Calculation of Magneto-Conductivity Tensor for Semiconductors with Warped Energy Surfaces

Abstract

The energy surfaces for the holes near the top of the valence band in Ge, Si and diamond consist of two sets of warped spheres, which are degenerate at $\overrightarrow k = 0$ . Owing to the complicated form of these surfaces a lengthy numerical calculation is, in general, required to solve the Boltzmann equation and obtain the magneto-conductivity tensor. In weak magnetic fields an expansion in powers of H is possible, and was used by Lax and Mavroides^1,2 to discuss d.c. galvanomagnetic effects in p-type Ge and Si. A formal method was given by McClure,³ based on a Fourier expansion of the carrier velocity in a plane normal to $\overrightarrow H$ . This can be applied to warped spheres^4,5 but in general a large number of Fourier components is required. An approximate solution of the high frequency problem was used by Zeiger, Lax and Dexter⁶ (ZLD) in the analysis of cyclotron resonance, and involved a Fourier expansion of the perturbed distribution function. A similar approach is used in the present work, which is aimed at deriving the high frequency magneto-conductivity tensor components. for arbitrary field strengths, in a form suitable for computer programming.