Auger decay of excitons in ${\mathrm{Cu}}_2\mathrm{O}$

The nonradiative recombination of an exciton due to a collision with another exciton (i.e., Auger recombination) is the dominant loss mechanism for excitons at high densities in photoexcited ${\mathrm{Cu}}_2\mathrm{O}.$ The principal evidence is that (a) the observed lifetime of excitons shortens substantially at high densities, and (b) the exciton density increases sublinearly with increasing excitation power. To achieve exciton densities at which this two-body decay process comes into play, the particles are produced within a few micrometers of the crystal surface using intense pulsed excitation with photon energies well above the semiconductor band gap. In the past, determination of the “Auger constant” A in the two-body decay rate, $1/\tau =An,$ was limited by insufficient knowledge of the exciton density n. In the present work, we have determined the density of excitons by (a) measuring their absolute brightness in a calibrated optical system and (b) measuring the expanding volume occupied by the excitons. The luminescence signal following subnanosecond laser excitation exhibits a decay rate which is strongly dependent on the particle density. While some modeling is required to determine the volumes at earliest times, we believe that we have determined the Auger constant to within a factor of 2. The experimental value, $A=7\mathrm{}\times {10}^{-17}\hspace{0.5em}{\mathrm{cm}}^3/\mathrm{n}\mathrm{s},$ is nearly two orders of magnitude larger than that derived from spectroscopic analysis. Such a strong Auger decay prevents the gas from achieving average densities in the quantum statistical regime of an ideal gas.