Faraday effect in semiconductors

Abstract

This paper first reviews the general macroscopic and quantum mechanical formulae necessary for the calculation of Faraday rotations and Voigt shifts in semiconductors. The general formulae are then applied to calculate Faraday rotations, θ , in semiconductors as caused by: (i) allowed direct band-to-band transitions, (ii) forbidden direct transitions, (iii) indirect (‘phonon-assisted’) transitions, and (iv) transitions by electrons in donor states. The dependence of the contributions (i) to (iii) on frequency ω is slower than would correspond to a single classical oscillator; for (i) it diverges as ω g — ω) -1/2 as ω tends towards the band-gap, ω g , and for (ii) and (iii) it tends to finite limit at the absorption edge. At low frequencies all three sources give contributions varying as ω 2 . Electrons bound in donor states behave like hydrogenic atoms and yield an obvious quantum generalization of the classical formula at low fields (equation (6.7)). At high field strengths the expression obtained is similar to that for free electrons except that the free electron cyclotron resonance frequency, ω c , is replaced by ω c + Δ/ h , where Δ/ h depends logarithmically on field strength (equation (6.9)).