Multiple scattering in a vacuum barrier obtained from real-space wavefunctions

Abstract

We have developed a method for simulating multiple electron scattering in a vacuumbarrier using real-space single-electron wavefunctions for the separate surfaces. The Greenfunctions in the vacuum barriers are calculated to first order in the Dyson series. We findthat the zero-order current is equal to the usual Bardeen approach only in the limit ofzero bias and derive the modifications in the finite bias regime. We also derive afirst-principles formulation for the energy of interaction between the two surfaces,and show that it is proportional to the tunnelling current. With this method thetunnelling current can in principle be computed to any order in the Dyson expansion.