Theory of the Galvanomagnetic Effects in Germanium

Abstract

In this paper a simple anisotropic theory of the galvanomagnetic effects in germanium is presented. It is assumed that the energy as a function of momentum has a number of extrema; near the extrema the energy is approximated by a quadratic function of momentum, and the relaxation time is assumed to be a function of energy only. Equations for the galvanomagnetic coefficients in any crystallographic direction are derived. The dependence of the coefficients on magnetic field strength is calculated and an expression for the ratio between Hall mobility and conduction mobility is obtained. The calculated values of the magnetoresistance are compared with measurements of Pearson and Suhl. The agreement between the calculated and the observed values is satisfactory in $n$-germanium, but not in $p$-germanium.