Charge and Energy Transport in a Nondegenerate Electron Gas

Abstract

In the preceding chapters, we have seen that a mobile charge carrier in a semiconductor has an effective mass m which is different from the free electron mass m 0. The effective mass takes care of the fact that the carrier is subject to the crystal field. In discussing the velocity distribution of the gas of carriers, we found that the Fermi-Dirac distribution holds in general and that the Maxwell-Boltzmann distribution f (v) ∝ exp (− m v 2/2 k B T) is an approximation of the former which is valid for nondegenerate semiconductors. Here the carrier density is small compared with the effective density of states N c in the conduction band and N v, in the valence band (3.1.12). For these distributions, no externally applied electric fields were assumed to be present. Instead, the calculations were based on the assumption of thermal equilibrium.