Diffusive semiconductor moment equations using Fermi-Dirac statistics
type: Item
instance of: scholarly article
title: Diffusive semiconductor moment equations using Fermi-Dirac statistics
zbMATH Open document ID: 1276.82063
author: Stefan Krause
author: Paola Pietra
author: Ansgar Jüngel
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2013-02-04T00:00:00Z
review text: Extending a previous work, the authors formulate a diffusive moment model for charge transport in semiconductors using a Fermi-Dirac statistics instead of the previously employed Maxwell-Boltzmann one. The balance equations are derived by using the moments of the Boltzmann equation written in the diffusion scaling. The closure relations are obtained by applying the maximum entropy principle with a generalized Fermi-Dirac statistics, and by performing a Chapman-Enskog expansion. The weight functions entering in the definition of the moments are taken as powers of the energy. Under the main assumption that the collision term can be split into the sum of a dominant term conserving the basic moments and a second-order correction, along with some technical assumptions, a general model of diffusive macroscopic equations is obtained. A symmetric formulation is also deduced with the introduction of appropriate entropic variable. This allows to get an entropy-entropy dissipative relation. For particular choices of the energy band and moments, explicit drift-diffusion and energy transport models are obtained, and their degeneracy limit is studied.
reviewed by: Vittorio Romano
Mathematics Subject Classification ID: 82D37
Mathematics Subject Classification ID: 35Q20
Mathematics Subject Classification ID: 82C70
zbMATH DE Number: 6134348
zbMATH Keywords: semiconductor Boltzmann equation
zbMATH Keywords: moment method
zbMATH Keywords: Fermi-Dirac statistics
zbMATH Keywords: entropy maximization
zbMATH Keywords: drift-diffusion equations
zbMATH Keywords: energy-transport equations
MaRDI profile type: Publication
full work available at URL: s00033-010-0106-z
OpenAlex ID: W2157006389
cites work: Thermodynamic design of energy models of semiconductor devices
cites work: Thermodynamic derivation of the hydrodynamical model for charge transport in semiconductors
cites work: On a hierarchy of macroscopic models for semiconductors
cites work: An energy-transport model for semiconductors derived from the Boltzmann equation.
cites work: Diffusion Approximation and Homogenization of the Semiconductor Boltzmann Equation
cites work: Asymptotic behaviour of a finite-volume scheme for the transient drift-diffusion model
cites work: FINITE VOLUME APPROXIMATION FOR DEGENERATE DRIFT-DIFFUSION SYSTEM IN SEVERAL SPACE DIMENSIONS
cites work: High electric field approximation to charge transport in semiconductor devices
cites work: Maximisation of the entropy in non-equilibrium
cites work: On the approximation of the Fokker-Planck equation by moment systems
cites work: Semiconductor Equations for variable Mobilities Based on Boltzmann Statistics or Fermi-Dirac Statistics
cites work: Q4031474
cites work: On fluid limit for the semiconductors Boltzmann equation
cites work: Existence of weak solutions to a degenerate time-dependent semiconductor equations with temperature effect
cites work: ON THE EXISTENCE AND UNIQUENESS OF TRANSIENT SOLUTIONS OF A DEGENERATE NONLINEAR DRIFT-DIFFUSION MODEL FOR SEMICONDUCTORS
cites work: Numerical Approximation of a Drift‐Diffusion Model for Semiconductors with Nonlinear Diffusion
cites work: Q4869443
cites work: A Nonlinear Drift ‐ Diffusion System with Electric Convection Arising in Electrophoretic and Semiconductor Modeling
cites work: A Hierarchy of Diffusive Higher-Order Moment Equations for Semiconductors
cites work: A Discretization Scheme for a Quasi-Hydrodynamic Semiconductor Model
cites work: Moment closure hierarchies for kinetic theories.
cites work: Q4296241
cites work: Charge transport in semiconductors with degeneracy effects
cites work: Q4283530
DOI: 10.1007/S00033-010-0106-Z
description: scientific article; zbMATH DE number 6134348