Coulomb lifetime and electronic distribution function in a drifting two-dimensional electron gas.

Abstract

The nonequilibrium distribution function of a two-dimensional electron gas (2DEG) drifting under a high electric field is calculated within the Lei-Ting approach of high-field transport. The separation of the center-of-mass motion from the relative motion of the electrons leads to anisotropic interactions with impurities and phonons that disturb the relative electron gas from a thermodynamic equilibrium state. The correcting amount to the equilibrium momentum distribution function turns out to be the product of the impurity and phonon interactions scattering rate by the particle Coulomb lifetime. This last one is expressed from the full spectral density functions so that its validity extends beyond the quasiparticle theory frame. The importance of a self-consistent calculation is first illustrated by a study of the zero-temperature many-body properties of the Coulomb gas: the plasmaron is shown to be an actual excitation; the threshold for plasmon emission is softened, and undamped Fermi-level particles are found to have a spectral weight nearly equal to unity. Then, within the drifting hot-electron gas, the Doppler shift of the LO-phonon frequencies is shown to enhance the plasmon--LO-phonon coupling. Since the electron--LO-phonon scattering rate is similar to the Coulomb damping rate that characterizes the electron-electron interaction strength, the linear handling of the electron--LO-phonon interaction is questionable for a 2DEG drifting under a high electric field.