Optical Absorption in Amorphous Semiconductors: The Independent Band Model and its Experimental Basis

  • George D. Cody
Part of the Institute for Amorphous Studies Series book series (IASS)


A major source of information on the electronic properties of amorphous semiconductors is experimental data on the optical properties close to the absorption edge. An important theoretical tool in interpreting this data is a simple physical model for the optical absorption which was introduced about twenty years ago.1 This model which can be described as the “independent band model”2 assumes that the amorphous semiconductor has no positional order but that its valence and conduction band wave functions are linear functions of Bloch functions of a corresponding “virtual” crystal. Based on these assumptions, a simple formula for the magnitude and spectral dependence of the imaginary part of the complex dielectric constant (ɛ2(E)) can be derived which depends on the optical matrix element of the “virtual” crystal and the density of states of the amorphous semiconductor. This formula has been used to define an optical gap, as well as to derive the energy dependence of the conduction and valence band density of states.3 Despite its wide spread use, the assumptions of the independent band model have yet to be critically examined. For example, there have been relatively few attempts to relate the matrix element of this model to those of the corresponding “virtual” crystal.4 Indeed there have been few attempts to identify the “virtual” crystal at all! Furthermore, while the model has been often used to predict the spectral dependence of ɛ2 from models for the density of states, the magnitude of ɛ2 has been relatively ignored until recently.5


Valence Band Optical Absorption Band Edge Spectral Dependence Amorphous Semiconductor 
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  1. 1.
    J. Tauc, R. Grigorovici and A. Vancu, Phys. Status Solidi 15, 627 (1966);CrossRefGoogle Scholar
  2. J. Tauc, in Optical Properties of Solids ed. by F. Abeles (North Holland, Amsterdam, 1972) p. 279;Google Scholar
  3. J. Tauc in Amorphous and Liquid Semiconductors ed. by J. Tauc (Plenum, New York, 1974) p. 159.CrossRefGoogle Scholar
  4. 2.
    For a recent review of experiment and theory with respect to the optics of this model see: K. C. Hass and H. Ehrenreich to be published in Annals of Physics (1985).Google Scholar
  5. 3.
    G. D. Cody in Semiconductors and Semimetals, Vol. 21B ed. by J. Pankove (Academic Press, 1984) p. 11.Google Scholar
  6. 4.
    K. Maschke and P. Thomas, Phys. Stat. Solidi 41, 743 (1970);ADSCrossRefGoogle Scholar
  7. W. Paul, G. A. N. Connell and R. J. Temkin, Adv. in Phys. 22, 529 (1973);ADSCrossRefGoogle Scholar
  8. 5.
    W. B. Jackson, S. M. Kelso, C. C. Tsai, J. W. Allen and S.-J. Oh, Phys. Rev B (1985);Google Scholar
  9. W. B. Jackson, S.-J. Oh, C. C. Tsai and J. W. Allen, Phys. Rev. Letters 53, 1481 (1984).ADSCrossRefGoogle Scholar
  10. 6.
    N. F. Mott, Phil. Mag. 22, 7 (1970).ADSCrossRefGoogle Scholar
  11. 7.
    S. Abe and Y. Toyazawa, J. Phys. Soc. Japan 50, 2185 (1981).ADSCrossRefGoogle Scholar
  12. 8.
    C. R. Wronski, B. Abeles, T. Tiedje and G. D. Cody, Solid State Com. 44, 1423 (1982);ADSCrossRefGoogle Scholar
  13. M. Vanacek, J. Kocka, J. Stuchlik, T. Kozisek, O. Stika and A. Triska, Solar Energy Materials 8, 411 (1983).ADSCrossRefGoogle Scholar
  14. 9.
    G. D. Cody, B. G. Brooks and B. Abeles, Solar Energy Materials 4, 231 (1982).ADSCrossRefGoogle Scholar
  15. 10.
    M. V. Kurik, Phy. Stat. Solid A 8, 9 (1971).ADSCrossRefGoogle Scholar
  16. 11.
    T. Tiedje in Semiconductors and Semimetals, Vol. 21C ed. by J. Pankove (Academic Press, 1984 ) p. 207.Google Scholar
  17. 12.
    C. M. Soukoulis, M. H. Cohen and E. N. Economou, Phys. Rev. Letters 53, 616 (1984).ADSCrossRefGoogle Scholar
  18. 13.
    N. Amer and W. Jackson in Semiconductors and Semimetals, Vol. 21B ed. by J. Pankove (Academic Press, 1984 ) p. 83.Google Scholar
  19. 14.
    B. G. Bagley, D. E. Aspnes, G. K. Celler and A. C. Adams, in Laser and Electron Beam Intractions with Solids, ed. by B. R. Apple ton and G. K. Celler ( Elsevier, Amsterdam, 1982 ) p. 483.Google Scholar
  20. 15.
    D. Ewald, M. Milleville and G. Weiser, Phil Mag B40, 291 (1979);Google Scholar
  21. L. Pajasova, A. Abraham, I. Gregora and M. Zavetova, Solar Energy Materials 4, 1 (1980);ADSCrossRefGoogle Scholar
  22. G. Weiser, D. Ewald and M. Milleville, J. Non-cryst. Solids 35&36, 447 (1980);CrossRefGoogle Scholar
  23. N. Sawides, D. R. McKenzie and R. C. McPhedran, Solid State Commun. 48, 189 (1983).ADSGoogle Scholar
  24. 16.
    W. A. Harrison and S. T. Pantelides, Phy. Rev. B14, 691 (1976).ADSCrossRefGoogle Scholar
  25. 17.
    S. H. Wemple, J. Chem. Phys. 67, 2151 (1977).ADSCrossRefGoogle Scholar
  26. 18.
    G. D. Cody, B. G. Silbernagel and L. A. Gebhard, to be published.Google Scholar
  27. 19.
    N. F. Mott and E. A. Davis, Electronic Processes in Non-crystalline Materials, 2nd ed. ( Oxford Univ. Press, London and New York, 1979 ).Google Scholar
  28. 20.
    D. E. Aspnes and A. A. Studna, Phys. Rev. B27, 985 (1982).ADSGoogle Scholar

Copyright information

© Plenum Press , New York 1985

Authors and Affiliations

  • George D. Cody
    • 1
  1. 1.Exxon Research & Engineering CompanyCorporate Research Science LaboratoriesAnnandaleUSA

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