Magnetic-Field Dependence of Free-Carrier Absorption in Semiconductors

A plane-wave semiclassical analysis of the amplitude of an electromagnetic wave transmitted through a semiconductor in the presence of a magnetic field is discussed and some theoretical predictions are compared with experimental measurements. The Faraday and the Voigt configurations, longitudinal and transverse, respectively, are specifically considered. The theoretical results, obtained formally in terms of the high-frequency conductivity tensor, are applied to the isotropic, one-carrier semiconductor model. The general expression, covering all ranges of frequency and magnetic field within the extent of validity of the model, is derived and reduced to simple forms applicable to specific experimental situations. The problem is then generalized to ellipsoidal surfaces of constant energy, and to systems involving more than one type of carrier. Results of room temperature microwave experiments carried out in the Faraday configuration on silicon and germanium show, in general, good agreement with the theoretical analysis. Effects of magnetodichroism, observed in $n$-type silicon in this configuration, are reported. It is finally noted that the theoretical analysis of the Voigt configuration predicts the major features of the line shapes observed in far infrared experiments by other workers.