Finite Element Modeling of Space Charge Phenomena on the Nanoscale

Donald R. Franceschetti

doi:10.4028/www.scientific.net/AST.46.120

Paper Titles

Diffusivity, Solubility and Speciation of Sulphur in Silicate Melts
p.93

Influence of Elasticity of Dislocations on Thermal Motion of Trapped Liquid Pb Inclusions in Al
p.98

Heat Transport in Superlattices and Nanocomposites for Thermoelectric Applications
p.104

In Situ Ultrahigh Vacuum Transmission Electron Microscope Investigations of Dynamical Changes of Nanostructures on Silicon
p.111

Finite Element Modeling of Space Charge Phenomena on the Nanoscale
p.120

Atom Probe Tomography: Studying Reactions on Top of the Tip
p.126

Periodic Pattern Formation in Metal-Ceramic Reactions
p.136

Growth and Characterization of (012)- and (001)-Oriented Epitaxial Anatase Thin Films
p.146

Study on Microstructure and Magnetic Properties of TM-Mg (TM: Fe, Co) Alloys Synthesized by Mechanical Alloying
p.152

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Finite Element Modeling of Space Charge Phenomena on the Nanoscale

Abstract:

The NernstPlanckPoisson (NPP) system of equations provides a continuum model for the behavior of interfacial charge in solid ionic conductors. Despite the obvious limitations in using such models to describe systems a few atomic diameters in extent, the success of the PoissonBoltzmann equation in modeling the electrostatic interactions of individual molecules with their ionic atmospheres suggests that continuum solutions have some value as a first approximation in describing charge distributions in nanoparticles and thin layers. Except for static charge distributions onedimensional geometries, solution of the NPP equations requires numerical approximation. Here we examine the applicability of the finite element method to the study of space charge phenomena in selected 1 and 2dimensional geometries, comparison to exactly soluble onedimensional cases to gauge the validity of the results.