Temperature-dependent exciton linewidths in semiconductors

The temperature-dependent linewidths of excitons in semiconductors due to the interaction of the exciton with both LO phonons and with acoustic phonons are studied with use of a Green's-function approach in which the exciton-phonon interaction is treated perturbatively. The interaction between the excitons and the LO phonons is taken to be of the Fr\"ohlich form, and the contribution to the linewidth is obtained in closed form. In this case it is found that scattering of the exciton to both bound and continuum states is important and that it is important to treat the continuum states fully as Coulomb scattering states. In describing optical-absorption processes, the fact that absorption occurs from polariton states, which are states composed of excitons coupled to light, is taken into account. The linewidths due to the exciton--LO-phonon interaction are evaluated for a series of II-VI and III-V compound semiconductors, and are shown to account for the existing experimental results for temperatures \ensuremath{\gtrsim}80 K. The contributions to the linewidth due to the interaction of excitons with acoustic phonons via both the deformation potential and the piezoelectric couplings are treated, and it is found that the deformation-potential coupling dominates for all of the materials considered. Because of the small velocity of sound, scattering to only intraband intermediate states, i.e., those in which the internal exciton quantum numbers do not change, is found to contribute to the linewidth. In the case of acoustic phonons, it is found to be important to treat optical absorption as originating from polariton states in order to evaluate properly the magnitude of this contribution to the linewidth. The acoustic-phonon contribution to the linewidths is compared with experiment for temperatures \ensuremath{\lesssim}80 K, for which it dominates the temperature dependence.