Spectroscopy of a high-mobility GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As one-side-modulation-doped quantum well

We report the results of low-temperature photoluminescence and photoluminescence excitation spectroscopy experiments performed on a 150-Å-thick GaAs-${\mathrm{Ga}}_{0.61}$ ${\mathrm{Al}}_{0.39}$As one-side-modulation-doped quantum well. An interpretation of the excitation and luminescence spectra has been obtained, yielding a GaAs band-gap renormalization of 19 meV for an areal electron concentration of 4.5×${10}^{11}$ ${\mathrm{cm}}^{\mathrm{-}2}$.