Well-width and aluminum-concentration dependence of the exciton binding energies in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells

A photoluminescence-excitation (PLE) study of the exciton binding energy in GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum-well (QW) structures is reported. A line-shape fit of the PLE spectra, based on a correct evaluation of the absorption probability in QW’s, is proposed as a powerful tool in order to deduce accurately the exciton binding energies even in samples where the 2s peak is unresolved. The experimental results obtained are in good agreement with recent accurate theories. In particular, we find a strong dependence of the heavy-hole exciton binding energy ${\mathit{E}}_1$ on the aluminum concentration of the ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As barrier, in agreement with the predicted importance of the dielectric mismatch and conduction-band nonparabolicity in enhancing ${\mathit{E}}_1$. Finally, evidence of exciton binding energies larger than the two-dimensional limit in GaAs is found even in relatively thick QW’s (50 Å) with AlAs barriers.