Electronic – How to there be electrons in the Fermi level

physics

The probability of electron occurring in fermi level is half. In case of intrinsic semiconductors the fermi level lies halfway between the valence band and conduction band i.e. in the band gap. How can electrons occur in the band gap?
Correct me if am wrong anywhere. Thanks for your replies!!

Best Answer

From Wikipedia:

The Fermi-Dirac distribution \$F(\epsilon)\$ gives the probability that (at thermodynamic equilibrium) an electron will occupy a state having energy ϵ.

That is, the Fermi-Dirac distribution doesn't give the probability of the existence of an electron at a certain energy. Rather, if there is a state at that energy, it gives the probability of the state being occupied.

So if there are no states, there won't be any electrons regardless of the Fermi level.