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 |
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EDP SCIENCES S A
1994
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/85589 |
| _version_ | 1848764745905078272 |
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| author | Miller, J.J.H. Wang, Song |
| author_facet | Miller, J.J.H. Wang, Song |
| author_sort | Miller, J.J.H. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T11:24:15Z |
| format | Journal Article |
| id | curtin-20.500.11937-85589 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:24:15Z |
| publishDate | 1994 |
| publisher | EDP SCIENCES S A |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-855892021-10-01T00:13:31Z An analysis of the Scharfetter-Gummel box method for the stationary semiconductor device equations Miller, J.J.H. Wang, Song Science & Technology Physical Sciences Mathematics, Applied Mathematics NONSYMMETRIC LINEAR-SYSTEMS DISCRETIZATION ALGORITHM CONTINUITY EQUATIONS MODELS 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. 1994 Journal Article http://hdl.handle.net/20.500.11937/85589 10.1051/m2an/1994280201231 English EDP SCIENCES S A unknown |
| spellingShingle | Science & Technology Physical Sciences Mathematics, Applied Mathematics NONSYMMETRIC LINEAR-SYSTEMS DISCRETIZATION ALGORITHM CONTINUITY EQUATIONS MODELS Miller, J.J.H. Wang, Song An analysis of the Scharfetter-Gummel box method for the stationary semiconductor device equations |
| title | An analysis of the Scharfetter-Gummel box method for the stationary semiconductor device equations |
| title_full | An analysis of the Scharfetter-Gummel box method for the stationary semiconductor device equations |
| title_fullStr | An analysis of the Scharfetter-Gummel box method for the stationary semiconductor device equations |
| title_full_unstemmed | An analysis of the Scharfetter-Gummel box method for the stationary semiconductor device equations |
| title_short | An analysis of the Scharfetter-Gummel box method for the stationary semiconductor device equations |
| title_sort | analysis of the scharfetter-gummel box method for the stationary semiconductor device equations |
| topic | Science & Technology Physical Sciences Mathematics, Applied Mathematics NONSYMMETRIC LINEAR-SYSTEMS DISCRETIZATION ALGORITHM CONTINUITY EQUATIONS MODELS |
| url | http://hdl.handle.net/20.500.11937/85589 |