Dispersion Surfaces

  • David B. Williams
  • C. Barry Carter


The analysis of Bloch waves we gave in the previous chapter is closely related to the classical analysis of waves that you’ve seen in solid-state physics or semiconductor theory. In semiconductors in particular, we often talk of indirect and direct band gaps. We use terms like conduction bands, valence bands, and Brillouinzone boundaries (BZBs). We visualize these quantities by drawing diagrams of E(k), the electron energy (which is a function of k) versus k, the wave vector. This plot of E(k) versus k is known as a dispersion diagram. For example, the band gap in Si is 1.1 eV, but the energy of most electrons in this material is somewhat smaller. We now follow the same approach to represent pictorially what we described in equations in Chapters 13 and 14. Remember that the difference to the solid-state physics approach is that, in TEM, the energy of the electrons is ≥ 100 keV.


Wave Vector Planar Defect Bloch Wave Dispersion Surface Dispersion Diagram 
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General References

  1. Ashcroft, N.W. and Merman, N.D. (1976) Solid State Physics, W.B. Saunders Co., Philadelphia.Google Scholar
  2. Kittel, C.J. (1986) Solid-State Physics,6th edition, John Wiley & Sons, New York. Chapters 1, 10, and 11 are particularly relevant.Google Scholar
  3. Metherell, A.J.F. (1975) in Electron Microscopy in Materials Science,II (Eds. U. Valdrè and E. Ruedl), p. 397, CEC, Brussels. The reference.Google Scholar

Specific References

  1. Kato, N. (1958) Acta. Cryst. 11, 885.CrossRefGoogle Scholar
  2. Hirsch, P.B., Howie, A., Nicholson, R.B., Pashley, D.W., and Whelan, M.J. (1977) Electron Microscopy of Thin Crystals, 2nd edition, Krieger, Huntington, New York. Chapter 9.Google Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • David B. Williams
    • 1
  • C. Barry Carter
    • 2
  1. 1.Lehigh UniversityBethlehemUSA
  2. 2.University of MinnesotaMinneapolisUSA

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