Time-dependent behavior in electron-hole condensation

The dominant relaxation rates in electron-hole condensation are calculated from the stochastic rate equations proposed in a previous paper. These govern the time scale for the nucleation of electron-hole droplets and for fluctuations in the number of electron-hole pairs bound to a nucleation center. The calculational procedure makes use of exact recursion relations for the temporal moments of the probability distribution. It is found that metastable states of electrons and holes can exist at high temperatures ($T\gtrsim 2°$K in Ge), for a limited range of ex`citon densities. At low temperatures the finite carrier lifetimes lead to measureably short relaxation times. The importance of the time dependence of the exciton density in experiments at fixed generation rates is stressed. Some of the reported discrepancy between spectroscopic and thermodynamic values of the work function may be ascribed to supersaturation effects.