Exciton-exciton and exciton-charge carrier interaction and the exciton collisional broadening in GaAs/AlGaAs quantum wells

TL;DR

This paper calculates exciton wave functions and interaction constants in GaAs/AlGaAs quantum wells of various widths, analyzing collisional broadening effects due to exciton and charge carrier interactions.

Contribution

It provides detailed numerical calculations of exciton wave functions, interaction constants, and scattering matrix elements across a range of quantum well widths, advancing understanding of exciton interactions.

Findings

Calculated exciton wave functions for various well widths.

Determined exciton-exciton, exciton-electron, and exciton-hole interaction constants.

Analyzed collisional broadening of exciton resonance as a function of particle densities.

Abstract

Wave functions of heavy-hole excitons in GaAs/Al$_{0.3}$Ga$_{0.7}$As square quantum wells (QWs) of various widths are calculated by the direct numerical solution of a three-dimensional Schr\"odinger equation using a finite-difference scheme. These wave functions are then used to determine the exciton-exciton, exciton-electron and exciton-hole fermion exchange constants in a wide range of QW widths (5-150 nm). Additionally, the spin-dependent matrix elements of elastic exciton-exciton, exciton-electron and exciton-hole scattering are calculated. From these matrix elements, the collisional broadening of the exciton resonance is obtained within the Born approximation as a function of the areal density of excitons, electrons and holes respectively for QW widths of 5, 15, 30 and 50 nm. The obtained numerical results are compared with other theoretical works.