Phonon-assisted optical absorption by excitons in semiconductor quantum wells

The optical-absorption edge in the region below the lowest exciton peak is studied theoretically for semiconductor quantum-well systems. At finite temperatures this edge is due to the creation of an exciton and the absorption of a LO phonon. The optical-absorption process is treated perturbatively in the light-exciton and the exciton–LO-phonon interactions which gives the absorption in terms of a sum over intermediate states involving the bound and scattering states of the interacting electron-hole system. The absorption corresponding to the lowest-lying exciton state is calculated by treating the electron-hole states as two dimensional, and the summation over the intermediate states is performed exactly. It is shown that this complete summation is necessary in order to obtain a quantitative understanding of the absorption process. The contributions of absorption processes involving higher-lying final exciton states and the effects of finite quantum-well thickness are discussed qualitatively. The present results account for recent experimental data on GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As quantum wells.