Suppose there is a semiconductor with Fermi energy $E_f$ and that there are $N$ bound electron states.
I'd like to know why the mean number of excited electrons takes the form $$\bar n={N\over \exp\beta(\mu-E_f)+1}$$
where $\mu$ is the chemical potential.
I can see that the Fermi Dirac statistics say that for one fermion the mean occupation number is $$\bar n = {1\over \exp\beta(E-\mu)+1}$$ I am not sure however as to how for the semi-conductor it should assume the above form. The $N$ is clearly due to the $N$ bound $e^-$ states. I am not quite so confident as to why $$\mu\to E_f$$ $$E\to \mu$$
Could someone please explain?
Anybody? :(