Theory of Impurity Bands in Magnetic Fields. II. Transport Properties

Abstract

The Hall coefficient and the magnetoresistance in a weak magnetic field are investigated for the impurity conduction processes based on a simplified model where the impurity potential is short-ranged. The formation of the impurity band and the modification of the intrinsic band are treated on the same footing by the Green function method. It is shown that the sign of the Hall coefficient is always electronic for n-type semiconductors irrespective of the degree of compensation. Two origins of the magneto-resistance, the Zeeman spin splitting and the Landau orbital motion, are separately calculated and both longitudinal and transverse magnetoresistances are shown to be of the same order of magnitude in the impurity band region. Numerical calculations of these transport coefficients are carried out as functions of the impurity concentration and of the degree of compensation. Intuitive discussion is made on the intrinsic nature of the impurity conduction processes. Further, the relation between the Hall coefficients in this model and in the Matsubara-Toyozawa model is discussed.