# A new exponentially fitted triangular finite element method for the continuity equations in the drift-diffusion model of semiconductor devices

• Volume: 33, Issue: 1, page 99-112
• ISSN: 0764-583X

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## Abstract

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In this paper we present a novel exponentially fitted finite element method with triangular elements for the decoupled continuity equations in the drift-diffusion model of semiconductor devices. The continuous problem is first formulated as a variational problem using a weighted inner product. A Bubnov-Galerkin finite element method with a set of piecewise exponential basis functions is then proposed. The method is shown to be stable and can be regarded as an extension to two dimensions of the well-known Scharfetter-Gummel method. Error estimates for the approximate solution and its associated flux are given. These h-order error bounds depend on some first-order seminorms of the exact solution, the exact flux and the coefficient function of the convection terms. A method is also proposed for the evaluation of terminal currents and it is shown that the computed terminal currents are convergent and conservative.

## How to cite

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Wang, Song. "A new exponentially fitted triangular finite element method for the continuity equations in the drift-diffusion model of semiconductor devices." ESAIM: Mathematical Modelling and Numerical Analysis 33.1 (2010): 99-112. <http://eudml.org/doc/197559>.

@article{Wang2010,
abstract = { In this paper we present a novel exponentially fitted finite element method with triangular elements for the decoupled continuity equations in the drift-diffusion model of semiconductor devices. The continuous problem is first formulated as a variational problem using a weighted inner product. A Bubnov-Galerkin finite element method with a set of piecewise exponential basis functions is then proposed. The method is shown to be stable and can be regarded as an extension to two dimensions of the well-known Scharfetter-Gummel method. Error estimates for the approximate solution and its associated flux are given. These h-order error bounds depend on some first-order seminorms of the exact solution, the exact flux and the coefficient function of the convection terms. A method is also proposed for the evaluation of terminal currents and it is shown that the computed terminal currents are convergent and conservative. },
author = {Wang, Song},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {exponential fitting; finite element method; semiconductors.; drift-diffusion model; semiconductor devices; Scharfetter-Gummel method; error bounds},
language = {eng},
month = {3},
number = {1},
pages = {99-112},
publisher = {EDP Sciences},
title = {A new exponentially fitted triangular finite element method for the continuity equations in the drift-diffusion model of semiconductor devices},
url = {http://eudml.org/doc/197559},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Wang, Song
TI - A new exponentially fitted triangular finite element method for the continuity equations in the drift-diffusion model of semiconductor devices
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 1
SP - 99
EP - 112
AB - In this paper we present a novel exponentially fitted finite element method with triangular elements for the decoupled continuity equations in the drift-diffusion model of semiconductor devices. The continuous problem is first formulated as a variational problem using a weighted inner product. A Bubnov-Galerkin finite element method with a set of piecewise exponential basis functions is then proposed. The method is shown to be stable and can be regarded as an extension to two dimensions of the well-known Scharfetter-Gummel method. Error estimates for the approximate solution and its associated flux are given. These h-order error bounds depend on some first-order seminorms of the exact solution, the exact flux and the coefficient function of the convection terms. A method is also proposed for the evaluation of terminal currents and it is shown that the computed terminal currents are convergent and conservative.
LA - eng
KW - exponential fitting; finite element method; semiconductors.; drift-diffusion model; semiconductor devices; Scharfetter-Gummel method; error bounds
UR - http://eudml.org/doc/197559
ER -

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