A multi-scale modeling of 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 Mo/GaAs (001) interface show that variations of the electronic properties with the distance from the interface have a strong impact on the transport characteristics. In particular, the calculated tunneling barrier differs dramatically from that of the ideal Schottky model of an abrupt metal-semiconductor interface. The band gap narrowing near the interface lowers resistivity by more than one order of magnitude: from 2.1×10-8 Ωcm² to 4.7×10-10 Ωcm². The dependence of the electron effective mass from the distance to the interface also plays an important role bringing resistivity to 7.9×10-10 Ωcm².