Cyclotron Resonance and the Free‐Carrier Magneto‐Optical Properties of a Semiconductor

Abstract

Abstract The high frequency conductivity tensor σ ij is calculated for a semiconductor with a quadratic band structure in a magnetic field. The existence of an energy‐dependent relaxation time τ( E ) is assumed. For both an isotropic band and a band with a many‐valley structure, σ ij can be expressed in terms of three similar functions, σ ± and σ. For an isotropic band, σ ± is the conductivity for a circularly polarized electric field and σ is the conductivity for zero magnetic field. It is shown that these coefficients satisfy certain sum rules. When τ ∼ E p , they are given by tabulated integrals. The results are applied to cyclotron resonance and compared with experimental measurements on n‐CdTe. The assumption that p = 3/2 (ionized impurity scattering) gives the best agreement with experiment. The free carrier magneto‐optical properties can be calculated if σ ij is known, and under low loss conditions the Faraday rotation and ellipticity, and the Voigt effect, may be expressed fairly simply in terms of σ ± and σ. The Faraday rotation in n‐Ge is calculated as a function of magnetic field, and the results are compared with experiment.