Fill factor: how square is the curve?
Sweep the voltage across a solar cell under light and the current stays almost constant, then collapses near the open-circuit voltage Voc. The fill factor is the area of the largest power rectangle that fits under the curve, divided by the area of the outer box.
A perfectly square curve would give FF = 1. The best silicon cells sit near 0.85. Organic cells are all over the place, from below 0.3 to about 0.8.
A border nobody could explain
We plotted fill factor against voltage loss, the gap between the optical gap and Voc, for a large set of organic cells. Two things stand out. The best achievable FF rises as voltage loss falls, as theory for an ideal diode predicts. But at the smallest losses there is a sharp edge: FF drops steeply, forming a "left border".
That border is the trade-off. Push voltage loss down and fill factor falls off a cliff.
Points in the drawing are schematic, after Fig. 1b of the paper.
Slow charges and recombination are not enough
The textbook explanation for a low FF is transport: charges move too slowly and recombine before they are collected. That picture reproduces the upper envelope, but not the border.
For one blend, PTO2:Y1, transport and recombination alone predict FF = 0.58. The measured value is 0.27. Time-delayed collection-field experiments show the missing piece: the number of free charges generated depends on the applied voltage, and it falls as the cell approaches Voc.
From exciton to charge pair
Light does not create free charges directly in an organic semiconductor. It creates an exciton, a tightly bound electron–hole pair, here in the acceptor. The exciton wanders until it meets the donor, where the hole hops across and leaves a charge-transfer (CT) state: electron and hole on neighbouring molecules, still attracted.
The energy step from exciton to CT state is the offset ΔE. A large offset makes the hop easy but throws away voltage. Modern low-loss blends have offsets of only a few tens of meV.
The electric field moves the CT energy
A CT state is a dipole about 3.5 nm long. Inside a working cell the field is roughly 105 V cm−1 (1 V across 100 nm). The energy of a dipole in a field shifts by
That is as large as the thermal energy kBT and as large as the offset itself. Interfaces facing one way have their CT energy pushed down and become easy doors; interfaces facing the other way are pushed up and close. Electroabsorption spectra confirm the first-order (dipole) Stark effect dominates; the second-order term is a thousand times smaller.
Near Voc, the doors close
At short circuit the internal field is strong, and an exciton finds a favourable interface easily. As the voltage approaches Voc, the field fades, the helpful energy shift disappears, and the small offset alone is not enough. Fewer excitons become charges, the current sags early, and the J–V curve rounds off.
Bias-dependent photoluminescence shows the same thing directly: excitons are quenched less as the field drops. This is field-dependent free-charge generation, and it gets worse the smaller the offset, which is exactly the left border.
Exciton lifetime decides who wins
Every exciton is racing two clocks: finding a good interface, or decaying back to the ground state. When the field is weak, good interfaces are rarer, so the exciton needs more time to find one.
A longer exciton lifetime buys that time. In the simulation on the right, the same blend is shown with a short and then a long lifetime. Drift–diffusion modelling in the paper predicts that lifetimes above about 1 ns can lift FF above 82% even with minimal voltage loss.
A guest that lends time
PM6:L8-BO has a long exciton lifetime (990 ps) and FF = 79.5%, with a voltage loss of 0.545 V. PM6:Y18-C3 loses less voltage (0.502 V) but its lifetime is shorter (690 ps) and FF drops to 68.8%.
Mixing the two acceptors 0.86 : 0.14 gives an exciton lifetime of 870 ps, FF = 81.1%, voltage loss 0.516 V, and 20.1% efficiency. Fill factor and voltage both improve, breaking the trade-off. Morphology barely changes, which points to exciton dynamics as the cause.
Why the Y6 era jumped ahead
Grouping published acceptors by era shows the same story. Y6-type acceptors after 2019 combine higher fill factors with lower voltage losses than ITIC-based ones (2015–2019) and older systems. They also have longer exciton lifetimes.
The design rule that follows is simple to state: when you shrink the energy offset to save voltage, give the exciton more time.