Boltzmann approximation ($f(E)\simeq e^{-(E-\mu )/(kT)}$)

When $E-\mu \gg kT$, the unit term in the denominator of the Fermi-Dirac distribution is negligible. The resulting exponentially small occupation is the Boltzmann approximation. It justifies the usual nondegenerate semiconductor carrier formulas; it fails near strongly occupied band states.