The Einstein relation in Kane-type semiconductors

Abstract

An attempt is made to investigate the Einstein relation for the diffusivity-mobility ratio of the carriers in degenerate Kane-type semiconductors, taking n-Cd3As2 as an example, on the basis of a newly derived dispersion relation of the conduction electrons allowing various types of anisotropies in the band parameters within the framework of k⋅p formalism. It is found that the above ratio increases with increasing carrier degeneracy and is in quantitative agreement with the suggested experimental method of determining the Einstein relation in degenerate semiconductors having an arbitrary dispersion relation. In addition, the corresponding results for an isotropic three-band Kane model are also obtained from the expressions derived.