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Finding the maxima or minima of band-edges?

  1. May 5, 2015 #1
    I'm working on a hw assignment and I'm completely stuck on this last problem. I'm not even sure what ∇KE=0 even means to begin with. I understand the difference between indirect and direct bandgap but I'm just confused on how to find the maxima and minima to determine this. Any help would be greatly appreciated.

    Direct Indirect Bandgap.PNG
     
  2. jcsd
  3. May 5, 2015 #2

    ZapperZ

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    This really should be posted in the HW/Coursework forum.

    First of all, don't you remember from your calculus class that a maximum and minimum will have zero gradient? ∇KE=0 is exactly that, except that this is obviously a gradient in 3D k-space. So find the k values for each one of them where the gradient is zero. If the k values you found for each band is the same, then the max and min occurs at the same k values and so, you have a direct band gap. If not, you have an indirect gap.

    Zz.
     
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