Why a third component raises, pins or lowers the voltage

Up, flat or down

A ternary organic solar cell (TOSC) is a host binary blend (one donor, one acceptor) plus a guest component. Record efficiencies come from such cells. At first the guest was added to absorb more light, but it can also change the open-circuit voltage V_OC, and nobody agreed on why.

The authors built six dual-acceptor systems. In each one a fullerene (PC₇₁BM or Bis-PC₆₂BM) gradually replaces the non-fullerene acceptor: PM6:Y6, PBDB-T:Y1, PM6:IT-M (twice, with two fullerenes), PM6:ITCC and PBDB-T:IEICO-4F. Depending on the system, V_OC rises, stays pinned or falls as the fullerene content goes up.

Trend shapes schematic, after Fig. 1b; no values read off the plot.

Alloy or parallel?

Two models were in use. The alloy model assumes the two acceptors mix well and form one phase with an averaged charge-transfer (CT) state. The parallel model assumes poor mixing, so the cell behaves like two binary cells side by side.

Each works in some systems and fails in others. The alloy model cannot explain tunable V_OC in some cells with two similar fullerenes. Some "parallel-like" cells have V_OC pinned to the lower binary value instead of a linear mix. Most of all, both tie V_OC only to the CT-state energy E_CT. Neither considers how the guest changes recombination, even though the non-radiative loss is a major part of the voltage loss.

Schematic morphologies; not from a figure in the paper.

Radiative limit minus non-radiative loss

Detailed balance (assuming near thermal equilibrium) splits the voltage into two measurable pieces:

V_OC^rad = (kT/q) ln(J_SC/J_0,rad) comes from the photovoltaic quantum efficiency EQE_PV. J_SC weights it with the solar spectrum, which is nearly flat here. J_0,rad weights it with 300 K black-body radiation, which grows exponentially towards low photon energy. So J_0,rad is set by the weak absorption tail.

EQE_EL is the electroluminescence efficiency of the cell run as an LED. Computed this way, V_OC follows the measured trends in all six systems.

Spectra schematic; the equations are Eqs. 1–4 of the paper.

Does the guest change the host?

Treat the guest as forming its own binary blend with the donor (the "guest binary"). Then compare the ternary EQE_PV with the composition-weighted sum of the two binary spectra.

Case-1 (five systems): the two match. The ternary behaves like a linear combination of two binaries, and the morphology hardly changes. For PM6:Y6:PC₇₁BM, calorimetry (DSC) and X-ray scattering (GIWAXS) look like those of PM6:Y6.

Case-2 (PBDB-T:IEICO-4F:PC₇₁BM): the ternary absorption edge shifts further to the blue as fullerene is added. PC₇₁BM suppresses aggregation of IEICO-4F: its melting endotherm at about 325 °C disappears and its diffraction peak broadens.

Schematic, after Fig. 2a,b and Fig. 4a.

V_OC^rad barely moves

In Case-1, J_SC and J_0,rad of the ternary are weighted sums of the binary values. Write the guest's values as J_SC^G = a·J_SC^H and J_0,rad^G = b·J_0,rad^H. For guest fraction x:

In the measured systems a is 0.5–1.5 and b spans 10⁻⁵ to 10¹. With a = 1, a guest with smaller J_0,rad (b < 1) gains at most about 20 mV at 50%. With b = 1 nothing changes. A guest with larger J_0,rad (b > 1) pulls V_OC^rad down quickly. So in Case-1 the radiative limit leaves little room. In Case-2 the equation fails, because the host itself changes.

Curves drawn from Eq. 5 with a = 1 at 300 K, as in Fig. 2f,g.

Three EQE_EL trends

The host binaries emit at least ten times more efficiently than the guest binaries. In the host blends CT and local-exciton (LE) states lie only about 30–80 meV apart. They hybridise, and the bright LE state is thermally populated. In the fullerene guest blends the gap is about 150–340 meV, and the emission is pure, dim CT emission.

As the guest is added, EQE_EL follows one of three trends. It stays pinned at the host value up to about 80% guest (PM6:Y6, PBDB-T:Y1, PM6:IT-M:Bis-PC₆₂BM). It falls steadily (PM6:ITCC, PM6:IT-M:PC₇₁BM). Or it rises up to about 80% and then drops (the Case-2 IEICO-4F system). In the electroluminescence spectra, guest CT emission shows up only in the systems where EQE_EL falls.

Trend shapes schematic, after Fig. 3a–c; offsets from the text.

Excitations sit where energy is lowest

Whether guest CT emission appears depends on where the guest CT state lies. In the "falling" systems E_CT of the guest is below that of the host. In the "pinned" systems it is above. Near thermal equilibrium, excitations spread over all states according to the Boltzmann factor. A low-lying dim state collects them and becomes the main loss channel.

The authors extend their three-state model to four states: LE_H 1.50 eV, CT_H 1.45 eV, LE_G 1.80 eV, and CT_G moved from 1.60 to 1.30 eV. If E_CT,G > E_CT,H, the simulated EQE_EL stays pinned to the host. If it is lower, EQE_EL falls continuously with guest content. If the two are equal, EQE_EL is roughly a linear mix of the two binaries. Thermal population alone reproduces all the Case-1 trends.

Level energies from Fig. 3g; the dots are a Boltzmann illustration, not the paper's simulation.

Less aggregation, brighter host

The rise in the IEICO-4F system needs one more ingredient. When PC₇₁BM breaks up IEICO-4F aggregates, aggregation-caused quenching (ACQ) is suppressed. The PLQY and the exciton lifetime of IEICO-4F rise with fullerene content (transient absorption shows the longer lifetime is not a fluence effect). In the model, a higher LE_H PLQY lifts the flat part of the EQE_EL curve, so EQE_EL first rises and then falls, as measured.

Trap passivation could give a similar effect. Space-charge-limited-current measurements rule it out here. So in Case-2 both parts can improve: the blue-shifted edge raises V_OC^rad, and the brighter host lowers ΔV_nr.

Schematic, after Fig. 3c,i and Fig. 4e.

Two rules for the guest

Rule 1 (Case-1). Use a guest whose binary blend emits more efficiently than the host (EQE_EL^G > EQE_EL^H): a luminescent guest with a small CT–LE offset. Keep its CT energy close to the host's (E_CT,G ≅ E_CT,H). Too low, and absorption from those low states raises J_0,rad (b > 1), so V_OC^rad falls by more than ΔV_nr gains.

Rule 2 (Case-2). Use a guest that mixes well with the low-gap component of the host, so that it suppresses aggregation. Such a guest does not even need to be a semiconductor; an insulator could work, as long as it does not harm the electronic properties.

The two cases can overlap: one guest can meet both rules. The authors note that they do not exclude other mechanisms in other material combinations.

Schematic, after Fig. 4c.