Raman scattering in a two-dimensional electron gas: Boltzmann equation approach

The inelastic light scattering in a 2-d electron gas is studied theoretically using the Boltzmann equation techniques. Electron-hole excitations produce the Raman spectrum essentially different from the one predicted for the 3-d case. In the clean limit it has the form of a strong non-symmetric resonance due to the square root singularity at the electron-hole frequency $\omega = vk$ while in the opposite dirty limit the usual Lorentzian shape of the cross section is reestablished. The effects of electromagnetic field are considered self-consistently and the contribution from collective plasmon modes is found. It is shown that unlike 3-d metals where plasmon excitations are unobservable (because of very large required transfered frequencies), the two-dimensional electron system gives rise to a low-frequency ($\omega \propto k^{1/2}$) plasmon peak. A measurement of the width of this peak can provide data on the magnitude of the electron scattering rate.