Scattering time and single-particle relaxation time in a disordered two-dimensional electron gas

Abstract

We calculate the scattering time (which determines the conductivity) and the single-particle relaxation time (which determines the density of states) for a disordered two-dimensional electron gas in lowest order of the electron-impurity interaction. Analytical results and numerical results for remote impurity doping, homogeneous background doping, interface roughness scattering, and alloy disorder scattering in ${\mathrm{In}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Ga}}_{\mathrm{x}}$As quantum wells are presented. Self-consistency effects are also included and provide a theoretical frame for estimating the validity of the results calculated in lowest order of the electron-impurity interaction. A logarithmic singularity is found for the single-particle relaxation time in the case of homogeneous background doping.