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How to calculate the gap for a solid?

  1. Jun 8, 2009 #1


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    Hello everyone:

    Do you know how to calculate the energy gap (the forbitten band) for a solid from the Kroning-Penney model?
  2. jcsd
  3. Jun 10, 2009 #2

    Dr Transport

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    check any solid state book, Kittel comes to mind as does Ashcroft and Mermin.
  4. Jun 11, 2009 #3
    It has been a while since I have done this.

    But I believe the answer you are looking for is:

    Set up a simple infinite potenential field consisting of a perriodic array of potential bumps. (i think the only one I have worked out for my self is the case of a Delta function comb)

    Then you have a parametric equation with sines in it. Because the solution can not be greater than 1 (maximum of sin(x) = 1) you find areas where there is no solution. Those are you gaps.

    I know I have seen this in Kittel, Griffiths (quantum mechanics) and a couple other places.
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