How to calculate the gap for a solid?

[gcc]

Hello everyone:

Do you know how to calculate the energy gap (the forbitten band) for a solid from the Kroning-Penney model?

 

[Dr Transport]

check any solid state book, Kittel comes to mind as does Ashcroft and Mermin.

 

[sfarrel2]

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.