The Faraday Effect in Non-degenerate Semiconductors

The theory of the Faraday effect, due to free charge carriers, is developed for non-degenerate semiconductors with spherical energy surfaces. General expressions for the Faraday rotation θ and the ellipticity δ are given, which are valid for all frequencies from the microwave region to the infra-red, and for all magnetic field strengths within the limitations of the Boltzmann equation. The cases of lattice scattering and impurity scattering are considered separately and the numerical calculations are based on experimental data for n-type germanium. The rotation θ changes sign at the cyclotron resonance frequency in strong fields and at a lower frequency (determined by the relaxation time) in weak fields. The ellipticity δ passes through zero at a frequency corresponding to maximum θ, and reaches a maximum when θ is zero. In the limit of high frequencies and weak fields θ (but not δ) is independent of the relaxation mechanism. Both θ and δ vary linearly with field strength in weak fields but subsequently pass through a maximum. The temperature dependence of θ and δ is examined in the range 100-300°K for lattice scattering and 15-100°K for impurity scattering. As the temperature is lowered, in general θ and δ both increase in the case of lattice scattering, and both decrease in the case of impurity scattering.