Hostname: page-component-788cddb947-w95db Total loading time: 0 Render date: 2024-10-15T14:42:05.737Z Has data issue: false hasContentIssue false
  • English
  • Français

Study of Oxygen Diffusion and Clustering in Silicon Using an Empirical Interatomic Potential

Published online by Cambridge University Press:  26 February 2011

Z. Jiang  and
R. A. Brown
Z. Jiang
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
R. A. Brown
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
Get access

Abstract

The diffusion path and diffusivity of oxygen in crystalline silicon are computed using an empirical interatomic potential which was recently developed [1] for modelling the interactions between oxygen and silicon atoms. The diffusion path is determined by constrained energy minimization, and the diffusivity is computed using jump rate theory. The calculated diffusivity D=0.025 exp(-2.43eV/kBT) cm2/sec is in excellent agreement with experimental data. The same interatomic potential also is used to study the formation of small clusters of oxygen atoms in silicon. The structures of these clusters are found by NPT molecular dynamics simulations, and their free energies are calculated by thermodynamic integration. These free energies are used to predict the temperature dependence of the equilibrium partitioning of oxygen atoms into clusters of different sizes. The calculations show that, for given total oxygen concentration, most oxygen atoms are in clusters at temperature below 1300K, and that the average cluster size increases with decreasing temperature. These results are in qualitative agreement with the effects of thermal annealing on oxygen precipitation in silicon crystals.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 378: Symposium B – Defect and Impurity-Engineered Semiconductors and Devices , 1995 , 89
Copyright
Copyright © Materials Research Society 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Jiang, Z. and Brown, R. A., Chem. Eng. Sci. 49, 2991 (1994).Google Scholar
[2] Zulehner, W. and Huber, D., in Crystals: Growth. Properties and Application 8, edited by Grabmaier, J. (Springer, New York, 1982).Google Scholar
[3] Brown, R. A., AIChE Journal 34, 881 (1988); T. A. Kinney and R. A. Brown, J. Crystal Growth 132, 551 (1993).Google Scholar
[4] Corbett, J. W., McDonald, R. S., and Watkins, G. D., J. Phys. Chem. Solids 25, 873 (1964).Google Scholar
[5] Yamagishi, H., Fusegawa, I., Fujimaki, N. and Katayama, M., Sem. Sci. Tech.7, A135 (1992).Google Scholar
[6] Mikkelsen, J. C. Jr., Appl. Phys. Lett. 40, 336 (1982).Google Scholar
[7] Lee, S. T. and Nichols, D., Appl. Phys. Lett. 47, 1001 (1985).Google Scholar
[8] Gass, J., Muller, H. H., Stussi, H., and Schweitzer, S., J. Appl. Phys. 51, 2030 (1980).Google Scholar
[9] Itoh, Y. and Nozaki, T., Jnp. J. Appl. Phys. 24, 279 (1985).Google Scholar
[10] Stavola, M., Patel, J.R., Kimerling, L.C., and Freeland, P. E., Appl. Phys. Lett. 42,73 (1983).Google Scholar
[11] Newman, R. C., Tucker, J. H., and Livingston, F. M., J. Phys. C 16, L151 (1983).Google Scholar
[12] Mikkelsen, J. C. Jr., Mat. Res. Soc. Symp. Proc. 59, 19 (1986).Google Scholar
[13] Needels, M., Joannopoulos, J. D., Bar-Yam, Y., Pantelides, S. T., and Wolfe, R. H., Mat. Res. Soc. Symp. Proc. 209, 103 (1991); Phys. Rev. B 43, 4208 (1991).Google Scholar
[14] Oshiyama, A. and Saito, M., in Defect Control in Semiconductors, edited by Sumino, K. (Elsevier Science Publishers, North-Holland, 1990).Google Scholar
[15] Saito, M. and Oshiyama, A., Phys. Rev. B 38, 10711 (1988).Google Scholar
[16] Snyder, L. C. and Corbett, J. W., Mat. Res. Soc. Symp Proc. 59, 207 (1986); 104, 179 (1988).Google Scholar
[17] Kelly, P. J., Mat. Sci. Forum 38–41, 269 (1989).Google Scholar
[18] Jiang, Z. and Brown, R. A., Phys. Rev. Lett. 74, 2046 (1995).Google Scholar
[19] Wert, C. and Zener, C., Phys. Rev. 76,1169 (1949); K. Weiser, Phys. Rev. 126, 1427 (1962).Google Scholar
[20] Vineyard, G. H., J. Phys. Chem. Solids 3, 121 (1957); J. H. Harding, Rep. Prog. Phys. 53, 1403 (1990).Google Scholar
[21] Stillinger, F. H. and Weber, T. A., Phys. Rev. B 31, 5262 (1985).Google Scholar
[22] van Beest, B. W., Kramer, G. J., and van Santen, R. A., Phys. Rev. Lett. 64,1955 (1990).Google Scholar
[23] Greig, D. M., Optimisation. (Longman, London, 1980).Google Scholar
[24] Haas, C., J. Phys. Chem. Solids 15, 108 (1960).Google Scholar
[25] Andersen, H. C., J. Chem. Phys. 72, 2384 (1980).Google Scholar
[26] Gear, C. W., Numerical Initial Value Problems in Ordinary Differential Equations. (Prentice_Hall, Englewood Cliffs, NJ, 1971).Google Scholar
[27] McQuarrie, D. A., Statistical Mechanics. (Harper and Row, New York, 1976).Google Scholar
[28] Ataka, M. and Ogawa, T., J. Mater. Res. 8, 2889 (1993).Google Scholar
[29] Gosele, U. and Tan, T. Y., Appl. Phys. A 28,79 (1982).Google Scholar