Exact analytical solution of a two diode circuit model for organic solar cells showing S-shape using Lambert W-functions

Abstract

Organic solar cells (OSCs) often show a kink, also called S-shape, in the current-voltage (I-V) characteristics, that has been attributed to different physical phenomena such as poor quality of cathode-active layer interface or unbalance charge carrier mobilities. This non-ideal behaviour can be electrically modelled including a second diode, in reverse bias, together with an extra shunt resistance (R-P2) in the traditional solar cell equivalent circuit. In this paper, we solve without approximations the transcendental equation system derived from this modified circuit. We have obtained an analytical expression for I-V curves decoupling the voltage drop in each diode using Lambert W function. This expression has been fitted to experimental data in order to obtain circuital parameters. Simulations varying saturation current of reverse diode (I-02) and R-P2 have been performed in order to study the dependence of S-shape with these parameters.