Does heat help charges escape? Thermally activated charge separation

Barrier or no barrier?

An exciton that reaches the donor–acceptor interface first forms a charge-transfer (CT) state: an electron on the acceptor and a hole on the donor, still bound by their Coulomb attraction. In fullerene cells, an empirical rule said the CT state had to lie about 0.3 eV below the lowest excited state for the pair to split efficiently. Non-fullerene acceptors (NFAs) broke this rule, and efficiencies passed 19%.

How the pairs separate with so little excess energy was debated. One low-offset NFA blend showed thermally activated CT states. Another, PM6:Y6, showed barrierless, temperature-independent generation, explained by the large quadrupole moment of the acceptor. Most studies looked at a single blend, and "low offset" was defined differently from paper to paper.

Schematic.

Measuring the offset in the working device

Offsets from UPS or cyclic voltammetry vary a lot between groups, and they are measured on the neat materials. They miss the band bending from the acceptor's quadrupole moment and the vacuum-level shift from interface dipoles.

The authors use the blend itself. The offset is E_g − E_CT^0K. E_g comes from the probability distribution of the EQE spectrum (the E_g^PV definition). E_CT^0K comes from extrapolating V_OC versus temperature to 0 K, where qV_OC and the CT energy coincide. The uncertainty is ±0.01 eV. This offset follows the UPS offset monotonically and agrees between labs.

Schematic of the method; the measured V_OC–T data are in the Supporting Information (Fig. S4).

Below about 0.2 eV, the efficiency falls

For each blend the charge separation efficiency (CSE) is estimated as J_SC/J_SQ: the measured short-circuit current divided by the current a cell with 100% EQE above the gap would give. The authors call this a rough estimate, but good enough to see the trend.

Table 1 covers offsets from 0.03 to 0.63 eV. Above a transition range near 0.2 eV, CSE is roughly constant. Below it, CSE drops steeply: from 76% for PM6:Y6 (0.32 eV) to 3% for PM6:IEICO (0.03 eV). Literature data added in Fig. 1 follow the same trend.

All 14 points from Table 1 (J_SC/J_SQ vs E_g − E_CT^0K). Transition band approximate, after Fig. 1.

Same acceptor, three donors

Could morphology or disorder cause the drop instead? To check, the authors compare three blends of the acceptor Y1 with three closely related donors: PM5 (PBDB-T), PM6 (PBDB-T-2F) and PM7 (PBDB-T-2Cl). The offset goes 0.23 → 0.17 → 0.11 eV, and the CSE 59 → 44 → 22%.

GIWAXS and GISAXS show similar crystallinity, pure-domain and mixed-domain sizes in all three. The Urbach energies are all 22–24 meV, and the donor HOMO disorder is similar. So neither morphology nor CT-state disorder explains the difference. The offset is the variable that changes.

Offsets, J_SC/J_SQ and Urbach energies from Table 1 and the text.

Where the charges are lost

Transient absorption with 800 nm pulses excites only Y1, since the donors do not absorb there. In PM5:Y1 the acceptor bleach fades over 1–100 ps while the donor bleach grows: holes move from Y1 to the donor and stay separated. In PM6:Y1 and PM7:Y1, both bleaches already decay on a tens-of-ps time scale. This is geminate recombination: with a small offset, holes can transfer back to the acceptor and re-form its excited state, which then decays quickly.

The authors take the total bleach area (donor plus acceptor) at 100 ps relative to the area just after excitation. This gives about 50%, 29% and 25% for PM5:Y1, PM6:Y1 and PM7:Y1, close to the J_SC/J_SQ values.

Curve shapes schematic, after Fig. 2; the 100 ps ratios are from the text.

Current that grows with temperature

Next the cells are measured from 200 to 305 K under weak light (0.26 mW cm⁻², about 10⁻³ sun), so that bimolecular recombination is negligible. Exciton dissociation at the interface hardly depends on temperature or offset here, so the change in current tracks the separation of CT states into free charges.

For high-offset PTO2:IT-4F (0.35 eV), the current stays the same: separation is already efficient at 200 K. For PM7:IEICO-4F (0.11 eV), the current at 305 K is twice that at 200 K. The pairs need thermal energy to get over the Coulomb barrier. An Arrhenius fit of the current gives an activation energy E_a for each blend.

Curves computed here as J(T)/J(200 K) = exp[−E_a/k_B(1/T − 1/200 K)] with the Table 1 E_a; they agree with the data of Fig. 3a within reading accuracy (×2.0 for PM7:IEICO-4F at 305 K).

Activation energy and efficiency move in opposite directions

Plotted against offset, E_a and CSE are mirror images. In high-offset blends, E_a is below the thermal energy at room temperature (about 26 meV) and CSE is high. PTO2:IT-4F has only 1.9 meV.

In low-offset blends E_a rises above 26 meV: 35–39 meV for PM7:Y1, PM6:IEICO-4F and PM7:IEICO-4F, and 44 meV for PM6:IEICO. These pairs face a real Coulomb barrier and many fail to separate at room temperature. The CSE that remains in these blends is partly thanks to heat.

Points from Table 1, as in Fig. 3b. P3HT:o-IDTBR (0.63 eV, 14.6 meV, 36%) lies off the right edge and is not in Fig. 3b.

Shrinking the offset helps only up to a point

High offset: excess energy separates the charges, and CSE stays high as the offset shrinks while V_OC rises (with the same low-gap material). PM6:Y6 (0.32 eV) → PM7:Y6 (0.22 eV): V_OC goes from 0.83 to 0.87 V with no change in CSE.

Low offset: CSE falls sharply, but V_OC no longer improves. The CT state and the local exciton are thermally populated together, so non-radiative recombination is dominated by the exciton of the low-gap material, and V_OC is set by its luminescence yield. PM6:Y1 (0.17 eV) → PM7:Y1 (0.11 eV): CSE halves, V_OC stays the same.

Mid offset: a narrow range in between, where excess energy and thermal energy together keep CSE high while V_OC is already at its maximum.

Schematic, after Fig. 5; example values from the text.

About 15 meV is enough

How large may E_a be? Starting from the measured temperature dependence of PTO2:IT-4F (E_a = 1.9 meV), the authors model the power output versus temperature for larger activation energies. The higher E_a, the higher the temperature at which output peaks. Measured cells follow the same trend (Fig. 4b). An E_a close to 15 meV is still enough for optimal CSE at room temperature; much higher values will likely hurt.

PM1:BTP-eC9, one of the best binary blends (PCE over 19%), fits this picture: offset ≈ 0.2 eV, voltage loss 0.5 V, E_a ≈ 8 meV and CSE 81%. The authors' advice: don't aim for zero offset. Aim for the mid-offset range and tune the activation energy, for example through hybridisation, interface dipoles or quadrupole moments. These results are for weak light. At 1 sun, bimolecular recombination at low temperature changes the picture.

Curves schematic, after Fig. 4a (the peak shifts to higher T as E_a grows). PM1:BTP-eC9 values from the text.