Long-range exciton di ﬀ usion in non-fullerene acceptors and coarse bulk heterojunctions enable highly e ﬃ cient organic photovoltaics †

We investigated singlet exciton di ﬀ usion in three ITIC derivatives used as electron acceptors in organic photovoltaics (OPVs) by time-resolved photoluminescence volume quenching and exciton – exciton annihilation. The exciton di ﬀ usion coe ﬃ cient was found to be in the range of 0.003 – 0.007 cm 2 s (cid:1) 1 which leads to a three-dimensional exciton di ﬀ usion length of up to 31 nm. We fabricated solar cells using bulk heterojunctions of these acceptors with the electron donor PTB7-Th which showed (cid:3) 7% e ﬃ ciency and large scale phase separation. Our results show that long range exciton di ﬀ usion and large domains o ﬀ er signi ﬁ cant advantages for OPVs.

The use of abundant and clean solar power to generate electricity is a very promising direction for renewable power. Organic photovoltaics (OPVs) are expected to play a major role in future power generation because of their simple fabrication enabling the deposition of solar cells on exible substrates by printing from solution or spray-coating. Recently, the development of non-fullerene electron acceptors (NFAs), which replace fullerene derivatives, has led to important advances in both efficiency and stability. 1,2 In contrast to fullerene derivatives, the absorption of NFAs extends over the visible spectral range and so improves light harvesting. The ionisation potentials and electron affinities of NFAs can be adjusted to achieve lower losses of open-circuit voltage (V oc ). 1,3 Organic solar cells using NFAs in binary and ternary blends to form bulk heterojunctions (BHJ) have reached power conversion efficiencies (PCE) of more than 17%. 4,5 The use of NFAs also signicantly increases the stability of solar cells with projected lifetimes up to 20 years. 6 With high efficiency and other desirable properties such as light weight, low production cost, tuneable bandgaps and mechanical exibility, OPVs offer low energy payback time compared to other photovoltaic technologies such as commercially available silicon. The energy payback time of OPVs with PCEs of 15% is predicted to be 0.5 weeks compared to 0.5 years for silicon. 7 The bandgap tuneability of NFAs has led to the development of near-infrared absorbers 8 which enable the production of semi-transparent or even fully transparent cells for their possible integration into buildings. 9 Furthermore, OPVs are made from "green" materials compared to other solution or spray coated photovoltaic materials such as leadcontaining hybrid perovskites.
The length-scale of phase separation between donor and acceptor is an important consideration in BHJ solar cells. Large scale phase separation is helpful for efficient charge extraction, as it reduces the area of the BHJ and so reduces charge recombination losses. 10 However, this needs to be balanced against the need for efficient exciton harvesting (charge generation), which requires that the length-scale of phase separation should be comparable to the exciton diffusion length (L D ) which is typically less than 10 nm in many solution-processed OPV materials. 10,11 Increasing exciton diffusion length is very desirable because it provides a way of overcoming this trade-off by enabling efficient exciton harvesting in larger domains.
BHJs made from NFAs have shown large donor and acceptor domains (20-50 nm) and high domain purity. 12 Despite these large domains, efficient exciton dissociation is observed in BHJs with NFAs which suggests that exciton diffusion lengths in NFAs are on a length-scale comparable to these domains. Despite the rapid development of materials and device engineering, photophysical investigations of NFAs are less developed, with only a couple of reports of measurements of exciton diffusion in NFAs (abbreviated names IDIC, INIC and its uorinated derivative FINIC) using exciton-exciton annihilation measurements. 13,14 Here we investigated exciton diffusion in a family of efficient NFA materials shown in Fig. 1 (abbreviated names ITIC, 15 ITIC-Th 16 and IT-4F 17 ). Time-resolved photoluminescence (PL) volume quenching and exciton-exciton annihilation measurements gave consistent values of exciton diffusion coefficient in all three materials investigated, which leads to three-dimensional exciton diffusion lengths between 18 and 31 nm. We fabricated solar cells using blends of these NFAs with the widely used donor polymer PTB7-Th which showed PCEs of more than 7%, consistent with previous reports. 15,18 The analysis of PL decays measured in these photovoltaic blends suggests large and pure NFA domains of up to 32 nm in diameter.
Absorption and PL spectra of neat lms of the three electron acceptors studied are shown in Fig. 1. ITIC has an absorption peak around 707 nm which corresponds to a 0-0 vibronic transition and a shoulder around 642 nm which can be attributed to a vibronic 0-1 transition. The absorption of ITIC-Th is slightly blue-shied compared to ITIC with a strong 0-0 peak at around 703 nm whilst absorption of IT-4F is red-shied with a 0-0 peak around 723 nm and a 0-1 shoulder around 659 nm. All these molecules show a single emission peak in thin lms: ITIC emits around 772 nm, ITIC-Th around 763 nm and IT-4F around 795 nm.
First we investigated singlet exciton diffusion in lms of these electron acceptors using PL quenching by DR3TBDTT molecules dispersed at low concentrations in the volume of electron acceptor lms. The resulting uorescence decays are plotted in Fig. S1. † For accurate measurement of exciton diffusion, homogenous dispersion of the quencher is required.
To check this, we measured a range of quencher concentrations and determine the rate of quenching for each concentration (as shown in Fig. S2 †). The rate of quenching shows a linear dependence at low concentration of quencher and deviates from the linear regime at high concentration. For exciton diffusion measurement, we only use the linear regime.
At low concentration, PL quenching is controlled by exciton diffusion to the quencher. For a given concentration, PL will decay faster if exciton diffusion is faster, so the decay can be used to measure exciton diffusion. As there is a nite spectral overlap of the PL spectra of the studied electron acceptors with the absorption of DR3TBDTT, therefore, Förster resonance energy transfer (FRET) to dispersed DR3TBDTT molecules can occur followed by electron transfer from DR3TBDTT to the electron acceptor which results in PL quenching (Fig. 2). For analysis it is convenient to take a ratio of the PL decay in lms with a quencher to the PL decay without a quencher to account for the natural exciton decay in neat electron acceptor lms. At high concentrations of dispersed DR3TBDTT molecules the direct FRET to the quencher dominates and the natural logarithm of the PL ratio is proportional to the square root of time as explained in ESI and has been observed before. 19,20 This allows us to estimate the Förster radius R 0 for FRET from electron acceptors to DR3TBDTT.
Aer determining R 0 , the diffusion coefficient is tted to the PL decays (Fig. 2d) using the formula developed by Gösele et al. for the case of diffusion mediated FRET to quenchers 21,22 as described further in ESI. † From this tting we obtain exciton diffusion coefficients of (3.4 AE 0.8) Â 10 À3 cm 2 s À1 for ITIC, (7.0 AE 2.0) Â 10 À3 cm 2 s À1 for ITIC-Th and (4.5 AE 0.8) Â 10 À3 cm 2 s À1 for IT-4F.
To verify these results we investigated exciton diffusion using singlet-singlet exciton annihilation. Excitons diffuse in the lms and when two excitons approach each other one exciton transfers its energy onto the other which goes into a higher excited state. The higher energy state usually relaxes to the lowest excited state and one exciton is lost per annihilation event. We used time-resolved PL measured at different initial excitation densities to study this process and the results are shown in Fig. 3. PL intensity is proportional to the density of singlet excitons N and described by the rate equation Here G is the generation rate which in our case is instantaneous (i.e. within the duration of the excitation pulse of 200 fs), k is the natural decay rate constant in the absence of annihilation and g is the annihilation constant. In order to determine k we measured the PL decays using very low excitation density (<10 15 cm À3 ) which is two orders of magnitude lower than the densities at which exciton-exciton annihilation is observed (Fig. S3 †). Then we tted the PL decay at this low excitation density with a sum of two exponential functions ( Fig. S4 and Table S1 in ESI †) and used it to solve eqn (1) numerically and model the PL decays at high excitation densities with the annihilation constant g as a tting parameter. The best ts were obtained with values of These results are summarised in Table 1. The g values are among the highest reported in organic semiconductors. [23][24][25][26][27] Although a substantially higher value g ¼ 2.5 Â 10 À7 cm 3 s À1 has been reported in the non-fullerene acceptor IDIC, 13 the authors of this report did not reach annihilation-free conditions and so used the excited-state This journal is © The Royal Society of Chemistry 2020 lifetime of IDIC diluted in a polystyrene matrix as a reference.
Since the exciton decay in a neat lm is usually faster than in a matrix, the extracted g value using too slow a reference decay may be substantially overestimated.
The kinematic model of diffusion-limited exciton-exciton annihilation in unrestricted three-dimensional space relates the annihilation constant g to the exciton diffusion coefficient D as where R a is the so called annihilation radius. 28 Using D values measured by volume quenching we determine R a values of 2.4 nm, 1.5 nm and 1.8 nm for ITIC, ITIC-Th and IT-4F, respectively. These values are slightly larger than the d 100 lamellar spacing but similar to the backbone spacing reported in these materials by grazing-incidence wide-angle X-ray scattering (GIWAXS, see Table 1). 29,30 The d 100 spacing is the shortest distance two excitons can approach each other when diffusing along the p-p stacks, hence R a is expected to be slightly larger than the d 100 spacing. Based on these considerations the agreement between the two techniques to measure exciton diffusion is very good.
The obtained values of diffusion coefficient are more than an order of magnitude higher than for the widely used fullerene derivative PC 71 BM (D ¼ 1.6 Â 10 À4 cm 2 s À1 ) measured using volume quenching. 31 It is interesting to note that ITIC-Th has been reported to show about ve times higher electron mobility as compared to ITIC and 1.4 times higher than IT-4F 32 suggesting a possible correlation between exciton diffusivity and electron mobility. It is very likely that both are enhanced by the large (010) coherence length in ITIC-Th along the p-p stacks up to 4 nm measured using GIWAXS. 33 Normally, the lower value of exciton diffusion coefficient (D) in solution-processed organic semiconductors is associated with energetic disorder that is typically larger than thermal energy at room temperature, thus reducing the available density of states for exciton hopping. 10,11 In the case of highly disordered materials, dispersive exciton transport is observed where the distribution of energy states has a strong inuence on the rate of hopping i.e. exciton diffusion will be faster initially while relaxing within the density of states and become slower at longer time due to the unavailability of energetically accessible sites. Experimentally it leads to strong time-dependent PL quenching. 34 However, in the case of NFAs, we observed a timeindependent rate of PL quenching both in exciton-exciton annihilation (where a single time-independent gamma is used to describe the decay) and volume quenching measurements (at low quencher concentration where exciton diffusion is the dominant process). This indicates that fast exciton diffusion in NFAs is due to their higher energetic and structural order.
The charge generation efficiency depends on the ability of each exciton to reach a heterojunction which in turn depends on the exciton diffusion length and the donor and acceptor domain sizes. In BHJ geometry, three-dimensional exciton diffusion length is relevant, therefore, we estimated the threedimensional exciton diffusion length using L 3D ¼ ffiffiffiffiffiffiffiffi 6Ds p . Here s is the exciton decay time in the absence of annihilation. The PL decays were non-exponential even for the low excitation density so we took s to be the time taken for PL to fall to 1/e of its initial value in our estimation of exciton diffusion length. The 1/e Fig. 3 Singlet-singlet annihilation measurements showing PL decays in neat films of ITIC derivatives measured at different initial excitation densities given in the legend. Solid lines are the numerical fits using eqn (1) with a time-independent g as a fitting parameter given in Table  1. Table 1 Singlet exciton diffusion coefficient D, singlet-singlet annihilation constant g, annihilation radius R a , singlet exciton lifetime s and threedimensional exciton diffusion length L 3D obtained from results in Fig. 2 and 3 (Table 1). We also measured singlet exciton diffusion in PTB7-Th lms using PL quenching by dispersed low concentrations of ITIC or IT-4F molecules. This gives the values of (1.0 AE 0.1) Â 10 À3 cm 2 s À1 for exciton diffusion coefficient and 12 nm for the 3D diffusion length in PTB7-Th (details are given in ESI †).
To investigate the effect of exciton diffusion on the photovoltaic device performance, we fabricated solar cells using these NFAs as acceptors. We followed a simple protocol for device fabrication without any extra processing (e.g. thermal or solvent vapor annealing) or additives. For all three NFAs, we used the same donor: acceptor blend weight ratio of 1 : 1.3, (with a total concentration of 23 mg mL À1 ) for easy comparison between the exciton diffusion length and solar cell device performance. For donor, we selected the widely used polymer PTB7-Th, whose molecular structure is shown in Fig. 4a. The photovoltaic J-V characteristics are shown in Fig. 4b and the external quantum efficiency (EQE) spectra are shown in Fig. 4c. All the photovoltaic performance parameters are given in Table 2. Our solar cell efficiencies are comparable to previously reported values using PTB7-Th as donor and ITIC as acceptor. 15,18 Though all the three PTB7-Th:NFA blends showed power conversion efficiency (PCE) close to 7%, the blend, PTB7-Th:ITIC-Th showed the highest average (7%) and champion efficiency of 7.45%. The illuminated current density-voltage curve given in Fig. 4b shows that the blend with IT-4F has a higher short circuit current (J SC ) density. This is due to enhanced absorption of this molecule in the region between 550 nm and 850 nm compared to the other two as shown in the absorption spectra in Fig. 1. The extended absorption range of this blend, PTB7-Th:IT-4F, is further re-ected in the EQE spectra shown in Fig. 4c. Overall the blends with these three NFAs show an EQE of more than 70% in the region between 550 nm and 750 nm.  the other two blends, the ideality factor (n) was estimated for the three blends. To obtain the value of n, we tted the I-V curves (Fig. S10 †) using the equation below.
The  Table 2. To understand the contribution of mobility in the high FF for the blend with ITIC-Th, the electron mobility of the three NFAs was also considered. Previous studies have reported electron mobilities of 1.10 Â 10 À4 cm 2 V À1 s À1 for ITIC, 6.10 Â 10 À4 cm 2 V À1 s À1 for ITIC-Th, and 4.37 Â 10 À4 cm 2 V À1 s À1 for IT-4F. 32 The higher electron mobility of ITIC-Th NFA compared to the other two will also be contributing to the higher FF for the blend containing this NFA.
The higher FF in the PTB7-Th:ITIC-Th blend also indicates improved dissociation of charge transfer states in competition with geminate recombination and better charge extraction. A previous study has established a positive correlation between the device FF, the coherence length of p-p stacking of ITIC-Th molecules and electron mobility. 33 We observed a higher exciton diffusion coefficient in ITIC-Th lms than the other derivatives. It is very likely that exciton diffusivity and electron mobility both increase as a result of the improved coherence length in ITIC-Th. Non-geminate recombination is more severe in nely mixed BHJs with large area of the donor-acceptor interface. To investigate this hypothesis we measured the domain size in the blends using time-resolved PL spectroscopy.
We can estimate the average domain size of non-fullerene acceptors assuming that the PL quenching in the blends is limited by exciton diffusion in acceptor domains to the boundary with PTB7-Th using a procedure previously described by Hedley et al. 31 and Jagadamma et al. 35 For this purpose we measured the PL decays in the blends of electron acceptors with PTB7-Th which were used to make solar cells and normalised them to the PL decays in neat electron acceptor lms to account for the natural exciton decay in non-fullerene acceptors (Fig. 4d). This approach is justied by good agreement of PL spectra measured in the blends and in neat acceptor lms which all are substantially red-shied relative to the PTB7-Th spectrum (Fig. S11 †). Time-resolved PL spectra of the blends show a red-shi within 10 ps aer excitation which can be attributed to energy transfer from PTB7-Th to electron acceptors (Fig. S12 †). This suggests that PTB7-Th domains are much smaller than L 3D in PTB7-Th of 12 nm or that these have some admixture of electron acceptor. The AFM image (Fig. S13 †) shows that at least on the surface the domains are approximately round rather than elongated, therefore, in order to estimate their size we assumed that they have spherical shape. Previous studies of PTB7-Th blends with ITIC derivatives deposited by one-step spin-coating also showed ne granular morphology with roughly round grains. 35,36 Recent reports show that high efficiency can also be achieved in sequentially deposited donor acceptor layers which may have very different needle-like morphology. 37,38 Hence, assuming that acceptor domains have a spherical shape with a radius r, the ratio g(t) of the PL decay in a blend to the PL decay in a neat acceptor lm is described by The radius of the sphere r is the only tting parameter in this case as the exciton diffusion coefficient D was determined for each non-fullerene acceptor in the annihilation and volume quenching measurements described above. For the tting, eqn (4) was multiplied by the uorescence intensity in the absence of quencher and then used to t the PL decays of the blends. A domain size of approximately 17 nm was obtained for ITIC, 32 nm for ITIC-Th and 14 nm for IT-4F. Large domains in the case of ITIC-Th are consistent with the higher ll factor observed. These results can be compared to the long-period (domain spacing) which was measured at around 95 nm in PTB7-Th:ITIC-Th blend using R-SoXS. 33 Our method gives us a size estimate of pure acceptor domains because any mixture of the donor polymer would give faster PL quenching as compared to quenching solely at the domain boundaries. According to R-SoXS results, the domain purity in PTB7-Th:ITIC-Th blend is not the highest among other blends, hence, we consider our ndings compatible with the reported R-SoXS results. However, large domains could limit exciton harvesting as excitons have further to diffuse to a heterojunction. We therefore estimated the charge generation efficiency in these blends using the PL decays in the presence and absence of quencher as where s blend is the lifetime of blend and s neat is the lifetime of neat acceptor lm. We made an assumption here that every exciton that is quenched generates a charge. PL Table 2 Photovoltaic parameters of PTB7-Th:NFAs. F gen is the charge generation efficiency estimated using fluorescence decay time. The solar cell performance parameters are the average and standard deviation of ten devices

Conclusions
In conclusion, we measured the exciton diffusion coefficient in a family of fused ring non-fullerene acceptors and found values of exciton diffusion coefficient that are higher than many OPV materials, including fullerene derivatives. Furthermore, we found that exciton diffusion is time-independent, suggesting that there is less energetic and structural disorder in these materials. The high exciton diffusion coefficient leads to threedimensional diffusion lengths of up to 31 nm, which allow blends with large domain sizes to be made using these NFAs. Our measurement of large exciton diffusion length along with large domains gives further understanding of why NFAs are such attractive materials for organic solar cells.

Absorption measurements
Materials for this study were purchased from 1-Material. The absorption of lms were measured using a Cary 300 UV-Vis spectrophotometer. Film thicknesses of 40-50 nm were used for these measurements.

Time-resolved PL measurements
Time-resolved PL decays were measured with Hamamatsu C6860 streak camera in synchroscan mode. In the volume quenching and low excitation density measurements of neat lms, the excitation was with 100 fs pulses at an excitation wavelength of 515 nm and a repetition rate of 80 MHz. For exciton-exciton annihilation measurements, the lms were excited using 200 fs pulses at 640 nm with 100 kHz repetition rate generated by an optical parametric amplier pumped by Pharos regenerative amplier. For exciton-exciton annihilation measurements lms of thickness 40-50 nm were used, so that the excitation density was close to uniform throughout the lm. The thickness of photovoltaic blends used in time resolved study was around 100 nm as optimised for the best device efficiency.
For volume quenching measurement, the solutions of NFAs and donor (DR3TBDTT) was prepared separately using chlorobenzene and were kept overnight at 60 C inside the glovebox. These solutions were mixed together and lms were made by spin-coating the solution at 2000 rpm for 60 s inside the glovebox.

Device fabrication and characterisation
Inverted organic solar cells were fabricated on pre-patterned ITO-coated glass. The ITO-coated glass substrates were cleaned in detergent (Hellmanex, Sigma Aldrich), successively ultrasonicated in deionized water, acetone, and isopropyl alcohol, and exposed to an oxygen plasma for 3 minutes. The blend solutions of PTB7-Th:NFAs were prepared by dissolving the components in a ratio of 1 : 1.3 (by weight), with a total concentration of 23 mg mL À1 in chlorobenzene. The solution was kept stirring at 60 C for $8 hours before spin-coating.
In all the inverted organic solar cells fabricated, the electron transporting layer was amorphous ZnO (a-ZnO) thin lm having a thickness of $25 nm and was prepared according to a previous report. 39 The active layer was deposited by spincoating (at 1500 rpm for 45 s) on glass/ITO/a-ZnO substrates inside a nitrogen lled glove box. The samples were then transferred to a thermal evaporator (1 Â 10 À6 mbar base pressure) in the glove box and the hole transporting layer of MoO x (7 nm) and anode Ag (100 nm) deposited through a shadow mask. The active area of the device was 0.07 cm 2 .
Aer the electrode deposition, the devices were encapsulated with an UV optical adhesive and a glass coverslip. The currentvoltage characteristics were determined under an illumination intensity of 100 mW cm À2 in air using an air mass 1.5 global (AM 1.5 G) Sciencetech solar simulator and a Keithley 2400 source-measure unit. The illumination intensity was veried with a calibrated mono-silicon detector and a KG-5 lter. The external quantum efficiency (EQE) measurements were performed at zero bias by illuminating the device with monochromatic light supplied from a xenon arc lamp in combination with a Bentham TMc300 monochromator. The number of photons incident on the sample was calculated for each wavelength by using a silicon photodiode calibrated by the National Physical Laboratory (NPL).

Conflicts of interest
There are no conicts to declare.