Single-particle relaxation time versus scattering time in an impure electron gas

Abstract

Relative magnitudes of the single-particle relaxation time and the scattering time that enters in conductivity are given for two- and three-dimensional electron gases in the presence of random distributions of charged Coulomb scattering centers. We find that for accessible electron densities in the usual three-dimensional metallic systems the scattering time is at most a factor of \ensuremath{\sim}2 larger than the single-particle relaxation time whereas in high-mobility GaAs-based heterojunctions the spatial separation between the impurities and the carriers gives rise to scattering times which can be as much as two orders of magnitude larger than the corresponding single-particle relaxation times.