Energy exchange in 2D electron-electron collisions with dynamic screening

The rapidity of thermalization processes within an excited electron gas is determined by the rate at which substantial energy exchanges can occur. To calculate the rate of such processes, as distinct from calculating the rate of scattering (which is the rate usually calculated), it is necessary to take into account the dynamic nature of screening. It is shown that this can be carried out analytically for the case of a non-degenerate electron gas in a 2D quantum well within the random-phase approximation. The results indicate resonant screening and anti-screening effects associated with the response of the polar lattice in a semiconductor. These effects are illustrated in the case of GaN at 77 K.