## INTRODUCTION

At the end of the solar cell manufacturing process the current–density versus voltage curves (*J*(*U*) curves) are measured to determine the solar cell's efficiency, the maximum power point and the mechanisms limiting the efficiency as there are resistive losses and recombination of electron hole pairs. An accurate and robust analysis of the measured curves is essential for the output power of the module and for the evaluation of the ongoing manufacturing process. The basic model for *J*(*U*) curves, which is important for the following considerations, is the two-diode model. The current density *J*(*U*) depends on the external voltage *U* in the following way.

*V*_{t} denotes the thermal voltage and *J*_{Ph} the photogenerated current density. The saturation current density *J*_{01} describes recombination of electron hole pairs in the base and in the emitter and *J*_{02} characterises recombination in the space charge region 1. As usual the ideality factor of the second diode *n*_{2} is set to *n*_{2} = 2 throughout this work. The two-diode model is a simple but useful model to describe the characteristics of crystalline silicon solar cells. In addition to the recombination losses (*J*_{01}, *J*_{02}) it includes the power losses due to series resistance (*R*_{S}) and parallel resistance (*R*_{P}). In this work *R*_{P} is assumed to be very large so that it does neither influence the cell's open circuit voltage nor its efficiency. Orthogonal distance regression based on weighted least-squares fitting 2 is one possibility to extract model parameters such as *J*_{01}, *J*_{02} and *R*_{S} from *J*(*U*) curves. Fischer *et al.*3 showed by simulations that the distributed character of the series resistance can cause severe deviations of the model parameters and misinterpretation of the measurements when fitting the two-diode model (Equation (1)) to measured *J*(*U*) curves. In the present work we investigated different types of solar cells produced at Fraunhofer ISE using industrial processes. For every solar cell Equation (1) has been fitted to dark and illuminated *J*(*U*) curves and to suns*V*oc curves using *J*_{Ph}, *J*_{01}, *J*_{02}, *R*_{S} and *R*_{P} as fit parameters. Comparing e.g. *J*_{02} from the illuminated fit with *J*_{02} from the dark fit, no good correlation is obtained. The same is valid for *J*_{01}. In general no consistent set of parameters can be found to describe all three curves with Equation (1), experimentally confirming Fischer's work. Besides, more interesting than the exact value of e.g. *R*_{S} or *J*_{02} is how much efficiency *η* is lost due to *R*_{S}, *J*_{02} and other mechanisms.

A fill factor analysis can have these advantages. No fit is needed and fill factor and efficiency losses are directly obtained. By shifting the suns*V*oc curve along the current density axis by *J*_{SC} (1 sun) the pseudo illuminated curve and the virtually series resistance free pseudo fill factor pFF are obtained. The difference between FF and pFF then gives the fill factor losses due to the series resistance (*R*_{S}) 4. The ideal fill factor FF_{0} is free from losses due to series resistance and free from losses due to recombination in the space charge region (References 5 (p. 96) and 1 (p. 138)). It is calculated numerically from the ideal *J*(*U*) curve:

The two parameters *J*_{Ph} and *J*_{01} can be determined from two points of the illuminated *J*(*U*) curve, e.g. under open circuit (*J*(*U* = *V*_{OC}) = 0) and under short circuit (*J*(*U* = 0) = *J*_{SC}) conditions since the influence of *J*_{02} on *V*_{OC} is small. The difference between FF_{0} and pFF quantifies the FF-losses due to recombination in the space charge region (*J*_{02}).