Relaxation kinetics of excitons in cuprous oxide

Cuprous oxide is a thoroughly s~udied semiconductor with long-lived, mobile excitons. The kinetic energy distribution of the excitons is reproduced in phonon-assisted luminescence spectra. When non-equilibrium excitons are produced by a laser pulse, nanosecond-time-resolved luminescence reveals the relaxation of their kinetic energy distribution. It has been known for several years that, when the excitons are produced with the highest attainable densities, the time-sequence of exciton kinetic energy distributions closely resembles a sequence of Bose-Einstein distributions, with apparent temperatures greater than that of the lattice. A widely used hypothesis is that the excitons exchange energy through elastic collisions quickly enough to establish a quasi-equilibrium, with the exciton gas having a temperature distinct from that of the lattice. The transient kinetic energy distributions have thus been interpreted simply as quasi-equilibrium distributions, with the gas density near enough the quantum density that the Bose statistics of the excitons is noticeable. This work is an experimental and theoretical study of such luminescence spectra. The absolute brightness of the photoluminescence, compared with that of a known number of excitons, indicates that the density of excitons is at all times too low to reveal their Bose statistics-assuming they act as an ideal gas. The assumption of a quasi-equilibrium among the excitons is abandoned, and the relaxation problem is treated through a Boltzmann equation. Only relaxation processes which have been measured experimentally are included: acoustic phonon emission and absorption, interconversion between spin states, and non-radiative two-exciton decay. Numerical modeling reproduces most of the experimental observations, without invoking Bose statistics.U of I OnlyThesi