Exciton binding energies in shallow GaAs-${\mathrm{Al}}_{\mathit{y}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{y}}$As quantum wells

Strong enhancements of the exciton binding energy (${\mathit{E}}_{\mathit{x}}$), compared to bulk GaAs, are deduced from high-resolution spectroscopic studies of shallow GaAs-${\mathrm{Al}}_{\mathit{y}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{y}}$As quantum wells, with aluminum concentrations of (1–4.5)%. A clear increasing trend in ${\mathit{E}}_{\mathit{x}}$ from 5.9 meV at 1% aluminum to 7.0 meV at 4.5% is deduced, in good agreement with the predictions of variational calculations. Even at 1%, the value of ${\mathit{E}}_{\mathit{x}}$ represents an enhancement of 40% over that in three-dimensional GaAs. The similarity of all the spectra supports strongly the marked two dimensionality of the lowest exciton states, even for very low barrier heights.