Theory of the Effect of a Magnetic Field on the Absorption Edge in Semiconductors

Oscillatory non-resonant interband Faraday rotation in InSb and PbTe—a new magneto-optical effect

Oscillations in the magnetic field dependence of interband Faraday rotation in degenerate samples of InSb and PbTe at low temperatures have been observed for photons having a wide range of energies which are less than that corresponding to the forbidden energy gap. These oscillations are attributed to the imbalance of contributions from right and left circularly polarized modes to the total rotation, caused by the blocking of certain interband absorptions by conduction-band electrons. The perturbing effect of the variation of carrier concentration is used as an experimental variable. The relative strengths of the oscillations have been reasonably well accounted for by analysis of the interband selection rules and transition strengths given by a theory due to Boswarva & Lidiard. The positions of the oscillations, which depend on the population of Landau levels in the conduction band, have a reciprocal magnetic field dependence as for the de Haas-van Alphen effect, and have yielded quantitative determinations of energy-band parameters.

Stimulated spin-flip Raman scattering: a magnetically tunable infrared laser. I

A microscopic theory of spin-flip Raman scattering from conduction electrons in semiconductors has been set out both in terms of appropriate general scattering theory and of detailed calculation of the electron band states of a solid in a magnetic field. From the latter, matrix elements determining the scattering cross-section have been evaluated as a function of frequency and magnetic field for the various ‘anharmonic’ processes involved in indium antimonide. New experimental results on magnetic field dependence of gain and loss, of direct relevance to comparison with microscopic theory, are presented and discussed. These results, together with earlier work, confirm the basic theoretical model and clearly demonstrate the potential of this continuously tunable infrared laser.

Faraday effect in semiconductors

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)).