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

Quasiequilibrium relaxational thermodynamics is developed to understand LA-phonon-assisted thermalization of Bose-Einstein distributed excitons in quantum wells. We study quantum-statistical effects in the relaxational dynamics of the effective temperature of excitons $T=T\left(t\right).$ 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 $T\left(t\right)\mathrm{}\propto 1/\ln t.\mathrm{}$ We also analyze the optical decay of Bose-Einstein distributed excitons in perfect quantum wells, and show how nonclassical statistics influences the effective lifetime ${\tau }_{\mathrm{opt}}.$ In particular, ${\tau }_{\mathrm{opt}}$ 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 ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum wells.