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Semiconductor Statistics

  • Karlheinz Seeger
Part of the Springer Study Edition book series (SSE)

Abstract

The periodic potential distribution of an electron in a crystal shown in Fig.2.5 involves N discrete levels if the crystal contains N atoms as we have seen in Fig. 2.9. A discussion of these levels can be confined to the first Brillouin zone. We have seen in the last chapter that due to the crystal periodicity the electron wave functions, which in one dimension are ψ(x) = u(x) exp(ikx), have also to be periodic (“Bloch functions”). Hence from
(3.1)
and
(3.2)
we obtain
(3.3)
or
(3.4)
where a is the lattice constant. We notice that Eq.(3.1) is actually valid for a ring-shaped chain which means that we neglect surface states (see Chap. 14a). Since for the first Brillouin zone k has values between −π/a and +π/a, we find that the integer n is limited to the range between −N/2 and +N/2. In Fig.3.1 the discrete levels are given for a “crystal” consisting of N = 8 atoms.

Keywords

Fermi Energy Band Edge Entropy Density Impurity Level Fermi Statistics 
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. [1]
    This calculation has been adapted from E.Spenke,: Electronic Semiconductors, chap. VIII. New York,: McGraw-Hill. 1958.Google Scholar
  2. [1]
    This calculation has been adapted from E.Spenke,: Electronic Semiconductors, chap. VIII. New York,: McGraw-Hill. 1958.Google Scholar
  3. [2]
    See e.g. E.Schrödinger,: Statistical Thermodynamics. Cambridge,: Univ.Press. 1948.Google Scholar
  4. [3]
    J.S.Blakemore,: Semiconductor Statistics, appendix B. Oxford,: Pergamon. 1962Google Scholar
  5. [1]
    H.Fritzsche, Phys.Rev. 120 (1960) 1120.Google Scholar
  6. [1]
    H.Fritzsche, Phys.Rev. 120 (1960) 1120.Google Scholar
  7. [2]
    S.H.Koenig, R.D.Brown III, and W.Schillinger, Phys.Rev.128 (1962) 1668, and literature cited there. See also D.Long, C.D.Motchenbacher, and J.Myers, J.Appl.Phys.30 (1959) 353; J.Blakemore,: Semiconductor Statistics, Chap.3.2.4. Oxford,: Pergamon. 1962.Google Scholar
  8. [3]
    J.S.Blakemore, Phil.Mag. 4 (1959) 560.ADSCrossRefGoogle Scholar
  9. [4]
    N.B.Hannay,: Semiconductors (N.B.Hannay,ed.) p. 31. New York,: Reinhold Publ.Co. 1959Google Scholar
  10. [5]
    For the occupation probabilility of double donors see e.g. E.Spenke,: Electronic Semiconductors, chap. VIII, I. New York,: McGraw-Hill. 1965.Google Scholar
  11. [7]
    For a review see e.g. E.M.Conwell, Proc.IRE 46 (1958) 1281; T.H.Geballe in ref.4,p.341 and 342.Google Scholar

Copyright information

© Springer-Verlag Wien 1973

Authors and Affiliations

  • Karlheinz Seeger
    • 1
    • 2
  1. 1.Ludwig Boltzmann-Institut für FestkörperphysikWienÖsterreich
  2. 2.Institut für Angewandte PhysikUniversität WienÖsterreich

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