Charged grain boundaries reduce the open-circuit voltage of polycrystalline solar cells—An analytical description

Abstract

Analytic expressions are presented for the dark current-voltage relation <i>J</i>(<i>V</i> ) of a <i>pn</i>⁺ junction with positively charged columnar grain boundaries with high defect density. These expressions apply to non-depleted grains with sufficiently high bulk hole mobilities. The accuracy of the formulas is verified by direct comparison to numerical simulations. Numerical simulations further show that the dark <i>J</i>(<i>V</i> ) can be used to determine the open-circuit potential <i>V</i>_oc of an illuminated junction for a given short-circuit current density <i>J</i>_sc. A precise relation between the grain boundary properties and <i>V</i>_oc is provided, advancing the understanding of the influence of grain boundaries on the efficiency of thin film polycrystalline photovoltaics like CdTe and Cu(In<i>,</i> Ga)Se₂.