Electron-Hole Condensation in Semiconductors

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Abstract
In Ge and Si, and also in Ge-Si alloys (74), there is extensive evidence for the stable binding of electrons and holes into a cold plasma of constant density, which undergoes a phase separation. Liquid metallic drops 1 to 300 µm in size are formed, with lifetimes ranging from 0.1 to 600 µsec. For Ge a surprising amount is known: the phase diagram, the surface energy, the work function, the decay kinetics. Much less is known for Si. There is good agreement between theoretical and experimental values of the liquid density, the critical density, the critical temperature, and the binding energy. The stability of the liquid phase is strikingly dependent on band structure. The multivalley structure and mass anisotropy of Si, Ge, and Ge-Si, together with their indirect band gap, are no doubt responsible for the observed stability in these crystals. In the similar semiconductor gallium phosphide, drops have not yet been observed, most likely because the high impurity content traps the excitons. In gallium arsenide the existence of drops is controversial (75). Undoubtedly drops will be found to exist in other semiconductors, perhaps at even higher temperatures. This is an exciting field for the experimentalist; new phenomena are being rapidly discovered, usually before they are predicted. For the theorist, the electron-hole drop is of high intrinsic interest. It represents the first example of a quantum liquid of constant density in a periodic crystal lattice. A number of challenging experimental and theoretical problems remain.