Voltage-current characteristics of a $pn$-diode from a drift-diffusion model with nonlinear diffusion
Authors:
Ansgar Jüngel and Christian Schmeiser
Journal:
Quart. Appl. Math. 55 (1997), 707-721
MSC:
Primary 78A55; Secondary 35R35
DOI:
https://doi.org/10.1090/qam/1486544
MathSciNet review:
MR1486544
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Abstract: A drift-diffusion model with density-dependent diffusion coefficients for the flow of electrons and holes in a semiconductor crystal is considered. It contains a new class of models for recombination-generation effects as well as boundary conditions modelling Ohmic contacts. Existence of steady-state solutions is proven. For a planar $pn$-diode the qualitative properties of steady-state solutions in dependence on the applied voltage is examined and, in particular, voltage-current characteristics are discussed.
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- A. Unterreiter, Vacuum and non-vacuum solutions of the quasi-hydrodynamic semiconductor model in thermal equilibrium, Math. Methods Appl. Sci. 18 (1995), no. 3, 225–254. MR 1317017, DOI https://doi.org/10.1002/mma.1670180304
A. Jüngel, The free boundary problem of a semiconductor in thermal equilibrium, Math. Meth. in the Appl. Sci. 18, 387–412 (1995)
A. Jüngel, Numerical approximation of a drift-diffusion model for semi-conductors with nonlinear diffusion, ZAMM 75, 783–799 (1995)
P. A. Markowich, C. Ringhofer, and C. Schmeiser, Semiconductor Equations, Springer-Verlag, Wien, 1990
P. A. Markowich and A. Unterreiter, Vacuum solutions of a stationary drift-diffusion model, Ann. d. Scuola Normale Sup. Pisa 20, 371–386 (1993)
A. Unterreiter, Vacuum and non-vacuum solutions of the quasi-hydrodynamic semiconductor model in thermal equilibrium, Math. Meth. in the Appl. Sci. 18, 225–254 (1995)
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Article copyright:
© Copyright 1997
American Mathematical Society
