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...

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Main Authors: Miller, J.J.H., Wang, Song
Format: Journal Article
Language:English
Published: EDP SCIENCES S A 1994
Subjects:
Online Access:http://hdl.handle.net/20.500.11937/85589
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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.
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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