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. 2023 Feb 16;14(7):1999–2005. doi: 10.1021/acs.jpclett.2c03585

Spatiotemporal Mapping Uncouples Exciton Diffusion from Singlet–Singlet Annihilation in the Electron Acceptor Y6

Giulia Lo Gerfo M †, Luca Bolzonello †, Francisco Bernal-Texca †, Jordi Martorell †,‡, Niek F van Hulst †,¶,*
PMCID: PMC9940293  PMID: 36794828

Abstract

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Understanding the spatial dynamics of nanoscale exciton transport beyond the temporal decay is essential for further improvements of nanostructured optoelectronic devices, such as solar cells. The diffusion coefficient (D) of the nonfullerene electron acceptor Y6 has so far only been determined indirectly, from singlet–singlet annihilation (SSA) experiments. Here, we present the full picture of the exciton dynamics, adding the spatial domain to the temporal one, by spatiotemporally resolved photoluminescence microscopy. In this way, we directly track diffusion and we are able to decouple the real spatial broadening from its overestimation given by SSA. We measured the diffusion coefficient, D = 0.017 ± 0.003 cm2/s, which gives a Y6 film diffusion length of Inline graphic nm. Thus, we provide an essential tool that enables a direct and free-of-artifacts determination of diffusion coefficients, which we expect to be pivotal for further studies on exciton dynamics in energy materials.

The advent of nonfullerene acceptor (NFA)1 molecules in the world of organic solar cells (OSCs) brought a notable increase in power conversion efficiences (PCEs) compared to fullerene based photovoltaics, reaching values over 19%.2−5 As numerical device simulations suggest,6 such an increase is just the kick-off for higher OSCs efficiencies, which can be increased up to 25%. Still, the available room of improvement can be gained only by cells designed with materials exhibiting optimized characteristics.

A promising candidate is the acceptor Y6 (also known as BTP-4F), on which most of the binary OSCs with efficiencies higher than 16% are based.7−10 Among the Y6 benefits are the ability to harvest light in the infrared range and the ultrafast and efficient charge separation even at a low driving force.11−13 This leads to low voltage losses (0.5 eV14) and consequently to a remarkably high open-circuit-voltage (VOC = 0.834–0.867 V15) which implies a high overall efficiency of the cell.16 More specifically regarding exciton properties, currently most OSCs are based on bulk heterojunctions where a short exciton diffusion is bypassed using nanodomains whose size is well below the exciton diffusion length. However, recent studies17 indicate that going back to the bilayer heterojunctions would be beneficial for a fine regulation of morphology and carriers pathways, therefore simplifying the fabrication process and leading toward a more accessible industrial OSCs production. In this scenario, the exciton diffusion coefficient and lifetime are key factors to allow long-range exciton transport and consequently to optimize the thickness and morphology of bilayer devices.18 Y6 outperforms its NFA analogues due to a longer exciton lifetime of τ = 800 ps19 and due to its large diffusion coefficient D up to 0.05 cm2/s,20,21 1 order of magnitude larger than those of fullerene acceptors.

Unfortunately, the reported large exciton diffusion values have only been determined indirectly from exciton–exciton annihilation dynamics by means of transient absorption spectroscopy.22,23 The transient approach is penalized by two major drawbacks. First, high laser intensities are required, far above sun conditions, to create enough absorption contrast and exciton density for the annihilation to occur. Photodamage of the sample is very probable in these conditions, leading to materials constants which are not representative for the desired behaviors (under 1 Sun illumination). Second, interpretation of the transient data requires a numerical solution, with a-priori knowledge of the initial exciton density and the exciton–exciton annihilation, as well as an exact expression that links the annihilation rate to the diffusion coefficient D, all susceptible to the specific interpretation.24,25

Beyond transient absorption spectroscopy several alternative techniques are reported in the literature26 to address the exciton diffusion, such as fluorescence quenching in bilayers,27−29 fluorescence volume quenching,30 and photocurrent31 and microwave conductivity32,33 measurements. However, none of these are able to directly resolve and disentagle diffusion in both space and time. The microscopic version of transient absorption spectroscopy (TAM)34 can provide a spatiotemporal map yet still requires fluences above 1 excitation/spot. In systems where the singlet–singlet annihilation (SSA) coefficient is very high, it may not be possible to use TAM with negligible SSA.

Here, we present a novel spatiotemporal method which readily tracks exciton diffusion in space and time by means of sensitive fluorescence readouts35−37 and moreover decouples the diffusion from exciton–exciton annihilation artifacts, due to the possibility of reducing the excitation fluences to the limit of negligible SSA. Doing so, we obtain a quantitative and accurate D value: (1) analytically determined without any initial numerical or physical assumption and (2) free of overestimation due to nonlinear exciton–exciton annihilation interference,38 since the bimolecular deactivation process is decoupled while still considered in the method.

A general equation to describe spatiotemporal exciton diffusion in molecular films reads:39

graphic file with name jz2c03585_m002.jpg 1

where n(x, t) represents the spatiotemporal distribution of excitons; D(x, t, n) is the diffusion coefficient dependent on space, time, and exciton density; k(t) is the rate of monomolecular deactivation, which can be time-dependent and is given by the sum of radiative krad and nonradiative decay knrad; and γ is the rate of bimolecular deactivation (i.e., singlet–singlet annihilation (SSA) for excitons or Auger recombination (AR) for charge carriers), dependent on the diffusion coefficient D and on RA, the radius of annihilation.

In the limit of exciton densities approaching zero, SSA becomes negligible since it scales with the square of n. Moreover, assuming the medium to be isotropic, exciton-hopping to be the only mechanism of diffusion, and D to be density independent, the diffusion equation reduces to the so-called heat equation:

graphic file with name jz2c03585_m003.jpg 2

While eq 1 only admits numerical solutions, eq 2 can be solved analytically. Assuming a Gaussian-shaped excitation spot, which produces an initial Gaussian-shaped exciton distribution n(x, 0),

graphic file with name jz2c03585_m004.jpg 3

and a compressed exponential decay40,41 (details in Supporting Information), the time-dependent density becomes

graphic file with name jz2c03585_m005.jpg 4

which is still a Gaussian distribution, with a time-dependent full width at half-maximum (FWHM):

graphic file with name jz2c03585_m006.jpg 5

As a result, the diffusion coefficient can be directly obtained as the slope of the squared width of the exciton distribution against time.

Eq 5 is true in the hypothesis of negligible SSA. However, the impact of SSA on the retrieved D becomes more and more important in two cases: (1) when the diffusion coefficient is high and (2) when increasing the excitation fluence (i.e., the initial exciton density). In the first scenario, the fast diffusion of excitons enhances their probability to bump into each other in a certain time range, which leads to important annihilation effects even for fluences far below the saturation limit (see Supporting Information). In the second scenario, the SSA is increased because of exciton overcrowding. In this context, it is important to remark that the spatial diffusion coefficient itself does not depend on the exciton density. Therefore, any apparent dependency of D on the excitation fluence is a consequence of the SSA into eq 5, yielding an effective diffusion coefficient Deff, which overestimates D as it contains the effect of γ.

Consequently, in a first and second analysis, we extrapolate Deff to the limit of zero fluence with two different fitting methods, to obtain the real spatial diffusion coefficient D.

Eq 1 does describe the exciton diffusion taking into account the exciton–exciton annihilation term. Therefore, in a third analysis, we numerically solve eq 1, systematically varying density and SSA terms, to obtain the pure spatial coefficient D.

For the measurements, the polymer Y6 (Batch No. 20200318E, purchased from eflexPV) was used as received without any additional purification. To obtain homogeneous Y6 layers of thickness 50 and 300 nm, two different chloroform solutions of Y6 with concentrations of 6 and 25 mg/mL were used. Both were stirred at room temperature overnight and spin-coated at 1000 rpm onto a clean substrate. In order to avoid photobleaching, the samples were thermally annealed at 50 °C for 3 min and consequently encapsulated with glass and sealed with an UV curable adhesive (Norland Optical Adhesive 73, 1.5 min curing) before testing. All procedures were performed in a N2-filled glovebox.

A 150-fs-pulsed Ti:sapphire laser with a repetition rate of 76 MHz and wavelength 800 nm was used as excitation source.42 The beam was cleaned spatially and dispersion compensated temporally using respectively a telescope with a pinhole and prism compressors. Then, a galvo-mirror followed by a second telescope allowed the scanning of the beam over the sample plane. The spatial displacement was quantified by calibrating the galvo-mirror (see Supporting Information). A Nikon Plan APO λ NA 1.40 60x oil immersion objective focused the beam to a spot of FWHM of 390 nm. The Y6 fluorescence signal, which peaks at 870 nm wavelength, was confocally collected in reflection through a 15 μm pinhole corresponding to a central spot size of 250 nm diameter in the sample plane, and separated from the excitation beam by a 830 nm long-pass filter. The detector was a Single Photon Avalanche Diode (SPAD) from the MPD series with an instrument response function of 50 ps. A schematic illustration can be found in the Supporting Information.

According to eq 1, excitons created in the excitation spot can either decay radiatively or nonradiatively, decay via exciton–exciton annihilation, or transfer energy to the closest molecule via Förster resonant energy transfer (FRET). The fluorescence collected from the spot of excitation on a Y6 film decays following a compressed exponential function exp(−(t/τeff)β) (see Supporting Information) with lifetime τ = 839 ± 13 ps, β = 1.35 and τ = 908 ± 14 ps, β = 1.25, respectively for the 50 and 300 nm film (at 13 nJ/cm2). If the excitation spot is moved away from the detection spot (Figure 1(d)), excitons are detected with a certain delay due to the time required to move from the position they are generated to the confocal detection spot. Such delay depends on the distance between the two spots and can be identified in an effective increase of the lifetime of fluorescence. Therefore, the lifetime change is a direct measurement of exciton diffusion.

Figure 1.

Figure 1

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(a) Normalized spatiotemporal exciton distribution (at F = 300 nJ/cm2). The fluorescence decay signal is collected every 100 nm along the cross-section of the excitation beam and each 20 ps of time-delay. The white lines represent the trend of the 2D spatiotemporal fit. (b) Distribution normalized at each spatial position, highlighting the decay in time. (c) Distribution normalized at each time delay, highlighting the width broadening. (d) Scheme of the setup. (e) Plot and fit of the monoexponential decay at positions x = 0 (brown) and x = 600 nm (orange) (at 100 nJ/cm2, 300 nm thick). (f) Plot and fit of the Gaussian distribution in space at time t = 0 (brown) and t = 1400 ps (orange) (at 100 nJ/cm2, 300 nm thick).

Integrating the collected fluorescence intensity I(x, t) every 20 ps at each position along the cross-section of the excitation profile, we reconstructed a 2D map which provides a direct visualization of the spatiotemporal exciton distribution (Figure 1(a)). The signal decays with time on a ps-ns scale and broadens in space on a nm-μm scale.

In Figure 1(b) the 2D distribution is normalized at each spatial displacement to visualize the delays of decay in time. We observe a clear elongation of the decay moving away from the excitation spot (Figure 1(e)). Next, to fully describe diffusion, we turn to the spatial broadening coordinate. To this end, in Figure 1(c) the 2D map is normalized at each time delay. Indeed, a broadening of the profile is readily observed (Figure 1(f)).

If singlet–singlet annihilation is not included in the model, the diffusion coefficient is only effective and Deff can be analytically obtained in two ways.

In the first method, the time and space coordinates are separated and a monodimensional fit is performed along each coordinate. Regarding the temporal coordinate, a plot of τeff obtained with a compressed exponential fit with fixed β = 1.35 at different positions and different fluences is presented in Figure 2(a). The concavity along the spatial coordinate is a result of both spatial diffusion (the further from the center, the higher the delay for excitons to be detected, and the higher the increase of τeff) and temporal exciton–exciton annihilation (the further from the center, the lower the excitation fluence, and the lower the annihilation and therefore the longer the τeff). Clearly, moving from high to low fluences, the annihilation effect becomes negligible, and consequently the concavity reduces, while the lifetime shifts toward higher values. At the lowest fluence (5 excitations/pulse), the lifetime change is purely caused by the spatial exciton diffusion.

Figure 2.

Figure 2

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(a) 1D fit: τeff at different positions and different fluences (50 nm thick film). (b) 1D fit: squared width of the exciton distribution against time to retrieve Deff from its slope (at 100 nJ/cm2, 50 nm thick). The shaded blue area represents the error margins of the squared FWHM. In gray the control measurement on a buffer of Y6, showing no diffusion properties. (c) 1D fit: logarithmic dependence of Deff on excitation fluence. (d) 2D fit: τeff at different positions and different fluences. (e) 2D fit: slope corresponding to the fitted Deff (at 100 nJ/cm2, 50 nm thick). The shaded blue area corresponds to the margins of error of D. (f) 2D fit: logarithmic dependence of Deff on excitation fluence

The spatial change in lifetime already provides a meaningful qualitative insight in the dynamic of the system. However, to quantitatively and directly determine the diffusion coefficient, we turn to the spatial broadening coordinate.

We fitted the normalized fluorescence intensity at each time delay with a Gaussian profile. The effective diffusion coefficient is then extracted from the slope of the squared FWHM against time (eq 5), as shown in Figure 2(b)(blue line). The gray line represents a control measurement performed on a solution of Y6, where transport should not happen because of the large distance between free molecules. As expected, no temporal change is observed in the width of the exciton distribution and therefore no spatial diffusion in such solution.

In the second method, a 2D-fit is performed on the whole spatiotemporal map (by means of eq 2) and Deff and τeff are obtained as its output parameters. The results of τeff coming from the 2D complete fit, still with β fixed at 1.35, are shown in Figure 2(d). Deff was directly obtained as the output of the fit, and its corresponding slope is shown in Figure 2(e) for the sake of comparison with the 1D-fit.

Following the behavior of lifetimes τeff with different fluences, we expect Deff to increase in the high fluence regime because of the significant change of τeff in space. In contrast, like in the case of τeff, moving toward low fluences, Deff reaches a plateau where the SSA is negligible. Figures 2(c) and (f) illustrate such a trend of Deff with fluence for both thicknesses of the sample (50 and 300 nm, respectively) for the 1D- and the 2D-fits. Independently from the chosen way of analysis, the diffusion in the 300 nm layer is slower compared to the 50 nm layer, indicating differences in spatial dynamics as a function of layer thickness. The two ways of fitting give the same result within error margins, therefore confirming the solidity of this model. In the limit of low fluences, the real diffusion coefficients extrapolated for the thicknesses of 50 and 300 nm are respectively limF→0Deff = D = 0.020 ± 0.006 cm2/s and D = 0.012 ± 0.006 cm2/s for the 1D-fit and D = 0.024 ± 0.003 cm2/s and D = 0.014 ± 0.003 cm2/s for the 2D-fit (Table 1).

Table 1. Diffusion Coefficient Decoupled from SSA Obtained with the Different Fitting Methods.

graphic file with name jz2c03585_0004.jpg

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In order to directly account for the SSA term at any fluence, we numerically solved the complete eq 1 and fitted it to our data set as a third method of analysis.

The equation depends on five parameters (D, γ, k(t), and the initial exciton distribution n(x, 0)), of which we only know k(t), with τ and β being well determined. The other three parameters were left free for the optimization, which was performed contemporaneously on a system of three data sets (obtained at 25, 100, 300 nJ/cm2). While D and γ were set to be constant, independent of the excitation fluence, the initial exciton density was forced to change proportionally to fluence itself. From the correlation matrix of the fitted parameters, we found that while n0 and γ are highly correlated (r = 0.99), D is independent from both n0 and γ (r < 0.1) and thus correctly determined to be D = 0.017 ± 0.003 cm2/s for the 50 nm sample (τ = 839 ± 13 ps and β = 1.35) and D = 0.012 ± 0.003 cm2/s for the 300 nm sample (τ = 908 ± 14 ps and β = 1.25). A further confirmation of the accuracy in the determination of D comes from fits with n0 fixed and only γ and D allowed to change (or similarly γ fixed, leaving n0 and D free). We observe that while γ (or n0) is susceptible of a large variance in its optimized values, there is no change in the optimal outcome for D, even with changing the γ and n0 fixed initial values.

Clearly the numerical solution stands-out to be an ideal candidate to quickly decouple real spatial diffusion from exciton–exciton annihilation, leading to an accurate determination of D and further confirming the results obtained with effective 1D- and 2D-fits.

We further supported our results by means of Monte Carlo simulation. Starting from an initial Gaussian distribution of random points (representing excitons), each excited state was left free to evolve according to the scheme in Figure 3(a). The initial parameters were chosen in the following way: the rate of monomolecular decay (nonradiative knrad plus radiative krad) was set equal to the inverse of the 50 nm film fluorescence lifetime τ–1 = (840 ps)−1; the rate of exciton transfer kET, the number of coordination, the geometry, and the distance between molecules were determined based on computational models and experimental results presented in the literature. From kinetic Monte Carlo simulations on push–pull systems similar to Y643 and molecular dynamics on Y6 itself,44 the average exciton transfer time was estimated to be tET = 0.1–1.0 ps. Further computational results,45 reinforced by experimental data,46 found a squared (N = 4) configuration with terminal–terminal interactions and lattice distances of about d = 2 nm in Y6 thin films. Therefore, for the Monte Carlo simulation we chose a squared lattice with dET = 2 nm and tET = 0.5 ps (Figure 3(a)).

Figure 3.

Figure 3

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Monte Carlo simulation. (a) Squared lattice found in Y6 single-crystals and thin films. (b) Scheme of the chosen parameters and geometry. (c) Fit of the broadening of the simulated exciton distribution width.

The number of iterations was chosen such that its expected value would equal τ/tET, which is the number of hops allowed before the exciton decays. As soon as the exciton decayed, a new point on the simulated mesh was marked.

To reproduce experimental results, we got a snapshot of the simulation every 20 ps, therefore obtaining a time-dependent representation of the system. At each time gap, the two-dimensional distribution was fitted with a 2D Gaussian shape, which squared FWHM2 was plotted against time as shown in Figure 3(b). Exactly like in the experimental treatment, from its slope we determined the simulated diffusion coefficient Dsim to be 0.023 cm2/s, with a 30% uncertainty when the input parameters kET and tET were varied by 30%.

It should be noticed that the exciton–exciton annihilation term was not included in the simulation for simplicity reasons. Therefore, the obtained value of diffusion corresponds to the one expected from a real system in the limit of low fluences.

To sum up, we analyzed the data in three different ways, namely the 1D-fit of the distribution broadening in space, the 2D-spatiotemporal fit which adds the temporal decay, and the 2D-spatiotemporal numerical fit that includes the singlet–singlet annihilation term. Monte Carlo simulations further supported our experiment. We found a very good agreement between the analytical 1D-fit and the numerical 2D-fit, while the analytical 2D-fit slightly overestimates the coefficient compared to the first two methods. Indeed, the 1D analytical fit outperforms in robustness not being based on any model assumption and with being D the only parameter to optimize, but it suffers from low signal-to-noise ratio when applied in the low fluence regime. Similarly, the analytical 2D-fit adds the temporal decay coordinate as a second parameter to be optimized, therefore increasing the model dependence and the signal-to-noise ratio, but it still does not provide any additional useful information for the determination of D. Finally, the numerical 2D-fit boasts completeness being omni-comprehensive (SSA is included in the model and quickly decoupled from D) and applied to a concatenated data set which allows for even higher signal-to-noise ratio. Therefore, the Y6 diffusion coefficient was accurately determined in the absence of SSA to be D = 0.017 ± 0.003 cm2/s and D = 0.012 ± 0.003 cm2/s for 50 and 300 nm film thicknesses, respectively (Table 1). These values are indeed lower than previously reported data that might be affected by overestimation (D up to 0.05 cm2/s), yet they are still 1 order of magnitude larger than the characteristic ones of fullerene acceptors (C71BM, D = 1.6 × 104 cm2/s47) and of other organic films (P3HT, D = 1.8 × 103 cm2/s;48 PPV derivatives, D = 3 × 103 cm2/s;49 PCPDTBT, D = 3 × 103 cm2/s50). Combined with Y6’s respectively long exciton lifetimes of τ = 840 ps and 908 ps, they allow for long exciton diffusion distances of Inline graphic nm, therefore confirming Y6 to be well-performing for photoactive organic layers in OSCs. Recently, new organic materials with diffusion coefficients higher than those of Y6 have been synthesized (PDHF nanofibers, D = 0.5 cm2/s51). Determining D corrected for SSA in their two-dimensional analogues would be of high interest for photovoltaic applications.

In conclusion, most of the available methods in the literature that aim to study nanoscale transport lack a direct spatial visualization of diffusion and/or rely only on numerical solutions susceptible to uncertainty in the initial necessary assumptions. Others, such as transient absorption microscopy, might require high excitation fluences and therefore not always can operate in a negligible-SSA regime, leading to an overestimation of the diffusion coefficient in samples where SSA is very high. In this work, we used spatially and time-resolved fluorescence microscopy to directly visualize diffusion. We could avoid photobleaching as well as decouple our measurements from exciton–exciton annihilation due to the low fluences regime (about 10 Suns) allowed and to the additional independent spatial coordinate.

Decoupling exciton–exciton annihilation from real diffusion, as well as a direct track of spatial broadening, is of ultimate importance to avoid overestimation of D and consequently to accurately determine the diffusion coefficients and length. Still, controlling exciton diffusion in new materials remains a challenging topic to be further investigate. Here, we provided a necessary and free-of-artifacts tool from which deeper and more methodical investigation on how diffusion is affected by geometry, temperature, or thickness may rise, leading to novel insights on how to optimize materials and explore the still available room of improvement in organic solar cells.

Acknowledgments

The authors acknowledge support through the MCIN/AEI projects PRE2019-091051 and PGC2018-096875-B-I00, the “Severo Ochoa” program for Centers of Excellence in R&D CEX2019-000910-S, the Catalan AGAUR 2017SGR1369, Fundació Privada Cellex, Fundació Privada Mir-Puig, and the Generalitat de Catalunya through the CERCA program. L.B. received funding from the Clean Planet Program supported by Fundació Joan Ribas Araquistain (FJRA). N.F.v.H. acknowledges the financial support by the European Commission (ERC Advanced Grant 670949-LightNet). J.M. and F.B. acknowledge the financial support by the European Commission (951843), Spanish MINECO (MAT2017-89522-R) and MCIN/AEI (PRE2018-084881). This work was partially funded by Ministerio de Ciencia e Innovación (grant No. PID2020-112650RB-I00).

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpclett.2c03585.

  • Figure S1: Compressed exponential fit. Figure S2: Saturation curve of the 50 nm layer. Figure S3: Galvo-mirror calibration. Figure S4: Experimental setup. Figure S5: Gaussian broadening and lifetime elongation. Figures S6–S7: Spatiotemporal fit residuals and offset. (PDF)

The authors declare no competing financial interest.

Supplementary Material

jz2c03585_si_001.pdf (731.3KB, pdf)

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