"Migration energy" for impurity diffusion in crystalline solids: A closer look

Journal of Applied Physics

Volumn 96, Issue 12, 2004, Pages 7095-7107

  Ramanarayanan, Panchapakesan ^a,c   Srinivasan, Balaji ^b   Cho, Kyeongjae ^a   Clemens, Bruce M ^a  

^a Stanford University   (United States)

^b Department of Aeronautics and Astronautics Department of Mechanical Engineering and Industrial for Computational and Mathematical Engineering   (United States)

^c INTEL CORPORATION   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CRYSTALLINE SOLIDS; MICROSCOPIC PROCESSES; MIGRATION ENERGY; TRANSITION STATE THEORY;

ACTIVATION ENERGY; COMPUTER SIMULATION; CRYSTAL LATTICES; DIFFUSION; GROUND STATE; IMPURITIES; MONTE CARLO METHODS; NUMERICAL METHODS;

CRYSTALLINE MATERIALS;

EID: 11044226007     PISSN: 00218979     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1809254     Document Type: Article

References (26)

1. P. Ramanarayanan, K. Cho, and B. M. Clemens, J. Appl. Phys. 94, 174 (2003).
2. S. M. Hu, Phys. Rev. 180, 773 (1969).
3. J. R. Manning, Phys. Rev. Lett. 1, 365 (1958).
4. A. D. LeClaire, Philos. Mag. 7, 141 (1962).
5. S. T. Dunham and C. D. Wu, J. Appl. Phys. 78, 2362 (1995).
6. O. Pankratov, H. Huang, T. D. de la Rubia, and C. Mailhiot, Phys. Rev. B 56, 13172 (1997).
7. O. Sugino and A. Oshiyama, Phys. Rev. B 46, 12335 (1992).
8. We assume, for the sake of simplicity, that the jump frequency depends only on the identity of the atom with which the vacancy jumps. The entire discussion can be easily extended to more complicated situations where the jump frequency depends on the identities of the nth neighbors of the vacancy and the jumping atom.
9. This assertion, of course, depends on the assumption that the jump frequency depends only on the identity of the jumping atom. If it has other dependencies, then the assertion is accordingly modified as, for example, the number of times the vacancy would jump with an A atom with the vacancy's first nearest neighbor being B and the A atom's first nearest neighbor atom being, say, C and so on.
10. S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943).
11. M. E. Glicksman, Diffusion in Solids: Field Theory, Solid-State Principles, and Applications (Wiley, New York, 2000).
12. J. Bardeen and C. Herring, in Imperfections in Nearly Perfect Crystals, edited by W. Shockley (Wiley, New York, 1952), p. 261.
13. J. R. Manning, Phys. Rev. 116, 819 (1959).
14. J. R. Manning, Phys. Rev. B 4, 1111 (1971).
15. R. A. Tahir-Kheli and R. J. Elliott, Phys. Rev. B 27, 844 (1983).
16. R. A. Tahir-Kheli, Phys. Rev. B 28, 3049 (1983).
17. R. A. Tahir-Kheli, Phys. Rev. B 35, 5503 (1987).
18. Y. Suzuki, K. Kitahara, Y. Fujitani, and S. Kinouchi, J. Phys. Soc. Jpn. 71, 2936 (2002).
19. The impurity concentration, though higher than in the case discussed earlier, is still assumed to be low. If the impurity concentration is higher, this model will no longer be applicable. One would, then, need to further extend this model in a fashion similar to what has been done here.
20. G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993).
21. G. Kresse and J. Hafner, Phys. Rev. B 49, 14251 (1994).
22. G. Kresse and J. Furthmüller, Comput. Mater. Sci. 6, 15 (1996).
23. G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996).
24. H. Monkhorst and J. Pack, Phys. Rev. B 13, 5188 (1976).
25. H. Jónsson, G. Mills, and K. W. Jacobsen, in Classical and Quantum Dynamics in Condensed Phase Simulations, edited by B. J. Berne G. Ciccotti, and D. F. Coker (World Scientific, Singapore, 1998), Chap. 16.
26. M. J. Aziz, Appl. Phys. Lett. 70, 2810 (1997).