Landauer formula for transmission across an interface

We reconsider the classical problem of the quantum-mechanical resistance due to a quantum-mechanical reflection off a heterostructure interface. In the presence of a current, the electron distribution in the vicinity of the interface is different from that in the bulk due to the angular dependence of the reflection coefficient. The interface also modifies the electron concentration, leading to a violation of the local neutrality. This creates a self-consistent electric field and affects the angular distribution. The interface resistance depends on the actual form of the electron distribution. Incorporating all these factors in a kinetic transport model, we have reduced evaluation of the resistance to an integral equation. The equation is solved analytically in the limits of either strong or weak reflection. A simple model shows an appreciable difference between our results and the conventional Landauer approach.