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    An analysis of the Scharfetter-Gummel box method for the stationary semiconductor device equations

    Access Status
    Open access via publisher
    Authors
    Miller, J.J.H.
    Wang, Song
    Date
    1994
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Miller, J.J.H. and Wang, S. 1994. An analysis of the Scharfetter-Gummel box method for the stationary semiconductor device equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modelisation Mathematique et Analyse Numerique. 28 (2): pp. 123-140.
    Source Title
    ESAIM: Mathematical Modelling and Numerical Analysis - Modelisation Mathematique et Analyse Numerique
    DOI
    10.1051/m2an/1994280201231
    ISSN
    0764-583X
    Faculty
    Faculty of Science and Engineering
    School
    School of Elec Eng, Comp and Math Sci (EECMS)
    URI
    http://hdl.handle.net/20.500.11937/85589
    Collection
    • Curtin Research Publications
    Abstract

    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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