Effect of charge-carrier screening on the exciton binding energy in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells

Exciton binding energies of heavy- and light-hole excitons affected by charge-carrier screening in GaAs-${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells are calculated by the variational-perturbation method. The exciton binding energies are found to decrease rapidly when the screening length is less than 30${\mathit{a}}_{\mathit{B}}^{\mathit{h}}$ (effective exciton Bohr radius). This screening length corresponds to a carrier density of 7.0×${10}^{13}$/${\mathrm{cm}}^3$ at T=10 K. In the calculation, the Debye screening model is used for charge carriers. The exciton binding energies as functions of the screening length, carrier density, and quantum-well parameters have been calculated. The critical carrier densities, above which no excitons can be formed, are obtained at different well thickness. The effects of charge-carrier screening to the exciton photoluminescence are also discussed.