Accuracy of expressions for the fill factor of a solar cell in terms of open-circuit voltage and ideality factor

An approximate expression proposed by Green predicts the maximum obtainable fill factor (FF) of a solar cell from its open-circuit voltage (V_oc). The expression was originally suggested for silicon solar cells that behave according to a single-diode model and, in addition to V_oc, it requires an ideality factor as input. It is now commonly applied to silicon cells by assuming a unity ideality factor - even when the cells are not in low injection - as well as to non-silicon cells. Here, we evaluate the accuracy of the expression in several cases. In particular, we calculate the recombination-limited FF and V_oc of hypothetical silicon solar cells from simulated lifetime curves, and compare the exact FF to that obtained with the approximate expression using assumed ideality factors. Considering cells with a variety of recombination mechanisms, wafer doping densities, and photogenerated current densities reveals the range of conditions under which the approximate expression can safely be used. We find that the expression is unable to predict FF generally: For a typical silicon solar cell under one-sun illumination, the error is approximately 6% absolute with an assumed ideality factor of 1. Use of the expression should thus be restricted to cells under very low or very high injection.