High-bias quantum electron transport

Abstract

High-bias, steady-state electron transport in small systems is modeled using the non-equilibrium Green's function formalism of Keldysh, Kadanoff and Baym. Using a model of local oscillators for the phonons simplifies the coupled equations for G ≶, G R, Σ ≶ and Σ R. The equations are numerically solved in real-space, r and r′ and energy, E. When an Einstein phonon spectrum is used for the oscillators, the local oscillator model corresponds precisely to dispersionless, deformation-potential, optical phonons. The electron-phonon interaction is treated in the self-consistent first- Born approximation. Example calculations are presented showing the effect of inelastic scattering on the energy dependence of the current density through a 1-D, multi-resonant-state, double-barrier structure and the occupation of an emitter quasi-bound state in a 3-D double-barrier structure.