Many-particle effects in Be-δ-doped ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum wells

We have performed photoluminescence (PL) and photoluminescence excitation measurements on two series of center-δ-doped $p$-type ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum wells, with variable well width and doping concentration. The experimental data are compared with self-consistent field calculations. The effects of exchange and correlation were found to be extremely important and various models for the hole exchange and correlation are compared with the experimental data. It is found that the model recently proposed by Bobbert et al. [P. A. Bobbert et al., Phys. Rev. B 56, 3664 (1997)] consistently describes our experimental observations. Furthermore, for well widths $w>~600\AA$ clear excitonic effects were observed, for hole densities as high as $12\times {10}^{12}{\mathrm{cm}}^{\mathrm{-}2},$ which is explained in terms of small spatial overlap between the screening particles and the exciton along the growth direction. In contrast to earlier work on similar samples, we found no indication for a Fermi-edge singularity in the PL spectra of our samples. Peaked structures at the high-energy side of the PL spectra are shown to arise from bulk transitions.