Effect of disorder on exciton binding in semiconductor alloys

We apply the coherent-potential approximation to the Wannier exciton and show that broadening of the conduction and valence bands, which pushes down the absorption edge relative to the virtual-crystal band position, has less influence on the exciton states, thus reducing the binding energy. We also show that the effective interaction induced by simultaneous scattering of the electron and hole by the same impurity can be either attractive or repulsive depending on the band lineup. In most semiconductor alloys, this turns out to be attractive and cancels partially the binding-energy reduction due to bowing. These results are obtained by an approximate solution to the Bethe-Salpeter equation appropriate to a disordered system. Our theory is compared with available experimental data in Ga (As,P).