Distribution function of a drifting electron gas for general energy-band structures.

Abstract

The usual application of the Lei-Ting balance equation method for treating electron transport problems makes use of a Fermi distribution function for the electron motion relative to the center of mass. It is pointed out that this presumes the existence of a moving frame of reference that is dynamically equivalent to the rest frame of reference, and this is only true for electrons with a constant effective mass. The method is thus inapplicable to problems where electrons governed by a general energy-band dispersion E(k) are important (such as in miniband conduction). It is demonstrated that this difficulty can be overcome by introducing a distribution function for a drifting electron gas by maximizing the entropy subject to a prescribed average drift velocity. The distribution function reduces directly to the usual Fermi distribution for electron motion relative to the center of mass in the special case of E(k)=${\mathrm{\ensuremath{\Elzxh}}}^{2}$\ensuremath{\Vert}k${\mathrm{\ensuremath{\Vert}}}^{2}$/2${\mathit{m}}^{\mathrm{*}}$. This maximum entropy treatment of a drifting electron gas provides a physically more direct as well as a more general basis for the application of the balance equation method.