Indirect Transitions at the Center of the Brillouin Zone with Application to InSb, and a Possible New Effect

Abstract

The theory of indirect optical transitions is extended to the case where both the valence and the conduction band extrema occur at the center of the Brillouin zone. For this band structure, the dominant electron transition involves a virtual optical transition to a conduction band state, accompanied by scattering to a real state in the conduction band by absorption of a long-wavelength optical mode phonon. An analogous transition may also occur for holes. It is likely that the hole transition will be dominant over the electron transition when the curvature of the conduction band is greater than that of the valence band. It is shown that the absorption edge data on InSb are in agreement with this theory. The experimental evidence on InSb is reviewed and found to be consistent with degenerate valence bands at the center of the Brillouin zone. The absence of any evidence of indirect transitions involving acoustic modes tends to indicate that the shift of the valence maximum away from k=0 due to spin-orbit energy terms is small. A new effect is predicted involving the modulation of the indirect absorption constant by the selective excitation of the long-wavelength optical modes. A simplified theory of this effect is presented and the experimental possibilities of observing it in InSb are discussed. Its existence would verify the proposed indirect transition process as well as indicating the position of the band extrema.