Exciton formation rates in GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As quantum wells

A theoretical investigation of the exciton formation process from free carriers in a single GaAs/ ${\mathrm{Al}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Ga}}_{\mathrm{x}}$As quantum well is presented. The mechanism for the formation processes is provided by the interaction of the electrons and holes with phonons. The contributions from both the acoustic and optical phonons are considered. The relative importance of exciton creation from a thermalized electron-hole gas (bimolecular formation) versus a direct creation of excitons from the crystal ground state through the electromagnetic field (geminate formation) is discussed. The formation process is analyzed for different densities and temperature of the free carriers, and for different intensities of the exciting optical pump. The results compare reasonably well with recent experiments.