Global zero-relaxation limit of the non-isentropic Euler–Poisson system for ion dynamics

2020 ◽  
Vol 120 (3-4) ◽  
pp. 301-318
Author(s):  
Yuehong Feng ◽  
Xin Li ◽  
Shu Wang
Keyword(s):  
Relaxation Time ◽  
Energy Estimates ◽  
Ion Dynamics ◽  
Poisson System ◽  
Smooth Solutions ◽  
Drift Diffusion ◽  
Limit System ◽  
Momentum Relaxation ◽  
Global Zero ◽  
Compactness Arguments

This paper is concerned with smooth solutions of the non-isentropic Euler–Poisson system for ion dynamics. The system arises in the modeling of semi-conductor, in which appear one small parameter, the momentum relaxation time. When the initial data are near constant equilibrium states, with the help of uniform energy estimates and compactness arguments, we rigorously prove the convergence of the system for all time, as the relaxation time goes to zero. The limit system is the drift-diffusion system.

ON THE 3-D BIPOLAR ISENTROPIC EULER–POISSON MODEL FOR SEMICONDUCTORS AND THE DRIFT-DIFFUSION LIMIT

2000 ◽  
Vol 10 (03) ◽  
pp. 351-360 ◽  
Author(s):  
CORRADO LATTANZIO
Keyword(s):  
Relaxation Time ◽  
Weak Solutions ◽  
Hydrodynamic Model ◽  
Poisson Model ◽  
Diffusion System ◽  
Diffusion Limit ◽  
Poisson System ◽  
Drift Diffusion ◽  
Bipolar Hydrodynamic Model

The aim of this paper is the study of the relaxation limit of the 3-D bipolar hydrodynamic model for semiconductors. We prove the convergence for the weak solutions to the bipolar Euler–Poisson system towards the solutions to the bipolar drifthyphen;diffusion system, as the relaxation time tends to zero.

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.

Acoustic Phonon and Surface Roughness Spin Relaxation Mechanisms in Strained Ultra-Scaled Silicon Films

2013 ◽  
Vol 854 ◽  
pp. 29-34 ◽  
Author(s):  
Dmitry Osintsev ◽  
V. Sverdlov ◽  
Siegfried Selberherr
Keyword(s):  
Surface Roughness ◽  
Relaxation Time ◽  
Spin Relaxation ◽  
Momentum Space ◽  
Acoustic Phonon ◽  
Soi Mosfet ◽  
Momentum Relaxation ◽  
Strained Films ◽  
The Impact ◽  
Strong Spin

We consider the impact of the surface roughness and phonon induced relaxation on transport and spin characteristics in ultra-thin SOI MOSFET devices. We show that the regions in the momentum space, which are responsible for strong spin relaxation, can be efficiently removed by applying uniaxial strain. The spin lifetime in strained films can be improved by orders of magnitude, while the momentum relaxation time determining the electron mobility can only be increased by a factor of two.

RELAXATION TIME APPROXIMATION FOR ELECTRON-PHONON INTERACTION IN SEMICONDUCTORS

1995 ◽  
Vol 05 (04) ◽  
pp. 519-527 ◽  
Author(s):  
PETER A. MARKOWICH ◽  
CHRISTIAN SCHMEISER
Keyword(s):  
Relaxation Time ◽  
Hydrodynamic Limit ◽  
Asymptotic Methods ◽  
Drift Diffusion Model ◽  
Phonon Interaction ◽  
Drift Diffusion ◽  
Time Model ◽  
Electron Phonon Interaction ◽  
Relaxation Time Approximation ◽  
Equilibrium Distributions

A Boltzmann equation for semiconductors is considered. Physical assumptions include the parabolic band approximation and a new relaxation time model for electron-phonon interaction. Thermal equilibrium distributions for this scattering mechanism are products of Maxwellian distributions with periodic functions of the energy, where the period is the energy of a phonon. The hydrodynamic limit is considered and a drift-diffusion model is derived by formal asymptotic methods.

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