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

Abstract

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.

Acceptor formation in Mg-doped, indium-rich Ga x In1−xN: evidence for p-type conductivity

“…Therefore, the observed weak temperature dependence is more likely to be associated with the latter, i.e. the screening of polar interaction with high carrier density [25,26]. …”

“…m *,  ℏω LO ,  k B ,  T L and τ m are respectively, the effective mass, optical phonon energy Boltzmann's constant, lattice temperature and electron-LO phonon scattering (momentum relaxation) time which is given by [2,25,26]…”

Dynamically screened electron electron scattering in two dimensions

“…Our approach follows that of [26] which we outline here for convenience. We will regard the rate of electron-electron scattering by electrons with the same spin as negligible because of exchange and interference effects.…”

“…Dynamic effects enter into screening via the factor q • v cm , where v cm is the velocity of the centre of mass [29]. It is straightforward to show that this factor is nothing but (E 1 − E 1 )/h which is the frequency associated with the energy loss by the incident electron [26].…”

“…In some studies employing Monte Carlo techniques, details of the interaction are entirely hidden, whether static or dynamic screening is assumed. It is, however, now generally accepted that the ee interaction is, in general, dynamically screened [23][24][25][26][27]. Here, we give an analytic/numerical description of energy and momentum exchange via the dynamically screened ee interaction in a polar lattice.…”