# Fermi and Boltzmann distribution of carriers in semiconductor

What are the requirements for describing charge carriers (e.g. electrons) in a semiconducting material by - Fermi distribution - Boltzmann distribution

When do we apply the one or the other? If the explanation to this question is in Ashcroft/Mermin, reference to the relevant chapter would be appreciated.

I don't agree with both commentators so far.

Edit Consider Eq. 21 in Sze, PHysics of Semiconductor Devices:

$$n = N_C exp\left(-\frac{E_C-E_F}{kT}\right)$$

or Eq. 2.16 in Pierret, Semiconductor device fundamentals.

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Can you please clarify your question a bit? Are you asking about limits of application or something else? In case this may be important, Fermi (or Bose, if you are dealing with bosons - not in this case, of course) distribution is applicable when quantum effects become important, e.g. at very low temperature. –  Eugene B Mar 19 '13 at 11:50

I would suggest that it is always better to use Fermi distribution when dealing with semiconductors. This is clear even from the wikipedia page. Anyway, I don't think I've even met semiconductors described via Boltzmann distribution. Moreover, if you find a system that would actually be well-described by Boltzmann distribution, you still can apply Fermi distribution to it, as Boltzmann distribution can be treated as a classical limit of Fermi or Bose distribution, so you shouldn't go wrong anyway. Similarly, you can apply special relativity to classical mechanics problems.

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