Hierarchies of transport equations for nanopores: Equations derived from the Boltzmann equation and the modeling of confined structures

Clemens Heitzinger, Christian Ringhofer

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

We review transport equations and their usage for the modeling and simulation of nanopores. First, the significance of nanopores and the experimental progress in this area are summarized. Then the starting point of all classical and semiclassical considerations is the Boltzmann transport equation as the most general transport equation. The derivation of the drift-diffusion equations from the Boltzmann equation is reviewed as well as the derivation of the Navier–Stokes equations. Nanopores can also be viewed as a special case of a confined structure and hence as giving rise to a multiscale problem, and therefore we review the derivation of a transport equation from the Boltzmann equation for such confined structures. Finally, the state of the art in the simulation of nanopores is summarized.

Original languageEnglish (US)
Pages (from-to)801-817
Number of pages17
JournalJournal of Computational Electronics
Volume13
Issue number4
DOIs
StatePublished - Dec 1 2014

Keywords

  • Boltzmann equation
  • Confined structure
  • Drift-diffusion-Poisson system
  • Model hierarchy
  • Nanopore
  • Navier–Stokes equation

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Modeling and Simulation
  • Electrical and Electronic Engineering

Fingerprint Dive into the research topics of 'Hierarchies of transport equations for nanopores: Equations derived from the Boltzmann equation and the modeling of confined structures'. Together they form a unique fingerprint.

  • Cite this