Numerical Approximation of a Drift‐Diffusion Model for Semiconductors with Nonlinear Diffusion

DOI10.1002/zamm.19950751016zbMath0866.35056OpenAlexW2110017567MaRDI QIDQ5691223

Ansgar Jüngel

Publication date: 24 July 1997

Published in: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/zamm.19950751016

zbMATH Keywords

vacuum solutionsmixed exponential fitting method

Mathematics Subject Classification ID

Degenerate parabolic equations (35K65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Motion of charged particles (78A35)

Related Items (13)

Stationary equations for charge carriers in semiconductors including electron-hole scattering ⋮ Positive Scharfetter-Gummel finite volume method for convection-diffusion equations on polygonal meshes ⋮ FINITE VOLUME APPROXIMATION FOR DEGENERATE DRIFT-DIFFUSION SYSTEM IN SEVERAL SPACE DIMENSIONS ⋮ Exponential decay of a finite volume scheme to the thermal equilibrium for drift-diffusion systems ⋮ Computational and analytical comparison of flux discretizations for the semiconductor device equations beyond Boltzmann statistics ⋮ Diffusive semiconductor moment equations using Fermi-Dirac statistics ⋮ Solution of variable‐order partial integro‐differential equation using Legendre wavelet approximation and operational matrices ⋮ A finite volume scheme for convection-diffusion equations with nonlinear diffusion derived from the Scharfetter-Gummel scheme ⋮ Discrete duality finite volume schemes for two‐dimensional drift‐diffusion and energy‐transport models ⋮ Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis ⋮ Numerical solutions of Euler-Poisson systems for potential flows ⋮ Unnamed Item ⋮ On a quasilinear degenerate system arising in semiconductor theory. Part II: Localization of vacuum solutions

Cites Work

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• On steady state Euler-Poisson models for semiconductors
• The thermal equilibrium state of semiconductor devices
• A Singular Perturbation Analysis of the Fundamental Semiconductor Device Equations
• Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations
• Two-Dimensional Exponential Fitting and Applications to Drift-Diffusion Models
• Vacuum and non‐vacuum solutions of the quasi‐hydrodynamic semiconductor model in thermal equilibrium
• Semiconductor Equations for variable Mobilities Based on Boltzmann Statistics or Fermi-Dirac Statistics
• The free boundary problem of a semiconductor in thermal equilibrium
• A Singularly Perturbed Boundary Value Problem Modelling a Semiconductor Device

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