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Computer Simulation of Atomic Collision Processes in Solids

Published online by Cambridge University Press:  25 February 2011

Mark T. Robinson
Mark T. Robinson*
Affiliation:
Solid State Division, Oak Ridge National Laboratory, Post Office Box 2008, Oak Ridge, Tennessee 37831–6032
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Abstract

Computer simulation is a major tool for studying the interactions of swift ions with solids which underlie processes such as particle backscattering, ion implantation, radiation damage, and sputtering. Numerical models are classed as molecular dynamics or binary collision models, along with some intermediate types. Binary collision models are divided into those for crystalline targets and those for structureless ones. The foundations of such models are reviewed, including interatomic potentials, electron excitations, and relationships among the various types of codes. Some topics of current interest are summarized.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 279: Symposium A – Beam-Solid Interactions–Fundamentals and Applications , 1992 , 3
Copyright
Copyright © Materials Research Society 1993

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References

REFERENCES

[1] Alder, B. J. and Wainwright, T. E., J. Chem. Phys 27, 1208 (1957); 31, 459 (1959).Google Scholar
[2] Bredov, M. M., Lang, I. G., and Okuneva, N. M., Zh. Tekh. Fiz. 28, 252 (1958) [Engl. transi.: Sov. Phys.-Tech. Phys. 3, 228 (1958)].Google Scholar
[3] Goldman, D. T., Harrison, D. E. Jr, and Coveyou, R. R., U. S. Atomic Energy Commission Report ORNL-2729 (1959).Google Scholar
[4] Gibson, J. B., Goland, A. N., Milgram, M., and Vineyard, G. H., Phys. Rev. 120, 1229 (1960). See also J. Appl Phys. 30, 1322 and cover (1959).Google Scholar
[5] Beeler, J. R. Jr, and Besco, D. G., Radiation Damage in Solids, Vol. I (I. A. E. A. Vienna, 1962), p. 43.Google Scholar
[6] Robinson, M. T., Holmes, D. K., and Oen, O. S., Le Bombardement Ionique (C. N. R. S.Paris, 1962), p. 105.Google Scholar
[7] Robinson, M. T. in Sputtering by Particle Bombardment I, edited by Behrisch, R. (Springer, Berlin, 1981), pp. 73–144.Google Scholar
[8] Yurasova, V. E. and Eltekov, V. A., Vacuum 32, 399 (1982).CrossRefGoogle Scholar
[9] Beeler, J. R. Jr, Radiation Effects Computer Experiments (North-Holland, Amsterdam, 1983).Google Scholar
[10] Harrison, D. E. Jr, Radiat. Eff. 70, 1 (1983).CrossRefGoogle Scholar
[11] Andersen, H. H., Nucl. Instrum. Methods B 18, 321 (1987).CrossRefGoogle Scholar
[12] Biersack, J. P., Nucl. Instrum. Methods B 27, 21 (1987).CrossRefGoogle Scholar
[13] Harrison, D. E. Jr, CRC Crit. Rev. Sol. State Mater. Sci. 14, S1 (1988).Google Scholar
[14] Dodson, B. W., Mater. Res. Soc. Symposium Proc. 128, 137 (1989).Google Scholar
[15] Mashkova, E. S. and Molchanov, V. A., RadiAt. Eff. 108, 307 (1989).CrossRefGoogle Scholar
[16] Barrett, J. H., Nucl. Instrum. Methods B 44, 367 (1990).CrossRefGoogle Scholar
[17] Eckstein, W., Computer Simulation of Ion-Solid Interactions (Springer, Berlin, 1991).CrossRefGoogle Scholar
[18] Smith, R. and Webb, R., Nucl. Instrum. Methods B 67, 373 (1992).Google Scholar
[19] Robinson, M. T., Dan, K.. Vidensk. Selsk. Mat. Fys. Medd. (1993) to be published.Google Scholar
[20] Nieminen, R. M., Dan, K.. Vidensk. Selsk. Mat. Fys. Medd. (1993) to be published.Google Scholar
[21] Johnson, R. E., Dan, K.. Vidensk. Selsk. Mat. Fys. Medd. (1993) to be published.Google Scholar
[22] Reimann, C. T., Dan, K.. Vidensk. Selsk. Mat. Fys. Medd. (1993) to be published.Google Scholar
[23] Abraham, F. F., Adv. Phys. 35, 1 (1986).CrossRefGoogle Scholar
[24] Hoover, W. G., Molecular Dynamics (Springer, Berlin, 1986).Google Scholar
[25] Allen, M. P. and Tildesley, D. J., Computer Simulation of Liquids (Clarendon Press, Oxford, 1987).Google Scholar
[26] Harrison, D. E. Jr, and Jakas, M. M., Radiat. Eff. 99, 637 (1986).CrossRefGoogle Scholar
[27] Bohr, N., Dan, K.. Vidensk. Selsk. Mat. Fys. Medd. 18, no. 8 (1948).Google Scholar
[28] Kennard, E. H., Kinetic Theory of Gases (McGraw-Hill, New York, 1938), especially pp. 97–134.Google Scholar
[29] Wannier, G. H., Statistical Physics (Wiley, New York, 1966), especially pp. 385–468.Google Scholar
[30] Robinson, M. T., Phys. Rev. B 40, 10717 (1989).Google Scholar
[31] Robinson, M. T.: Radiat. Eff. (1993) to be published.Google Scholar
[32] Sigmund, P., Robinson, M. T., Baskes, M. I., Hautala, M., Cui, F. Z., Eckstein, W., Yamamura, Y., Hosaka, S., Ishitani, T., Shul'ga, V. I., Harrison, D. E. Jr, Chakarov, I. R., Karpuzov, D. S., Kawatoh, E., Shimizu, R., Valkealahti, S., Nieminen, R. M., Betz, G., Husinsky, W., Shapiro, M. H., Vicanek, M., and Urbassek, H., Nucl. Instrum. Methods B 36, 110(1989).CrossRefGoogle Scholar
[33] Robinson, M. T., Nucl. Instrum. Methods B 48, 408 (1990); 67, 396 (1992).Google Scholar
[34] Robinson, M. T. and Torrens, I. M., Phys. Rev. B 9, 5008 (1974).Google Scholar
[35] Biersack, J. P. and Haggmark, L. G., Nucl. Instrum. Methods 174, 257 (1980).Google Scholar
[36] Takeuchi, W. and Yamamura, Y., Radiat. Eff. 71, 51 (1983).Google Scholar
[37] Yamamura, Y., Nucl. Instrum. Methods 194, 515 (1982).Google Scholar
[38] Yamamura, Y., Nucl. Instrum. Methods B 33, 493 (1988); 45, 707 (1990).CrossRefGoogle Scholar
[39] Yamamura, Y., Nucl. Instrum. Methods B 62, 181 (1991).Google Scholar
[40] Yamamura, Y., Yamada, I., and Takagi, T., Nucl. Instrum. Methods B 37/38, 902 (1989).Google Scholar
[41] Yamamura, Y. and Takeuchi, W., Nucl. Instrum. Methods B 29, 461 (1987).Google Scholar
[42] Schlaug, R. N., Thesis, University of California, Berkeley, 1965 (University Microfilms, Inc., Ann Arbor, Michigan, 1966).Google Scholar
[43] Torrens, I. M., J. Phys. F 3, 1771 (1973).Google Scholar
[44] Schwartz, D. M., Schiffgens, J. O., Doran, D. G., Odette, G. R., and Ariyasu, R. G., Computer Simulation for Materials Applications, edited by Arsenault, R. J., Beeler, J. R. Jr, and Simmons, J. A., Nucl Metall. 20, 75 (1976).Google Scholar
[45] Heinisch, H. L., Schiffgens, J. O., and Schwartz, D. M., J. Nucl. Mater. 85/86, 607 (1979).Google Scholar
[46] Gombás, P., Handbuch der Physik, edited by Fluegge, S., (Springer, Berlin, etc., 1956), Vol. XXXVI, pp. 109–231.Google Scholar
[47] Gordon, R. G. and Kim, Y. S., J. Chem. Phys. 56, 3122 (1972).Google Scholar
[48] Dodson, B. W., Nucl. lnstrum. Methods B 44, 273 (1990); 59/60, 481 (1991).Google Scholar
[49] Nakagawa, S. T., Radiat. Eff. 112, 1 (1990).Google Scholar
[50] Firsov, O. B., Zh. Eksp. Teor. Fiz. 33, 696 (1957) [Engl. transi.: Sov. Phys.-JETPS 6, 534 (1958)].Google Scholar
[51] Lindhard, J., Nielsen, V., and Scharff, M., Dan, K.. Vidensk. Selsk. Mat. Fys. Medd. 36, no. 10 (1968).Google Scholar
[52] Molière, G., Z. Naturforsch. 2a, 133 (1947).Google Scholar
[53] Ziegler, J. F., Biersack, J. P., and Littmark, U., Stopping Powers and Ranges of Ions in Matter (Pergamon, New York, 1985), pp. 25ff.Google Scholar
[54] Nakagawa, S. T. and Yamamura, Y., Radiat. Eff. 105, 239 (1988);Google Scholar
Nakagawa, S. T., Radiat. Eff. 116, 21 (1991).Google Scholar
[55] Broomfield, K., Stansfield, R. A., and D. C Clary, Surface Sci. 202, 320 (1988).Google Scholar
[56] Hou, M. and Robinson, M. T., Appl Phys. 18, 381 (1979).Google Scholar
[57] Fano, U. and Lichten, W., Phys. Rev. Lett. 14, 627 (1965).Google Scholar
[58] Kessel, Q. C. and Everhart, E., Phys. Rev. 146, 16 (1966).Google Scholar
[59] Garcia, J. D., Fortner, R. J., and Kavanagh, T. M., Rev. Mod. Phys. 45, 111 (1973).Google Scholar
[60] Grizzi, O. and Baragiola, R. A., Phys. Rev. A 35, 135 (1987).CrossRefGoogle Scholar
[61] Yu, M. L., Sputtering by Particle Bombardment III, edited by Behrisch, R. and Wittmaack, K. (Springer, Berlin, 1991) 91.Google Scholar
[62] Diaz de la Rubia, T., Averback, R. S., Benedek, R., and King, W. E., Phys. Rev. Lett. 59, 1930, (1987).CrossRefGoogle Scholar
[63] Averback, R. S., Diaz de la Rubia, T., and Benedek, R., Nucl. lnstrum. Methods B 33, 693, (1988).Google Scholar
[64] Diaz de la Rubia, T., Averback, R. S., Hsieh, H., and Benedek, R., J. Mater. Res. 4, 579 (1989).Google Scholar
[65] Caro, A., Victoria, M., and Averback, R. S., J. Mater. Res. 5, 1409 (1990).Google Scholar
[66] Shul'ga, V. I. and Sigmund, P., Nucl. lnstrum. Methods B 47, 236 (1990).Google Scholar
[67] Pan, Z. and Sigmund, P., Nucl. lnstrum. Methods B 51, 344, (1990).Google Scholar
[68] Averback, R. S., Diaz de la Rubia, T., Hsieh, H., and Benedek, R., Nucl. lnstrum. Methods B 59/60, 709 (1991).Google Scholar
[69] Shul'ga, V. I., Nucl. lnstrum. Methods B 58, 422 (1991).Google Scholar
[70] Shul'ga, V. I. and Sigmund, P., Nucl. lnstrum. Methods B 62, 23 (1991).Google Scholar
[71] Pan, Z., Nucl. lnstrum. Methods B 66, 325 (1992).Google Scholar
[72] Yurasova, V. E., Nucl. lnstrum. Methods B (1993) to be published.Google Scholar
[73] Harrison, D. E. Jr, Avouris, P., and Walkup, R., Nucl. lnstrum. Methods B 18, 349 (1987).Google Scholar
[74] Lo, D. Y., Shapiro, M. H., Tombrello, T. A., Garrison, B. J., and Winograd, N., Matt. Res. Soc. Sym., Proc. 74, 449 (1987).Google Scholar
[75] Shapiro, M. H. and Tombrello, T. A., Nucl. lnstrum. Methods B 18, 355 (1987).Google Scholar
[76] Mazzone, A. M., Nucl. lnstrum. Methods B 33, 776 (1988).Google Scholar
[77] Shapiro, M. H., Tombrello, T. A., and Harrison, D. E. Jr, Nucl. lnstrum. Methods B 30, 152(1988).Google Scholar
[78] Shapiro, M. H. and Fine, J., Nucl. lnstrum. Methods B 44, 43, (1989).Google Scholar
[79] Smith, R. and Harrison, D. E. Jr, Phys. Rev. B 40, 2090, (1989).Google Scholar
[80] Antonov, S. L., Ivanov, I. N., Orlikovsky, A. A., Vasi'chenko, V.Yu., and Yurasova, V. E., Nucl. lnstrum. Methods B 48, 553, (1990).Google Scholar
[81] Broomfield, K., Stansfield, R. A., and Clary, D. C., Surface Sci. 227, 369 (1990).Google Scholar
[82] Diaz de la Rubia, T. and Guinan, M. W., J. Nuclear Mater. 174, 151 (1990).Google Scholar
[83] Shapiro, M. H. and Tombrello, T. A., Phys. Rev. Lett. 65, 92 (1990).Google Scholar
[84] Shapiro, M. H. and Tombrello, T. A., Nucl. lnstrum. Methods B 48, 557, (1990).Google Scholar
[85] Betz, G., Pellin, M. J., Burnett, J. W., and Gruen, D. M., Nucl. lnstrum. Methods B 58, 429,(1991).Google Scholar
[86] Pelletier, J. D., Shapiro, M. H., and Tombrello, T. A., Nucl. Instrum. Methods B 67, 296 (1992).CrossRefGoogle Scholar
[87] Shapiro, M. H. and Tombrello, T. A., Nucl. Instrum. Methods B 58, 161, (1991).Google Scholar
[88] Shapiro, M. H. and Tombrello, T. A., Nucl. Instrum. Methods B 62, 35, (1991).Google Scholar
[89] Shapiro, M. H. and Tombrello, T. A., Phys. Rev. Lett. 68, 1613 (1992); Nucl. Instrum. Methods B 66, 317 (1992).Google Scholar
[90] Finnis, M. W. and Sinclair, J. E., Phil. Mag. A 50, 45 (1984).Google Scholar
[91] Carlsson, A. E., Solid State Physics 43, 1 (1990).Google Scholar
[92] Cyrot-Lackmann, F., J. Phys. Chem. Solids 29, 1235 (1968).CrossRefGoogle Scholar
[93] Ducastelle, F., J. Phys. (Paris) 31, 1055 (1970).Google Scholar
[94] Daw, M. S. and Baskes, M. I., Phys. Rev. B 29, 6443 (1984);CrossRefGoogle Scholar
Foiles, S. M., Baskes, M. I., and Daw, M. S., Phys. Rev. B 33, 7983 (1986).Google Scholar
[95] Johnson, R. A., Phil. Mag. A 63, 865 (1991).Google Scholar
[96] van Midden, H. J. P. and Sasse, A. G. B. M., Phys. Rev. B 46, 6020 (1992).Google Scholar
[97] Garrison, B. J., Winograd, N., Deaven, D. M., Reiman, D. T., Lo, D. Y., Tombrello, T. A., Harrison, D. E. Jr, and Shapiro, M. H., Phys. Rev B 37, 7197 (1988).Google Scholar
[98] Chen, S. P., Voter, A. F., Albers, R. C., Boring, A. M., and Hay, P. J., J. Mater. Res. 5, 955(1990).Google Scholar
[99] Guellil, A. M. and Adams, J. B., J. Mater. Res. 7, 639 (1992).Google Scholar
[100] Igarashi, M., Kanta, K., and Vitek, V., Phil. Mag. B 63, 603 (1991).Google Scholar
[101] Loisel, B., Lapujoulade, J., and Pontikis, V., Surface Sci. 256, 247 (1991).Google Scholar
[102] Gades, H. and Urbassek, H. M., Nucl. Instrum. Methods B 69, 232 (1992).Google Scholar
[103] Hsieh, H., Averback, R. S., Sellers, H., and Flynn, C. P., Phys. Rev. B 45, 4417 (1992).Google Scholar
[104] Baskes, M. I., J. Nucl. Mater. 28/129, 676 (1984).Google Scholar
[105] Lo, D. Y., Tombrello, T. A., Shapiro, M. H., Garrison, B. J., Winograd, N., and Harrison, D. E. Jr, J. Vac. Sci. Technol. A 6, 708 (1988).CrossRefGoogle Scholar
[106] Karetta, F. and Urbassek, H. M., J. Appl Phys. 71, 5410 (1992).Google Scholar
[107] Wucher, A. and Garrison, B. J., Surface Sci. 260, 257 (1992); Phys. Rev. B 46, 4855 (1992).Google Scholar
[108] Wucher, A., Watgen, M., Moessner, C., Oechsner, O., and Garrison, B. J., Nucl. Instrum. Methods 67, 531 (1992).CrossRefGoogle Scholar
[109] Wucher, A. and Garrison, B. J., Nucl. Instrum. Methods B (1993) to be published.Google Scholar
[110] Betz, G. and Kirchner, R., Nucl. Instrum. Methods B (1993) to be published.Google Scholar
[111] Diaz de la Rubia, T. and Guinjan, M. W., J. Nuclear Mater. 174, 151 (1990).Google Scholar
[112] Chou, S. P. and Ghoniem, N. M., Phys. Rev. B 43, 2490 (1991).Google Scholar
[113] Diaz de la Rubia, T. and Guiñan, M. W., Phys. Rev. Lett. 66, 2766 (1991).Google Scholar
[114] Proennecke, S., Caro, A., Victoria, M., Diaz de la Rubia, T., and Guinan, M. W., J. Mater. Res. 6, 483 (1991).Google Scholar
[115] StiHinger, F. H. and Weber, T. A., Phys. Rev. B 31, 5262 (1985).Google Scholar
[116] Tersoff, J., Phys. Rev. Lett B 56, 632 (1986).Google Scholar
[117] Brenner, D. W. and Garrison, B. J., Phys. Rev B 34, 1304 (1986).CrossRefGoogle Scholar
[118] Biswas, R. and Hamann, D. R., Phys. Rev. B 36, 6434 (1987).Google Scholar
[119] Baskes, M. I., Phys. Rev. Lett. 59, 2666 (1987).Google Scholar
[120] Dodson, B. W., Phys. Rev. B 35, 2795 (1987).Google Scholar
[122] Tersoff, J., Phys. Rev. B 37, 6991 (1988).Google Scholar
[123] Tersoff, J., Phys. Rev. Lett. 61, 2879 (1988); Phys. Rev. B 38, 9902 (1988).Google Scholar
[124] Brenner, D. W., Phys. Rev. B 42, 9458 (1990).Google Scholar
[125] Smith, R., Nucl. Instrum. Methods. B 67, 335 (1992).Google Scholar
[126] Dodson, B. W., Phys. Rev. B 36, 1068 (1987); Appl Surface Sci. 29, 334 (1987).Google Scholar
[127] Dodson, B. W., and Taylor, P. A., J. Mater. Res. 2, 805 (1987).Google Scholar
[128] Smith, R., Harrison, D. E. Jr, and Garrison, B. J., Phys. Rev. B 40, 93 (1989); Nucl. Instrum. Methods B 46, 1 (1990).Google Scholar
[129] Smith, R., and Webb, R. P., Nucl. Instrum. Methods B 59/60, 1378 (1991).Google Scholar
[130] Mowrey, R. C., Brenner, D. W., Dunlap, B. I., Mintmire, J. W., and White, C. T., J. Phys. Chem. 95, 7138 (1991).Google Scholar
[131] Smith, R., and Webb, R. P., Nucl. Instrum. Methods B (1993) to be published.Google Scholar
[132] Echenique, P. M., Flores, F., and Ritchie, R. H., Solid State Physics 43, 229 (1990).Google Scholar
[133] Brandt, W. and Kitigawa, M., Phys. Rev. B 25, 5631 (1982).Google Scholar
[134] Flynn, C. P. and Averback, R. S., Phys. Rev. B 38, 7118 (1988).Google Scholar
[135] Sigmund, P. in Interaction of Charged Particles with Solids and Surfaces, edited by Gras-Marti, A. et al., NATO ASI Series, Vol. 271 (Plenum, New York, 1991), p.73.Google Scholar
[136] Mikkelsen, H. H., Meibom, A., and Sigmund, P., Phys. Rev. A (1992), in press.Google Scholar
[137] Lindhard, J. and Scharff, M., Phys. Rev. 124, 128 (1961).CrossRefGoogle Scholar
[138] Firsov, O. B., Zh. Eksp. Teor. Fiz. 36, 1517 (1959) [Engl. transl.: Sov. Phys.-JETP 36, 1076(1959)].Google Scholar
[139] Oen, O. S. and Robinson, M. T., Nucl. Instrum. Methods 132, 647 (1976).Google Scholar
[140] Kaneko, T., Surface Science 236, 203 (1990); Nucl. Instrum. Methods B 48, 83 (1990).Google Scholar
[141] Schiwietz, G., Phys. Rev. A 42, 296 (1990).Google Scholar
[142] Grande, P. L. and Schiwietz, G., Phys. Rev. A 44, 2984 (1991).Google Scholar
[143] Jakas, M. M. and Harrison, D. E. Jr, Phys. Rev. B 30, 3573 (1984).Google Scholar
[144] Harrison, D. E. Jr, and Jakas, M. M., Nucl. Instrum. Methods B 15, 25 (1986).Google Scholar
[145] Valkealahti, S. and Nieminen, R. M., Nucl. Instrum. Methods B 18, 365 (1987).Google Scholar
[146] Caro, A. and Victoria, M., Phys. Rev. A 40, 2287 (1989).Google Scholar
[147] Lindhard, J., Nielsen, V., Scharff, M., and Thomsen, P. V., Dan, K.. Vidensk. Selsk. Mat. Fys. Medd. 33, no. 10 (1963).Google Scholar
[148] Robinson, M. T. and Oen, O. S., J. Nucl. Mater. 110, 147 (1982).Google Scholar
[149] Norgett, M. J., Robinson, M. T., and Torrens, I. M., Nucl. Engineer. Design 33, 50 (1975).Google Scholar
[150] Robinson, M. T., J. Appl Phys. 54, 2650 (1983).Google Scholar
[151] Eckstein, W. and Biersack, J. P., Nucl. Instrum. Methods B 2, 550 (1984).Google Scholar
[152] Biersack, J. P. and Eckstein, W., Appl Phys. A 34, 73 (1984).Google Scholar
[153] Jakas, M. M. and Harrison, D. E. Jr, Phys. Rev. B 32, 2752 (1985).Google Scholar
[154] Chang, C. -C., Winograd, N., and Garrison, B. J., Surface Sci. 202, 309 (1988).Google Scholar
[155] Karpuzov, D. S. and Yurasova, V. E., Phys. Stat. Solidi 47, 41 (1971).Google Scholar
[156] Hou, M. and Robinson, M. T., Nucl. Instrum. Methods 132, 641 (1976).Google Scholar
[157] Shu'ga, V. I., Vicanek, M., and Sigmund, P., Phys. Rev. A 39, 3360 (1989).Google Scholar
[158] Brown, W. L., Jarrold, M. F., McEachern, R. L., Sosnowski, M., Takaoka, G., Usui, H., and Yamada, I., Nucl. Instrum. Methods B 59/60, 182 (1991).Google Scholar
[159] Beuhler, R. J., Friedlander, G., and Friedman, L., Phys. Rev. Lett. 63, 1292 (1989).Google Scholar
[160] Beuhler, R. J., Chu, Y. Y., Friedlander, G., Friedman, L., and Kunnmann, W., J. Phys. Chem. 94, 7665 (1990).Google Scholar
[161] Fallavier, M., Kemmler, J., Kirsch, R., Poizat, J. C., Remillieux, J., and Thomas, J. P., Phys. Rev. Lett. 65, 621 (1990).Google Scholar
[162] Beuhler, R. J. and Friedman, L., Chem. Rev. 86, 521 (1986).Google Scholar
[163] Cleveland, C. L. and Landman, U., Science 257, 355 (1992).Google Scholar
[164] Sigmund, P., J. Phys. (Paris), Coll. C-2 50, 175 (1989).Google Scholar
[165] Mueller, K.-H., J. Appl Phys. 61, 2516 (1987).Google Scholar
[166] Biswas, R., Grest, G. S., and Soukoulis, C. M., Phys. Rev. B 38, 8154 (1988).Google Scholar
[167] Kwon, I., Biswas, R., Grest, G. R., and Soukoulis, C. M., Phys. Rev. B 41, 3678 (1990).Google Scholar
[168] Hsieh, H., and Averback, R. S., Phys. Rev. B 42, 5365 (1990).Google Scholar
[169] Yamamura, Y. and Muramoto, T., Nucl. Instrum. Methods B (1993) to be published.Google Scholar