An analysis of the Scharfetter-Gummel box method for the stationary semiconductor device equations
An exponentially fitted box method, known as the Scharfetter-Gummel box method, for the semiconductor device équations in the Slotboom variables is analysed. The method is formulated as a Petrov-Galerkin finite element method with piecewise exponential basis functions on a triangular Delaunay mes...
| Main Authors: | , |
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| Format: | Journal Article |
| Language: | English |
| Published: |
EDP SCIENCES S A
1994
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/85589 |
| Summary: | An exponentially fitted box method, known as the Scharfetter-Gummel box
method, for the semiconductor device équations in the Slotboom variables is analysed. The
method is formulated as a Petrov-Galerkin finite element method with piecewise exponential
basis functions on a triangular Delaunay mesh. No restriction is imposed on the angles in the
triangulation, The stability of the method is proved and an error estimate for the Slotboom
variables in a discrete energy norm is given. When restricted to the two continuity équations the
error estimate dépends only on the first-order seminorm of the exact flux and the approximation
error ofthe zero order and inhomogeneous terms. This is in contrast to standard error estimâtes
which depend on the second order seminorm of the exact solution. The évaluation of the ohmic
contact currents is discussed and it is shown that the approximate ohmic contact currents are
convergent and conservative. |
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