# 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 (2010)

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

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topWang, 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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