Fermi enhancement and band-gap renormalization of ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs modulation-doped quantum wells

A comparative study of photoluminescence and photoluminescence-excitation spectra of thin n- and p-type modulation-doped ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs quantum wells is presented for sheet carrier densities up to ${10}^{12}$ ${\mathrm{cm}}^{\mathrm{-}2}$. Photoluminescence-excitation spectra reveal a rather weak enhancement of the oscillator strength at the Fermi edge which is not observable in the emission spectra. The renormalization of the quasi-two-dimensional band gap is obtained by comparison with undoped quantum wells of the same width. The experimental data compare favorably with our calculations of the band-gap renormalization within the local-density approximation as well as with the self-energy shifts of electron and hole subbands calculated within the random-phase approximation. The importance of a detailed line-shape analysis for the separation of intrinsic and extrinsic components in the photoluminescence spectra is emphasized.