Fermi-Distribution:

The Fermi-Distribution fn(E) = {1 + exp[(E - EF)/kT]}-1 indicate the probability if a state located at the energy E is occupied by an electron. This propability depends on temperature T. At T=0K the distribution looks like a hutch. The energy where the propability drops from 1 to 0 (at T=0K) is called the Fermi-Energy EF:

Fermi-Distribution fn(E) in dependence of energy E for different temperatures T.