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# Design rules for minimizing voltage losses in high-efficiency organic solar cells

## Abstract

The open-circuit voltage of organic solar cells is usually lower than the values achieved in inorganic or perovskite photovoltaic devices with comparable bandgaps. Energy losses during charge separation at the donor–acceptor interface and non-radiative recombination are among the main causes of such voltage losses. Here we combine spectroscopic and quantum-chemistry approaches to identify key rules for minimizing voltage losses: (1) a low energy offset between donor and acceptor molecular states and (2) high photoluminescence yield of the low-gap material in the blend. Following these rules, we present a range of existing and new donor–acceptor systems that combine efficient photocurrent generation with electroluminescence yield up to 0.03%, leading to non-radiative voltage losses as small as 0.21 V. This study provides a rationale to explain and further improve the performance of recently demonstrated high-open-circuit-voltage organic solar cells.

## Main

A major breakthrough in organic solar cell (OSC) development was the discovery of the donor–acceptor (D:A) bulk heterojunction (BHJ) concept1, which in many material systems provides a fast (sub-100 fs) and efficient route for exciton dissociation2. This concept formed the basis for the general paradigm of OSC advances and led to devices with high photovoltaic external quantum efficiencies (EQEPV)3 and high photocurrent4. However, the gain in the number of extracted charges was achieved at the expense of large photovoltage losses5,6. In comparison to efficient inorganic and hybrid perovskite solar cells, it is clear that one of the main challenges in OSCs is the optimization of the device voltage with respect to the optical absorption spectrum7.

Previous studies have shown that the open-circuit voltage (VOC) in OSCs is determined by the energy of charge-transfer (CT) states at D:A interfaces, as well as recombination processes8,9,10. According to the classical Mulliken theory11, the CT state energy is close to that of the ‘effective gap’ between the ionization potential (IP, or more crudely, highest occupied molecular orbital (HOMO)) of the D, and the electron affinity (EA, or lowest unoccupied molecular orbital (LUMO)) of the A. For this reason, a large number of recent efforts directed towards reducing voltage losses have been focused on increasing the energy of CT states by minimizing the energetic offset between D and A (more precisely, the offset between either the IPs or the EAs of the two components). The increase in CT energy, however, leads to a lower driving force for exciton dissociation (ΔGLE-CT, defined as the energy difference between the local excited (LE) state and the CT state). Although polymer:fullerene blends generally tend to show low efficiencies with low driving forces5,12, there are exceptions13,14, and recent polymer:non-fullerene materials exhibit efficient charge separation despite low (<0.1 eV) ΔGLE-CT values15,16. The detailed molecular mechanism behind this improved performance is still unclear17.

Apart from effective-gap optimization, functional strategies for reducing non-radiative recombination are still needed. Based on detailed-balance considerations, radiative recombination of excitons is an unavoidable process accompanying the absorption, and non-radiative recombination always constitutes an additional, particularly detrimental, loss channel18,19,20. Therefore, to maximize VOC, the yields of photoluminescence and electroluminescence processes in OSC materials need to be enhanced 21.

Here, we formulate key design rules for combining low voltage losses with efficient photocurrent generation, and demonstrate a set of existing as well as unreported material systems that effectively apply these rules to achieve high power conversion efficiency (PCE). We show that the high-performance regime is achieved in these OSCs due to charge dynamics that differ from those observed in ‘conventional’ polymer:fullerene materials. These non-typical photophysics are induced by a concerted combination of two factors: (1) low energy offset between D and A molecular states and (2) high photoluminescence yield of the blend components. As a result, CT excitons formed after initial charge transfer become hybridized with emissive LE states. This leads to slow charge separation, as observed in ultrafast photoluminescence and transient absorption measurements, and also to the minimization of non-radiative relaxation to the ground state. As a result, the studied low-ΔGLE-CT OSC systems show small non-radiative recombination and high VOC similar to that of devices based on pristine D or A.

## Materials and photovoltaic performance

Our study involves D:A blends consisting of five polymers and five small molecules acting as the D and A components, respectively. The polymers comprise different conjugated backbones representative of the D polymers currently used in the OSC community, including polythiophene-22, naphthobisoxadiazole-23, thieno[3,4-b]thiophene-24, quinoxaline-25 and difluorinated triazole-based polymers26. The A components include both non-fullerene materials (indacenodithieno[3,2-b]thiophene- and indacenodithiophene-based small molecules)27,28 and PC71BM. Non-fullerene-based OSCs have continued to attract attention during the past several years, with systems achieving PCEs over 13% (refs 29,30,31). The particular material combinations were chosen to achieve low D:A energy offsets and hence close alignment of CT absorption with that of the red absorber (D or A) in the blend.

The chemical structures of the materials are shown in Fig. 1a alongside sketches of the state energies for the D:A combinations in Fig. 1b. Apart from the PTB7-Th:PC71BM blend, which is used here as a state-of-the-art reference, the energy offsets are small in all cases. Figure 1c compares the current density–voltage (J–V) curves under illumination of the studied D:A systems with those of the narrow-gap component of the blend. For all the material systems, photocurrent generation is significantly enhanced in a BHJ compared to the pristine-material devices. However, in striking contrast to the PTB7-Th:PC71BM reference blend, where VOC decreases dramatically on forming the BHJ, the VOC values in the other material systems are almost identical to those of the respective single-component devices. Therefore, the formation of a BHJ significantly facilitates charge separation without a corresponding decrease in VOC. Consequently, the voltage losses in these systems are around or even below 0.6 V (Table 1). The PNOz4T:PC71BM blend is one of the few fullerene-based devices where high efficiency (~9%) is possible in spite of a small energy offset14. Most of the blends investigated in this work show reasonably high values of EQEPV in the range of 45−70% as well as good PCEs (Table 1).

### Energies of molecular states

Measurements of the energetics on isolated D and A neglect the influences of film morphology and interfacial effects when D and A are mixed32,33. An appropriate approach to investigate the energy offsets in the D:A blends is to perform measurements on complete devices34,35. We therefore used highly sensitive Fourier-transform photocurrent spectroscopy (FTPS) to measure the sub-gap FTPS-EQE of the devices based on BHJ blends and pristine films.

Figure 2a–f compares the FTPS-EQE and electroluminescence spectra (see Supplementary Fig. 6 for the bias dependence of the electroluminescence spectra) of the studied blends with that of the corresponding low-gap components (in orange in Fig. 1b). For all the low-ΔGLE-CT material systems, the FTPS-EQE and electroluminescence spectra of the blends and low-gap components largely overlap (Fig. 2a–e), without showing the strongly redshifted features typical of polymer:fullerene CT state formation36, as demonstrated in the PTB7-Th:PC71BM reference (Fig. 2f). Such behaviour might originate from two scenarios. On the one hand, the absence of redshifted absorption in the blend may arise from CT states that are degenerate or hybridized with the singlet excitons and therefore absorb and emit in the same region. On the other hand, the CT state may indeed have a lower energy, but the resultant red shoulder might be undetectable by optical measurements if the electronic coupling between the CT and ground states is very weak. Extrapolating the temperature-dependent VOC data reveals the energy at which the electron and hole recombine. For systems with small voltage losses, this energy is indeed comparable for the blend and low-gap component (Supplementary Fig. 7), being consistent with their overlapping optical spectra. This finding is also reflected in the dark J–V curves in Supplementary Fig. 8, where the recombination-dominated exponential region is less shifted than the PTB7-Th:PC71BM reference.

### Charge generation

We have shown that using low D:A band offsets brings the effective energy gap of the blend close to that of the low-gap component. However, this also decreases the driving force for exciton dissociation to CT states, which could be detrimental to the efficiency of charge generation. Indeed, for a range of polymer:fullerene blends, it was shown that the yield of free carriers exponentially decreases with decreasing driving energy37. To investigate the efficiency and dynamics of the charge generation process, we used steady-state and time-resolved photoluminescence as well as transient absorption spectroscopy.

Photoluminescence quenching measurements provide a straightforward approach to estimate the exciton dissociation efficiency. Although it is common to compare photoluminescence in pristine and blend films, the material morphologies in these two cases are different. In the blend, one material is dispersed in the matrix of another, while in the pristine films, identical molecules are closely packed, potentially leading to strong photoluminescence self-quenching38. Therefore, as a ‘pure’ reference sample we blended the insulating polymer polystyrene (PS) with materials with lower optical gaps, aiming to mimic the dispersed morphology in the active layer of the device. Although the PS blend does not replicate the exact morphology in the active layer, it still provides a qualitative similarity. While the possibility for substantial aggregation and self-quenching may still exist in the PS blend, this will only lead to a decrease in the estimated quenching efficiency. We indeed find that the photoluminescence intensity of the pristine materials is significantly enhanced following the addition of PS (Supplementary Fig. 9), where the peak shift might be due to variations in the morphology of the materials after blending. Supplementary Fig. 10 and Supplementary Table 4 compare the photoluminescence quantum efficiencies (PLQEs) in the D:PS or PS:A combinations with that of the D:A blends. Although reasonable quenching of the excitonic luminescence is achieved in the low-ΔGLE-CT systems, the quenching is not as pronounced as in the reference PTB7-Th:PC71BM blend.

Concomitant with the steady-state photoluminescence findings, time-resolved photoluminescence measurements (Fig. 2g–k) show shortening of the photoluminescence lifetime following blending. Interestingly, the timescale on which the photoluminescence quenching occurs is surprisingly slow in the low-ΔGLE-CT materials. Although photoluminescence quenching in PTB7-Th:PC71BM is resolution limited (10 ps), quenching in the other materials typically happens in timescales of 10–30 ps. This is still faster than the radiative decay and leads to fairly efficient exciton dissociation, in agreement with steady-state measurements (Supplementary Table 5).

Figure 3 gives a more detailed insight into the charge separation dynamics by summarizing the results of transient absorption experiments on the five most efficient blends and devices. Transient absorption was measured in the 900–1,500 nm region following excitation at the red edge of the blend absorption (Supplementary Fig. 11); additional control measurements were performed in the 450–800 nm region (Supplementary Fig. 12 and Supplementary Table 6) and with wide-gap component excitation (Supplementary Fig. 13a). Singular-value decomposition (SVD) was then applied to identify the contributions of different excited states to the response39. We note that although SVD does not guarantee the complete separation of responses from different species, it is a robust mathematical procedure39 that can be applied to all the studied systems without additional adjustments. This makes SVD a very efficient tool for capturing the key parameters describing the interconversion of excited states, like excitons to charges.

The dynamics of the extracted SVD components are presented in Fig. 3a–f, and Fig. 3g–l presents a comparison of the representative kinetics measured in films and working devices. The behaviour of the reference blend PTB7-Th:PC71BM (Fig. 3a) is consistent with the existing paradigm of charge generation in BHJs40. The exciton lifetime of PTB7-Th (~70 ps in the PS matrix) is dramatically shortened in the blend with PC71BM due to CT occurring on the sub-300 fs timescale. Charge generation is also observed as the appearance of a strong, long-lived polaron absorption in the sub-picosecond timescale (Fig. 3a). This signal slightly evolves in the ~0.1–1 ns time range, which is suggestive of long-range charge separation and/or relaxation within the density of states.

In agreement with the time-resolved photoluminescence, the transient absorption data show much slower exciton quenching in the low-ΔGLE-CT materials. Compared to the pure materials, the excitonic response in the blends decays only slightly faster within the first ~10 ps (Supplementary Fig. 13b). Accordingly, the polaronic response in the low-ΔGLE-CT systems emerges at slower timescales (15–30 ps). This could be the result of either very slow CT, or strong phase segregation whereby excitons require a considerable time to reach the D:A interface14. The latter option is unlikely; taking the PTB7-Th:IEICO blend as an example we find that (1) efficient energy transfer occurs between D and A, as observed after D excitation (Supplementary Fig. 13a), implying domain sizes of <20 nm, and (2) the dynamics are different in the PS matrix and in the pure materials, suggesting that large domains of the pure phase are not formed in the blends. Therefore, all the presented data indicate that the materials invoke a very slow CT process, at least 100 times longer than in conventional OSCs.

The observation of slow charge separation in the low-ΔGLE-CT systems indicates that, in comparison to most polymer:fullerene blends41,42, a conceptually different mechanism is responsible for photocurrent generation. Instead of ultrafast charge carrier generation assisted by electronic delocalization typical for polymer:fullerene blends2,43,44, 100 times slower exciton and/or CT state dissociation is observed in the low-ΔGLE-CT systems. The exciton dissociation rate can be reduced by a decrease in electronic coupling and/or by the increase of the dissociation barrier through the lowering of ΔGLE-CT. In the low-ΔGLE-CT systems, the presence of such a barrier is in fact confirmed by transient absorption measurements on films and devices. While PTB7-Th:PC71BM and other previously studied high-performance45 systems show no external-field effect on the separation of charges (Fig. 3g), the yield of charge carriers in the low-ΔGLE-CT systems exhibits a sensitivity towards a weak external field inside the device (Fig. 3h–l). This effect mostly manifests itself at early times (~10 ps), which suggests that the electric field is more likely influencing exciton dissociation rather than the dynamics of the CT states 46.

### Modelling of excitonic and CT states

To obtain more insight into the difference between typical polymer:fullerene blends and the low-offset systems, we compare, as an example, PTB7-Th:IEICO and PTB7-Th:PC71BM blends. The results of density functional theory (DFT) calculations (see Methods and Supplementary Table 7) are in agreement with the experimental data, indicating that IEICO and PC71BM have comparable LUMO energies, while IEICO and PTB7-Th have comparable HOMO energies.

The excited state calculations performed on both model and optimized PTB7-Th:IEICO and PTB7-Th:PC71BM complexes (Supplementary Figs. 14 to 16 and Supplementary Table 8) show that the lowest CT states in both materials have similar energies and that the absolute value of ΔGLE-CT is ~0.2–0.3 eV smaller in PTB7-Th:IEICO than in PTB7-Th:PC71BM. For PTB7-Th:IEICO, ΔGLE-CT is estimated to be ~80 meV (Fig. 4). Based on the DFT-derived electronic couplings (Supplementary Table 8) and using Marcus semi-classical electron transfer theory (see Methods) we estimate that the exciton dissociation rate (kLE→CT) in PTB7-Th:IEICO is ~1 × 1012 s−1. This result is in good agreement with the photoluminescence quenching data. As seen from Fig. 4b,c, the back electron transfer rate (kCT→LE) is also rapid in this system. In contrast, recombination of the CT state (kCT→GS) is very slow due to the large ΔGCT-GS and small electronic couplings. However, our model does not account for the triplet states that can provide an additional pathway for deactivation of the CT states13. Although this recombination channel still needs to be investigated, based on the experimental observations we conclude that the lifetime of the CT states in PTB7-Th:IEICO is sufficiently long to ensure their dissociation into free charges.

The calculated energetics are concordant with the steady-state spectroscopic data and have important consequences for the charge dynamics. The rate constants of both non-radiative (knr) and radiative (kr) transitions from the CT state to the ground state are proportional to the square of the CT→S0 electronic coupling. Given that the CT energies and reorganization energies in PTB7-Th:IEICO and PTB7-Th:PC71BM are comparable, we expect that both knr and knr are larger in PTB7-Th:PC71BM due to the larger electronic coupling (Supplementary Table 8). In the case where only relaxation directly from the CT state is considered, the EQE of emission (EQEEL $$\propto k_{\mathrm{r}}$$/$$(k_{\mathrm{r}} + k_{\mathrm{nr}})$$) is independent of electronic coupling20; therefore, the coupling variation cannot be solely responsible for the change in VOC. However, the picture changes significantly when rules (1) and (2) formulated in this study are applied. First, hybridization of the CT state with the highly emissive LE state due to small energy offset ΔGLE-CT between D and A will increase the radiative ability of the CT state through the intensity borrowing mechanism47,48. More importantly, when ΔGLE-CT is small, an efficient transition from the CT state back to the LE state is possible. This opens an additional radiative relaxation pathway from the CT state through the highly emissive (rule (2)) LE state. If this radiative relaxation channel is efficient, the non-radiative voltage loss should decrease. When ΔGLE-CT is well above the thermal energy (kT), as in PTB7-Th:PC71BM, the non-radiative rate is solely determined by the properties of the CT state and increases rapidly as the energy of the CT state decreases20. Along the same vein, in the process of bimolecular recombination, the similarity of the HOMO (ionization potential) energies in PTB7-Th and IEICO allows holes to transfer directly from PTB7-Th to IEICO and form an IEICO LE state, which can then contribute to radiative recombination.

As shown above, slow but efficient charge separation and strong photoluminescence intensity can coexist in OSC blends, which is beneficial for a high VOC according to18

$$V_{\mathrm{OC}} = V_{\mathrm{OC}}^{\mathrm{rad}} - \frac{{kT}}{q}{\mathrm{ln}}\left( {\frac{1}{{{\mathrm{EQE}}_{\mathrm{EL}}}}} \right)$$
(1)

where $$V_{\mathrm{OC}}^{\mathrm{rad}}$$ denotes the maximum VOC of the device when only radiative recombination exists, T is the temperature, k is Boltzmann’s constant, q is the elementary charge, and EQEEL is the radiative quantum efficiency of the solar cell. We summarize the EQEEL data for all systems (Table 1) and find that the VOC values are similar for the pristine and blend devices when their EQEEL values are comparable. The PDCBT-2F:IT-M blend exhibits a high EQEEL of ~0.03%, resulting in a small loss of ~0.21 V due to non-radiative recombination. In addition, we observe no tradeoff between the EQEEL and the PCE. For instance, the PvBDTTAZ:O-IDTBR blend shows a high EQEEL of ~0.008% and a high PCE of 11.4%. This indicates that the PCE of the PvBDTTAZ:O-IDTBR blend could potentially be further improved by decreasing the non-radiative recombination in O-IDTBR. These discussed systems have the lowest non-radiative recombination losses reported to date for OSCs, similar to those found in inorganic thin-film technologies6,7.

Our results indicate that the luminescence properties of the low-gap components are key parameters for designing efficient OSC systems. For example, the PBQ-QF:IEICO-4F blend exhibits a relatively low EQEEL of ~1 × 10−5, representing a voltage loss of ~0.30 V due to non-radiative recombination. This value is larger than those for the other four systems with negligible energetic offset. When comparing the pristine IEICO-4F and PBQ-QF:IEICO-4F, it becomes clear that the low EQEEL of the blend is due to the relatively low EQEEL (2.7 × 10−5) of pristine IEICO-4F itself. As EQEEL requires electrical injection of electrons and holes, the EQEEL values might underestimate the luminescence properties of the active materials in cases of non-ohmic contacts or low-conductivity materials; however, the PLQE measurements (Supplementary Fig. 10) show that the PLQE is also low in IEICO-4F, which further confirms the poor luminescence properties of the pristine material.

To further demonstrate that the luminescence properties of the low-gap materials are key to determining the non-radiative recombination in the blend, we also investigated the non-radiative recombination at different weight ratios (Supplementary Table 10 and Supplementary Fig. 17). We found that the VOC only shows a slight dependence on the weight ratio. These results are fully consistent with our argument that VOC is determined by the low-gap materials in the blends. The minor difference at high weight ratios might be due to a change in the aggregation states of the materials, resulting in a slight difference in the non-radiative recombination.

### Outlook

The present study introduces a set of rules for the design of OSC devices with high output voltages. We show that combining high VOC and charge generation efficiency is possible when two key factors work together to bring the photophysics of the blend into the new regime: (1) there is a low energy offset between the D and A molecular states and (2) the low-gap component is highly luminescent. We illustrate that the application of these design rules to a range of existing and unreported material systems allows the construction of devices with decreased non-radiative losses and good photovoltaic performance.

In these systems, both VOC and JSC are determined by the energy of the excitonic states. This is conceptually different from conventional OSC systems such as PTB7-Th:PC71BM, where absorption and emission take place at different energies, so that the absorption edge (and thus JSC) is determined by the D and A materials while the VOC is determined by the CT states. The low-ΔGLE-CT materials behave similarly to other single-semiconductor-based photovoltaic materials in that the optical and electronic gaps converge to the same value; however, two materials are needed to form a BHJ for a high EQEPV. In the studied systems, this comes at the expense of substantially slowing (down to >10 ps) the rate of exciton dissociation and introducing a sensitivity to external fields, but still allows for fairly high photocurrent generation in the device. These findings open the route for the next prospect in the design of both pristine absorber materials and the BHJ. This prospect asserts that there is no additional intrinsic limit for the VOC and efficiency of OSCs compared with other photovoltaic technologies, which is an essential step towards the commercialization of OSCs.

## Methods

### Materials

PTB7-Th and PC71BM were purchased from Solarmer and Solennebv, respectively. PDCBT-2F, PBQ-QF, IT-M, IEICO and IEICO-4F were synthesized at the Institute of Chemistry, Chinese Academy of Sciences. PvBDTTAZ, O-IDTBR and PNOz4T were synthesized at the Hong Kong University of Science and Technology. The materials were all synthesized as reported previously.

### Time-resolved photoluminescence

Time-resolved photoluminescence measurements were performed at room temperature. A wavelength-tunable mode-locked Ti:sapphire laser was used as the excitation source; this has a repetition rate of 76 MHz and a pulse duration of 2 ps. Photoluminescence emission induced by the pulsed excitation laser was detected by a Hamamatsu streak camera combined with a single-grating monochromator.

### Devices

The device structure of PDCBT-2F:IT-M, PTB7-Th:IEICO and PBQ-QF:IEICO-4F based solar cells is indium tin oxide (ITO)/Poly(2,3-dihydrothieno-1,4-dioxin)-poly(styrenesulfonate) (PEDOT:PSS)/active layer/Poly[(9,9-bis(3′-((N,N-dimethyl)-N-ethylammonium)-propyl)-2,7-fluorene)-alt-2,7-(9,9-dioctylfluorene)] Dibromide (PFN-Br)/Al, with an active area of 4 mm2. The device structure of PNOz4T:PC71BM and PvBDTTAZ:O-IDTBR based solar cells is ITO/ZnO/active layer/V2O5/Al, with an effective area of 7 mm2 (measured with a mask of 5.9 mm2). The device structure of PTB7-Th:PC71BM, PNOz4T, IT-M, IEICO, IEICO-4F, O-IDTBR and PTB7-Th based solar cells is ITO/PEDOT:PSS/active layer/LiF/Al, with an effective area of 4 mm2. The effective areas of the devices were determined with the optical microscope. BHJ devices based on PDCBT-2F:IT-M, PNOz4T:PC71BM, PTB7-Th:IEICO, PvBDTTAZ:O-IDTBR and PTB7-Th:PC71BM were fabricated following conditions taken from the literature4,14,22,26,49. Devices based on PBQ-QF:IEICO-4F were prepared as a 1:1.5 (wt/wt) mixture from 12 mg ml−1 (total) in chlorobenzene. Devices based on pristine films were prepared from 10 mg ml−1 in chloroform or chlorobenzene. The devices were encapsulated and measured in air. J–V curves (measured in the forward direction, that is, from negative to positive bias, with a scan step of 0.04 V) were collected using a Keithley 2400 Source Meter under AM1.5 illumination provided by a solar simulator (LSH-7320 ABA LED solar simulator) with an intensity equivalent to 1,000 W m2 after spectral mismatch correction. The light intensity for the J–V measurements was calibrated with a reference Si cell (VLSI standards SN 10510-0524 certified by National Renewable Energy Laboratory). We compared the measurements (on the PvBDTTAZ:O-IDTBR device) with and without a mask in Supplementary Fig. 18. The absence of the mask had a negligible effect on VOC, but noticeable effects on JSC, possibly due to the extra light entering the side of device50 or extra photocurrent from the borders of the pixel. EQEPV spectra were recorded with an integrated quantum efficiency measurement system named QE-R3011 (Enli Technology Co.), which was calibrated with a crystal silicon photovoltaic cell before use. Temperature-dependent VOC values were obtained by characterizing the J–V curves in a vacuum probe system (Advanced Research Systems) under illumination provided by a solar simulator with an intensity of 1,000 W m−2.

### Electroluminescence and photoluminescence measurements

Electroluminescence and photoluminescence spectra were recorded with an Andor spectrometer (Shamrock sr-303i-B, coupled to a Newton EMCCD Si array detector cooled to −60 °C). The system was wavelength-calibrated by an argon lamp to a resolution better than 0.5 nm. A Keithley 2400 external current/voltage source meter was connected to prepared photovoltaic devices comprising pristine or blend films to support an external electric field for electroluminescence measurements. The pumping light sources used to measure photoluminescence were lasers with different wavelengths (532, 635, 670 and 780 nm) and power of 3–5 mW. PLQE values were obtained using an integrating sphere. The absolute value of EQEEL was recorded with a home-built system using a Hamamatsu silicon photodiode 1010B. A Keithley 2400 meter was used to supply voltages and record the injected current, and a Keithley 485 was used to measure the emitted light intensity.

### FTPS-EQE measurement

FTPS-EQE measurements were carried out using a Vertex 70 (Bruker Optics) with an external detector option. A low-noise current amplifier (SR570) was used to amplify the photocurrent generated from the solar cells with illumination light modulated by the Fourier transform infrared (FTIR) instrument.

### Transient absorption spectroscopy

Femosecond transient absorption spectroscopy was carried out using a commercial transient absorption spectrometer (HELIOS, Ultrafast Systems). Pump pulses, used to excite the samples, were generated from a frequency mixer (NIRUVis, Light Conversion) coupled to an optical parametric amplifier (TOPAS, Light Conversion), which in turn was seeded with 800 nm, <100 fs pulses from a 1 kHz Ti:sapphire regenerative amplifier (Spectra-Physics Solstice, Newport Corporation). These seed pulses were also used to provide the broadband near-infrared (900–1,500 nm) and visible (450–800 nm) probes, generated in an yttrium aluminium garnet and sapphire crystal, respectively. The pump was modulated at 500 Hz by a mechanical chopper, and the delay between the pump and probe pulses was controlled by a mechanical stage. Samples were held in a cuvette purged with nitrogen gas during measurements. SVD analysis was performed using Surface Xplorer software (Ultrafast Systems). Devices were measured in reflection geometry (one electrode present) under short-circuit conditions. Transmission measurements on devices (between metal electrodes) were also performed to verify that this geometry gave similar dynamics to the film on glass measurements.

### Electronic-structure calculations

Geometry optimizations of the isolated donor and acceptor small-molecular oligomers in neutral and charged configurations were performed by means of DFT calculations. Excited-state transition energies and oscillator strengths were obtained by time-dependent DFT calculations based on the Tamm–Dancoff approximation51. Calculations for the polymeric systems were based on oligomers with three repeat units except in the case of PTB7-Th:IEICO and PTB7-Th:PC71BM complexes, where pentamers were used for PTB7-Th. Model D:A complexes were constructed in a ‘face-on’ configuration as shown in Supplementary Figs. 14 and 15. In these calculations, the donor and acceptor geometries were kept at the optimized configurations of the isolated molecules (oligomers). The total energies of the complexes were obtained by means of the DFT-D3 method, which accounts for dispersion interactions52. In addition, to account for geometry relaxations, full geometry optimizations of these complexes were performed at the semi-empirical PM7 level53. Geometry optimizations of the isolated molecules were performed at the B3LYP/6-31G(d) level and using SRSH-ωPBEh, a PBE-based screened range-separated hybrid (SRSH) function (see Supplementary Information).

All electron transfer rates were derived using Marcus semi-classical electron transfer theory 54:

$$k = \frac{{2\pi }}{\hbar }\left| {V_{\mathrm{el}}} \right|^2\frac{1}{{\sqrt {4\pi \lambda k_{\mathrm{b}}T} }}{\mathrm{exp}}\left( { - \frac{{\left( {\lambda + \Delta G} \right)^2}}{{4\pi \lambda k_{\mathrm{b}}T}}} \right)$$

Here, Vel denotes the electronic coupling between the initial and final diabatic states, ħ is Planck’s constant, ΔG is the Gibbs free energy (driving force), λ is the reorganization energy, T is the temperature, and kb is Boltzmann’s constant. Electronic couplings between the local excitation state and ground state with the CT states were obtained in the framework of the generalized Mulliken–Hush approach55. Adiabatic energies for the LE state ($$E_{{\mathrm{LE}}}^{\mathrm{a}}$$) and CT state ($$E_{{\mathrm{CT}}}^{\mathrm{a}}$$) were obtained using the respective DFT energies computed at the ground-state geometry (vertical transition energies, Supplementary Table 8) and corrected for geometry relaxation: a value of 50 meV for the LE state (based on the Stokes shift) and a value of 0.27 eV for the CT state (0.17 eV from the computed intramolecular relaxation (Supplementary Table 9) and 100 meV to account for the medium effect). Geometry optimizations of the ground states at the DFT level were performed with Gaussian0956 and those at the PM7 level with Gaussian 1657. All excited state calculations were performed with the Q-chem 4 package58.

### Reporting Summary

Further information on experimental design is available in the Nature Research Reporting Summary linked to this article.

### Data availability

The data that support the plots within this paper are available from the corresponding author upon request.

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## Acknowledgements

The authors thank J. Durrant, J.-S. Kim, M. Pshenichnikov and D. Paraschuk for useful discussions. The research was supported by the Swedish Energy Agency Energimyndigheten (grant no. 2016-010174), the Swedish Research Council VR (grant nos 621-2013-5561, 2016-06146, and 2017-00744), the Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University (faculty grant no. SFO-Mat-LiU #2009-00971), the National Natural Science Foundation of China (grants nos 91633301, 51673201 and 21325419), the Chinese Academy of Sciences (grant no. XDB12030200), the China Scholarship Council (CSC) (no. 201306730002) and the Department of the Navy, Office of Naval Research, under the MURI ‘Center for Advanced Organic Photovoltaics’ (awards nos N00014-14-1-0580 and N00014-16-1-2520). F.G. is a Wallenberg Academy Fellow and O.I. is a Wallenberg Scholar. A.A.B. is a Royal Society University Research Fellow. This project has also received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement nos 639750 and 717026). W.T. acknowledges an Ambizione fellowship from the Swiss National Science Foundation.

### Competing interests

The authors declare no competing interests.

## Author information

### Affiliations

1. #### Department of Physics, Chemistry and Biology (IFM), Linköping University, Linköping, Sweden

• Deping Qian
• , Shula Chen
• , Xiao-Ke Liu
• , Liangqi Ouyang
• , Yingzhi Jin
• , Galia Pozina
• , Weimin M. Chen
• , Olle Inganäs
• , Fengling Zhang
•  & Feng Gao
2. #### School of Chemistry and Biochemistry and Center for Organic Photonics and Electronics, Georgia Institute of Technology, Atlanta, GA, USA

• Zilong Zheng
• , Veaceslav Coropceanu
•  & Jean-Luc Bredas
3. #### Beijing National Laboratory for Molecular Sciences, State Key Laboratory of Polymer Physics and Chemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing, China

• Huifeng Yao
• , Sunsun Li
• , Bowei Gao
•  & Jianhui Hou
4. #### Laboratory of Photonics and Interfaces (LPI), Institute of Chemical Sciences and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

• Wolfgang Tress
5. #### Department of Chemistry, Imperial College London, London, UK

• Thomas R. Hopper
• , Jiangbin Zhang
•  & Artem A. Bakulin
6. #### Department of Chemistry and Energy Institute, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong

• Jing Liu
• , Shangshang Chen
•  & He Yan
7. #### Cavendish Laboratory, University of Cambridge, Cambridge, UK

• Jiangbin Zhang

### Contributions

F.G. conceived and directed the project. D.Q. fabricated the solar cell devices, performed the FTPS, steady-state photoluminescence, electroluminescence and EQEEL experiments. Z.Z. carried out the DFT calculations. X.L. performed the PLQE measurements. S.C. and G.P. carried out the transient photoluminescence measurements. H.F.Y., J.L., S.S.C. and S.L. synthesized the materials. T.R.H. and A.A.B. carried out the transient absorption measurements. T.R.H., J.Z. and A.A.B. analysed the time-resolved data. B.G. and Y.J. fabricated the solar cell devices. L.O. performed the cyclic voltammetry measurements. D.Q. was supervised by F.G. and F.Z. J.B. and V.C. supervised the DFT calculations. J.H. and H.Y. supervised the materials synthesis and device fabrication. I.B. and W.C. supervised the transient photoluminescence measurements. W.T., O.I. and F.Z. participated in data interpretation. D.Q., W.T., T.R.H., V.C., A.A.B. and F.G. wrote the manuscript. All authors discussed the results and commented on the final manuscript.

### Corresponding authors

Correspondence to Veaceslav Coropceanu or Artem A. Bakulin or Feng Gao.

## Supplementary information

1. ### Supplementary Information

Supplementary Figures 1–18, Supplementary Tables 1–10, Supplementary References 1–8