Green’s-function approach to nonlinear electronic transport for an electron-impurity-phonon system in a strong electric field

Abstract

A Green’s-function approach to nonlinear electronic transport in a static electric field is developed microscopically for the system composed of interacting electrons with impurities and phonons. The essential idea is to separate the center-of-mass motion from the relative motion of electrons. An electron temperature is introduced as a measurement of the internal energy of the relative electrons without reference to any distribution function. By allowing different temperatures for decoupled electrons and phonons in the initial state, we obtain the density matrix for the electron-lattice system to the first order of interaction but under arbitrarily strong electric field. The frictional force experienced by the center of mass of electrons and the energy transfer rate from electron system to phonon system are derived by means of the Green’s-function technique, and the force- and energy-balance equations for steady state are obtained. These equations are applied to the calculations of the ratio of electron temperature to the lattice temperature and the electron resistivity as functions of drift velocity for impurity, acoustic-phonon, and optical-phonon scatterings. The dynamic nature of Coulomb screening by charge carriers is studied numerically. One of the interesting predictions is the possible cooling of electrons at low temperatures in samples with low impurity concentration.