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

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 (RP2) 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 (I02) and RP2 have been performed in order to study the dependence of S-shape with these parameters.

► We have obtained exact analytical expression for I–V curves for OSC showing S-shape. ► The model includes an extra diode (in reverse bias) and an extra parallel resistance. ► Simulations varying these extra parameters have been performed. ► Circuit parameters have been extracted by fitting the model to experimental data.