Dependence of the Free-Carrier Faraday Ellipticity in Semiconductors on Scattering Mechanisms

The theory of the Faraday ellipticity in semiconductors is developed, via the Boltzmann transport equation, under the assumption of an isotropic energy-dependent time of relaxation $\tau$. Equations relating ellipticity to semiconductor parameters are derived for various ranges of the collision, cyclotron, and applied frequencies. It is observed that, besides its dependence on the value of the scattering parameter, Faraday ellipticity is rather sensitive to the type of scattering mechanism as such, and to the distribution function. Some specific experiments are suggested in the ranges where ellipticity appears particularly promising as a tool for investigating these aspects of the scattering process. Numerical examples, calculated for thermal and ionized impurity scattering in nondegenerate carrier systems, are contrasted with the results of the constant-$\tau$ approximation, showing the inadequacy of the latter approach. Finally, the effect of spheroidal surfaces of constant energy on Faraday ellipticity is briefly discussed.