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Modelling nonlocal processes in semiconductor devices with exponential difference schemes

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Abstract

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.

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Authors and Affiliations

  1. Mathematical Modelling of Industrial Processes, CSIRO Mathematical and Information Sciences – Sydney, Locked Bag 17, North Ryde, NSW, 1670, Australia

    R.V.N. Melnik

  2. Department of Theoretical Physics, School of Physics, University of Sydney, NSW, 2006, Australia

    Hao He

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  2. Hao He
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Melnik, R., He, H. Modelling nonlocal processes in semiconductor devices with exponential difference schemes. Journal of Engineering Mathematics 38, 233–263 (2000). https://doi.org/10.1023/A:1004783723500

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