Modelling nonlocal processes in semiconductor devices with exponential difference schemes

In this paper nonlocal quasi-hydrodynamic mathematical models describing no n-equilibrium physical processes in semiconductor devices are considered. T hese processes cannot be adequately described with conventional drift-diffu sion models. The primary numerical difficulty arises in the energy balance equation. Details of the discretisation for the continuity equations will b e described along with a transformation of the energy balance equations to give computationally convenient forms. Effective exponential difference sch emes are constructed and applied to modelling transport phenomena in semico nductors. Stability conditions, computational convergence and algorithmic r ealisations of the proposed schemes are discussed and numerical examples ar e given.