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Energy Band Structure

  • Karlheinz Seeger

Abstract

The energy band structure is the relationship between the energy and momentum of a carrier in a solid. For an electron in free space, the energy is proportional to the square of the momentum. The factor of proportionality is l/(2m 0), where m 0 is the free electron mass. In the simple model of band structure, the same relationship between energy and momentum is assumed except that m 0 is replaced by an effective mass m. This may be larger or smaller than m 0. Why this is so will be seen later in this chapter. Quite often the band structure is more complex and can only be calculated semi-empirically even with computers. A short description of some typical band structures will be given in Sect. 2.4 and used for the calculation of charge transport in Chaps. 7, 8, while in Chaps. 4, 5, the transport properties will be calculated assuming the simple model of band structure (which is quite a good approximation for most purposes).

Keywords

Valence Band Band Structure Effective Mass Brillouin Zone Heavy Hole 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 2.1
    R. de Laer Kronig, W.J. Penney: Proc. Roy. Soc. London A130, 499 (1930)Google Scholar
  2. 2.2
    A. Nussbaum: Semiconductor Device Physics (Prentice-Hall, Englewood Cliffs, N.J. 1962) Sects. 1.9 and 1.13Google Scholar
  3. 2.3
    R.A. Smith: Wave Mechanics of Crystalline Solids, 2nd edn. (Chapman and Hall, London 1969) Sect. 6.2Google Scholar
  4. 2.4
    J.P. McKelvey: Solid-State and Semiconductor Physics (Harper and Row, New York 1966) Sect. 8.6Google Scholar
  5. 2.5
    E.O. Kane: J. Phys. Chem. Solids 1, 249 (1957)CrossRefGoogle Scholar
  6. 2.6
    W.A. Harrison: Electronic Structure and the Properties of Solids (Freeman, San Francisco 1980). In particular, the pages 140, 141, 150 contain comparisons of band structures of various semiconductorsGoogle Scholar
  7. M.L. Cohen, J.R. Chelikowsky: Electronic Structure and Optical Properties of Semiconductors, 2nd edn., Springer Ser. Solid-State Sci., vol. 75 (Springer, Berlin, Heidelberg 1989)CrossRefGoogle Scholar
  8. 2.7
    D. Long: Energy Bands in Semiconductors (Wiley, New York 1968) p.49Google Scholar
  9. 2.8
    D. Matz: J. Phys. Chem. Solids 28, 373 (1967)CrossRefGoogle Scholar
  10. 2.9
    S. Flügge: Rechenmethoden der Quantentheorie, 3rd edn. Heidelberger Taschenbücher, Vol. 6 (Springer, Berlin, Heidelberg 1966) Problem No.91Google Scholar
  11. 2.10
    F. Hund, B. Mrowka: Ber. Sächs. Akad. Wiss. 87, 185, 325 (1935)Google Scholar
  12. A.H. Wilson: The Theory of Metals, 2nd edn. (Cambridge Univ. Press, London 1965) pp.66–70, 83Google Scholar
  13. 2.11
    G.E. Kimball: J. Chem. Phys. 3, 560 (1935)CrossRefGoogle Scholar
  14. 2.12
    F. Hund: Theorie des Aufbaues der Materie (Teubner, Stuttgart 1961) Chap. VIIGoogle Scholar
  15. 2.13
    E. Wigner, F. Seitz: Phys. Rev. 43, 804 (1933)CrossRefGoogle Scholar
  16. 2.14
    J.C. Slater: Phys. Rev. 51, 846 (1937)CrossRefGoogle Scholar
  17. 2.15
    C. Herring: Phys. Rev. 57, 1169 (1940)CrossRefGoogle Scholar
  18. 2.16
    E. Antoncik: J. Phys. Chem. Solids 10, 314 (1959)CrossRefGoogle Scholar
  19. 2.17
    J.C. Phillips, L. Kleinman: Phys. Rev. 116, 287, 880 (1959)Google Scholar
  20. 2.18
    M.L. Cohen, V. Heine: Solid State Physics 24, 37 (Academic, New York 1970) (review)CrossRefGoogle Scholar
  21. 2.19
    J. Koringa: Physica 13, 392 (1947)CrossRefGoogle Scholar
  22. 2.20
    W. Kohn, N. Rostoker: Phys. Rev. 94, 1111 (1954)CrossRefGoogle Scholar
  23. 2.21
    N.W. Ashcroft, N.D. Mermin: Solid State Physics (Holt, Rinehart, and Winston, New York 1976) p.202Google Scholar
  24. 2.22
    W. Shockley: Electrons and Holes in Semiconductors (Van Nostrand, New York 1950)Google Scholar
  25. 2.23
    C. Kittel: Introduction to Solid State Physics, 7th edn, (Wiley, New York 1995)Google Scholar
  26. O. Madelung: Introduction to Solid-State Theory, Springer Ser. Solid-State Sci., Vol. 2 (Springer, Berlin, Heidelberg 1978)CrossRefGoogle Scholar
  27. 2.24
    R.A. Smith: Wave Mechanics of Crystalline Solids (Chapman and Hall, London 1961)Google Scholar
  28. 2.25
    H. Jones: The Theory of Brillouin Zones and Electronic States in Crystals (North-Holland, Amsterdam 1960)Google Scholar
  29. 2.26
    F. Seitz: Modern Theory of Solids (McGraw-Hill, New York 1940)Google Scholar
  30. 2.27
    L.P. Bouckaert, R. Smoluchowski, E.P. Wigner: Phys. Rev. 50, 58 (1936)CrossRefGoogle Scholar
  31. 2.28
    J. Callaway: Energy Band Theory (Academic, New York 1964)Google Scholar
  32. 2.29
    H.W. Streitwolf: Gruppentheorie in der Festkörperphysik (Geest und Portig, Leipzig 1967)Google Scholar
  33. 2.30
    D. Long: Energy Bands in Semiconductors (Wiley, New York 1968)Google Scholar
  34. 2.31
    C. Rigaux, G. Drilhorn: J. Phys. Soc. Jpn. 21, Suppl., 193 (1966) (Proc. Int’l. Conf. Phys. Semicond. Kyoto)CrossRefGoogle Scholar
  35. 2.32
    J.R. Drabble: In Progress in Semiconductors, Vol. 7, ed. by A.F. Gibson, R.E. Burgess (Temple, London 1963) p.45Google Scholar
  36. 2.33
    D.L. Greenaway, G. Harbeke: J. Phys. Chem. Solids 26, 1585 (1965)CrossRefGoogle Scholar
  37. 2.34
    I. Melngailis: J. Physique, Suppl. No.11–12, 29, C4–84 (1968)Google Scholar
  38. 2.35
    J.O. Dimmock, I. Melngailis, A.J. Strauss: Phys. Rev. Lett. 16, 1193 (1966)CrossRefGoogle Scholar
  39. 2.36
    C. Vérié: Festkörper-Probleme / Advances in Solid State Physics, X, 1–19 (Vieweg, Braunschweig 1970)CrossRefGoogle Scholar
  40. 2.37
    S. Groves, W. Paul: Phys. Rev. Lett. 11, 194 (1963)CrossRefGoogle Scholar
  41. 2.38
    R. Dornhaus, G. Nimtz: Springer Tracts Mod. Phys.78, 1–112 (Springer, Berlin, Heidelberg 1976)CrossRefGoogle Scholar
  42. 2.39
    M. Cardona, F.H. Pollak: Phys. Rev. 142, 530 (1966)CrossRefGoogle Scholar
  43. 2.40
    J.C. Phillips, D. Brust, F. Bassani: Proc. Int’l. Conf. Phys. Semicond., Exeter (The Institute of Physics, London 1962) p.564Google Scholar
  44. 2.41
    A.B. Pippard: Philos. Trans. A250, 325 (1957)CrossRefGoogle Scholar
  45. 2.42
    W. Brauer: Einführung in die Elektronentheorie der Metalle (Geest und Portig, Leipzig 1966)Google Scholar
  46. 2.43
    J.M. Ziman: Contemp. Phys. 3, 241 (1962)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Karlheinz Seeger
    • 1
    • 2
  1. 1.ViennaAustria
  2. 2.Institut für Materialphysik der UniversitätViennaAustria

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