Two dark triplets, one bright singlet: triplet–triplet annihilation in organic solar cells

Three in four recombinations go dark

A solar cell at open circuit is also a light-emitting diode. The more of its recombination gives light, the higher its voltage: the non-radiative loss is ΔV_nr = −k_BT ln(EQE_EL). The paper splits the electroluminescence efficiency into four factors (the first γ is a charge-balance factor, not the TTA rate used later):

EQE_EL = γ · φ_PL · χ · η_out

χ is the fraction of recombination events that can give light at all. When a free electron and hole meet, their spins are random: 25% of pairs form singlets and 75% form triplets. A triplet exciton on the acceptor decays without light, by triplet–charge annihilation (TCA) or on its own, which adds up to 60 mV to ΔV_nr.

In triplet–triplet annihilation (TTA), two triplets meet. One is lifted to the bright singlet S₁, and the other drops to the ground state. In OLEDs this raises χ from 0.25 to 0.625, and most commercial blue OLEDs rely on it. Its potential to raise the voltage of solar cells had not been considered, although TTA had been reported in fullerene cells. (A related explainer covers the other factors.)

Schematic, after Fig. 1b. Eq. 1, 75%, 60 mV, 0.25 and 0.625 from the introduction.

Same donor, swapped core

Y6 and Y11 are both A–DA′D–A acceptors from the Y-series. They differ only in the central acceptor unit A′: Y6 carries benzothiadiazole (BT), and Y11 carries benzotriazole (BTz).

Blended with the donor polymer PM6, both give efficient cells with nearly the same numbers: 15.2% for PM6:Y6 and 15.1% for PM6:Y11. Their triplets, however, behave very differently.

Device values from Fig. S1; molecules drawn as blocks, not to scale.

Triplets grow after the holes have left

Femtosecond transient absorption (TAS) follows the excited states. An 800 nm pulse excites mainly the acceptor. A photoinduced absorption (PIA) at 1500–1600 nm appears first. It belongs to an intermolecular charge-transfer state between neighbouring acceptor molecules (inter-CT), and it fades within about 100 ps as holes move to PM6.

After that, a second PIA grows at 1400–1450 nm: the acceptor triplet exciton, assigned from earlier sensitisation experiments on Y6. Its growth from about 100 ps onward depends on the excitation fluence. That makes it a bimolecular process, so the triplets come from free charges that meet again (non-geminate recombination).

Spectra schematic, after Fig. 2a; band positions and time scales from the text. PM6:Y6 shows the same two features.

In Y11, more light means faster triplet loss

The kinetics are normalised to the inter-CT signal at time zero. In PM6:Y6, a higher fluence makes the triplet maximum come earlier and sit higher, as expected: more charges, more recombination. PM6:Y11 does the opposite. At higher fluence its triplets start to decay at a lower normalised value.

Such rapid, strongly fluence-dependent quenching means the triplets are lost by a process of higher order in the triplet density than TCA. The authors fit the data with

dn_T/dt = −α dn_H/dt − β n_Hn_T − γ n_T²

Here α is the fraction of recombination that forms triplets, β is the TCA rate constant and γ is the TTA rate constant. Monomolecular decay is left out, because the triplets live longer than the 2 ns window.

Curves schematic, after Fig. 2c,d. Eq. 3.

TCA in Y6, TTA in Y11

The cross-sections of the hole polaron and the triplet are hard to measure, so the fit uses a "cross-section free" form with parameters A, B and G proportional to α, β and γ. In PM6:Y6, B = (6.3 ± 0.6) × 10¹⁰ s⁻¹ and G = (7 ± 2) × 10¹⁰ s⁻¹ are similar. Polarons far outnumber triplets, though, so TCA dominates. In PM6:Y11 only G could be extracted, (2.3 ± 0.2) × 10¹¹ s⁻¹, and TCA is negligible. Because of the normalisation, these numbers do not compare the two blends quantitatively.

Neat films measured with nanosecond TAS give G = 1.46 × 10¹¹ s⁻¹ (Y11) and 1.20 × 10¹¹ s⁻¹ (Y6). The neat films are about half as thick, so the same γ should give twice the G. Y6 fits this rule. Y11 does not: the blend has a much faster TTA rate than the neat film. Unlike the blend, the neat Y11 film was not annealed. An unannealed PM6:Y11 blend gives G = (1.7 ± 0.3) × 10¹¹ s⁻¹, which points to better order speeding up TTA.

Values from Table 1, Table S1 and Fig. S11. The dashed ticks (neat-film G ÷ 2) are derived here.

Triplets that make light

Photoluminescence-detected magnetic resonance (PLDMR, at 10 K) flips triplet spin sublevels with microwaves. The PL changes only if the triplets are coupled to light emission, for example through TTA. The broad feature is the acceptor triplet (zero-field splitting D = 930 MHz in PM6:Y11 and 990 MHz in PM6:Y6, plus a half-field signal at 167 mT). The narrow centre peak at 336.1 mT comes from distant spins such as CT states.

The "wings" are steeper in PM6:Y11. Its ordering factor λ_θ = 9.0 against 5.5 in PM6:Y6 means more out-of-plane order. The triplet signal rises as power^1.47 below about 10 mW and linearly above it, the pattern of TTA systems that become annihilation-limited. Relative to the CT peak, the triplet-sensitive PL is nine times larger in PM6:Y11 (0.45 against 0.05).

Spectra schematic, after Fig. 3a (D, λ_θ and field values from the text). Slopes 1.47 ± 0.05 and 1.00 ± 0.04 from Fig. 3c; the points are illustrative.

A bigger dipole, longer-range stacking

X-ray scattering (GIWAXS) shows that both neat acceptors stack face-on, with a π–π peak near q ≈ 1.7 Å⁻¹. In annealed PM6:Y11, a new out-of-plane peak appears near q ≈ 0.6 Å⁻¹, a sign of long-range order that PM6:Y6 lacks.

Density functional theory suggests why. BTz withdraws less electron density than BT, so in Y11 the end groups are no longer balanced by the core. Its dipole is 3.82 D, mostly in the molecular plane, against 0.97 D for Y6, mostly out of plane. A strong dipole pulls molecules together and drives crystallisation. More crystalline phases let triplets diffuse further, and TTA needs two triplets to meet.

Line cuts schematic, after Fig. 4d; dipoles from Table S4. The arrow direction is schematic.

How many millivolts could fusion win back?

Suppose a fraction ω of the triplets made by recombination come back as singlets. ω can be at most 0.5, because every TTA event sends one triplet to the ground state. In the best case every recycled singlet emits (Eq. 6). In the other case it may split into charges again with probability η_CT = 0.93 and go round the cycle (Eq. 7):

χ = (1 − α) + αω · χ = [1 − α + αω(1 − η_CT)] / (1 − αωη_CT)

Without TTA, χ = 1 − α. With α = 0.75 and ω = 0.5 the gain is about 24 mV in the best case and about 14 mV with re-dissociation. Near α = 0.95 it reaches about 60 and 28 mV. That is "several tens of mV" under the most favourable conditions.

Maps recomputed here from Eqs. 6 and 7 as ΔV = k_BT ln[χ/(1 − α)] with k_BT = 25.7 meV, after Fig. 5b,c. α is capped at 0.95, as in the paper.

Triplets must live about a microsecond

TTA is second order: it needs many triplets at once. Under 1 Sun the polaron density is about 4.5 × 10¹⁶ cm⁻³. If triplets live only 10–100 ns, they reach about 10¹⁵ cm⁻³ and simply decay on their own first. TTA becomes a major channel only if the triplet lifetime exceeds about 1 µs. The neat-film fits give 63 ± 7 ns for Y11 and 600 ± 400 ns for Y6. Some ITIC derivatives reach about 100 µs. The map assumes weak TCA, as in PM6:Y11. With the much stronger TCA of PM6:Y6, TTA stays minor (Fig. S20).

PM6:Y11 does lose less voltage (ΔV_nr 220 mV against 260 mV for PM6:Y6), but probably not because of TTA. A smaller S₁–CT offset or stronger hybridisation are likelier causes. The design rules: raise the intrinsic TTA rate through order (dipole, side chains, annealing, additives), and push the triplet lifetime toward about 1 µs. Longer-lived triplets also react more with oxygen, so the lifetime should not be pushed further than that.

Map recomputed here from Eqs. S7–S8 with the paper's inputs (n_P = 4.5 × 10¹⁶ cm⁻³, k₂ = 10⁻¹¹ cm³ s⁻¹, α = 0.75, β = 10⁻¹² cm³ s⁻¹), after Fig. 5d; the γ range is chosen here. ΔV_nr from Fig. S21.