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.