Two-dimensional modelling of electron flow through a poorly conducting layer

TL;DR

This paper develops a two-dimensional mathematical model for electron flow through a poorly conducting layer in solar cells, introducing a spectral method for numerical solutions and deriving asymptotic expressions for current density.

Contribution

It presents a novel spectral method for solving the drift-diffusion model and provides asymptotic formulas for current density in specific glass layer profiles.

Findings

Current short-circuits through thin glass regions.

Asymptotic expressions for average current density derived.

Validated spectral method for numerical solutions.

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.