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We have developed a three-dimensional numerical model of grain boundaries to simulate the electrical properties of polycrystalline silicon with doping densities larger than approximately 5×1017 cm–3. We show that three-dimensional effects play an important role in quantifying the minority-carrier properties of polycrystalline silicon. Our simulations reproduce the open-circuit voltage of a wide range of published experiments on thin-film silicon p-n junction solar cells, choosing a velocity parameter for recombination at the grain boundaries, S, in the order of 105–106 cm/s. The simulations indicate that, although S has been reduced by one order of magnitude over the last two decades, improvements in the open-circuit voltage have mainly been achieved by increasing the grain size. A few options are proposed to further reduce S.