<i>Ab initio</i> phonon dispersion curves of Si

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

doi:10.1103/PhysRevB.31.4089

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Ab initio phonon dispersion curves of Si

P. E. Van Camp and V. E. Van Doren

J. T. Devreese

University of Antwerpen Rijksuniversitair Centrum Antwerpen, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium

University of Antwerpen Rijksuniversitair Centrum Antwerpen, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium; and University of Antwerpen (Universitaire Instelling Antwerpen), Universiteitsplein 1, B-2610 Wilrijk-Antwerpen, Belgium; and Eindhoven University of Technology, 5600-MB Eindhoven, The Netherlands

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Phys. Rev. B 31, 4089(R) – Published 15 March, 1985

DOI: https://doi.org/10.1103/PhysRevB.31.4089

Abstract

We give phonon dispersion curves of Si in the Δ, Λ, and Σ directions. This calculation takes into account the linear response of the electron to an external potential caused by the displacements of the ions away from their equilibrium positions. The lattice constant is calculated from minimalization of the total crystal energy with respect to these displacements. The polarizability matrix is evaluated by means of a direct summation over the conduction bands. In previous work we used a moment expansion of the polarizability. The same exchange-correlation approximation in both the Hamiltonian and the dielectric matrix is taken into account. Furthermore, consistency between the electron-ion and the crystal pseudopotential has been achieved for the calculation of electron energies and wave functions.

References (18)

W. Kohn and L. Sham, Phys. Rev. 140, A1133 (1965).
M. T. Yin and M. L. Cohen, Phys. Rev. Lett. 45, 1004 (1980).
M. T. Yin and M. L. Cohen, Phys. Rev. B 25, 4317 (1982).
P. E. Van Camp, V. E. Van Doren and J. T. Devreese, Phys. Rev. Lett. 42, 1224 (1979).
P. E. Van Camp, V. E. Van Doren and J. T. Devreese, Phys. Rev. B 24, 1096 (1981).
P. E. Van Camp, V. E. Van Doren and J. T. Devreese, Phys. Status Solidi 110, K133 (1982); and (unpublished).
M. Schlüter, J. R. Chelikowsky, S. G. Louie and M. L. Cohen, Phys. Rev. B 12, 4200 (1975).
J. Donohue, The Structure of Elements (Wiley, New York, 1974).
See Ref. 4.
G. Dolling, Inelastic Scattering of Neutrons in Solids and Liquids (IAEA, Vienna, 1963), Vol. II, p. 37.
See Ref. 4.
P. E. Van Camp, V. E. Van Doren and J. T. Devreese, Phys. Rev. B 25, 4270 (1982).
D. J. Chadi and R. M. Martin, Solid State Commun. 19, 643 (1976).
H. Wendel and R. M. Martin, Phys. Rev. B 19, 5251 (1979).
See Ref. 2.
R. Resta and A. Baldereschi, Phys. Rev. B 24, 4839 (1981).
J. Ihm, M. T. Yin, M. L. Cohen, Solid State Commun. 37, 491 (1981).
B. N. Harmon, W. Weber and D. R. Hamann, J. Phys. (Paris) Colloq. 42, C6-628 (1981).

[c1] W. Kohn and L. Sham, Phys. Rev. 140, A1133 (1965).

[c2] M. T. Yin and M. L. Cohen, Phys. Rev. Lett. 45, 1004 (1980).

[c3] M. T. Yin and M. L. Cohen, Phys. Rev. B 25, 4317 (1982).

[c4] P. E. Van Camp, V. E. Van Doren and J. T. Devreese, Phys. Rev. Lett. 42, 1224 (1979).

[c5] P. E. Van Camp, V. E. Van Doren and J. T. Devreese, Phys. Rev. B 24, 1096 (1981).

[c6] P. E. Van Camp, V. E. Van Doren and J. T. Devreese, Phys. Status Solidi 110, K133 (1982); and (unpublished).

[c7] M. Schlüter, J. R. Chelikowsky, S. G. Louie and M. L. Cohen, Phys. Rev. B 12, 4200 (1975).

[c8] J. Donohue, The Structure of Elements (Wiley, New York, 1974).

[c9] See Ref. 4.

[c10] G. Dolling, Inelastic Scattering of Neutrons in Solids and Liquids (IAEA, Vienna, 1963), Vol. II, p. 37.

[c11] See Ref. 4.

[c12] P. E. Van Camp, V. E. Van Doren and J. T. Devreese, Phys. Rev. B 25, 4270 (1982).

[c13] D. J. Chadi and R. M. Martin, Solid State Commun. 19, 643 (1976).

[c14] H. Wendel and R. M. Martin, Phys. Rev. B 19, 5251 (1979).

[c15] See Ref. 2.

[c16] R. Resta and A. Baldereschi, Phys. Rev. B 24, 4839 (1981).

[c17] J. Ihm, M. T. Yin, M. L. Cohen, Solid State Commun. 37, 491 (1981).

[c18] B. N. Harmon, W. Weber and D. R. Hamann, J. Phys. (Paris) Colloq. 42, C6-628 (1981).

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Ab initio phonon dispersion curves of Si

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