Transport Properties of a Many-Valley Semiconductor

Abstract

The simple model of a semiconductor, based on a single effective mass for the charge carriers and a spherical shape for the surfaces of constant energy, is now known to be inadequate for most of the semiconductors which have been extensively studied experimentally. However, some of these do correspond to what may be called the “many-valley” model, a model for which the band edge occurs at a number of equivalent points K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(i)</sup> in wave number space, and for which the surfaces of constant energy are multiple ellipsoids, one centered on each of these points. This paper develops, for models of this type, the theory for: mobility (Section 2) and its temperature dependence (Section 3); thermoelectric power (Section 4); piezoresistance (Section 5); Hall effect (Sections 6 and 9); high-frequency dielectric constant (Section 7); and magnetoresistance (Sections 8 and 9). These phenomena are treated, for cases to which Maxwellian statistics apply, on the assumption that the scattering of the charge carriers is describable by a relaxation time which depends on energy only, but is otherwise unrestricted. This assumption can be shown to be justified in a large class of cases, although for some cases it fails, notably when ionized impurity scattering predominates and at the same time the effective mass is very anisotropic. Special attention is given to the role of inter-valley lattice scattering, i.e., to processes whereby a charge carrier is scattered from the neighborhood of one of the band edge points