I am having a hard time understanding the relation between the fermi distribution of electrons in a semiconductor, and the fact the electron energy states are discrete.
The fermi distribution is supposed to give us the probability of an energy level being occupied by electrons. It looks like this:
yet electrons are supposed to have discrete energy states, and no electron is supposed to be in the band gap:
I must be missing something here, how is it that electrons have a fairly high probability of being in the band gap ?