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

Analytic expressions are presented for the dark current-voltage relation J(V ) of a pn⁺ 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 J(V ) can be used to determine the open-circuit potential V_oc of an illuminated junction for a given short-circuit current density J_sc. A precise relation between the grain boundary properties and V_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, Ga)Se₂.