Pseudopotential Theory of Exciton and Impurity States

J. Hermanson; J. C. Phillips

doi:10.1103/PhysRev.150.652

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Pseudopotential Theory of Exciton and Impurity States

J. Hermanson^*,† and J. C. Phillips^‡

Department of Physics and Institute for the Study of Metals, University of Chicago, Chicago, Illinois

^*Xerox Fellow.
^†A. P. Sloan Fellow.
^‡Present address: Department of Physics, University of Illinois, Urbana, Illinois.

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Phys. Rev. 150, 652 – Published 14 October, 1966

DOI: https://doi.org/10.1103/PhysRev.150.652

Abstract

A formalism for studying central-cell corrections to the effective-mass equation is presented. A generalized impurity equation for excitons and impurity states is derived, including the effects of dielectric response and large- $k$ variation of the effective mass. Because of the presence of interband matrix elements of the impurity potential in the general case, this equation is not easily solved. By transforming to a representation in which the core parts of Bloch functions are removed, a pseudo-wave-equation is developed. In this equation the effective impurity potential is substantially cancelled within the central cell, so that interband matrix elements are sharply reduced, and the usual one-band approximation is valid.

References (29)

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[c1] W. Kohn, Solid State Phys. 5, 257 (1957)

[c2] R. S. Knox, Solid State Phys. Suppl. 5, 7 (1963)

[c3] G. H. Wannier, Phys. Rev. 52, 191 (1937)

[c4] G. Dresselhaus, J. Phys. Chem. Solids 1, 14 (1956)

[c5] W. Kohn and J. M. Luttinger, Phys. Rev. 98, 915 (1955)

[c6] T. P. Mc Lean, in Progress in Semiconductors (John Wiley & Sons, Inc., New York, 1961) Vol. 5, p. 55

[c7] J. Frenkel, Phys. Rev. 37, 17 (1931) ibid.37, 1276 (1931)

[c8] R. S. Knox, J. Phys. Chem. Solids 9, 238 (1959) ibid.9, 265 (1959)

[c9] P. O. Löwdin, Advan. Phys. 5, 1 (1956)

[c10] A. Gold, Phys. Rev. 124, 1740 (1961)

[c11] T. Keil and A. Gold, Phys. Rev. 136, A252 (1964)

[c12] O. Schnepp and K. Dressler, J. Chem. Phys. 33, 49 (1960) G. Baldini, Phys. Rev. 136, A248 (1964)

[c13] A. W. Overhauser, Phys. Rev. 101, 1702 (1956)

[c14] G. Baldini, Phys. Rev. 128, 1562 (1962)

[c15] J. C. Slater, Phys. Rev. 76, 1592 (1949) ibid.87, 807 (1952) G. F. Koster, ibid. 89, 67 (1953) W. Kohn, ibid. 115, 809 (1959)

[c16] J. C. Slater and W. Shockley, Phys. Rev. 50, 705 (1936)

[c17] E. I. Blount, Solid State Phys. 13, 305 (1962)

[c18] C. Herring, Phys. Rev. 57, 1169 (1940)

[c19] J. C. Phillips and L. Kleinman, Phys. Rev. 116, 287 (1959)

[c20] M. H. Cohen and V. Heine, Phys. Rev. 122, 1821 (1961)

[c21] B. J. Austin, V. Heine, and L. J. Sham, Phys. Rev. 127, 276 (1962)

[c22] M. Azuma, J. Phys. Soc. Japan 18, 194 (1963)

[c23] N. Wiser, Phys. Rev. 129, 62 (1963)

[c24] W. Kohn, Phys. Rev. 110, 857 (1958)

[c25] M. H. Cohen, Phil. Mag. 3, 762 (1958)

[c26] M. A. Biondi and J. A. Rayne, Phys. Rev. 115, 1522 (1959)

[c27] H. Nara, J. Phys. Soc. Japan 20, 778 (1965)

[c28] K. H. Bennemann, Phys. Rev. 133, A1045 (1964)

[c29] L. Kleinman and J. C. Phillips, Phys. Rev. 116, 880 (1959) ibid.117, 460 (1960) ibid.118, 1153 (1960)

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Pseudopotential Theory of Exciton and Impurity States

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