Polarons in Degenerate Semiconductors

G. D. Mahan; C. B. Duke

doi:10.1103/PhysRev.149.705

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Polarons in Degenerate Semiconductors

G. D. Mahan and C. B. Duke

General Electric Research and Development Center, Schenectady, New York

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Phys. Rev. 149, 705 – Published 16 September, 1966

DOI: https://doi.org/10.1103/PhysRev.149.705

Abstract

The second-order self-energies of an electron in a degenerate Fermi gas arising from polar coupling to longitudinal optic phonons and from both piezoelectric and deformation-potential coupling to (Debye) acoustic phonons are evaluated exactly and analytically. Numerical calculations of the resulting density of states for optical phonons exhibit logarithmic singularities at the Fermi energy $μ$ and at $μ + ω_{0}$ . Similar structure due to the electron's interaction with acoustical phonons is exhibited by the proper self-energy but is smoothed out in the density of states by the nonvanishing imaginary part of the self-energy. The singularities at the Fermi surface are removed by the random-phase-approximation screening of the electronphonon interaction due to mobile charge carriers. These results indicate that several proposed explanations for low-bias conductance anomalies in tunnel diodes are inapplicable.

References (28)

L. Esaki, Phys. Rev. 109, 603 (1957)
R. T. Shuey, Phys. Rev. 137, A1268 (1965)
R. N. Hall, J. H. Racette, and H. Ehrenreich, Phys. Rev. Letters 4, 456 (1960) R. N. Hall, in Proceedings of the International Conference on Semiconductors, Prague, 1960 (Academic Press Inc., New York, 1961), p. 193
R. A. Logan and J. M. Rowell, Phys. Rev. Letters 13, 404 (1964)
R. M. Williams and J. Shewchun, Phys. Rev. Letters 14, 824 (1965) ibid. 15, 160 (1965)
W. A. Harrison and C. B. Duke (unpublished)
A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinsky, Methods of Quantum Field Theory in Statistical Physics (Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1963), Chaps. 2 and 3
S. Engelsberg and J. R. Schrieffer, Phys. Rev. 131, 993 (1963)
T. Holstein, Ann. Phys. (N. Y.) 29, 410 (1964)
Omitted endnote
A. Ron, Phys. Rev. 132, 978 (1963)
J. R. Schrieffer, Theory of Superconductivity (W. A. Benjamin, Inc., New York, 1964), Chap. 6
L. V. Keldysh and Yu. V. Kopaev, Fiz. Tverd. Tela 5, 1411 (1963) [English transl.: Soviet Phys.—Solid State 5, 1026 (1963)]
A. H. Wilson, The Theory of Metals (Cambridge University Press, Cambridge, England, 1953), p. 77 R. Balian and D. R. Fredkin, Phys. Rev. Letters 15, 480 (1965)
J. Conley and J. J. Tiemann (private communication)
A. F. G. Wyatt, Phys. Rev. Letters 13, 401 (1964) L. Shen and J. M. Rowell, Bull. Am. Phys. Soc. 11, 224 (1966)
D. J. Kim, Phys. Letters 18, 215 (1965)
D. J. BenDaniel and C. B. Duke (to be published)
A. R. Hutson and D. L. White, J. Appl. Phys. 33, 40 (1962)
R. A. Cowley and G. Dolling, Phys. Rev. Letters 14, 549 (1965) W. Cochran, R. A. Cowley, G. Dolling, and M. M. Elcombe (to be published)
W. CochranR. A. CowleyG. DollingM. M. ElcombeHigher Transcendental Functions, edited by A. Erdilyi (McGraw-Hill Book Company, Inc., New York, 1953), Vol. 1, p. 31
[13]
C. B. Duke, Phys. Rev. 136, B59 (1964)
C. B. Duke and G. D. Mahan, Phys. Rev. 139, A1965 (1965)
Omitted endnote
J. J. Quinn and R. A. Ferrell, Phys. Rev. 112, 812 (1958)
D. F. DuBois, Ann. Phys. (Paris) 7, 174 (1959) ibid.8, 24 (1959)
D. J. W. Geldart and S. H. Vosko, J. Phys. Soc. Japan 20, 20 (1965)

[c1] L. Esaki, Phys. Rev. 109, 603 (1957)

[c2] R. T. Shuey, Phys. Rev. 137, A1268 (1965)

[c3] R. N. Hall, J. H. Racette, and H. Ehrenreich, Phys. Rev. Letters 4, 456 (1960) R. N. Hall, in Proceedings of the International Conference on Semiconductors, Prague, 1960 (Academic Press Inc., New York, 1961), p. 193

[c4] R. A. Logan and J. M. Rowell, Phys. Rev. Letters 13, 404 (1964)

[c5] R. M. Williams and J. Shewchun, Phys. Rev. Letters 14, 824 (1965) ibid. 15, 160 (1965)

[c6] W. A. Harrison and C. B. Duke (unpublished)

[c7] A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinsky, Methods of Quantum Field Theory in Statistical Physics (Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1963), Chaps. 2 and 3

[c8] S. Engelsberg and J. R. Schrieffer, Phys. Rev. 131, 993 (1963)

[c9] T. Holstein, Ann. Phys. (N. Y.) 29, 410 (1964)

[c10] Omitted endnote

[c11] A. Ron, Phys. Rev. 132, 978 (1963)

[c12] J. R. Schrieffer, Theory of Superconductivity (W. A. Benjamin, Inc., New York, 1964), Chap. 6

[c13] L. V. Keldysh and Yu. V. Kopaev, Fiz. Tverd. Tela 5, 1411 (1963) [English transl.: Soviet Phys.—Solid State 5, 1026 (1963)]

[c14] A. H. Wilson, The Theory of Metals (Cambridge University Press, Cambridge, England, 1953), p. 77 R. Balian and D. R. Fredkin, Phys. Rev. Letters 15, 480 (1965)

[c15] J. Conley and J. J. Tiemann (private communication)

[c16] A. F. G. Wyatt, Phys. Rev. Letters 13, 401 (1964) L. Shen and J. M. Rowell, Bull. Am. Phys. Soc. 11, 224 (1966)

[c17] D. J. Kim, Phys. Letters 18, 215 (1965)

[c18] D. J. BenDaniel and C. B. Duke (to be published)

[c19] A. R. Hutson and D. L. White, J. Appl. Phys. 33, 40 (1962)

[c20] R. A. Cowley and G. Dolling, Phys. Rev. Letters 14, 549 (1965) W. Cochran, R. A. Cowley, G. Dolling, and M. M. Elcombe (to be published)

[c21] W. CochranR. A. CowleyG. DollingM. M. ElcombeHigher Transcendental Functions, edited by A. Erdilyi (McGraw-Hill Book Company, Inc., New York, 1953), Vol. 1, p. 31

[c22] [13]

[c23] C. B. Duke, Phys. Rev. 136, B59 (1964)

[c24] C. B. Duke and G. D. Mahan, Phys. Rev. 139, A1965 (1965)

[c25] Omitted endnote

[c26] J. J. Quinn and R. A. Ferrell, Phys. Rev. 112, 812 (1958)

[c27] D. F. DuBois, Ann. Phys. (Paris) 7, 174 (1959) ibid.8, 24 (1959)

[c28] D. J. W. Geldart and S. H. Vosko, J. Phys. Soc. Japan 20, 20 (1965)

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Polarons in Degenerate Semiconductors

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