The Fermi Distribution Function
The Fermi distribution function: f(E) = 1/[1 + exp((E-Ef)/kT)]
where, E is the electron energy, Ef is the Fermi energy, and T is the absolute temperature.
Its physical meaning is that:
f(E) is the probability of occupancy for an electron energy state at energy E by an electron. That is, the probability that this state is occupied by an electron is f(E), and the probability that it is vacant is 1 - f(E).
As can be seen from the formula, the probability of occupancy for an arbitrary energy state at E depends on the value of Fermi energy Ef, and on the value of temperature T.
The effects of Ef and T on this probability distribution function can be seen from the following applet.
The Fermi probability distribution function