Analytical model for the open-circuit voltage and its associated resistance in organic planar heterojunction solar cells

We derive an analytical formula for the open-circuit voltage $\left(V_{\text{oc}}\right)$ of organic planar heterojunction solar cells under standard operating conditions. We find that the type of free carrier recombination at the interface between the donor and acceptor materials controls the slope of $V_{\text{oc}}$ vs incident light intensity. By using the same derivation, an equation for the resistance around $V_{\text{oc}}$ is obtained. From this, we investigate two parameters in more detail and compare them to experiments. The first is the work function of the cathode metal. We show that, within our model, $V_{\text{oc}}$ does not depend on this work function, while the cell resistance around $V_{\text{oc}}$ is strongly dependent on it. Second, we find that the asymptotic resistance around $V_{\text{oc}}$ is a third-order power function of the thickness of the organic layers (acceptor or donor). The model provides insights to achieve low-resistivity high open-circuit voltage organic solar cells.