Generalized Kane model for the band spectrum of diamond-like semiconductors. Nonparabolicity and anisotropy of the dispersion relations

Abstract

Available experimental data indicate that the Kane models for the band structure of diamond-like semiconductors do not sufficiently correctly describe the effects of the anisotropy and nonparabolicity of the valence bands. In [1], we carried out parallel examinations of the spectrum for all diamond-like semiconductors with a lower conduction band of the s-type within the four-band kp model, which is a generalization of both Kane models. We obtained a dispersion equation of fourth degree (DE-4s), allowing us to refine the range of applicability of the Kane models. This paper is a continuation of [1] in which we do a detailed analysis of the nonparabolicity and anisotropy of the dispersion relations for the holes. We show that neither of the Kane models correctly describe the state of the light-hole band over a broad energy range. At the same time, the heavy-hole band is correctly described by the Kane equation (1956); the conduction band and the split-off hole band are correctly described by the Kane theory (1957).