Numerical simulation of exciton dynamics in Cu(2)O at ultra-low temperatures within a potential trap

We have studied theoretically the relaxation behaviour of excitons in cuprous oxide (Cu(2)O) at ultra-low temperatures when excitons are confined within a potential trap by solving numerically the Boltzmann equation. As relaxation processes, we have included in this paper deformation potential phonon scattering, radiative and non-radiative decay and Auger decay. The relaxation kinetics has been analysed for temperatures in the range between 0.3 and 5?K. Under the action of deformation potential phonon scattering only, we find for temperatures above 0.5?K that the excitons reach local equilibrium with the lattice, i.e.?that the effective local temperature is coming down to the bath temperature, while below 0.5?K a non-thermal energy distribution remains. Interestingly, for all temperatures the global spatial distribution of excitons does not reach the equilibrium distribution, but stays at a much higher effective temperature. If we include further a finite lifetime of the excitons and the two-particle Auger decay, we find that both the local and the global effective temperature do not come down to the bath temperature. In the first case we find that a Bose-Einstein condensation (BEC) occurs for all temperatures in the investigated range. Comparing our results with the thermal equilibrium case, we find that BEC occurs for a significantly higher number of excitons in the trap. This effect could be related to the higher global temperature, which requires an increased number of excitons within the trap to observe the BEC. In the case of Auger decay, we do not find a BEC at any temperature due to the local heating of the exciton gas.