We present a discussion on the modeling of Schottky barrier rectifying contacts (diodes) within the framework of partial-differential-equation-based physical simulations. We propose a physically consistent generalization of the drift-diffusion model to describe the boundary layer close to the Schottky barrier where thermionic emission leads to a non-Maxwellian carrier distribution, including a novel boundary condition at the contact. The modified drift-diffusion model is validated against Monte Carlo simulations of a GaAs device. The proposed model is in agreement with the Monte Carlo simulations not only in the current value but also in the spatial distributions of microscopic quantities like the electron velocity and concentratio
