New theory of linewidths of radiative transitions due to disordering in semiconductor alloys

A quantum mechanical formalism for the excitonic photoluminescence linewidth in semiconductor alloys due to band gap fluctuations caused by the random distributions of alloy components is presented. Using a quantum mechanical description for the excitonic system, the mean deviation of its transition energy due to the statistical potential fluctuations is calculated using a first-order perturbation theory. We then apply this formalism to calculate the linewidth of the ground state excitonic transition as a function of composition. Specifically, the excitonic linewidth in AlxGa1−xAs alloy as a function of Al concentration is calculated and compared with earlier models and available low-temperature photoluminescence data.