Modelling Nonlocal Processes in Semiconductor Devices with Exponential Difference Schemes

Melnik, R.V.N. and He, Hao

Journal of Engineering Mathematics, 38(3), 233-263, 2000


In this paper nonlocal quasi-hydrodynamic mathematical models describing non-equilibrium physical processes in semiconductor devices are considered. These processes cannot be adequately described with conventional drift-diffusion models. The primary numerical difficulty arises in the energy balance equation. Details of the discretisation for the continuity equations will be described along with a transformation of the energy balance equations to give computationally convenient forms. Effective exponential difference schemes are constructed and applied to modelling transport phenomena in semiconductors. Stability conditions, computational convergence and algorithmic realisations of the proposed schemes are discussed and numerical examples are given.