Electron transport in the presence of random impurities: Transition from ballistic to diffusive regimes

A transport theory is developed for multibarrier mesoscopic devices that contain a random configuration of short-range impurity potentials. The theory is based on the self-consistent second Born approximation within the Keldysh formulation. The self-energy of the system is estimated to describe the average two-terminal resistance of an ensemble of nearly identical systems. The theory describes the transition from the ballistic to the diffusive regime of operation as a function of a disorder parameter characterizing the density as well as the strength of the impurities. It is shown that as the strengths of the elastic tunnel barriers are increased, the transition from ballistic to diffusion regime occurs at larger values of the disorder parameter.