Exciton spectrum of surface-corrugated quantum wells: the adiabatic self-consistent approach

Abstract

A theory for calculating the relaxation frequency $\nu$ and the shift $\delta\omega$ of exciton resonances in quantum wells with finite potential barriers and adiabatic surface disorder is developed. The adiabaticity implies that the correlation length $R_c$ for the well width fluctuations is much larger than the exciton radius $a_0$ ($R_c\gg a_0$). Our theory is based on the self-consistent Green's function method, and therefore takes into account the inherent action of the exciton scattering on itself. The self-consistent approach is shown to describe quantitatively the sharp exciton resonance. It also gives the qualitatively correct resonance picture for the transition to the classical limit, as well as within the domain of the classical limit itself. We present and analyze results for $hh$-exciton in a GaAs quantum well with Al$_{0.3}$Ga$_{0.7}$As barriers. It is established that the self-consistency and finite height of potential barriers significantly influence on the line-shape of exciton resonances, and make the values of $\nu$ and $\delta\omega$ be quite realistic. In particular, the relaxation frequency $\nu$ for the ground-state resonance has a broad, almost symmetric maximum near the resonance frequency $\omega _0$, while the surface-induced resonance shift $\delta\omega$ vanishes near $\omega_0$, and has different signs on the sides of the exciton resonance.