high as possible The upper limits depend on the problem itself For example if a high energy deposition profile as e g for MeV ion beam synthesis where sputtering is negligible shall be simulated a ver
14. as gt 22 i e numerically DNSOmencas gt 10 cm In this way the presence of the gaseous component is neglected for the depth scale calculation but not for the development of the collision cascades unless QUMAX 0 for the inert gas see 4 Example A TaC surface is bombarded with He Du to the more efficient momentum transfer carbon will be sputtered preferentially so that tantalum is chosen as the principal component Any swelling by incorporated helium shall be neglected With Om 16 6 g cm and My 180 95 g mole DNSOm 5 5310 cm according to eq 19 Similarly for the compound with Prc 13 9 g cm and M 12 0 g mole and DNSOmec 8 68 10 cm according to eq 20 From eq 21 DNSO 2 02 10 cm and according to eq 22 DNSOp 10 cm Note For compounds with a very high atomic density the atomic density of the non principal component may become negative according to eq 21 This represents no problem for the processing in TRIDYN 6 Incident Energies 6 1 Molecular Bombardment In many cases such as for molecular ion implantation or in the case of plasma enhanced chemical vapour deposition the incident species are molecules e g A Ba For each of the constituents the beam fractions QUBEAM and the incident energies EO T have to be defined consistently For incident energies being sufficiently large compared the molecular binding energies surface collisions will cause an
15. f JCP1 0 JCP1 and JCP2 recoils of all components are treated Integer NH 70 lt IQOUT lt NH Default IQOQUT NH 5 generation of Frenkel pairs for Integer 1 lt JFRP lt 5 Default 1 components with number gt JFRP only meaningful for static output see below output of profiles for components Integer 1 lt INRM amp S Default 1 with number gt JNRM only meaningful for static output Ben TI T FLC total fluence of all projectiles Real FLC gt 0 10 cm index for model of inelastic Integer 1 2 3 Default 1 1 inelastic interaction interaction nonlocal 2 local 3 equipartition maximum order of weak Integer 1 2 3 Default 1 projectile target collisions index of diffusion model for Integer 0 1 0 diffusion and atoms exceeding maximum atomic reemission 1 reemission fraction see QUMAX below Tr target thickness A Real TT gt 0 YN depth range for dynamic Real TTDYN gt 0 simulation A NQX number of depth intervals within Integer 100 lt NQX lt 500 depth for dynamic simulation DSF averaging depth for surface Real O9S lt DSFSTTDYN composition A IOXN IQXX profile output only for depth Integer OSIQXNSIQXX 1SIQXX lt NOQX intervals with numbers between Default IQXN 0 IQXX NQX if IQXN and IQXX IQXN 0 output for all intervals Number of component for Integer O lt I
16. hickness and or composition of multicomponent targets during high dose ion implantation or ion beam assisted deposition It is based on TRIM using the binary collision approximation BCA model for ballistic transport The main fields of application of TRIDYN include high fluence ion implantation ion beam synthesis sputtering and ion mixing of polyatomic solids ion beam or plasma assisted deposition of thin films and ion beam or plasma assisted etching Ballistic effects such as projectile deposition and reflection sputtering and ion mixing are computed for a target at zero temperature Radiation damage is not taken into account The target and the grown layers are assumed to be amorphous Each simulated projectile pseudoprojectile represents a physical increment of incident fluence incident particles per unit area Up to 5 different atomic species in the target and or in the beam may be considered with different energies and angles of incidence for the beam components Initially homogeneous as well as initially inhomogeneous and layered targets may be treated TRIDYN allows to calculate the depth profiles of all atomic species in the target as function of the incident fluence Additionally sputtering yields total areal densities surface concentrations and re emitted amounts are calculated as function of fluence as well as the surface erosion when sputtering prevails or the grown layer thickness in the deposition regime The p
17. hysical background of TRIDYN is described in the papers given in the refs 1 4 A simple diffusion procedure which is described in this manual can be included in addition to ballistic transport of atoms TRIDYN covers only non thermal processes Due to the binary collision approximation its lower energy limit is in the order of 10 eV Nevertheless experience shows that also collisional processes with slightly lower characteristic energies such as sputtering are predicted quite accurately The upper energy limit is given by feasible times of computation Nevertheless TRIDYN is less suitable for energies in the MeV range and above It does not contain a collision frequency reduction such as in TRIM for higher energies The following files are available to run TRIDYN_FZR input f and input exe source code and dialog program for preparing the input files elements dat file containing atomic data of the elements tridynfzr f and tridynfzr exe source code and executable program Running the Programme under MS DOS Window Step 1 Creating Standard Input Files Dialog using the program input exe Command input exe Creates namexxxx IN and optionally namexxxx LAY Note For all questions Yes No the Yes answer can be chosen by small or capital Y or by pressing the Enter button and the answer No can be chosen by small or capital N Input of parameters for beam and target co
18. ialog are used After that the dialog program is finished Inhomogeneous target from a file This option allows the use of a target structure obtained by a previous calculation The name of the output file namePRxx DAT of the previous calculation which contains the depth profiles of the atomic components is prorapted This file must be in the current directory From this the input file namexxxx LAY is created Be careful with this option In any case the number of ion beam and target components and their sequence must be the same as in the previous calculation If necessary a beam component can be 3 switched off by setting its fraction in the beam to zero Check that the depth for dynamic simulation the number and width of depth intervals and other parameters are the same as in the previous simulation General Note Not all parameters of the simulation are prompted during the input dialog Some of the default parameters of the standard input file namexxxx IN are not optimized for an efficient simulation See notes below for an appropriate choice of all input parameters which can be adjusted by editing the standard input file For example the standard choice of the cutoff energies is always on the safe side but will generally cause unnecessarily long computing times Moreover it is often inconvenient to use the input dialog program repeatedly such as in the case of performing a series of calculations with similar
19. ith L denoting Avogadro s number and M the atomic masses Then the atomic density of the non principal component is calculated from eq 18 according to 21 1 DNSO zim 1 n 1 DNS pon m DNSO Due to the definition of pseudoprojectiles which represent increments of fluence i e atoms per unit area the natural depth scale of TRIDYN is an areal density with each depth interval given by the total number of atoms per unit area in this interval For the resulting depth profiles geometrical depths are calculated by dividing the areal density of each depth interval by its total atomic density according to eq 18 Example The ion beam assisted deposition of Ta 0 by tantalum evaporation and oxygen ion bombardment shall be simulated Obviously the principal component is tantalum with Or 16 6 g cm and Mna 180 95 g mole and according to eg 19 DNSOp 5 53 10 cm Similarly for the compound Pros 7 5 g cm and Mo 16 0 g mole and according to eq 20 DNSOpa205 7 16 10 cm From this and eq 21 the input atomic density for the oxygen component results as DNSO 8 11 10 cm For the bombardment with inert gas atoms their incorporation might cause a swelling of the material due to high pressure gas filled voids The density of the gas within these bubbles and their volume fraction are mostly unknown Therefore one might simply discard the swelling by 15 setting DNS O inertG
20. mponents At first the name of the run to be performed 4 ASCH characters example AIN5 is prompted The file namexxxx IN will contain all necessary input information excluding the target structure information in the case of an inhomogeneous target Then prompts for the beam components their energies and angles of incidence fractions in the beam maximum possible fractions in the target energy parameters bulk binding energies surface binding energies and atomic volumes appear During the input of energy and atomic volume parameters the values for pure elements from the file elements dat are proposed If the maximum target fraction of any component is set to less then 100 a diffusion model can be chosen with Yes for diffusion of excess atoms to the nearest depth interval with an atomic fraction less than the maximum one and No for reemission of excess atoms Subsequently target components and their parameters are prompted Input of calculation and target parameters Target thickness and the thickness for dynamic simulation in which the dynamic change of target composition is considered and the number of depth intervals within the range for dynamic simulation are prompted followed by the target structure Two different types of inputs for the initial target structure are possible Homogeneous target The whole initial target is considered as homogeneous The fractions of components from the first part of the d
21. nergy matrix for Real Default SBV LJ are equal for all component number I with respect components J to surface component number J The default values are recommended to be used for all variables which are not prompted during the input dialog J 1 NCP eV Choice of Input Parameters Hints and Formulas 1 Target Intervals and Thickness The thickness of the initially equidistant depth intervals which is equal to TIDYN NQX should be small enough to allow for a sufficient resolution within the depth range of interest However too thin intervals might result in an artificial broadening due to the algorithm of interval splitting and combination A choice below about 2 A is not meaningful in view of the typical atomic distances The stability of the results against the interval thickness should always be checked The range of dynamic relaxation TTDYN may be larger than the target thickness TT This is helpful if the modification e g ion mixing of a thin layer by a high energy ion beam with a range much larger than the depth range of interest shall be simulated In this way the high energy pseudoprojectile is suppressed after the passage through TT saving computer time and the depth range of interest can be resolved sufficiently 2 Total Fluence and Number of Pseudoprojectiles Mostly one will aim at reducing computer time by reducing the number of pseudoprojectile histories at
22. o two component targets A Bm With respect to eq 4 a more realistic approach is to take into account the heat of formation of a specific compound but still to define surface binding energies being associated to the individual atoms independent of the actual surface composition Conservation of energy requires n SBE m SBE n AH m AHS AH 7 where AH denotes the formation enthalpy per molecule of the compound If the heat of formation is small it might simply be added to the enthalpy of sublimation of one of the constituents e g B This results in SBE SBV SBV AH 8 P 8 SBE SBV SBV pg AH AH m 10 This formalism may also be employed if AH is large but if the surface composition remains far from the pure component B Then with eq 8 the surface binding energy of the pure A surface is approximately correct and eq 7 is fulfilled Physically this model is justified if e g preferential sputtering or thin film deposition result in a surface composition between that of the stoichiometric compound and an enrichment of the component A Example Preferential sputtering of TaC by He at keV energies results in an enrichment of Ta at the surface Therefore the choice of the surface binding energies should be good for the compound itself and for the limit of a pure Ta surface With AH 8 1 eV AH 7 41 eV and AH fac 1 54 eV itis reasonable to set SBE SBVzura
23. obtain Therefore it is often simply set to zero with good results e g for sputtering yields if other standard parameters as described here are chosen It is also known from TRIM experience that an increase of the bulk binding energies to up to a few eV requires a corresponding decrease of the surface binding energies in order to obtain the same sputtering yields It is recommended to set the bulk binding energies to the default value of zero 3 3 Surface Binding Energy The surface binding energies determine critically the sputtering yields Theoretically the sputtering yield is proportional to the inverse of the surface binding energy In TRIDYN the effective surface binding energy of each target component can be chosen in dependence on the actual surface composition With c denoting the surface atomic fractions of the target atoms j 1sjsNCP amp c 1 the surface binding energy of a surface atom i is given by NCP SBE gt SBV c 2 ja with the matrix components SBV Eq 2 includes the simple choice of surface binding energies which are independent of the surface composition by the default setting SBVy SBE for all components j In the following recipes of increasing complexity will be given for the choice of the surface binding energies 3 3 1 Neglecting the projectile species at the surface For some applications the surface composition of a target does not change significantly during the
24. s of the pure element can be used The corresponding atomic volumes are taken from the file elements dat In the case of compound materials TRIDYN calculates the local total atomic density DNS linearly from the atomic densities of the individual components DNSO according to 14 1 NCP C 18 DNS gt Dnso a8 Similar to the choice of surface binding energies see 3 3 in dependence on the actual problem it has to be decided which limiting cases shall be reproduced correctly In a solid solid compound with little chemical interaction the choice of the pure element atomic densities for DNSO trivially reproduces the atomic densities of the pure elements and yields a good approximation for the whole range of concentrations In a highly covalent solid solid compound or in a solid gas compound normally the density of the stoichiometric compound and that of one of the constituents should be reproduced correctly In a solid gas compound the atomic density of the pure gaseous component is ill defined anyway Again the following recipe shall be restricted to a two component compound A B Starting from the mass density p of the principal component A the nongaseous component or the component for which the pure elemental density shall be reproduced correctly and the mass density of the compound 2 the corresponding atomic densities are Pal 19 DNSO A DNS n m AnBn 20 AnBm lM mM w
25. the stoichiometric fraction Excess gas atoms behave similarly to nonreactive gases see 4 1 Therefore if not known better the maximum atomic fraction should be chosen equal to the stoichiometric value Example For the implantation of nitrogen into silicon with the stoichiometric compound SiN QUMAXs 1 QUMAXy 0 571 If an additional gas take up such as in gas filled voids is known from experiment QUMAX may be increased correspondingly 4 3 Excess Atoms Using the parameter IDIFF there are two possibilities to steer the behavior of atoms whose concentration exceeds the maximum atomic fraction QUMAX The simplest choice is to discard them IDIFF 1 which corresponds physically to a direct reemission into the vacuum Alternatively a simple diffusion model can be employed IDIFF 0 In this case excess atoms are moved from their original depth interval to the nearest interval with a concentration of this species below QUMAX within the dynamic range TTDYN If the concentration is QUMAX in all depth intervals the excess atoms are reemitted Note The simple diffusion picture is realistic only for some specific systems such as the formation of a buried oxide in silicon by oxygen implantation It is not appropriate for a corresponding formation of a buried nitride This indicates that any generalization of the simple diffusion model is not justified 5 Atomic Density Depth Scale For monoatomic materials the atomic densitie
26. tories pseudoprojectiles 3 Deposited depth is larger than dynamic depth range Output profile might be in error Increase TTDYN and NQX Decrease the total fluence or increase the depth for dynamic simulation and number of intervals if the same depth interval is required to avoid this problem 4 Recoil storage capacity exceeded The total number of recoils for each projectile is limited by a definite number default 20000 If this limit is exceeded this occurs only for very high ion energies the program is stopped 19 References 1 W M ller and W Eckstein Nucl Instr and Meth in Phys Res B 2 1984 814 2 W M ller W Eckstein and J P Biersack Comput Phys Commun 51 1988 355 3 W M ller and W Eckstein Report IPP 9 64 Max Planck Institute of Plasma Physics Garching 1988 4 W Eckstein and J P Biersack Appl Phys A 37 1985 95 5 R Kelly Surf Science 100 1980 85 20
27. using the parameter MAXCHA The output listing file nameOUT DAT contains the parameter MAXCHA For results with sufficient statistical quality and precision MAXCHA should be less than 0 05 An increase of the number of pseudoparticles NH and a reduction of the total fluence FLC result in a decrease of MAXCHA Error messages During the simulation the error messages are written on the screen and into the output listing file nameOUT DAT if certain program parameters were not chosen properly Some of the errors can stop the program before the regular end of simulation The following error messages may occur 1 Projectile recoils range exceeds dynamic composition range Increase TTDYN This message appears when the projectile or a recoil went out of the limit of dynamic composition range The simulation is stopped after the accumulation of a definite number default 5 of the number of projectiles of such events The depth of dynamic simulation should be increased to avoid this problem 2 Depth interval completely depleted Decrease FLC or increase NH This message appears if the change of the composition induced by a projectile in a certain depth interval is so high that the interval is completely depleted The simulation is stopped after accumulation of a definite number default 1 of the number of projectiles of such events The problem can be avoided by decreasing of total fluence or by increasing the number of ion his
28. y high cutoff energy sometimes up to several keV can be chosen being only limited by the artificial distortion of the resulting profile at a too high cutoff energy In general the choice of the cutoff energies must be consistent with the characteristic energies of the governing processes For 8 example if sputtering is to be treated correctly the cutoff energies of the target components must be equal or less than the surface binding energies SBE D see below so that the surface binding energies are a good choice also for the cutoff energies In order to further reduce the computer time for certain problems it may be adequate to increase the cutoff energy of a projectile according to the energy transfer to the target atoms resulting in EF m pr FM arget F SBE 1 pro target 4M pos arg ot as e g for gaseous projectiles which are not trapped in the target see 4 Note In general it is not justified to identify the cutoff energies with the displacement threshold energies see 3 4 which are in the order of several 10 eV This would reduce the computing time significantly but suppress all cascade development below these energies and thus e g result in a drastic underestimation of sputtering 3 2 Bulk Binding Energy In a BCA simulation the bulk binding energy BE D is subtracted from the energy transfer to the recoil atom before it is set in motion A well defined value for this energy is difficult to
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