Effect of the Relativistic Operators on the Band Shapes of Anisotropic Semiconductors

Abstract

The effect of the spin-orbit, Darwin and mass-velocity operators on the non-relativistic self-consistent valence and conduction band edges of trigonal Te is studied with the degenerate first order perturbation theory. It is found that: (1) the k dependence of all the three relativistic corrections is essential for the proper description of the band edges on the meV scale. (2) The Darwin correction cancels out a part of the mass-velocity correction to the shape of the band edges. (3) The spin-orbit and the joint Darwin-mass-velocity correction to the shape of the band edges are of the same order of magnitude. Therefore the neglect of the latter correction is not entirely justified. The calculated pressure dependence of the valence band edge of Te agrees closely with the conduction measurement of Koma et al. The experimental difference between the valence band minimum and the saddle point, Δϵ, by Glushkov et al. decreases about twice as fast as the calculated Δϵ. Therefore the α-β fine structure in the infrared absorption spectrum does not seem to be directly related to the valence band edge.