Ab-Initio Calculation of the Phonon Frequencies in Covalent Semiconductors Using the Dielectric Screening Method

  • J. T. Devreese
  • P. E. Van Camp
  • V. E. Van Doren

Abstract

The theory of the lattice dynamics of covalent semiconductors has been developed in the late sixties and early seventies [1]. The essence of this theory is the description of the density distribution of the valence electrons between the ions at their arbitrary and instantaneous positions. Originally this part of the electron distribution due to deviations of the ions from their equilibrium positions is derived from linear response theory. Subsequently phonon dispersion curves can be obtained from this dielectric screening method. From 1972 the present authors started their efforts to calculate phonon frequencies using this method. A presentation of linear response and dielectric screening theory is given in these proceedings in the paper by J.T. Devreese and F. Brosens.

Keywords

Local Density Approximation Phonon Frequency Dynamical Matrix Reciprocal Lattice Vector Linear Response Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L.J. Sham, Phys. Rev. 188, 1431 (1969).CrossRefGoogle Scholar
  2. R.M. Pick, M.H. Cohen and R.M. Martin, Phys. Rev. B2, 910 (1970).Google Scholar
  3. F.A. Johnson, Proc. Roy. Soc. A310, 79 (1969);Google Scholar
  4. F.A. Johnson, ibid. A310, 89 (1969);Google Scholar
  5. F.A. Johnson, ibid. A310, 101 (1969).Google Scholar
  6. D.C. Wallace, “Thermodynamics of Crystals”, J. Wiley, New York (1972).Google Scholar
  7. 2.
    P.E. Van Camp, V.E. Van Doren, J.T. Devreese, Inst. Phys. Conf. Ser. 43, 685 (1979).Google Scholar
  8. P.E. Van Camp, V.E. Van Doren, J.T. Devreese, Phys. Stat. Sol. (b) 93, 483 (1979).CrossRefGoogle Scholar
  9. P.E. Van Camp, V.E. Van Doren, J.T. Devreese, Phys. Rev. Lett. 42, 1224 (1979).CrossRefGoogle Scholar
  10. J.T. Devreese, P.E. Van Camp, V.E. Van Doren, Int. J. Quant. Chem. 18, 317 (1980).CrossRefGoogle Scholar
  11. 3.
    H. Ehrenreich, M.H. Cohen, Phys. Rev. 115, 786 (1959).CrossRefGoogle Scholar
  12. S. Adler, Phys. Rev. 126, 413 (1962).CrossRefGoogle Scholar
  13. N. Wiser, Phys. Rev. 129, 62 (1963).CrossRefGoogle Scholar
  14. 4.
    W. Kohn, L. Sham, Phys. Rev. 136, B864 (1964).CrossRefGoogle Scholar
  15. 5.
    P.E. Van Camp, V.E. Van Doren, J.T. Devreese, Phys. Rev. B24, 1096 (1981).Google Scholar
  16. 6.
    J.C. Slater, Phys. Rev. 81, 385 (1951).CrossRefGoogle Scholar
  17. 7.
    P.E. Van Camp, V.E. Van Doren, J.T. Devreese, Phys. Stat. Sol. (b) 110, K133 (1982).CrossRefGoogle Scholar
  18. 8.
    P.E. Van Camp, V.E. Van Doren, J.T. Devreese, unpublished results.Google Scholar
  19. 9.
    M. Schlüter, J. Chelikowsky, S. Louie, M.L. Cohen, Phys. Rev. B12, 4200 (1975).CrossRefGoogle Scholar
  20. 10.
    W. Topp, J. Hopfield, Phys. Rev. B7, 1295 (1973).CrossRefGoogle Scholar
  21. 11.
    M.L. Cohen, T. Bergstresser, Phys. Rev. 141, 789 (1966).CrossRefGoogle Scholar
  22. 12.
    P.E. Van Camp, V.E. Van Doren, J.T. Devreese, in “Ab-Initio Calculation of Phonon Spectra”, eds. J.T. Devreese, V.E. Van Doren, P.E. Van Camp, Plenum, New York (1983).Google Scholar
  23. P.E. Van Camp, V.E. Van Doren, J.T. Devreese, Phys. Rev. B25, 4270 (1982).CrossRefGoogle Scholar
  24. 13.
    J. Donahue, “The Structure of Elements”, Wiley, New York (1972).Google Scholar
  25. 14.
    G. Nilson, G. Nelin, Phys. Rev. B6, 3777 (1972). 15Google Scholar
  26. 15.
    P.E. Van Camp, J.T. Devreese, in. Devreese, in “Proceedings of the Supercomputer Applications Symposium”, to be published (1984).Google Scholar

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • J. T. Devreese
    • 1
    • 2
    • 3
  • P. E. Van Camp
    • 1
  • V. E. Van Doren
    • 1
  1. 1.University of Antwerp (RUCA)AntwerpenBelgium
  2. 2.Department of PhysicsUniversity of Antwerp (UIA)Antwerpen-WilrijkBelgium
  3. 3.University of TechnologyEindhovenThe Netherlands

Personalised recommendations