Bose-Einstein statistics in thermalization and photoluminescence of quantum well excitons

TL;DR

This paper develops a thermodynamic model to understand how Bose-Einstein statistics affect the thermalization and photoluminescence of excitons in quantum wells, revealing density-dependent dynamics and slowed thermalization at low temperatures.

Contribution

It introduces a quantum-statistical thermodynamic framework for exciton thermalization and photoluminescence in quantum wells, highlighting nonexponential behavior and lifetime modifications due to Bose-Einstein effects.

Findings

Thermalization slows down at low temperatures, with $T(t) \, \propto \, 1/\ln t$.

Optical lifetime of degenerate excitons is doubled compared to intrinsic lifetime.

Photoluminescence dynamics depend on exciton density and degeneracy.

Abstract

Quasi-equilibrium relaxational thermodynamics is developed to understand LA-phonon-assisted thermalization of Bose-Einstein distributed excitons in quantum wells. We study the quantum-statistical effects in the relaxational dynamics of the effective temperature of excitons $T = T(t)$. When $T$ is less than the degeneracy temperature $T_0$, well-developed Bose-Einstein statistics of quantum well excitons leads to nonexponential and density-dependent thermalization. At low bath temperatures $T_b \to 0$ the thermalization of quantum-statistically degenerate excitons effectively slows down and $T(t) \propto 1 / \ln t$. We also analyze the optical decay of Bose-Einstein distributed excitons in perfect quantum wells and show how nonclassical statistics influences the effective lifetime $\tau_{opt}$. In particular, $\tau_{opt}$ of a strongly degenerate gas of excitons is given by $2 \tau_R$, where $\tau_R$ is the intrinsic radiative lifetime of quasi-two-dimensional excitons. Kinetics of resonant photoluminescence of quantum well excitons during their thermalization is studied within the thermodynamic approach and taking into account Bose-Einstein statistics. We find density-dependent photoluminescence dynamics of statistically degenerate excitons. Numerical modeling of the thermalization and photoluminescence kinetics of quasi-two-dimensional excitons are given for GaAs/AlGaAs quantum wells.