Multi-scale modelling of the electron transport via a metal-semiconductor interface is carried out by coupling ab initio calculations with three-dimensional finite element ensemble Monte Carlo simulations. The results for the studied Mo/GaAs structure show that the metal's effect on the electronic properties of the semiconductor varies with the distance from the interface. Introducing this variation into Monte Carlo simulations strongly impacts the resultant transport characteristics of the system. We find that, in the case of an atomically abrupt interface, the variation in the electronic properties is on a large enough scale that treating the interface as abrupt in transport simulations is invalid. In particular, the band gap narrowing near the interface lowers the interface resistivity by more than one order of magnitude with respect to that calculated for the idealized Schottky contact: from 2.1×10 −8 to 4.7×10 −10 cm 2 . The dependence of the electron effective mass from the distance to the interface also plays an important role bringing the resistivity to 7.9×10 −10 cm 2 .