Offset energies at organic semiconductor heterojunctions and their influence on the open-circuit voltage of thin-film solar cells

Organic semiconductor heterojunction (HJ) energy level offsets are modeled using a combination of Marcus theory for electron transfer, and generalized Shockley theory of the dark current density vs voltage $\left(J\text{−}V\right)$ characteristics. This model is used to fit the $J\text{−}V$ characteristics of several donor-acceptor combinations commonly used in thin film organic photovoltaic cells. In combination with measurements of the energetics of donor-acceptor junctions, the model predicts tradeoffs between the junction open-circuit voltage $\left(V_{\mathrm{OC}}\right)$ and short-circuit current density $\left(J_{\mathrm{SC}}\right)$. The $V_{\mathrm{OC}}$ is found to increase with light intensity and inversely with temperature for 14 donor-acceptor HJ materials pairs. In particular, we find that $V_{\mathrm{OC}}$ reaches a maximum at low temperature $(\sim 175\mathrm{K})$ for many of the heterojunctions studied. The maximum value of $V_{\mathrm{OC}}$ is a function of the difference between the donor ionization potential and acceptor electron affinity, minus the binding energy of the dissociated, geminate electron-hole pair: a general relationship that has implications on the charge transfer mechanism at organic heterojunctions. The fundamental understanding provided by this model leads us to infer that the maximum power conversion efficiency of double heterostructure organic photovoltaic cells can be as high as 12%. When combined with mixed layers to increase photocurrent and stacked cells to increase $V_{\mathrm{OC}}$, efficiencies approaching 16% are within reach.