Interband spectroscopy of a quasi-three-dimensional electron gas in wide parabolic (Al,Ga)As quantum wells

The quasi-three-dimensional electron gas found in wide n-type parabolic ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells has been studied through photoluminescence spectroscopy in perpendicular and in-plane magnetic fields. The conduction-band subband structure composed of several occupied closely spaced levels (δE≊1 meV) can be clearly identified from the spectra, aided by the sharpening of the luminescence emission into narrow peaks by Fermi-edge singularity effects (many-electron–one-hole exciton). The luminescence behavior in magnetic fields shows clearly the relative importance of the following energies in the problem: the Fermi energy, the subband spacing, the cyclotron energy, and the Coulomb perturbation by the photoholes. In the limit where the cyclotron energy dominates, an accurate measurement of the thickness of the electron slab is spectroscopically determined. A magnetic-field anomaly in the quantum limit near filling factor ν=2/3 has been observed.