The Electronic Structures of Disordered Materials

  • Morrel H. Cohen


A brief review is given of current understanding of the electronic structures of disordered materials, with emphasis on work by the author and his associates. Formal arguments are omitted; simple physical arguments are used instead to build up a coherent conceptual structure. Disordered materials are briefly introduced followed by the notion of universal features in the electronic structures of classes of materials. These are summarized for crystals, and an elementary semiclassical argument is used to elicit them for disordered materials. The basic band model for disordered materials is introduced and used to explain the basic experimental facts about amorphous semiconductors. The history of localization theory, which gives the formal justification of the basic band model, is then reviewed and its present status assessed. Eggarter’s theory of electron mobility of gaseous He is reviewed. Some recent results on localization in one dimension are presented and discussed. Localized states found by Eggarter and Kirkpatrick for lattices with vacancies are also discussed. Both the one-dimensional and the vacancy results shed light on the Cohen-Sak theory of the metal-semiconductor transition in disordered materials. Mott hopping between localized states in disordered materials is next reviewed, with application to the properties of homogeneously stacked organic or metallo-organic salts. Finally, remarks are made on the relevance of these considerations for the theory of metal-ammonia solutions.


Extended State Universal Feature Root Singularity Amorphous Semiconductor Mobility Edge 
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  1. 1.
    Cohen, M. H.: In: Amorphous and liquid semiconductors, p. 391. N. F. Mott (Ed.): Amsterdam: North-Holland Publishing Company (1970).Google Scholar
  2. 2.
    Cohen, M. H.: J. Non-Crystalline Solids 2, 432 (1970).CrossRefGoogle Scholar
  3. 3.
    Cohen, M. H.: Proceedings of the Tenth International Conference on the Physics of Semiconductors. Cambridge, Mass. S. K. Keller, J. C. Hensel, F. Stern (Eds.), p. 645. Springfield: USAEC Division of Technical Information 1970.Google Scholar
  4. 4.
    Cohen, M. H.: Physics Today 24, 26 (1971).CrossRefGoogle Scholar
  5. 5.
    Ziman, J.M.: J. Phys. Cl, 1532 (1968).Google Scholar
  6. 6.
    Shante, V. K. S., Kirkpatrick, S.: Advan. Phys. 20, 325 (1971).CrossRefGoogle Scholar
  7. 7.
    Anderson, P. W.: Phys. Rev. 109, 1492 (1958).CrossRefGoogle Scholar
  8. 8. a)
    Thouless, D. J.: J. Non-Crystalline Solids 8–10, 461 (1972).CrossRefGoogle Scholar
  9. Economou, E. N., Cohen, M.H.: Phys. Rev. 5, 2931 (1972).CrossRefGoogle Scholar
  10. Ziman, J.M.: J. Phys. C2, 1230 (1969).Google Scholar
  11. 9.
    Mott, N. F.: Advan. Phys. 16, 49 (1967).CrossRefGoogle Scholar
  12. 10.
    Cohen, M. H., Fritsche, H., Ovshinsky, S. R.: Phys. Rev. Letters 22, 1065 (1969).CrossRefGoogle Scholar
  13. 11.
    See for example Stuke, J.: In: Mott, N. F. (Ed.): Amorphous and liquid semiconductors. Amsterdam: North-Holland Publishing Company 1970.Google Scholar
  14. 12.
    Kubo, R.: J. Phys. Soc. Japan 12, 470 (1957).Google Scholar
  15. 13.
    Lifschitz, I. M.: Advan. Phys. 13, 483 (1964).CrossRefGoogle Scholar
  16. 14.
    Friedman, L.: J. Non-Crystalline Solids 6, 329 (1971).CrossRefGoogle Scholar
  17. 15.
    Mott, N.F.: Phil. Mag. 26, 1015 (1972).CrossRefGoogle Scholar
  18. 16.
    Freed, K. F.: Phys. Rev. B5, 4802 (1972).Google Scholar
  19. 17.
    Lukes, T.: J. Non-Crystalline Solids 8-10, 470 (1972).Google Scholar
  20. 18.
    Anderson, P. W.: Proc. Natl. Acad. Sci. US. 69, 1097 (1972).CrossRefGoogle Scholar
  21. 19.
    Cohen, M.H., Jortner, J.: Phys. Rev. Lett. 30, 698 (1973).Google Scholar
  22. 20.
    Weaire, D., Thorpe, M. F., Heine, V.: J. Non-Crystalline Solids 8-10, 128 (1972).Google Scholar
  23. 21.
    Mott, N. F.: Phil. Mag. 13, 989 (1966).CrossRefGoogle Scholar
  24. 22.
    Mott, N.F.: J. Non-Crystalline Solids 1, 1 (1968).CrossRefGoogle Scholar
  25. 23.
    Mott, N. F.: Phil. Mag. 17, 1259 (1968).CrossRefGoogle Scholar
  26. 24.
    Mott, N. F.: Phil. Mag. 19, 835 (1969).CrossRefGoogle Scholar
  27. 25.
    Mott, N.F.: Rev. Mod. Phys. 40, 677 (1968).CrossRefGoogle Scholar
  28. 26. a)
    Levine, J.L., Sanders, T.M.: Phys. Rev. 154, 138 (1967).CrossRefGoogle Scholar
  29. b).
    Harrison, H. R.: Ph. D. Thesis, University of Michigan, Ann Arbor (unpublished).Google Scholar
  30. 27.
    Eggarter, T.P., Cohen, M. H.: Phys. Rev. Letters 27, 129 (1971).CrossRefGoogle Scholar
  31. 28.
    Eggarter, T. P.: Phys. Rev. A5, 2496 (1972).Google Scholar
  32. 29.
    Kirkpatrick, S.: Phys. Rev. Letters 27, 1722 (1971).CrossRefGoogle Scholar
  33. 30.
    Mott, N. F., Twose, W. D.: Advan. Phys. 96, 1208 (1954).Google Scholar
  34. 31.
    Borland, R.: Proc. Roy. Soc. (London) A 274, 529 (1963).CrossRefGoogle Scholar
  35. 32.
    Bush, R. L.: Phys. Rev. 56, 1182 (1972).Google Scholar
  36. 33.
    Economou, E.N., Papatriantafillou, C.: Solid State Comm 11, 191 (1972).CrossRefGoogle Scholar
  37. 34.
    Papatriantafillou, C.: Phys. Rev: B (in press).Google Scholar
  38. 35.
    Eggarter, T. P.: Unpublished.Google Scholar
  39. 36.
    Kirkpatrick, S., Eggarter, T. P.: Phys. Rev. B15 (in press); Computational Methods For Large Molecules And Localized States in Solids, ed. Herman, F., McLean, A.O., Nesbet, R.K., p. 327, Plenum Press, 1972.Google Scholar
  40. 37. a)
    Enderby, J., Simmons, C. J.: Phil. Mag. 20, 125 (1969)CrossRefGoogle Scholar
  41. Enderby, J.: Non-Crystalline Solids (in press).Google Scholar
  42. 37. b)
    Mott, N.F.: Phil. Mag. 22, 1 (1970); 24, 1 (1971).Google Scholar
  43. 38.
    Cohen, M. H., Sak, J.: Non-Crystalline Solids 8–10, 696 (1972).CrossRefGoogle Scholar
  44. 39.
    Cohen, M. H., Jortner, J.: To be published.Google Scholar
  45. 40.
    Bruggeman, D.A. G.: Ann. Phys. (Leipzig) 24, 836 (1935).Google Scholar
  46. 41.
    Landauer, R.: J. Appl. Phys. 23, 779 (1952).CrossRefGoogle Scholar
  47. 42.
    Cohen, M. H., Jortner, J.: Phys. Rev. Lett. 30, 696 (1973).CrossRefGoogle Scholar
  48. 43.
    Mott, N. F.: Phil. Mag. 19, 835 (1969)CrossRefGoogle Scholar
  49. Mott, N. F.: Festkörperprobleme 9, 22 (1969).Google Scholar
  50. 44.
    Ambegaokar, V., Halperin, B. I., Langer, J.: Phys. Rev. B 4, 2612 (1967).CrossRefGoogle Scholar
  51. 45.
    Miller, A., Abrahams, E.: Phys. Rev. 120, 745 (1960).CrossRefGoogle Scholar
  52. 46.
    Ambegaokar, V., Halperin, B. I., Langer, J.: J. Non-Crystalline Solids 8–10, 492 (1972).CrossRefGoogle Scholar
  53. 47.
    Shante, V.K.S.: To be published.Google Scholar
  54. 48.
    Leblanc, O.H.: In: Physics and chemistry of the organic solid state, Vol. III, Chapter 3. New York: Interscience 1967.Google Scholar
  55. 49.
    Epstein, A. J., Etemad, S., Garito, A. F., Heeger, A. J.: Phys. Rev. B 5, 952 (1972)CrossRefGoogle Scholar
  56. Etemad, S., Garito, A. F., Heeger, A. J.: Phys. Letters 40 A, 45 (1972)Google Scholar
  57. Chaiken, P. M., Garito, A. F., Heeger, A. J.: Phys. Rev. B 5, 4966 (1972)CrossRefGoogle Scholar
  58. Coleman, L. B., Cohen, J. A., Garito, A. F., Heeger, A. J. (in press)Google Scholar
  59. Ehrenfreund, E., Etemad, S., Coleman, L. B., Rybaczewski, E. F., Garito, A. F., Heeger, A. J.: Phys. Rev. Letters 29, 269 (1972)CrossRefGoogle Scholar
  60. Coleman, L.B., Cohen, J.A., Garito, A. F., Heeger, A.J.: Phys. Rev. B (in press)Google Scholar
  61. Ehrenfreund, E., Rybaczewski, E. F., Garito, A. F., Heeger, A. J.: Phys. Rev. Letters 28, 873 (1972)CrossRefGoogle Scholar
  62. Ehrenfreund, E., Rybaczewski, E. F., Garito, A. F., Heeger, A. J., Pincus, P.: Phys. Rev. B (Jan. 1973).Google Scholar
  63. 50.
    Bloch, A., Weissman, B., Verna, C.: Phys. Rev. Letters (1971).Google Scholar
  64. 51. a)
    Papatriantafillou,C.: To be published.Google Scholar
  65. b).
    Bush, R. L.: To be published.Google Scholar
  66. 52.
    Cohen, M. H., Thompson, J. C.: Advan. Phys. 17, 857 (1968).CrossRefGoogle Scholar

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© Springer-Verlag, Berlin · Heidelberg 1973

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  • Morrel H. Cohen

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