Kinetics of radiative recombination in quantum wells

A theory of radiative-recombination kinetics which treats free carriers, excitons, and photon recycling in a quantum-well system is presented. An expression for the temporal decay of excess carriers which encompasses large- and small-signal regimes is derived. When excitons are present the decay can be approximated by two exponentials in general, and in the large-signal regime the photoluminescence time constant is half as long as that associated with photoconductivity. Explicit expressions for the recombination coefficients are given and their magnitudes discussed for nondegenerate and degenerate populations in GaAs. Excitons are shown to enhance the temperature dependence. A simple model of exciton screening is used to illustrate the dependence of radiative time constants on background carrier density, which deviates significantly from the conventional free-carrier dependence. The magnitudes of radiative time constants in real systems depend, in addition to material characteristics, upon the details of exciton screening, the overlap of the electron and hole wave functions in the quantum well, and the probability of photon reabsorption, all of which are specimen specific. It is pointed out that the transition from a degenerate to a nondegenerate population may be misinterpreted in terms of Auger processes.