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Computer simulation of ion-beam assisted film growth
Nuclear Instruments and Methods in Physics Research B 89 (1994) 322-324
k!Nil B
Beam Interactions with Materials&Atoms
Computer simulation of ion-beam assisted film growth Wolfhard Miiller Max-Planck-Institut fiir Plasmaphysik, EURATOM-Association,
Ion bombardment in connection with physical or chemical thin film deposition techniques offers new possibilities of tailoring specific material properties. It has therefore attracted considerable interest for industrial application [1,2]. In connection with this, a large number of scientific studies have been performed in order to characterize the effects of ion bombardment and to delineate their physical origin [3-121. However, most of these studies only present empirical correlations of process parameters such as the ion energy or flwr with the film properties and growth rate. They rarely aim at an understanding on the basis of the elementary ion bombardment effects such as implantation, radiation damage, sputtering, ion mixing or ioninduced diffusion. Due to the complexity of these effects, analytical approaches are of rather limited capability. Nevertheless, simple rate equation models have been formulated for specific problems of stoichiometry formation [13-151, stress formation and reduction [16], and ioninduced densification [17-191. However, the evaluation of such models often requires computer-generated profiles of ion deposition and radiation damage, such as from the TRIM program [20-221. For more detailed and reliable model predictions, computer simulation programs - both of the molecular dynamics (MD) and the binary collision approximation (BCA) type - have been applied in recent years to problems of ion-assisted thin film deposition. Two different modes are available for both types of programs: In static mode, the accumulating effects of ion bombardment are neglected. Nevertheless, information can be gained on the effects of atomic mechanisms such as sputtering or mixing. Dynamic modes provide a realistic model of the modification of the substance, including the film growth. A recent review has been given in ref. [23]. The ultimate aim of the computer simulations is the simultaneous treatment of fast collisional effects such as ion deposition or atomic relocation and slow thermal and chemical effect such as the establishment of chemical bonds, diffusion, and the formation of point or extended defects. Although the present state-of-the0168-583X/94/$07.00
D-85748 Garching, Germany
art is far away from a realization, MD simulations of the present type should be able to fulfil the requirements in the future, provided suitable interatomic potentials can be provided and the computer capacity can be significantly increased. Presently, MD calculations only address specific problems and suffer from often excessive computing times. This limits the size of the computing cell and the time interval allowed for slowing down of the individual cascades and the thermalization of the substance. A specific problem arises for the timescale of MD simulations when the normal case of ion assisted growth with single ions or atoms (rather than large clusters) is considered: in order to obtain reasonable information within acceptable computing times, the rate of incidence of projectiles in present calculations amounts to about lo’* s-l on a surface area of about 50 x 50 atoms, which represents a flux which is by many orders of magnitude higher than any flux attainable in a real deposition process. Nevertheless, promising results have been obtained: early two-dimensional simulations with a simple two-body potential by Miiller [24] already demonstrated a densification of the growing film at increasing particle energies. Under more realistic conditions with the embedded-atom potential [25] and including surface temperature, Gilmore and Sprague [26,27] demonstrated a transition from Volmer-Weber (island) growth to Frank-van-der-Merwe (layer-bylayer) growth for the deposition of thermal and energetic (10 eV) silver atoms. Calculations on the film formation by energetic multiatomic copper clusters have been published by Averback et al. [28]. Also thin films involving directed bonds have been treated by MD simulations: Using a Stillinger-Weber [29] potential, Pailthorpe [30] investigated the penetration of up to several hundred eV carbon atoms incident onto a diamond surface using static calculations. Atoms with an incident energy above 60 eV remain in a stable position below the surface. Maximum stress, which might be necessary for the formation of tetragonal bonds, appears around this energy. Kaukonen and Nieminen [31] performed a dynamic growth simulation of hydrogen-free hard carbon films using a Tersoff [32]
0 1994 - Elsevier Science B.V. All rights reserved
SSDI 0168-583X(93)E0771-8
W. Miiller / Nucl. Instr. and Meth. in Phys. Res. B 89 (1994) 322-324
potential. The densest films containing most sp3 coordinated carbon are formed at an incident energy of the carbon atoms of again 40-70 eV. Also employing a Tersoff potential, Kitabatake and Greene [331 studied the final positions and the role of defects for 50 eV Si incident on a reconstructed crystalline Si surface. With a Stillinger-Weber potential, Gilmer [34] studied the deposition of Si clusters, including dimers, on a Si surface. Also mechanisms involving hydrogen were addressed: Brenner [35] developed a Tersoff-type potential also for different hydrocarbon configurations, and applied it to possible surface processes occurring during diamond growth. Biswas [36] studied the hydrogen deposition in amorphous hydrogenated silicon, with a potential describing both the Si-Si and the Si-H interactions. Maximum sticking of hydrogen occurs around 50 eV. Thus, nowadays MD simulation are applicable to relatively low bombarding energies only, but are capable of describing detailed atomic effects which occur during the thermalization of the collision sequences. The treatment of stationary growth involving higher, such as keV, energies is at present excluded. Such simulations, however, can be performed using BCA simulations [22]. These are only capable of describing events at sufficiently high energy (larger than some eV) and thereby not applicable to thermalization or structural effects such as the formation of defects. However, these purely “collisional” calculations provide valuable information about film growth and stoichiometry, with the often complicated interplay of atom and ion deposition, sputtering, and atomic relocation [23]. For this purpose, dynamic BCA codes such as TRIDYN
[21,22,37,38],
T-DYN
[39,40] and
DYNA
[41]
have been employed. Li et al. [42] studied the interface mixing during the ion-beam assisted deposition (IBAD) of metal films. The formation of silicon nitride films under reactive bombardment with 1 keV nitrogen ions was simulated by Zhou et al. [43]. Konoplev [41] described the ion plating with copper ions in the keV range. Biersack et al. [40] studied the growth of titanium film during 800 eV Ar bombardment. MBller, Bouchier et al. [44-461 treated the reactive IBAD of boron nitride in the keV range in comparison to detailed experimental information. For sufficiently low ion(nitrogen)-to-neutrakboron) ratios, excellent agreement between simulation and experiment was found. Being characteristic for reactive IBAD, the neutral constituent, which impinges at thermal energy, is enriched close to the surface due to the penetration depth of the ionic species. At high nitrogen fluxes which would result in the formation of superstoichiometric films, excess nitrogen atoms diffuse to the surface and are partly trapped there to nitride the boronrich surface layer. This process can also be included in the simulation in an empirical way, but requires fitting
323
to the experimental data in contrast to the purely collisional simulation which is free of any fit parameters. A special advantage of the BCA simulations is the possibility of quick variations of process parameters such as ion-to-neutral ratio, ion energy or ion angle of incidence. In this way, special effects occuring during ion-assisted growth can be identified. In particular, a very delicate balance often exists between mechanisms of deposition and removal, so that net deposition or net erosion can be obtained at only slightly varying conditions. For nuclear fusion application, Eckstein and Roth [47] simulated the bombardment of tungsten with 6 keV carbon ions. At normal incidence, a carbon film is built up. At 35 degrees with respect to the surface normal, a turnover from deposition to erosion occurs in agreement with experimental findings, which is due to the increased sputter yield at oblique incidence. By comparing silicon and platinum substrates for IBAD of titanium films, Nender et al. [39] simulated selective deposition for 800 eV argon bombardment at an ion-to-neutral ratio of 1: 1. A growing film appears on silicon, whereas platinum is eroded due to the increased flux reversion by the heavier substrate, with a shallow stationary titanium profile. Under certain conditions, it is even possible to obtain a film of stationary thickness much larger than the ion range without any net growth or erosion, as shown in simulations of titanium IBAD on silicon by Miiller [23]. Concluding, dynamic BCA simulations allow a very detailed insight into the individual, counteracting mechanisms which are effective during ion-assisted film formation, with partly excellent predictive power on film growth and stoichiometry. However, future developments will increasingly utilize MD codes, as these will in addition be able to treat structural effects which to a large extent influence the properties of the films. References [l] E. Mall and E. Bergmann, Surf. Coat. Technol. 37 (1989) 483. [2] B. Lux, R. Haubner and C. Wohlrab, Surf. Coat. Technol. 38 (1989) 267. [3] J.M.E. Harper, in: Plasma Surface Interactions and Processing of Materials, eds. 0. Auciello, A. Gras-Marti, J.A. Valles-Abarca and D.L. Flamm, NATO ASI Series E, Vol. 176 (Kluwer, Dordrecht, 1990) p. 251. [4] J.E. Greene, S.A. Barnett, J.-E. Sundgren and A. Rockett, ibid., p. 281. [S] D.M. Mattox, J. Vat. Sci. Technol A 7 (1989) 1105. [6] S.M. Rossnagel and J.J. Cuomo, Thin Sol. Films 171 (1989) 143. [7] G.K. Wolf, Nucl. Instr. and Meth. B 46 (1990) 369. [8] H. Oechsner, Thin Sol. Films 175 (1989) 119. [9] S. VepFek, Surf. Coat. Technol. 43/44 (1990) 154. [lo] K. Reichelt and X. Jiang, Thin Sol. Films 191 (1990) 91. VIII. BEAM MODIFICATION
324
W. Miiller / Nucl. Instr. and Meth. in Phys. Res. B 89 (1994) 322-324
[ll] G.K. Wolf, Surf. Coat. Technol. 43/44 (1990) 920. [12] J.K. Hirvonen, Mater. Sci. Rep. 6 (1991) 215. [13] G. Carter, I.V. Katardjiev and M.J. Nobes, Vacuum 39 (1989) 571. [14] D. Van Vechten, G.K. Hubler, E.P. Donovan and F.D. Correll, J. Vat. Sci. Technol. A 8 (1990) 821. [15] G.K. Hubler, C.A. Carosella, E.P. Donovan, D. Van Vechten, R.H. Bassel, T.D. Andreadis, M. Rosen and G.P. Mueller, Nucl. Instr. and Meth. B 46 (1990) 384. 1161 H. Windischmann, J. Appl. Phys. 62 (1987) 1800. [17] K.-H. Miiller, Appl. Phys. A 40 (1986) 209. [18] K.-H. Miiller, J. Appl. Phys. 59 (1986) 2803. [19] 0. Vancauwenberghe, N. Herbots and O.C. Hellman, J. Vat. Sci. Technol. B 9 (1991) 2027. [20] J.P. Biersack and L.G. Haggmark, Nucl. Instr. and Meth. 174 (1980) 257. [21] W. Moller, in: Materials Modification by High-Fluence Ion Beams, eds. R. Kelly and M.F. da Silva, NATO AS1 Series E, Vol. 155 (Kluwer, Dordrecht, 1989) p. 151. [22] W. Eckstein, Computer Simulation of Ion-Solid Interactions, Springer Series in Materials Science Vol. 10 (Springer, Berlin, 1991). [23] W. Moller, Thin Sol. Films 228 (1993) 319. [24] K.-H. Miiller, Phys. Rev. B 35 (1987) 7906. [25] MS. Daw and M.I. Baskes, Phys. Rev. B 29 (1984) 6443. [26] C.M. Gilmore and J.A. Sprague, Phys. Rev. B 44 (1991) 8950. [27] C.M. Gilmore and J.A. Sprague, J. Vat. Sci. Technol. A 10 (1992) 1597. [28] R.S. Averback, T. Diaz de la Rubia, H. Hsieh and R. Benedek, Nucl. Instr. and Meth. B 59/60 (1991) 709. [29] F.H. Stillinger and T.A. Weber, Phys. Rev. B 31 (1985) 5262. [30] B.A. Pailthorpe, J. Appl. Phys. 70 (1991) 543.
[31] H.-P. Kaukonen and R.M. Nieminen, Phys. Rev. Lett. 68 (1992) 620. 1321 J. Tersoff, Phys. Rev. 39 (1989) 5566. [33] M. Kitabatake and J.E. Greene, J. Appl. Phys. 73 (1993) 3183. [34] G.H. Gilmer, in: Proc. Int. Conf. on Computer Simulation of Radiation Effects in Solids, Berlin 1992, Rad. Eff. Def. Sol. (in press). [35] D.W. Brenner, Phys. Rev. B 42 (1990) 9458. 1361 R. Biswas, J. Appl. Phys. 73 (1993) 3295. [37] W. Moller and W. Eckstein, Nucl. Instr. and Meth. B 2 (1984) 814. [38] W. Miiller, W. Eckstein and J.P. Biersack, Comp. Phys. Comm. 51 (1988) 355. [39] C. Nender, S. Berg and J.P. Biersack, Thin Sol. Films 193/194 (1990) 13. [40] J.P. Biersack, S. Berg and C. Nender, Nucl. Instr. and Meth. B 59/60 (1991) 21. [41] V.M. Konoplev, Nucl. Instr. and Meth. B 42 (1989) 229. [42] W.-Z. Li, F.-Z. Cui, Y. Liao and H.-D. Li, Vacuum 40 (1990) 289. [43] J. Zhou, Y. Chen, X. Liu and S. Zou, Nucl. Instr. and Meth. B 39 (1989) 182. [44] W. Moller, D. Bouchier, 0. Burat and V. Stambouli, Surf. Coat. Technol 45 (1991) 73. [45] D. Bouchier and W. Mdller, Surf. Coat. Technol. 51 (1992) 190. [46] W. Miiller, in: Low Energy Ion Beam and Plasma Modification of Materials, ed. J.M.E. Harper, K. Miyake, J.R. McNeil and S.M. Gorbatkin, Materials Research Society Symp. Proc., Vol. 223 (Materials Research Society, Pittsburgh, 1991). [47] W. Eckstein and J. Roth, Nucl. Instr. and Meth. 53 (1991) 279.
k!Nil B
Beam Interactions with Materials&Atoms
Computer simulation of ion-beam assisted film growth Wolfhard Miiller Max-Planck-Institut fiir Plasmaphysik, EURATOM-Association,
Ion bombardment in connection with physical or chemical thin film deposition techniques offers new possibilities of tailoring specific material properties. It has therefore attracted considerable interest for industrial application [1,2]. In connection with this, a large number of scientific studies have been performed in order to characterize the effects of ion bombardment and to delineate their physical origin [3-121. However, most of these studies only present empirical correlations of process parameters such as the ion energy or flwr with the film properties and growth rate. They rarely aim at an understanding on the basis of the elementary ion bombardment effects such as implantation, radiation damage, sputtering, ion mixing or ioninduced diffusion. Due to the complexity of these effects, analytical approaches are of rather limited capability. Nevertheless, simple rate equation models have been formulated for specific problems of stoichiometry formation [13-151, stress formation and reduction [16], and ioninduced densification [17-191. However, the evaluation of such models often requires computer-generated profiles of ion deposition and radiation damage, such as from the TRIM program [20-221. For more detailed and reliable model predictions, computer simulation programs - both of the molecular dynamics (MD) and the binary collision approximation (BCA) type - have been applied in recent years to problems of ion-assisted thin film deposition. Two different modes are available for both types of programs: In static mode, the accumulating effects of ion bombardment are neglected. Nevertheless, information can be gained on the effects of atomic mechanisms such as sputtering or mixing. Dynamic modes provide a realistic model of the modification of the substance, including the film growth. A recent review has been given in ref. [23]. The ultimate aim of the computer simulations is the simultaneous treatment of fast collisional effects such as ion deposition or atomic relocation and slow thermal and chemical effect such as the establishment of chemical bonds, diffusion, and the formation of point or extended defects. Although the present state-of-the0168-583X/94/$07.00
D-85748 Garching, Germany
art is far away from a realization, MD simulations of the present type should be able to fulfil the requirements in the future, provided suitable interatomic potentials can be provided and the computer capacity can be significantly increased. Presently, MD calculations only address specific problems and suffer from often excessive computing times. This limits the size of the computing cell and the time interval allowed for slowing down of the individual cascades and the thermalization of the substance. A specific problem arises for the timescale of MD simulations when the normal case of ion assisted growth with single ions or atoms (rather than large clusters) is considered: in order to obtain reasonable information within acceptable computing times, the rate of incidence of projectiles in present calculations amounts to about lo’* s-l on a surface area of about 50 x 50 atoms, which represents a flux which is by many orders of magnitude higher than any flux attainable in a real deposition process. Nevertheless, promising results have been obtained: early two-dimensional simulations with a simple two-body potential by Miiller [24] already demonstrated a densification of the growing film at increasing particle energies. Under more realistic conditions with the embedded-atom potential [25] and including surface temperature, Gilmore and Sprague [26,27] demonstrated a transition from Volmer-Weber (island) growth to Frank-van-der-Merwe (layer-bylayer) growth for the deposition of thermal and energetic (10 eV) silver atoms. Calculations on the film formation by energetic multiatomic copper clusters have been published by Averback et al. [28]. Also thin films involving directed bonds have been treated by MD simulations: Using a Stillinger-Weber [29] potential, Pailthorpe [30] investigated the penetration of up to several hundred eV carbon atoms incident onto a diamond surface using static calculations. Atoms with an incident energy above 60 eV remain in a stable position below the surface. Maximum stress, which might be necessary for the formation of tetragonal bonds, appears around this energy. Kaukonen and Nieminen [31] performed a dynamic growth simulation of hydrogen-free hard carbon films using a Tersoff [32]
0 1994 - Elsevier Science B.V. All rights reserved
SSDI 0168-583X(93)E0771-8
W. Miiller / Nucl. Instr. and Meth. in Phys. Res. B 89 (1994) 322-324
potential. The densest films containing most sp3 coordinated carbon are formed at an incident energy of the carbon atoms of again 40-70 eV. Also employing a Tersoff potential, Kitabatake and Greene [331 studied the final positions and the role of defects for 50 eV Si incident on a reconstructed crystalline Si surface. With a Stillinger-Weber potential, Gilmer [34] studied the deposition of Si clusters, including dimers, on a Si surface. Also mechanisms involving hydrogen were addressed: Brenner [35] developed a Tersoff-type potential also for different hydrocarbon configurations, and applied it to possible surface processes occurring during diamond growth. Biswas [36] studied the hydrogen deposition in amorphous hydrogenated silicon, with a potential describing both the Si-Si and the Si-H interactions. Maximum sticking of hydrogen occurs around 50 eV. Thus, nowadays MD simulation are applicable to relatively low bombarding energies only, but are capable of describing detailed atomic effects which occur during the thermalization of the collision sequences. The treatment of stationary growth involving higher, such as keV, energies is at present excluded. Such simulations, however, can be performed using BCA simulations [22]. These are only capable of describing events at sufficiently high energy (larger than some eV) and thereby not applicable to thermalization or structural effects such as the formation of defects. However, these purely “collisional” calculations provide valuable information about film growth and stoichiometry, with the often complicated interplay of atom and ion deposition, sputtering, and atomic relocation [23]. For this purpose, dynamic BCA codes such as TRIDYN
[21,22,37,38],
T-DYN
[39,40] and
DYNA
[41]
have been employed. Li et al. [42] studied the interface mixing during the ion-beam assisted deposition (IBAD) of metal films. The formation of silicon nitride films under reactive bombardment with 1 keV nitrogen ions was simulated by Zhou et al. [43]. Konoplev [41] described the ion plating with copper ions in the keV range. Biersack et al. [40] studied the growth of titanium film during 800 eV Ar bombardment. MBller, Bouchier et al. [44-461 treated the reactive IBAD of boron nitride in the keV range in comparison to detailed experimental information. For sufficiently low ion(nitrogen)-to-neutrakboron) ratios, excellent agreement between simulation and experiment was found. Being characteristic for reactive IBAD, the neutral constituent, which impinges at thermal energy, is enriched close to the surface due to the penetration depth of the ionic species. At high nitrogen fluxes which would result in the formation of superstoichiometric films, excess nitrogen atoms diffuse to the surface and are partly trapped there to nitride the boronrich surface layer. This process can also be included in the simulation in an empirical way, but requires fitting
323
to the experimental data in contrast to the purely collisional simulation which is free of any fit parameters. A special advantage of the BCA simulations is the possibility of quick variations of process parameters such as ion-to-neutral ratio, ion energy or ion angle of incidence. In this way, special effects occuring during ion-assisted growth can be identified. In particular, a very delicate balance often exists between mechanisms of deposition and removal, so that net deposition or net erosion can be obtained at only slightly varying conditions. For nuclear fusion application, Eckstein and Roth [47] simulated the bombardment of tungsten with 6 keV carbon ions. At normal incidence, a carbon film is built up. At 35 degrees with respect to the surface normal, a turnover from deposition to erosion occurs in agreement with experimental findings, which is due to the increased sputter yield at oblique incidence. By comparing silicon and platinum substrates for IBAD of titanium films, Nender et al. [39] simulated selective deposition for 800 eV argon bombardment at an ion-to-neutral ratio of 1: 1. A growing film appears on silicon, whereas platinum is eroded due to the increased flux reversion by the heavier substrate, with a shallow stationary titanium profile. Under certain conditions, it is even possible to obtain a film of stationary thickness much larger than the ion range without any net growth or erosion, as shown in simulations of titanium IBAD on silicon by Miiller [23]. Concluding, dynamic BCA simulations allow a very detailed insight into the individual, counteracting mechanisms which are effective during ion-assisted film formation, with partly excellent predictive power on film growth and stoichiometry. However, future developments will increasingly utilize MD codes, as these will in addition be able to treat structural effects which to a large extent influence the properties of the films. References [l] E. Mall and E. Bergmann, Surf. Coat. Technol. 37 (1989) 483. [2] B. Lux, R. Haubner and C. Wohlrab, Surf. Coat. Technol. 38 (1989) 267. [3] J.M.E. Harper, in: Plasma Surface Interactions and Processing of Materials, eds. 0. Auciello, A. Gras-Marti, J.A. Valles-Abarca and D.L. Flamm, NATO ASI Series E, Vol. 176 (Kluwer, Dordrecht, 1990) p. 251. [4] J.E. Greene, S.A. Barnett, J.-E. Sundgren and A. Rockett, ibid., p. 281. [S] D.M. Mattox, J. Vat. Sci. Technol A 7 (1989) 1105. [6] S.M. Rossnagel and J.J. Cuomo, Thin Sol. Films 171 (1989) 143. [7] G.K. Wolf, Nucl. Instr. and Meth. B 46 (1990) 369. [8] H. Oechsner, Thin Sol. Films 175 (1989) 119. [9] S. VepFek, Surf. Coat. Technol. 43/44 (1990) 154. [lo] K. Reichelt and X. Jiang, Thin Sol. Films 191 (1990) 91. VIII. BEAM MODIFICATION
324
W. Miiller / Nucl. Instr. and Meth. in Phys. Res. B 89 (1994) 322-324
[ll] G.K. Wolf, Surf. Coat. Technol. 43/44 (1990) 920. [12] J.K. Hirvonen, Mater. Sci. Rep. 6 (1991) 215. [13] G. Carter, I.V. Katardjiev and M.J. Nobes, Vacuum 39 (1989) 571. [14] D. Van Vechten, G.K. Hubler, E.P. Donovan and F.D. Correll, J. Vat. Sci. Technol. A 8 (1990) 821. [15] G.K. Hubler, C.A. Carosella, E.P. Donovan, D. Van Vechten, R.H. Bassel, T.D. Andreadis, M. Rosen and G.P. Mueller, Nucl. Instr. and Meth. B 46 (1990) 384. 1161 H. Windischmann, J. Appl. Phys. 62 (1987) 1800. [17] K.-H. Miiller, Appl. Phys. A 40 (1986) 209. [18] K.-H. Miiller, J. Appl. Phys. 59 (1986) 2803. [19] 0. Vancauwenberghe, N. Herbots and O.C. Hellman, J. Vat. Sci. Technol. B 9 (1991) 2027. [20] J.P. Biersack and L.G. Haggmark, Nucl. Instr. and Meth. 174 (1980) 257. [21] W. Moller, in: Materials Modification by High-Fluence Ion Beams, eds. R. Kelly and M.F. da Silva, NATO AS1 Series E, Vol. 155 (Kluwer, Dordrecht, 1989) p. 151. [22] W. Eckstein, Computer Simulation of Ion-Solid Interactions, Springer Series in Materials Science Vol. 10 (Springer, Berlin, 1991). [23] W. Moller, Thin Sol. Films 228 (1993) 319. [24] K.-H. Miiller, Phys. Rev. B 35 (1987) 7906. [25] MS. Daw and M.I. Baskes, Phys. Rev. B 29 (1984) 6443. [26] C.M. Gilmore and J.A. Sprague, Phys. Rev. B 44 (1991) 8950. [27] C.M. Gilmore and J.A. Sprague, J. Vat. Sci. Technol. A 10 (1992) 1597. [28] R.S. Averback, T. Diaz de la Rubia, H. Hsieh and R. Benedek, Nucl. Instr. and Meth. B 59/60 (1991) 709. [29] F.H. Stillinger and T.A. Weber, Phys. Rev. B 31 (1985) 5262. [30] B.A. Pailthorpe, J. Appl. Phys. 70 (1991) 543.
[31] H.-P. Kaukonen and R.M. Nieminen, Phys. Rev. Lett. 68 (1992) 620. 1321 J. Tersoff, Phys. Rev. 39 (1989) 5566. [33] M. Kitabatake and J.E. Greene, J. Appl. Phys. 73 (1993) 3183. [34] G.H. Gilmer, in: Proc. Int. Conf. on Computer Simulation of Radiation Effects in Solids, Berlin 1992, Rad. Eff. Def. Sol. (in press). [35] D.W. Brenner, Phys. Rev. B 42 (1990) 9458. 1361 R. Biswas, J. Appl. Phys. 73 (1993) 3295. [37] W. Moller and W. Eckstein, Nucl. Instr. and Meth. B 2 (1984) 814. [38] W. Miiller, W. Eckstein and J.P. Biersack, Comp. Phys. Comm. 51 (1988) 355. [39] C. Nender, S. Berg and J.P. Biersack, Thin Sol. Films 193/194 (1990) 13. [40] J.P. Biersack, S. Berg and C. Nender, Nucl. Instr. and Meth. B 59/60 (1991) 21. [41] V.M. Konoplev, Nucl. Instr. and Meth. B 42 (1989) 229. [42] W.-Z. Li, F.-Z. Cui, Y. Liao and H.-D. Li, Vacuum 40 (1990) 289. [43] J. Zhou, Y. Chen, X. Liu and S. Zou, Nucl. Instr. and Meth. B 39 (1989) 182. [44] W. Moller, D. Bouchier, 0. Burat and V. Stambouli, Surf. Coat. Technol 45 (1991) 73. [45] D. Bouchier and W. Mdller, Surf. Coat. Technol. 51 (1992) 190. [46] W. Miiller, in: Low Energy Ion Beam and Plasma Modification of Materials, ed. J.M.E. Harper, K. Miyake, J.R. McNeil and S.M. Gorbatkin, Materials Research Society Symp. Proc., Vol. 223 (Materials Research Society, Pittsburgh, 1991). [47] W. Eckstein and J. Roth, Nucl. Instr. and Meth. 53 (1991) 279.