Quantum mechanical theory of linewidths of localized radiative transitions in semiconductor alloys

A quantum mechanical formalism to calculate the effect of compositional disorder on the linewidth of localized radiative transitions in semiconducting alloys is developed. A variational-statistical approach is used to calculate the line broadening. The general theory is applied to the specific case of excitonic transitions in which the exciton is in the ground state. The linewidth as a function of alloy composition is derived and the results thus obtained are compared with those of previous theories. For illustration, the calculations are done for GaAlAs and the results are compared with the available low-temperature photoluminescence data.