A new expression for intrinsic fill factor of silicon solar cells

Green [1] and Swanson and Sinton [2] proposed two different approaches to predict the maximum obtainable fill factor (FF) from the open-circuit voltage (Voc) of a solar cell. This is convenient because the internal or implied open-circuit voltage of a solar cell can be measured at early stages of device processing (e.g., after passivation), giving rapid insight into expected device performance. However, these methods assume that recombination is linear in excess carrier density. In addition, both formulas also require that the ideality factor be known, and, while unity is often assumed, the ideality factor in fact varies with injection level. The expressions are often used in cases where these assumptions are clearly violated; here, we evaluate the accuracy in these cases. We find that the expressions are unable to predict the intrinsic FF generally, and their use must be restricted to very low or very high injection. We propose an alternative expression that is accurate for calculating the intrinsic-recombination-limited FF. With appropriate input parameters, e.g. wafer thickness, doping concentration and photogenerated current, the FF and Voc of solar cells can be predicted independent of each other. We investigate the accuracy of our proposed expression and see that its deviation from exact results are less than 0.3 % for FF and 1 mV for Voc.