Photoluminescence excitation spectroscopy of Be-remotely-doped wide parabolic GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells

p-type, remotely doped, wide (∼1000 Å) parabolic GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells were investigated by photoluminescence excitation spectroscopy. For three samples, with valence-band edge curvatures equivalent to the potentials of fictitious uniform slabs of charge with three-dimensional (3D) densities of 0.2, 3, and 4×${10}^{16}$ ${\mathrm{cm}}^{\mathrm{-}3}$, the spectra show uniformly spaced peaks with spacings which scale with these 3D densities. This peak structure is similar to that observed for n-type, remotely doped parabolic GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells. A simple single-particle model is presented which is quantitatively consistent with the spectra for the three samples, assuming the hole gas forms a wide slab in the valence band with density given by the designed 3D density. These results support the conclusions from transport measurements of the existence of wide hole-gas layers in these structures.