Abstract
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 where 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 is due to spin-orbit interaction. In InSb the effect is much greater, the result being . These are consistent with experimental results. For bands in which the transition probability vanishes at k=0, absorption peaks will also occur corresponding to but absorption edges occur for . 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.
- Received 14 July 1958
DOI:https://doi.org/10.1103/PhysRev.114.90
©1959 American Physical Society