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

The high frequency conductivity tensor σij 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, σij 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 ∼ Ep, 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 σij 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.

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