The Theory of the Faraday Effect in Anisotropic Semiconductors II: Application to n-type Germanium

Abstract

The theory of the anisotropic free-carrier Faraday effect in semiconductors, previously developed by the authors, is applied to n-type germanium, taking into account the detailed structure of the conduction band. The high-frequency magnetoconductivity tensors are derived from a closed solution of the Boltzmann equation and are evaluated for a non-degenerate system of electrons, considering lattice scattering only. The Faraday rotation Θ and ellipticity Δ are evaluated numerically, as functions of the direction of propagation in the crystal, for two cases, in which the magnetic field is confined to the (100) and (110) planes respectively. Over the range of field strengths considered (up to 30 kilo-oersteds), anisotropic changes in Θ and Δ of the order of 30% may be obtained in the microwave region, but decrease with increasing frequency, becoming negligible in the infra-red. For all directions of propagation, except [100] and [111], it is shown that Θ and Δ depend also upon the orientation of the initial plane of polarization with respect to the crystal axes. This effect is similar to the directional effect in magnitude, frequency dependence and field dependence, and is most pronounced for propagation along [110]-type directions.