Exciton dispersion in semiconductors with degenerate bands

Abstract

The problem of energy versus momentum dispersion is considered for excitons in semiconductors of the diamond and zincblende families, which are characterized by a fourfold degeneracy of the upper valence band (in the strong spin-orbit limit). This degeneracy results in the well-known impossibility of a complete decoupling of relative and translational dynamics of the electron-hole pair. It is shown, however, how the canonical transformation to the new coordinates can be optimized to reduce and simplify the coupling terms, and to obtain, on the basis of simple physical arguments, the description of the motion that is most convenient for practical calculations in a particular semiconductor. Results of such calculations are presented for several materials and are favorably compared with experimental information obtained by modulation spectroscopy. The striking deviations from the hydrogenic parabolic dispersion law that occur in some materials are briefly discussed.