Accurate theory of excitons in GaAs-Ga1−xAlxAs quantum wells

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Abstract
Binding energies of excitons in quantum wells are calculated including valence-band mixing and also other important effects, namely Coulomb coupling between excitons belonging to different subbands (which is predominantly with the exciton continuum), nonparabolicity of the bulk conduction band, and the difference in dielectric constants between well and barrier materials. All these effects are found to be of a comparable size, tend to increase the binding energies, and taken together result in very high binding energies, particularly in narrow GaAs/AlAs quantum wells. Binding energies can be even higher than the two-dimensional limit of four times the bulk Rydberg. Theoretical results agree within a few tenths of a milli-electron-volt with available photoluminescence excitation experiments. Valence-band mixing gives a finite oscillator strength to some excitons not in s states, but does not change the selection rules based on parity. Calculated oscillator strengths of the ground-state heavy- and light-hole excitons are found to be in good agreement with absorption and reflectivity experiments.