Two-body decay of thermalized excitons in ${\mathrm{Cu}}_2\mathrm{O}$

We have examined the decay of thermalized excitons in cuprous oxide $\left({\mathrm{Cu}}_2\mathrm{O}\right)$ and determined their lifetime against two-body decay (i.e., Auger recombination). The experiments are conducted at $T=70\mathrm{}\hspace{0.5em}\mathrm{K}$ with near-resonant picosecond excitation to ensure a thermal equilibrium between orthoexcitons, paraexcitons, and the crystal lattice. Time-resolved spectroscopy reveals the gas reaching equilibrium with the lattice temperature in 0.5 ns. The wavelength of the excitation photons and the spatial distribution of the laser beam are selected to produce a well defined spatial distribution of excitons. Time-resolved photoluminescence imaging measures the diffusion of excitons. From absolute measurements of the gas volume and the luminescence intensity, we determine the instantaneous gas density. At high excitation levels, a rapid nonexponential decay of the excitonic gas is observed. The decay curve is well explained by assuming that the local exciton density is governed by the rate equation $dn/dt=-{\mathrm{An}}^2-n/\tau ,$ with an Auger constant $A=0.6\mathrm{}\times {10}^{-16}\hspace{0.5em}{\mathrm{cm}}^3/\mathrm{n}\mathrm{s}$ and a residual decay time $\tau =300\mathrm{}\hspace{0.5em}\mathrm{ns}.$ This value of the Auger constant is comparable to that estimated previously for a nonthermalized exciton gas at a lattice temperature of 2 K, indicating that the Auger lifetime of an exciton is only weakly dependent on its kinetic energy. The Auger process characterized here defines the practical limits for exciton densities in cuprous oxide.