Plasma instabilities in quasi two-dimensional electron gases

Abstract

Recent pulsed optical experiments in n-doped quantum wells (Knox and co-workers, 1988) suggest that hot carriers relax in times as short as 10 fs. A 10 fs thermalization time is an order of magnitude shorter than the inverse plasma frequency. While Monte Carlo calculations (Goodnick and Lugli, 1988) can account for the trends in such hot carrier relaxation experiments, times as short as 10 fs are difficult to understand. As an alternative to single-particle relaxation mechanisms, we have considered the possibility of collective mode instabilities in these systems. In this paper, the longitudinal dielectric function for a quasi-two-dimensional electron gas is calculated, in the random phase approximation, for a plasma with a shell-like, excited component, analogous to that excited in the experiments of Knox, and co-workers. From this dielectric function, the plasma eigenfrequencies are determined. In this excited plasma, intrasubband plasma modes experience gain by inverse Landau damping, via coupling to the energetic electrons. Their repsonse contrast with the Landau damped behavior of the corresponding modes in a three dimensional plasma. The modes with gain are unstable, and experience amplification at rates on the order of the plasma frequency, relaxing energy from the excited distribution. While these growth rates are not fast enough to account for the observed relaxation rates in the n-doped quantum wells studied by Knox, and co-workers, the calculations do indicate an alternative relaxation path, whose rate increases linearly with density, and imply that two-dimensional plasmas are less stable than those in three dimensions.