A quantum statistical theory of linewidths of radiative transitions due to compositional disordering in semiconductor alloys

A quantum statistical formalism has been developed for the excitonic luminescence linewidths and line shapes in semiconductor binary alloys due to band-gap fluctuations caused by the random distributions of the alloy components in an applied magnetic field. The virtual crystal approximation is used to estimate the local band-gap variations. The shifts of the excitonic transition energy due to the band-gap fluctuations are obtained using the first-order perturbation theory. A Gaussian line shape is obtained for the excitonic transition using standard statistical techniques. This formalism is applied to calculate the linewidths and line shapes associated with the ground-state excitonic transition as a function of alloy composition and magnetic-field strength in AlxGa1−xAs and InxGa1−xP alloys. The resulting linewidths and line shapes are in good agreement with the available low-temperature photoluminescence data; however, the calculated linewidths are consistently smaller than the measured values. The possible mechanisms responsible for this discrepancy are discussed. A comparison of excitonic linewidths obtained from the present theory with those calculated earlier is also presented.