Abstract
In this paper we analyse a special-purpose finite difference scheme for the basic stationary semiconductor device equations in one space dimension. These equations model potential distribution, carrier concentration and current flow in an arbitrary one-dimensional semiconductor device and they consist of three second order ordinary differential equations subject to boundary conditions. A small parameter appears as multiplier of the second derivative of the potential, thus the problem is singularly perturbed. We demonstrate the occurence of internal layers at so called device-junctions, which are jump-discontinuities of the data, and present a finite difference scheme which allows for the resolution of these internal layers without employing an exceedingly large number of grid-points. We establish the relation of this scheme to exponentially fitted schemes and give a convergence proof. Moreover the construction of efficient grids is discussed.
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References
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© 1985 Birkhäuser Boston, Inc.
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Markowich, P.A. (1985). A Finite Difference Method for the Basic Stationary Semiconductor Device Equations. In: Ascher, U.M., Russell, R.D. (eds) Numerical Boundary Value ODEs. Progress in Scientific Computing, vol 5. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-5160-6_17
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DOI: https://doi.org/10.1007/978-1-4612-5160-6_17
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-9590-7
Online ISBN: 978-1-4612-5160-6
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