Experimental exciton binding energies in GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As quantum wells as a function of well width

In the low-temperature photoluminescence excitation spectra of high-quality GaAs/${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As single quantum wells, we have observed distinctive peaks arising from the first excited level (2s) in addition to the ground state (1s) of heavy- and light-hole excitons. We utilized this accurate determination of the 2s-1s splitting energies to derive the binding energies of the heavy- and light-hole excitons as a function of well width and found good agreement with other similar determinations and with recent theoretical calculations based on models of quantum wells which included valence-band coupling. The agreement with exciton binding energies derived from magneto-optical spectroscopic experiments is satisfactory when comparison is made with recent results.