The initial time layer problem and the quasineutral limit in the semiconductor drift-diffusion model

INGENUIN GASSER; C. DAVID LEVERMORE; PETER A. MARKOWICH; CHRISTIAN SCHMEISER

doi:10.1017/S0956792501004533

Abstract

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The classical time-dependent drift-diffusion model for semiconductors is considered for small scaled Debye length (which is a singular perturbation parameter). The corresponding limit is carried out on both the dielectric relaxation time scale and the diffusion time scale. The latter is a quasineutral limit, and the former can be interpreted as an initial time layer problem. The main mathematical tool for the analytically rigorous singular perturbation theory of this paper is the (physical) entropy of the system.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Gamba, Irene M. and Jüngel, Ansgar 2002. ASYMPTOTIC LIMITS FOR QUANTUM TRAJECTORY MODELS. Communications in Partial Differential Equations, Vol. 27, Issue. 3-4, p. 669.

Jüngel, Ansgar Li, Hailiang Markowich, Peter A. and Wang, Shu 2003. Hyperbolic Problems: Theory, Numerics, Applications. p. 217.

Jüngel, Ansgar and Wang, Shu 2003. Convergence of Nonlinear Schrödinger–Poisson Systems to the Compressible Euler Equations. Communications in Partial Differential Equations, Vol. 28, Issue. 5-6, p. 1005.

SCHMEISER, CHRISTIAN and WANG, SHU 2003. QUASINEUTRAL LIMIT OF THE DRIFT-DIFFUSION MODEL FOR SEMICONDUCTORS WITH GENERAL INITIAL DATA. Mathematical Models and Methods in Applied Sciences, Vol. 13, Issue. 04, p. 463.

Ben Abdallah, Naoufel Méhats, Florian and Vauchelet, Nicolas 2004. A note on the long time behavior for the drift-diffusion-Poisson system. Comptes Rendus. Mathématique, Vol. 339, Issue. 10, p. 683.

Jüngel, Ansgar 2004. Dispersive Transport Equations and Multiscale Models. Vol. 136, Issue. , p. 151.

Gasser, Ingenuin 2004. Dispersive Transport Equations and Multiscale Models. Vol. 136, Issue. , p. 107.

Brezzi, F. Marini, L.D. Micheletti, S. Pietra, P. Sacco, R. and Wang, S. 2005. Numerical Methods in Electromagnetics. Vol. 13, Issue. , p. 317.

Ben Abdallah, Naoufel and Tayeb, Mohamed Lazhar 2005. Diffusion Approximation and Homogenization of the Semiconductor Boltzmann Equation. Multiscale Modeling & Simulation, Vol. 4, Issue. 3, p. 896.

Wang, Shu 2005. Quasineutral Limit of Euler–Poisson System with and without Viscosity. Communications in Partial Differential Equations, Vol. 29, Issue. 3-4, p. 419.

Hsiao, Ling and Wang, Shu 2006. Quasineutral limit of a time-dependent drift–diffusion–Poisson model for p-n junction semiconductor devices. Journal of Differential Equations, Vol. 225, Issue. 2, p. 411.

Wang, Shu and Jiang, Song 2006. The Convergence of the Navier–Stokes–Poisson System to the Incompressible Euler Equations. Communications in Partial Differential Equations, Vol. 31, Issue. 4, p. 571.

WANG, SHU 2006. QUASINEUTRAL LIMIT OF THE MULTI-DIMENSIONAL DRIFT-DIFFUSION-POISSON MODELS FOR SEMICONDUCTORS WITH PN-JUNCTIONS. Mathematical Models and Methods in Applied Sciences, Vol. 16, Issue. 04, p. 537.

Wang, Shu Xin, Zhouping and Markowich, Peter A. 2006. Quasi-neutral Limit of the Drift Diffusion Models for Semiconductors: The Case of General Sign-Changing Doping Profile. SIAM Journal on Mathematical Analysis, Vol. 37, Issue. 6, p. 1854.

Liu, Hailiang and Wang, Zhongming 2007. A field-space-based level set method for computing multi-valued solutions to 1D Euler–Poisson equations. Journal of Computational Physics, Vol. 225, Issue. 1, p. 591.

Goudon, Thierry Miljanović, Vera and Schmeiser, Christian 2007. On the Shockley–Read–Hall Model: Generation-Recombination in Semiconductors. SIAM Journal on Applied Mathematics, Vol. 67, Issue. 4, p. 1183.

Li, Yeping 2007. Asymptotic profile in a one-dimensional steady-state nonisentropic hydrodynamic model for semiconductors. Journal of Mathematical Analysis and Applications, Vol. 325, Issue. 2, p. 949.

Liang, Bo and Zheng, Sining 2008. Exponential decay to a quantum hydrodynamic model for semiconductors. Nonlinear Analysis: Real World Applications, Vol. 9, Issue. 2, p. 326.

Hsiao, Ling Ju, QiangChang and Wang, Shu 2008. Quasi-neutral limit of the drift-diffusion model for semiconductors with general sign-changing doping profile. Science in China Series A: Mathematics, Vol. 51, Issue. 9, p. 1619.

Ju, Qiangchang Li, Fucai and Wang, Shu 2008. Convergence of the Navier–Stokes–Poisson system to the incompressible Navier–Stokes equations. Journal of Mathematical Physics, Vol. 49, Issue. 7,

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The initial time layer problem and the quasineutral limit in the semiconductor drift-diffusion model

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