Explainer · Advanced Materials 2020

Free charges without a barrier in PM6:Y6

An electron and a hole that have just been split at a donor–acceptor interface still attract each other strongly. In PM6:Y6 they escape anyway, with no help from the electric field and almost none from heat. The electrostatics of the Y6 molecule do the work.

L. Perdigón-Toro*, H. Zhang*, A. Markina, J. Yuan, S. M. Hosseini, C. M. Wolff, G. Zuo, M. Stolterfoht, Y. Zou, F. Gao, D. Andrienko, S. Shoaee, D. Neher. Barrierless free charge generation in the high-performance PM6:Y6 bulk heterojunction non-fullerene solar cell. Advanced Materials 32, 1906763 (2020). *Equal contribution. doi:10.1002/adma.201906763

1 / 9 · TWO WAYS IN

Light makes excitons, the interface makes charges

PM6 is a donor polymer and Y6 an acceptor molecule. A photon absorbed in either one creates an exciton, a tightly bound electron–hole pair on one material. Only at the interface between the two can the pair be pulled apart.

There are two channels. If PM6 absorbs, its electron drops into Y6 (channel I). If Y6 absorbs, its hole moves into PM6 (channel II). The singlet energies are 1.90 eV for PM6 and 1.42 eV for Y6, and the charge-transfer (CT) state lies at about 1.41 eV. So channel I has a driving force of ≈0.60 eV, channel II only ≤0.13 eV, and the ionization-energy offset is just 0.09 eV.

Energy levels after Fig. 1a (cyclic voltammetry, from ref. 4 of the paper).

2 / 9 · THE TRAP

The Coulomb trap

Right after transfer, the electron sits on Y6 and the hole on PM6, about a nanometre apart. This CT pair is still bound by Coulomb attraction. For an organic material with a dielectric constant around 3.5:

Eb ≈ q² / (4πε₀εrr) ≈ 0.4 eV at r = 1 nm

Theory for homogeneous media predicts a CT binding energy of around 400 meV, more than fifteen times the thermal energy at room temperature (kBT ≈ 26 meV). On paper, the pair should mostly fall back together.

The curve is the bare Coulomb potential; the paper quotes the ≈0.4 eV expectation from the literature.

3 / 9 · WHAT A BARRIER LOOKS LIKE

Fingerprints of a barrier

If the pair had to climb out of that well, two things would give it away. First, the yield of free charges would depend on the internal electric field: a strong field at reverse bias lowers the barrier, a weak field near open circuit does not. Second, cooling the device would cut the yield, because the pair would need heat to escape.

The curves on the right show what that looks like in a simple barrier model. They are an expectation, not data.

4 / 9 · THE MEASUREMENT

Counting charges with a delayed field

Time-delayed collection field (TDCF) separates generation from what happens later. The cell is held at a pre-bias Vpre, which sets the internal field. A ≈5 ns laser pulse creates charges. After 6 ns the voltage jumps to a strong reverse bias of −2.5 V and every free charge is swept out and counted.

The pulse is weak (0.05 µJ cm−2, in the regime where collected charge is strictly proportional to fluence), so charges barely meet each other before collection. The collected charge Q then measures how many free charges were generated at Vpre.

5 / 9 · FLAT

No field dependence, whatever you excite

For PM6:Y6 the collected charge does not change with pre-bias, even close to Voc. That holds at six photon energies: 2.76, 2.33 and 2.07 eV (mainly PM6, channel I), 1.55 and 1.41 eV (Y6, channel II), and 1.29 eV, inside the low-energy shoulder attributed to the CT state.

The internal quantum efficiency and the internal generation efficiency are both close to one and do not depend on photon energy. Extra driving force (channel I) and excess photon energy bring no benefit: generation proceeds through cold, relaxed CT states.

Schematic, after Fig. 1c; each curve is normalised to its value at −2 V.

6 / 9 · COLD

Six millielectronvolts

Cooling tests the second fingerprint. In TDCF, free charge generation drops by less than 10% from 320 K to 230 K and stays field independent. Low-intensity EQE measured versus temperature follows EQE = EQE₀·exp(−Ea/kBT) with Ea = 6 meV at every excitation energy.

Comparable studies on fullerene blends found a few tens to ≈100 meV. Generation stays efficient down to ≈125 K, and Voc rises linearly on cooling down to ≈100 K, so the free-carrier density is unaffected. Charge generation in PM6:Y6 is essentially barrierless.

Lines are Eq. (1) of the paper drawn with the quoted Ea values, not the measured points (Fig. 2c).

7 / 9 · NOT DISORDER

Order, not disorder

One popular explanation for easy charge separation is energetic disorder: a broad spread of site energies offers low-energy escape routes. Temperature-dependent space-charge-limited currents give a disorder of σIE = 83 meV for holes and σEA = 71 meV for electrons, and recombination is non-dispersive. Both point to a narrow density of states, too narrow to be the main driver.

Aggregation of Y6 does matter. In a dilute blend (PM6:Y6 = 10:1) where Y6 no longer aggregates, generation becomes field dependent and thermally activated with Ea ≈ 22 meV.

8 / 9 · WHY

The quadrupole flattens the hill

Y6 has an A–D′–A″–D′–A architecture. Its electrostatic potential is positive over the conjugated core and negative at the ends (Fig. 4a), giving a large quadrupole moment (Qxx = −120, Qyy = 80, Qzz = 40 D·Å). In the crystal, Y6 molecules pair up so that their dipoles cancel and the quadrupolar fields remain.

At a donor–acceptor interface the concentration of Y6 changes, so its crystal field bends. This bias potential B pushes electrons and holes away from the interface and shrinks the energy gap between the CT state and free charges. An upper-bound estimate gives B ≈ 1.1 eV for Y6; simulations suggest B > 1 is enough for barrierless CT dissociation.

Molecule and energy landscape are schematic, after Fig. 4a and the text.

9 / 9 · WHAT FOLLOWS

Generation is not the bottleneck

Because generation is the same at every bias, any slope of the J–V curve near short circuit must come from recombination of free charges. That recombination is bimolecular (order 2.14) with k2 = 1.7 × 10−17 m³ s−1, only about 30 times below the Langevin rate of 5.5 × 10−16 m³ s−1.

The devices reach 13.7% (Voc 0.856 V, Jsc 22.4 mA cm−2, FF 71.3%), and a certified 1 cm² cell 13.45%. They are limited by absorption and extraction, not generation. Simulations suggest more than 18% is within reach with a smaller k2 and ten times higher mobility.

J–V drawn with a diode model (ideality 1.17 from the paper) plus a linear collection loss, matched to Voc, Jsc and FF of Table S1; the generation line is schematic.

Try it

Escape from the Coulomb well

A deliberately simple toy model, built for intuition and not taken from the paper. A CT pair escapes with rate k = k₀·exp(−Ea/kBT) or recombines with rate kr = k₀/100. The barrier is Ea = Eb − ΔEB − ΔE(F): the Coulomb binding energy, minus an electrostatic compensation ΔEB, minus the lowering by the internal field F (Poole–Frenkel form, 100 nm device, built-in voltage 1 V). ΔEB stands in for the effect of the interfacial bias potential; it is not the paper's B, which is defined differently. The plot shows the free-charge yield against applied voltage, like the TDCF pre-bias scan.

–yield at short circuit
–yield near Voc / yield at −2 V
–apparent activation energy

Try this: with ΔEB = 0 the yield is small and falls toward open circuit. Raise ΔEB toward Eb and the curve goes flat and high. Then lower the temperature: with the barrier gone, cold barely matters.