Properties of the electron-hole drop inn-doped germanium and silicon

The gas-liquid transition of an electron-hole plasma is studied under the influence of a donor electron system of density $n_D^{-}$. It is found that the density of holes within the drop decreases with increasing $n_D^{-}$. The width of the electron-hole recombination line calculated from the joint density of states, is found to go through a minimum in agreement with experiment. It is further shown that the behavior of the linewidth reflects the nature of the impurity-induced semiconductor-metal transition. It is therefore possible to construct the underlying change of the free-carrier density with doping which is demonstrated for Si: P. Condensation seems to occur up to high doping levels. It might also be expected in a number of heavily doped (metallic) semiconductors, for which the metallic phase is not stable with respect to exciton formation under normal conditions.