Transients of the photoluminescence intensities of the electron-hole droplets in pure and doped Ge

We have measured the electron-hole-droplet (EHD) luminescence intensities in pure and doped Ge as a function of time at 2 and 4.2°K. Surface-excitation pulses 50 to 100 μsec in length were used. The EHD intensities were found to reach steady-state levels after several tens of microseconds. The decay of the EHD luminescence intensity in pure Ge at 4.2°K was too slow to be explained by the previously accepted model. The decay at 2°K of the luminescence intensity of the EHD in Ge doped with ∼ ${10}^{15}$ ${\mathrm{cm}}^{-3\mathrm{}}$ of impurities was found to be identical to that in pure Ge, i.e., exponential decay with lifetime of 37 μsec; however, very little effect due to evaporation of excitons was observed at 4.2°K. A new model of the decay of the luminescence intensity of EHD is presented. This model is based on the existence of a cloud of EHD's and it incorporates (i) exciton flow among EHD's in the cloud and (ii) exciton diffusion out of the cloud. This model explains the decay of the EHD luminescence in both pure and doped Ge. In particular, this model shows that the size of the cloud of EHD's can affect the EHD decay at high temperatures and the reduction of free-exciton diffusion length can shut off the effect of exciton evaporation on the decay transients in doped Ge.