Light scattering on free electrons in semiconductors in the presence of electron-relaxation processes

The cross section for the scattering of light is obtained for the screened single-particle excitations and the collective plasma modes of a single parabolic band, taking into account the different electron-scattering processes. The dielectric constant in the random-phase approximation is evaluated, including the effect of energy-dependent electron-relaxation processes. Thereby, the conservation of the local electron number is observed. We find that with an increasing scattering rate the line shape of the single-particle spectrum changes from a Gaussian to a Lorentzian form and the shape of the plasma-mode spectrum is shifted and broadened by the collisions. The details of the line shapes, as a function of the frequency $\omega$ and the temperature $T$, are determined by the energy dependence of the relaxation rate. The general theoretical results are used for a comparison with experimental data on GaAs.