Theory of Optical Magneto-Absorption Effects in Semiconductors

The theory of the effect of a magnetic field on the optical absorption in semiconductors is developed on the basis of the effective-mass approximation. For simple parabolic conduction and valence bands and a direct transition which is allowed at k=0, absorption peaks occur at energies above the zero-field gap. Since the selection rule for the transition is $\Delta n=0\mathrm{}$ where $n$ is the magnetic quantum number, the spacing between the peaks is the sum of the cyclotron frequencies for the two bands. For degenerate band edges, the spectrum is more complicated. A detailed treatment of the direct transition in germanium is given in which account is taken of the change in curvature of the bands away from k=0 and the results are in good agreement with the experimental measurements of Zwerdling, Lax, Roth, and Button. The k=0 conduction band mass is found to agree with predictions based on cyclotron resonance in the valence band. In addition, a gyromagnetic ratio for conduction electrons of -2.6 resulted from the calculations. The deviation from $g=2.0\mathrm{}$ is due to spin-orbit interaction. In InSb the effect is much greater, the result being $g=-50\mathrm{}$. These are consistent with experimental results. For bands in which the transition probability vanishes at k=0, absorption peaks will also occur corresponding to $\Delta n=\pm 1$ but absorption edges occur for $\Delta n=0\mathrm{}$. In the case of indirect transitions, the absorption does not exhibit oscillations but consists of a series of "steps" as has been observed in Ge by Zwerdling, Lax, Roth, and Button.