Mixed finite element approach and nonlinear implicit schemes for drift-diffusion equation solution of 2D heterojunction semiconductor devices
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A. EL Doukili [1] ; A. Marrocco [1]
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[1] French Institute for Research in Computer Science and Automation
French Institute for Research in Computer Science and Automation
Arrondissement de Versailles, Francia
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- Localización: Compel: International journal for computation and mathematics in electrical and electronic engineering, ISSN 0332-1649, Vol. 13, Nº 4, 1994, págs. 609-640
- Idioma: inglés
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Resumen
We present an abstract mathematical and numerical analysis for Drift‐Diffusion equation of heterojunction semiconductor devices with Fermi‐Dirac statistic. For the approximation, a mixed finite element method is considered. This can be profitably used in the investigation of the current through the device structure. A peculiar feature of this mixed formulation is that the electric displacement D and the current densities jn and jp for electrons and holes, are taken as unknowns, together with the potential φ and quas‐Fermi levels φn and φp. This enably D, jn and jp to be determined directly and accurately. For decoupled system, existence, uniqueness, regularity and stability results of the approximate solution are given. A priori and a posteriori error estimates are also presented. A nonlinear implicit scheme with local time steps is used. This algorithm appears to be efficient and gives satisfactory results. Numerical results for an heterojunction bipolar transistor, In two dimension, are presented.
