Ex3 Basic principles semiconductors

Physics Q&A
1

I have a question about this exercise. I was making it and using the expression Eh=-E relating the electron energy and the hole energy of the same band. And the Hamilton equations for the group velocity and the effective mass I kept deriving ve=-vh and me*=-mh* . However this does not make sense as a semi conductor is neutral in charge giving me a net current when a field is applied. Thus when making the exercise I noticed that the velocity in the same band should be of the same sign as the charges of holes and electrons are opposite sign. So I made up that in reciprocal space the wave numbers(k) need to be opposite In sign kh=-k such that this problem is fixed. I put my derivation in the image.

Question:Is this how you’re supposed to do this?Because when you take kh=-k you do get the correct expressions.

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2

Hi Kenichi,

Thanks for your question. Indeed, that approach is correct. If you check the lecture notes you can find that they arrive at the same conclusion.

If we have a full band and remove an electron with momentum k, the whole band has now only one unpaired electron with momentum -k, so that is the momentum of the hole. Since both energy and momentum have a negative sign and v=\frac{1}{\hbar}\frac{\partial E}{\partial k} you get that both have the same velocity.