A new model of organic solar cells reveals open circuit conditions and size dependent power loss induced by the finite conductivity of a transparent contact

We report on a new approach to modelling the effect of the size of organic solar cells on their efficiency. Experimental results show a drastic deterioration in performance when scaling up organic solar cells. This reduction reflects in key parameters such as the short circuit current (Isc), the maximum power point (Pm), and the Fill Factor (FF). It is attributed to the transparent anode that exhibits a relatively low conductivity (σ). Our unique approach is to account for the interplay between the two sub-domains of the solar cell. In the first domain, containing the electro-optic active materials, we solve the drift-diffusion model using a simplified model for the recombination to emphasize the role of the anode resistance. In the second domain, representing the anode, we solve only the Laplace equation. We introduce the coupling between these layers using the current of the active layer as the boundary condition for the anode and the position dependent potential of the anode as the boundary condition for the active layer. Our results reveal that as the length of the cell increases, the parts that are farther from the contact exhibit near open circuit conditions and do not contribute to the current. We found that the efficiency of the cell altered from linear to sub-linear behavior already at cell lengths of a few millimeters. The transition point strongly depends on the conductivity of the anode. The sub-linearity starts at 0.4, 0.5, and 0.7 cm for σ=100, 200, and 500 S/cm, respectively. Additionally, the efficiency begins to saturate sooner than both the short circuit current and the Fill-Factor. The saturation is observed at device lengths of 0.8, 1.2, and 2.1 cm for σ=100, 200, and 500 S/cm, respectively.