Optical Absorption Edge in CdTe: Theoretical

Optical absorption in the "edge region" (i.e., for photon energies just below the first exciton peak) due to the creation of direct excitons with the simultaneous absorption of one and two longitudinal optical phonons is calculated by perturbation theory for Wannier excitons formed from the conduction and valence bands around k=0. It is shown that the contributions from the $n>\mathrm{}1\mathrm{}$ exciton bands, neglected in earlier calculations, are quite important and are required for a quantitative study. The results quantitatively account for the magnitude and for the temperature and energy dependences of the absorption coefficient observed in CdTe using a (average) hole mass of $0.4m$, where $m$ is the free-electron mass. These results strongly support the assignment to CdTe of a "direct" minimum band gap at k=0, contrary to a number of recent contentions (also based on absorption measurements) that the material is "indirect." It is noted that the agreement between the calculated results (including a rough correction for level broadening) and the data extends up to the temperature range at which the absorption coefficient begins to exhibit Urbach's-rule behavior. It is argued from this fact that the mechanism employed in these calculations, as opposed to others recently considered, underlies Urbach's rule in, at least, the compound semiconductors.