Collective Behavior in Solid-State Plasmas

The conditions for the existence of plasma wave instabilities in the plasma formed by the electrons and holes in semiconductors are discussed. The dispersion relations for both the high-frequency optical mode in which electrons and holes move out of phase, and the low-frequency acoustic mode in which electrons and holes move in phase are calculated. Growing acoustic waves are shown to occur for a sufficiently large relative drift velocity of the electrons and holes, and the boundary between growing and damped waves is determined for various electron-hole temperature ratios. Growth rates are calculated for several cases of interest; when the influence of impurity and phonon scattering on the electron-hole behavior is taken into account it is concluded that InSb is perhaps the most promising semiconductor in which to observe such instabilities. An investigation of the hole and electron temperatures and the relative electron-hole drift velocity as a function of field strength is carried out for InSb. It is shown that moderate field strengths (100 v/cm) suffice to produce electron-hole drifts of the required order of magnitude for the observation of plasma wave instability; however, the scattering mechanisms present are sufficiently effective that it appears marginal whether the other condition (long hole relaxation times) necessary for the observation of the plasma wave instability is achievable in practice. In an Appendix the conditions for the occurrence of similar plasma wave instabilities in semimetals are analyzed briefly.