Excitons in square quantum wells: microscopic modeling and experiment

TL;DR

This paper presents a detailed microscopic calculation of exciton binding energies and radiative decay rates in GaAs-based quantum wells, comparing numerical solutions with experimental data to validate the models.

Contribution

It introduces a high-precision numerical approach for exciton modeling in quantum wells and compares it with variational methods and experimental results.

Findings

Calculated exciton binding energies agree within 0.1 meV of variational results.

Radiative decay rates from calculations match experimental data well.

The approach improves accuracy over earlier theoretical estimates.

Abstract

The binding energy and the corresponding wave function of excitons in GaAs-based finite square quantum wells (QWs) are calculated by the direct numerical solution of the three-dimensional Schroedinger equation. The precise results for the lowest exciton state are obtained by the Hamiltonian discretization using the high-order finite-difference scheme. The microscopic calculations are compared with the results obtained by the standard variational approach. The exciton binding energies found by two methods coincide within 0.1 meV for the wide range of QW widths. The radiative decay rate is calculated for QWs of various widths using the exciton wave functions obtained by direct and variational methods. The radiative decay rates are confronted with the experimental data measured for high-quality GaAs/AlGaAs and InGaAs/GaAs QW heterostructures grown by molecular beam epitaxy. The calculated and measured values are in good agreement, though slight differences with earlier calculations of the radiative decay rate are observed.