Resonant impurity and exciton states in a narrow quantum well

Abstract

An analytical investigation of resonant impurity and exciton states in a narrow quantum well (QW) is performed. We employ the adiabatic multisubband approximation assuming that the motions parallel and perpendicular to the heteroplanes separate adiabatically. The coupling between the Coulomb states associated with the different size-quantized subbands ($N=1$, 2, \dots{}) is taken into account. In the two- and three-subband approximation the spectrum of the complex energies of the impurity electron and the exciton optical absorption coefficient are derived in an explicit form. The spectrum comprises a sequence of series of quasi-Coulomb levels $(n)$ where only the series belonging to the ground subband $N=1$ is truly discrete while the excited series $N\ensuremath{\geqslant}2$ consist of quasi-discrete energy levels possessing non-zero widths ${\ensuremath{\Gamma}}_{Nn}$. Narrowing the QW leads to an increase of the binding energy and to a decrease of the resonant energy width ${\ensuremath{\Gamma}}_{Nn}$ and the resonant energy shift $\ensuremath{\Delta}{E}_{Nn}$ of the impurity electron. Displacing the impurity center from the midpoint of the QW causes the binding energy to decrease while the width ${\ensuremath{\Gamma}}_{Nn}$ and the corresponding shift $\ensuremath{\Delta}{E}_{Nn}$ both increase. A Lorentzian form is recovered for the exciton absorption profile. The absorption peak is narrowed and blue shifted for a narrowing of the quantum well. A successful comparison with existing numerical data is performed. For GaAs QW's it is shown that the resonant states analyzed here are sufficiently stable to be observed experimentally.