  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.
