Lifetime, surface tension, and impurity effects in electron-hole condensation

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Abstract
A theory of electron-hole condensation in germanium and silicon is developed in which recombination, evaporation, and exciton collection are treated as random processes. An expression is derived for the probability distribution of the number of electron-hole pairs bound to a nucleation center. Consideration of the effects of lifetime, surface tension, and nucleation center leads to: (i) the relation of multiexciton complexes to electron-hole droplets; (ii) stable droplet sizes which are strong functions of temperature but only weak functions of pair-generation rate; (iii) the possibility of determining the surface tension from size measurements; and (iv) deviations from the usual phase diagram for a liquid-gas transition at very low temperatures. Detailed numerical calculations are carried out for uniform excitation of germanium and compared to data available from laser excitation experiments.