Phonon-assisted relaxation kinetics of statistically-degenerate excitons in high-quality quantum wells
Acoustic-phonon-assisted thermalization kinetics of excitons in quantum wells (QWs) is developed for small concentrations of particles, $ρ_{\rm 2D} \lesssim 10^9$ cm$^{-1}$, when particle-particle interaction can be neglected while Bose-Einstein statistics already strongly influences the relaxation processes at low temperatures. In this case thermalization of QW excitons occurs through nonequilibrium states and is given by the following scenario. During the first transient stage, which lasts a few characteristic scattering times, the correlations with an initial distribution of QW excitons disappear. The next, adiabatic stage of thermalization usually takes many characteristic scattering times, depends only upon two control parameters, the lattice temperature $T_b$ and the degeneracy temperature $T_0 \propto ρ_{\rm 2D}$, and is characterized by a quasi-equilibrated distribution of high-energy QW excitons with effective temperature $T(t)$. We show that the thermalization law of high-energy particles is given by $δT(t) = T(t) - T_b \propto e^{-λ_0 t}/t$, where $λ_0$ is a marginal value of the continuous eigenvalue spectrum of the linearized kinetics. By analyzing the linearized phonon-assisted kinetics of statistically-degenerate QW excitons, we study the dependence $λ_0 =λ_0(T_b,T_0)$. Our numerical estimates refer to high quality GaAs and ZnSe QWs. Finally, we propose a special design of GaAs-based microcavities, which considerably weakens the bottleneck effect in relaxation of excitons (polaritons) and allows us to optimize the acoustic-phonon-assisted thermalization processes.