Derive the Fermi?Dirac distribution (25.8)

Start by considering a single electron state of energy E that is either occupied (n = 1) or not occupied (n = 0) by an electron. Now, consider coupling this two-state system to a thermal reservoir at temperature T so that not only energy but also particles can move between the smaller system and the reservoir. The entropy of the reservoir S (U, N) now depends on the total energy and total number of particles in the reservoir. Define E_F = ?T(?S/?N)|_U . Use an argument similar to that used to derive the Boltzmann distribution in ?8 to derive the Fermi?Dirac distribution (25.8)

- E /kBT 1 e p(E) %3D -E/kBT +e-EF(T)/kBT 1+e(E-Ef(T))/kgT