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References (12)
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M. Mock (1986)
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M. Mock (1983)
ANALYSIS OF A DISCRETIZATION ALGORITHM FOR STATIONARY CONTINUITY EQUATIONS IN SEMICONDUCTOR DEVICE MODELS, IICompel-the International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 3
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M. Sever, P. Markowich (1987)
The Stationary Semiconductor Device Equations.Mathematics of Computation, 49
- Publisher
- Emerald Publishing
- Copyright
- Copyright © Emerald Group Publishing Limited
- ISSN
- 0332-1649
- DOI
- 10.1108/eb010033
- Publisher site
- See Article on Publisher Site
Abstract
A new algorithm is presented for the discretization of semiconductor models in one space dimension plus time. A complete error analysis is given, showing that the discretization errors do not depend on any derivatives of illbehaved quantities such as carrier densities. In this algorithm, the electrostatic potential is updated from a discretization of the equation of total current continuity, and parabolic equations for the current densities are discretized, rather than those for the carrier densities. Projection methods, e.g. simple finiteelement methods, are used for the space discretization. The equations for the current densities are similar to the familiar ScharfetterGummel expressions in the stationary limit. However, the discrete timedependent current densities are required here to be H1 functions of x, obtained in a space with at least second order approximation property in L2. This method is fully compatible with recently developed methods for uncoupling the discrete systems to be solved at each time step, for an individual device or when a given problem involves multiple, coupled devices.
Journal
COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering – Emerald Publishing
Published: Mar 1, 1987