Convergence of a finite element method for the drift-diffusion semiconductor device equations: The zero diffusion case
In this paper a new explicit finite element method for numerically solving the drift-diffusion semiconductor device equations is introduced and analyzed. The method uses a mixed finite element method for the approximation of the electric field. A finite element method using discontinuous finite elements is used to approximate the concentrations, which may display strong gradients. The use of discontinuous finite elements renders the scheme for the concentrations trivially conservative and fully parallelizable. In this paper we carry out the analysis of the model method (which employs a continuous piecewise-linear approximation to the electric field and a piecewise-constant approximation to the electron concentration) in a model problem, namely, the so-called unipolar case with the diffusion terms neglected. The resulting system of equations if equivalent to a conservation law whose flux, the electric field, depends globally on the solution, the concentration of electrons. By exploiting the similarities of this system with classial scalar conservation laws, the techniques to analyze the monotone schemes for conservation laws are adapted to the analysis of the new scheme. The scheme, considered as a scheme for the electron concentration, is shown to satisfy a maximum principle and to be total variation bounded. Its covergence to the unique weak solution is proven. Numerical experiments displaying the performance of the scheme are shown. 40 refs., 4 figs, 3 tabs.
- OSTI ID:
- 6723045
- Journal Information:
- Mathematics of Computation; (United States), Journal Name: Mathematics of Computation; (United States) Vol. 59:200; ISSN 0025-5718; ISSN MCMPAF
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
426000* -- Engineering-- Components
Electron Devices & Circuits-- (1990-)
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
CALCULATION METHODS
CONSERVATION LAWS
CONVECTION
CONVERGENCE
DIFFUSION
ELECTRIC FIELDS
ELECTRON DRIFT
ENERGY TRANSFER
FINITE ELEMENT METHOD
HEAT TRANSFER
ITERATIVE METHODS
MASS TRANSFER
MATHEMATICAL MODELS
NUMERICAL SOLUTION
RUNGE-KUTTA METHOD
SEMICONDUCTOR DEVICES