Density dependence of electron scattering at low density

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Abstract
Several recent experiments have measured the rates of momentum relaxation and energy relaxation due to carrier-carrier scattering in GaAs as a function of density in three dimensions and in two dimensions. This paper examines the power laws for the density and temperature dependence of these rates based on the Boltzmann equation for electron-electron scattering, from both analytical arguments and numerical calculations. The experimental scaling with density is deduced for three-dimensional scattering over four orders of magnitude of density variation and two-dimensional scattering over two orders of magnitude. The effects of frequency-dependent terms in the random-phase approximation for the dielectric function are taken into account, as well as the effects of electron-hole scattering.