Excitons in the quasi-two-dimensional electron gas

The response of modulation-doped semiconductor quantum wells to a band-gap light field is discussed with special attention paid to excitons and screening. Absorption and luminescence spectra are calculated in a mean-field approximation, taking into account the confinement and finite mass of the particles, finite temperatures, and external magnetic fields. Bound excitonic states are found to dominate the low-temperature luminescence spectra for densities up to ≃${10}^{11}$ ${\mathrm{cm}}^{\mathrm{-}2}$. At higher densities the excitonic state can be recovered by applying a magnetic field. The reappearance of the excitonic state is accompanied by an abrupt blueshift and increased oscillator strength of the luminescence. An efficient method to solve the zero-field Bethe-Salpeter integral equation in two dimensions is based on the application of a small auxiliary magnetic field.