Exciton dispersion in degenerate bands

Abstract

The dispersion relations of band-gap excitons in covalent cubic crystals are investigated. For low momentum a perturbation method is used following Baldereschi and Lipari. At very low momentum the dispersion is strongly affected by a splitting of the fourfold $K=0\mathrm{}$ degeneracy for those materials with nonspherical conduction-band energy surfaces. In silicon and germanium this splitting leads to strong nonparabolic effects at energies in the 0.1-meV range. For large momentum a band decoupling scheme which generalizes the center-of-mass transformation method is derived and the concept of "light-mass" and "heavy-mass" excitons naturally results. Numerical values are given for germanium, silicon, and gallium arsenide.