The Electronic Bandstructure of Solids

  • Harald Ibach
  • Hans Lüth
Part of the Advanced Texts in Physics book series (ADTP)


Despite the success of the free-electron-gas model in describing electrons in crystals (Chap. 6), it must be recognized that the assumptions of the one-electron approximation and of a square-well potential, are oversimplifications. Thus one cannot expect this model to explain, for example, the fundamentally important optical and electronic properties of semiconductors. If one imagines, as discussed briefly in Chap. 1, that a solid is created by allowing initially free atoms to gradually approach one another, then the discrete nature of the energy levels of the isolated atoms should clearly be reflected in the properties of the solid. Indeed, discrete energy levels must be present in order to explain, e.g., the sharp resonance-like structures observed in the optical spectra of solids. An explanation of such features is beyond the scope of the free-electron-gas model. Furthermore, this model is unable to shed any light on the nature of semiconductors and insulators. To make further progress one has to take into account that the electronic states in solids form so-called bands. One can think of these as deriving from the states of the free atom.


Brillouin Zone Free Atom Bloch Wave Reciprocal Lattice Vector Discrete Energy Level 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. V.1
    M. Cardona, L. Ley (eds.): Photoemission in Solids 1, 11; Topics Appl. Phys., Vols. 26, 27 ( Springer, Berlin, Heidelberg 1979 )Google Scholar
  2. B. Feuerbacher, B. Fitton, R. F. Willis (eds.): Photoemission and the Electronic Properties of Surfaces ( Wiley, New York 1978 )Google Scholar
  3. H. Lüth: Solid Surfaces, Interfaces and Thin Films (Springer, Berlin, Heidelberg 2001) 4th. edn.Google Scholar
  4. S. Hüfner: Photoelectron Spectroscopy, 2nd edn., Springer Ser. Solid-State Sci., Vol. 82 ( Springer, Berlin, Heidelberg 1996 )Google Scholar
  5. V.2
    R. Courths, S. Hüfner: Physics Reports 112, 55 (1984)ADSGoogle Scholar
  6. V.3
    H. Lüth, G. W. Rubloff, W. D. Grobmann: Solid State Commun. 18, 1427 (1975)Google Scholar

Chapter 7

  1. 7.1
    W. Shockley: Electrons and Holes in Semiconductors ( Van Nostrand, New York 1950 )Google Scholar
  2. 7.2
    L.P. Howard: Phys. Rev. 109, 1927 (1958)ADSCrossRefGoogle Scholar
  3. 7.3
    B. Segall: Phys. Rev. 124, 1797 (1961)MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. 7.4
    R. Courths, S. Hüfner: Phys. Rep. 112, 55 (1984)ADSCrossRefGoogle Scholar
  5. 7.5
    H. Eckhardt, L. Fritsche, J. Noffke: J. Phys. F14, 97 (1984)ADSCrossRefGoogle Scholar
  6. 7.6
    F. Herman, R.L. Kortum, C.D. Kuglin, J.L. Shay: In II—VI Semiconducting Compounds, ed. by D.G. Thomas ( Benjamin, New York 1967 )Google Scholar
  7. 7.7
    T.H. Upton, W.A. Goddard, C.F. Melius: J. Vac. Sci. Technol. 16, 531 (1979)ADSCrossRefGoogle Scholar
  8. 7.8
    H. Haberland (ed.): Clusters of Atoms and Molecules I and II, Springer Series in Chem. Phys. 52, 56 (Springer, Berlin Heidelberg 1994 )Google Scholar

Further Reading

  1. Ashcroft, N.W., Mermin, N.D.: Solid State Physics (Hold, Rinehart and Winston, New York 1976 )Google Scholar
  2. Brillouin, L.: Wave Propagation in Periodic Structures ( Academic, New York 1960 )Google Scholar
  3. Callaway, J.: Energy Band Theory ( Academic, New York 1964 )zbMATHGoogle Scholar
  4. Harrison, W.A.: Pseudopotentials in the Theory of Metals ( Benjamin, New York 1966 )Google Scholar
  5. Herrmann, R., Preppernau, U.: Elektronen im Kristall ( Springer, Berlin Heidelberg 1979 )CrossRefGoogle Scholar
  6. Jones, H.: The Theory of Brillouin-Zones and Electronic States in Crystals ( North-Holland, Amsterdam 1962 )Google Scholar
  7. Loucks, T.L.: Augmented Plane Wave Method ( Benjamin, New York 1967 )Google Scholar
  8. Madelung, O.: Introduction to Solid-State Theory, Springer Ser. Solid State Sci., Vol. 2 ( Springer, Berlin Heidelberg 1978 )CrossRefGoogle Scholar
  9. Skriver, H.L.: The LMTO Method, Springer Ser. Solid-State Sci., Vol. 41 ( Springer, Berlin Heidelberg 1984 )Google Scholar
  10. Wilson, A.H.: The Theory of Metals, 2nd edn. ( Cambridge Univ. Press, London 1965 )Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Harald Ibach
    • 1
    • 2
  • Hans Lüth
    • 1
    • 2
  1. 1.Institut für Schichten und GrenzflächenForschungszentrum Jülich GmbHJülichGermany
  2. 2.Rheinisch-Westfälische Technische HochschuleAachenGermany

Personalised recommendations