scholarly journals On the entropy method and exponential convergence to equilibrium for a recombination–drift–diffusion system with self-consistent potential

2018 ◽  
Vol 79 ◽  
pp. 196-204 ◽  
Author(s):  
Klemens Fellner ◽  
Michael Kniely
Keyword(s):  
Exponential Convergence ◽  
Entropy Method ◽  
Diffusion System ◽  
Convergence To Equilibrium ◽  
Drift Diffusion ◽  
Self Consistent

scholarly journals Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model

2020 ◽  
Vol 6 (2) ◽  
pp. 529-598
Author(s):  
Klemens Fellner ◽  
Michael Kniely
Keyword(s):  
Intermediate Energy ◽  
Entropy Method ◽  
Mass Action ◽  
Convergence To Equilibrium ◽  
System Modelling ◽  
Trap Level ◽  
Drift Diffusion ◽  
Recombination System ◽  
State Approximation ◽  
Steady State Approximation

Abstract In this paper, we establish convergence to equilibrium for a drift–diffusion–recombination system modelling the charge transport within certain semiconductor devices. More precisely, we consider a two-level system for electrons and holes which is augmented by an intermediate energy level for electrons in so-called trapped states. The recombination dynamics use the mass action principle by taking into account this additional trap level. The main part of the paper is concerned with the derivation of an entropy–entropy production inequality, which entails exponential convergence to the equilibrium via the so-called entropy method. The novelty of our approach lies in the fact that the entropy method is applied uniformly in a fast-reaction parameter which governs the lifetime of electrons on the trap level. Thus, the resulting decay estimate for the densities of electrons and holes extends to the corresponding quasi-steady-state approximation.

scholarly journals On a Drift–Diffusion System for Semiconductor Devices

2016 ◽  
Vol 17 (12) ◽  
pp. 3473-3498 ◽  
Author(s):  
Rafael Granero-Belinchón
Keyword(s):  
Semiconductor Devices ◽  
Diffusion System ◽  
Drift Diffusion

scholarly journals Generalized Logarithmic Hardy–Littlewood–Sobolev Inequality

2019 ◽  
Author(s):  
Jean Dolbeault ◽  
Xingyu Li
Keyword(s):  
Sobolev Inequality ◽  
Nonlinear Diffusion ◽  
Opposite Sign ◽  
Entropy Method ◽  
Nonlinear Diffusion Equation ◽  
Sobolev Inequalities ◽  
Poisson System ◽  
Drift Diffusion ◽  
Reverse Inequality ◽  
Logarithmic Growth

Abstract This paper is devoted to logarithmic Hardy–Littlewood–Sobolev inequalities in the 2D Euclidean space, in the presence of an external potential with logarithmic growth. The coupling with the potential introduces a new parameter, with two regimes. The attractive regime reflects the standard logarithmic Hardy–Littlewood–Sobolev inequality. The 2nd regime corresponds to a reverse inequality, with the opposite sign in the convolution term, which allows us to bound the free energy of a drift–diffusion–Poisson system from below. Our method is based on an extension of an entropy method proposed by E. Carlen, J. Carrillo, and M. Loss, and on a nonlinear diffusion equation.

scholarly journals Uniform-in-time bounds for approximate solutions of the drift–diffusion system

2019 ◽  
Vol 141 (4) ◽  
pp. 881-916
Author(s):  
M. Bessemoulin-Chatard ◽  
C. Chainais-Hillairet
Keyword(s):  
Approximate Solutions ◽  
Diffusion System ◽  
Drift Diffusion ◽  
Time Bounds

On the Swendsen-Wang dynamics. I. Exponential convergence to equilibrium

1991 ◽  
Vol 62 (1-2) ◽  
pp. 117-133 ◽  
Author(s):  
Fabio Martinelli ◽  
Enzo Olivieri ◽  
Elisabetta Scoppola
Keyword(s):  
Exponential Convergence ◽  
Convergence To Equilibrium
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