Shunt screening, size effects and I /V analysis in thin-film photovoltaics

We present an analytical model that quantitatively describes the physics behind shunting in thin film photovoltaics and predicts size-dependent effects in the $\mathrm{I/V}$ characteristics of solar cells. The model consists of an array of microdiodes and a shunt in parallel between the two electrodes, one of which mimics the transparent conductive oxide and has a finite resistance. We introduce the concept of the screening length L, over which the shunt affects the system electric potential. The nature of this screening is that the system generates currents in response to the point perturbation caused by the shunt. L is expressed explicitly in the terms of the system parameters. We find the spatial distribution of the electric potential in the system and its $\mathrm{I/V}$ characteristics. The measured $\mathrm{I/V}$ characteristics depend on the relationship between the cell size l and L, being markedly different for the cases of small $\mathrm{(l\ll L)}$ and large $\mathrm{(l\gg L)}$ cells. We introduce a new regime of the large photovoltaic cell where all the characteristics are calculated analytically. Our model is verified both numerically and experimentally: good agreement is obtained.