An analytical model for polycrystalline photovoltaics

Despite decades of research, the role of grain boundaries in the photovoltaic behavior of thin film polycrystalline solar cells remains poorly understood. The high defect density of grain boundaries generally promotes recombination and reduces photovoltaic efficiency. However, thin film polycrystalline photovoltaics such as CdTe and Cu(In; Ga)Se2 exhibit high efficiencies despite a large density of grain boundaries.

I’ll present our analysis of recombination in a 2-d model of a pn+ junction containing columnar grains with positively charged grain boundaries. We restrict our attention to dark recombination at forward bias and derive the dark J-V relation. We formulate a physical picture of the electron/hole currents and recombination, and translate this picture into a simplified effective model which describes the essential features of the full system. A crucial simplification follows from that fact that electrons are electrostatically confined to the grain boundary core, so that parts of the problem can be reduced to 1 dimension.

The effective model we construct is amenable to simple analytic solutions. Under reasonable assumptions (such as non-depleted grains and reasonably high hole mobilities), we find that these analytic solutions successfully describe the results of full 2-d numerical simulations for a range of grain boundary orientations and defect structures. Numerical simulations further show that the dark J-V relation can be used to determine the open-circuit potential Voc of an illuminated junction for a given short-circuit current density Jsc. We can therefore provide a precise relation between grain boundary properties and Voc. This relation enables one to rationalize the (relatively) low Voc observed in polycrystalline CdTe and to formulate strategies to optimize grain boundary properties. I conclude by discussing approaches to experimentally test our results.