Two-dimensional modelling of electron flow through a poorly conducting layer
Analysis of PDEs
2014-12-08 v1
Abstract
Motivated by contact resistance on the front side of a crystalline silicon solar cell, we formulate and analyse a two-dimensional mathematical model for electron flow across a poorly conducting (glass) layer situated between silver electrodes, based on the drift-diffusion (Poisson-Nernst-Planck) equations. We devise and validate a novel spectral method to solve this model numerically. We find that the current short-circuits through thin glass layer regions. This enables us to determine asymptotic expressions for the average current density for two different canonical glass layer profiles.
Cite
@article{arxiv.1412.1986,
title = {Two-dimensional modelling of electron flow through a poorly conducting layer},
author = {J. P. Black and C. J. W. Breward and P. D. Howell},
journal= {arXiv preprint arXiv:1412.1986},
year = {2014}
}
Comments
30 pages, 19 figures, acceptor for publication by SIAM Journal on Applied Mathematics