Hostname: page-component-5c6d5d7d68-7tdvq Total loading time: 0 Render date: 2024-08-16T03:55:35.601Z Has data issue: false hasContentIssue false

First-Principles Calculation of Force Constants and Full Phonon Dispersions

Published online by Cambridge University Press:  01 January 1992

Siqing Wei
Affiliation:
Georgia Institute of Technology, School of Physics, Atlanta, GA 30332-0430
M. Y. Chou
Affiliation:
Georgia Institute of Technology, School of Physics, Atlanta, GA 30332-0430
Get access

Abstract

We calculated the real-space force constants and full phonon dispersion curves for elemental semiconductors (silicon and germanium) under the local-density approximation with the Hellmann-Feynman forces. The force constants are obtained through super- cell calculations for planar displacements in three different symmetry directions. From these real-space force constants the dynamical matrix for an arbitrary wave vector in the Brillouin zone can be constructed. The procedure is simple in concept and requires no complicated computer programing. It is also possible in principle to handle the anharmonic effects.

Type
Research Article
Copyright
Copyright © Materials Research Society 1993

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

REFERENCES

1. Bruesch, P., Phonons, Theory and Experiments (Springer-Verlay, New York 1982).Google Scholar
2. Sham, L. J., Dynamical Properties of Solids, edited by Horton, G. K. and Maradudin, A. A., (North-Holland, 1974), p. 301.Google Scholar
3. Sinha, S. K., CRC Crit. Rev. Sold State Sci. 3, 273 (1973).Google Scholar
4. Baroni, S., de Gironcoli, S. and Giannozzi, P., Phys. Rev. Lett. 65, 84 (1990).Google Scholar
5. Molinari, E., Baroni, S., Giannozzi, P., and de Gironcoli, S., Phys. Rev. B45, 4280 (1992).Google Scholar
6. Feynman, R. P., Phys. Rev. 56, 340 (1939), and Slater, J. C., J. Chem. Phys. 57, 2389 (1972), and Ihm, J., Zunger, A., and Cohen, M. L., J. Phys. C12, 4409 (1979).Google Scholar
7. Kunc, K. and Martin, Richard M., Phys. Rev. Lett. 18, 406 (1982).Google Scholar
8. Yin, M. T. and Cohen, M. L., Phys. Rev. B25, 4317 (1982).Google Scholar
9.See, for example Electronic Structure, Dynamics, and Quantum Structural Properties of Condensed Matter, edited by Devreese, J. T. and Van Camp, P. (Plenum, New York, 1985).Google Scholar
10. Baroni, S., Giannozzi, P. and Testa, A., Phys. Rev. Lett. 58, 1861 (1987).Google Scholar
11. Wei, Siqing and Chou, M. Y., to be published in PRB.Google Scholar
12. Wei, Siqing and Chou, M. Y., Phys. Rev. Lett. 69, 2799 (1992).Google Scholar
13. Hermann, Frank, J. Phys. Chem. Solids 8, 405 (1959).Google Scholar
14. Mazur, A. and Pollmann, J., Phys. Rev. B39, 5261 (1989).Google Scholar
15. Dolling, G., in Inelastic Scattering of Neutrons in Solids and Liquids, edited by Ekland, S. (IAEA, Vienna, 1963), Vol. II, p. 37; G. Nilsson and G. Nelin, Phys. Rev. B6, 3777 (1972).Google Scholar
16. Nilsson, G. and Nelin, G., Phys. Rev. B3, 364, (1971).Google Scholar
17. Ceperley, D. M. and Alder, B. J., Phys. Rev. Lett. 45, 566 (1980).Google Scholar
18. Troullier, N. and Martines, J. L., Phys. Rev. B43, 1993 (1990).Google Scholar