Where the voltage goes in Y6-type solar cells

A 0.6 V gap

Organic solar cells (OSCs) have improved fast. At the time of writing, the certified efficiency of single-junction cells had reached 17.4%. Peak external quantum efficiencies were above 80% and internal ones above 90%, so nearly every absorbed photon already becomes collected charge.

Voltage is where they fall short. The difference between the optical gap and the open-circuit voltage V_oc is usually around 0.6 V in state-of-the-art OSCs. That is 0.2–0.3 V more than in crystalline silicon or GaAs cells. The authors argue that V_oc may be the only avenue left for another big leap in efficiency.

Schematic bars; the 0.6 V and 0.2–0.3 V figures are from the text.

Splitting the loss into three

Using detailed balance, the paper writes the open-circuit voltage as the optical gap minus three losses:

ΔE₁ is radiative recombination above the gap. Every solar cell has it, because a cell that absorbs light must also emit it. ΔE₂ is extra radiative loss below the gap, from a soft absorption edge. In the latest low-offset OSCs it is already below 50 meV, as small as in inorganic or perovskite cells. ΔE₃ is non-radiative recombination: 200–300 meV in state-of-the-art OSCs, much more than in the best inorganic or perovskite cells.

Step heights are schematic (Eq. 1 of the paper); only the ΔE₂ and ΔE₃ ranges are from the text.

ΔE₃ is set by how well the cell glows

The non-radiative loss follows from a single number, the electroluminescence quantum efficiency EQE_EL. That is the fraction of injected charges that come out as photons when the solar cell is run as an LED:

Here k is Boltzmann's constant. At room temperature every factor of ten in EQE_EL is worth about 60 meV of voltage. A loss of 200–300 meV therefore means EQE_EL of only about 4 × 10⁻⁴ down to 1 × 10⁻⁵: at best one photon for every few thousand injected charges. To cut ΔE₃, make the cell a better LED.

Curve drawn from the equation at 300 K; the shaded band is the 200–300 meV range from the text.

What makes a cell emit

EQE_EL is a product of four probabilities:

f_e–h is the balance of injected electrons and holes (1 when they match). β is the chance that an injected pair forms an emissive exciton: spin statistics make singlets and triplets in a 1 : 3 ratio, and triplets usually end as heat, so β ≈ 25%. PLQY is the photoluminescence quantum yield of the blend. f_outcoupling is the share of emitted light that escapes the device, about 20% for a planar cell.

Three of the four are fixed by physics or device geometry. The one chemists can change is the PLQY.

Values 1, 25% and 20% are the assumptions the paper uses for Fig. 2.

Why small offsets do not have to hurt

In fullerene blends the non-radiative loss follows an energy-gap law tied to the charge-transfer (CT) state. That implied a trade-off: high current needed a large donor–acceptor offset, and a large offset cost voltage.

In the best non-fullerene blends the absorption and emission spectra of the blend often overlap those of the pure low-gap component, so the offset is small. When the singlet exciton S₁ and the CT state are close in energy they hybridise. The CT state then "borrows" brightness from the emissive S₁ (the three-state model). A bright low-gap material can then make the whole blend brighter and lower ΔE₃.

Schematic, after Fig. 3B (three-state model, Eisner et al.).

Anatomy of an A-DA′D-A acceptor

Y6 joins electron-accepting end groups (A) to a ladder-type fused core whose centre is itself electron deficient (A′, a benzothiadiazole), flanked by donor segments (D). Two sp² nitrogens in pyrrole rings carry alkyl side chains. These chains stand roughly perpendicular to the backbone and stop the core from over-aggregating. The molecule is C₂-symmetric and slightly curved.

In films its absorption shifts about 100 nm to the red compared with solution. A single Y6 molecule has only a small dipole moment but a strong quadrupole moment: the electron-withdrawing end groups are negative relative to the core. In the crystal the molecules pair up face to face, and this large quadrupole persists. The paper links the resulting narrow density of states to trap-free transport of both electrons and holes. Y6 also has a smaller local-exciton reorganisation energy than other NFAs, which helps keep voltage losses small.

Schematic, after Fig. 4A, 4C and 4E; not a real structure.

Change A′, gain light

PM6:Y6 still has a HOMO offset of about 0.1 eV, and its blend PLQY is only 2.8 × 10⁻⁴. That is about 70 times below the PLQY needed for 20% efficiency in the paper's model.

The proposed lever is the central A′ unit. Replacing benzothiadiazole (BT) with the less electron-withdrawing benzotriazole (BTA) gives Y11. With PM6 it has a smaller HOMO offset and a smaller optical gap, and the blend PLQY rises to 1.3 × 10⁻³, nearly five times higher. The non-radiative loss of PM6:Y11 devices drops to 0.20 eV.

PLQY values, the ≈70× and ≈5× ratios and ΔE₃ = 0.20 eV are from the text; the 2% target is the Fig. 2 scenario.

Order, morphology, third components

Disorder. Tail states below the gap open extra non-radiative channels. Sub-gap absorption follows the Urbach rule α = α₀ exp[(E − E_g)/E_U]; a smaller Urbach energy E_U means a sharper edge. Adding alkyl chains at the β position of the core gives a more uniform conformation: the electron mobility of Y18 in blends is five times that of Y3.

Morphology. Grazing-incidence X-ray scattering (GIWAXS) of PM6:Y11 blends shows a new out-of-plane (100) diffraction at 0.54–0.59 Å⁻¹, a sign of more regular acceptor stacking. Ternary blends can raise EQE_EL by reducing aggregation-induced quenching or trap states, at some risk to morphology and absorption. "Quasi-polymer" acceptors (oligomers, branched macromolecules) aim at stable, roll-coated modules.

Absorption tails schematic, after Fig. 6A (no measured E_U values shown).

No built-in trade-off

For years a donor–acceptor offset of about 0.3 eV was thought necessary to split excitons. The new acceptors reach internal quantum efficiencies of 90% with offsets close to zero. So there is no intrinsic compromise between photocurrent and V_oc.

The A-DA′D-A family went from 6% (BZIC, 2017) to 17% (Y18) in about three years. Getting past 20% now mainly means raising blend emission. Open questions remain: the roles of thermal motion, of triplet states (well studied in fullerene blends, little known for NFAs), and of domain purity.

Efficiency values from the text; bar lengths to scale.