An Energy-Gap Law for Photocurrent Generation in Fullerene-based

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An Energy-Gap Law for Photocurrent Generation in Fullerenebased Organic Solar Cells – The Case of Low-Donor Content-Blends Elisa Collado-Fregoso, Silvina N. Pugliese, Mariusz Wojcik, Johannes Benduhn, Eyal Bar-Or, Lorena Perdigon Toro, Ulrich Hörmann, Donato Spoltore, Koen Vandewal, Justin M Hodgkiss, and Dieter Neher J. Am. Chem. Soc., Just Accepted Manuscript • Publication Date (Web): 08 Jan 2019 Downloaded from http://pubs.acs.org on January 8, 2019

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Journal of the American Chemical Society

An Energy-Gap Law for Photocurrent Generation in Fullerene-based Organic Solar Cells – The Case of Low-Donor Content-Blends Elisa Collado-Fregoso1, Silvina N. Pugliese2,3, Mariusz Wojcik4, Johannes Benduhn5, Eyal Bar-Or1, Lorena Perdigon Toro1, Ulrich Hörmann1, Donato Spoltore5, Koen Vandewal6, Justin M. Hodgkiss2,3 and Dieter Neher1* 1

Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Straße 24–

25,14476 Potsdam-Golm, Germany 2

School of Chemical and Physical Sciences, Victoria University of Wellington, Wellington 6040,

New Zealand. 3

The MacDiarmid Institute for Advanced Materials and Nanotechnology, Wellington 6040, New

Zealand. 4

Institute of Applied Radiation Chemistry, Lodz University of Technology, Wroblewskiego 15, 93-

590 Lodz, Poland 5 Dresden

Integrated Center for Applied Physics and Photonic Materials (IAPP) and Institute for

Applied Physics, Technische Universität Dresden, Nöthnitzer Str. 61, 01187 Dresden, Germany 6

Institute for Materials Research (IMO-IMOMEC), Hasselt University, Wetenschapspark 1, 3590

Diepenbeek, Belgium

KEYWORDS. Organic photovoltaics, photocurrent generation, excited states, spectroscopy.

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ABSTRACT. The involvement of charge-transfer (CT) states in the photogeneration and recombination of charge carriers has been an important focus of study within the organic photovoltaic community. In this work, we investigate the molecular factors determining the mechanism of photocurrent generation in low-donor-content organic solar cells, where the active layer is composed of vacuum-deposited C60 and small amounts of organic donor molecules. We find a pronounced decline of all photovoltaic parameters with decreasing CT state energy. Using a combination of steady state photocurrent measurements and time-delayed collection field experiments, we demonstrate that the power conversion efficiency, and more specifically, the fill factor of these devices, is mainly determined by the bias dependence of photocurrent generation. By combining these findings with the results from ultrafast transient absorption spectroscopy, we show that blends with small CT energies perform poorly because of an increased non-radiative CT state decay rate, and that this decay obeys an energy-gap law. Our work challenges the common view that a large energy offset at the heterojunction and/or the presence of fullerene clusters guarantee efficient CT dissociation, and rather indicates that charge generation benefits from high CT state energies through a slower decay to the ground state.


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INTRODUCTION Free charge carrier and transport generation in organic solar cells (OSCs) has been optimized to such extent that they produce photocurrents comparable to their more efficient perovskite counterparts.1 This is surprising given the low dielectric constant of organic solids, which suggests the formation of bound pairs of charge carriers following photo-excitation. Various mechanisms have been proposed to explain this important fact,2 referring to a beneficial energetics, an advantageous morphology, or a combination of these two. Several groups proposed that photocurrent generation benefits from a high energy of the primarily-excited excitons relative to the energy of the final charge-separated (CS) states.3–5 A possible scenario is that singlet excitons dissociating at the donor-acceptor heterojunction form electroncally/vibronically "hot" chargetransfer (CT) states, and that these excited states split into free carriers prior to thermalizing to the lowest excited CT state manifold.6–10 In this picture, the charge generation efficiency correlates with the driving force for charge separation, Δ𝐸𝐺𝑆 defined as the difference in the enthalpy of the singlet exciton and of the separated polaron pair.11 In turn, charge generation should largely benefit from a large offset of the LUMO (lowest unoccupied molecular orbital) and/or HOMO (highest occupied molecular orbital) energy at the heterojunction. However, some recent solar cells exhibited very high photocurrent efficiencies despite low energy offsets at the heterojunction.12–14 The concept of an improved dissociation yield via “hot” CT states was also challenged by the observation that the excitation energy has little influence on the field- and temperature dependence of free charge formation.15–19 This led to a picture where the efficiency of charge generation is governed by the details of the pathway from the relaxed CT state to the charge-separated state. Additionally, and related to the concept of “cold” CT dissociation, free charge formation was proposed to benefit from the delocalization of CT states and charges on well-ordered molecular aggregates of the donor and acceptor.18,20–24 Charge delocalization was shown to reduce the CT state binding energies,25–28 rendering their dissociation into free charges more likely. According with this picture, a higher degree of phase separation in bulk heterojunction solar cells generally results in a more efficient and less field-dependent photocurrent generation.



Conclusions regarding the role of a given parameter on the efficiency of photocurrent generation are often deduced from the study of donor-acceptor bulk heterojunction systems, where the energetics are varied systematically through chemical modification of the constituents. However, the morphology of such systems is generally ill-defined and, more importantly, may undergo changes when modifying the chemical structure of the components forming the blend. This ambiguity of interpretation is avoided in solar cells comprising mainly fullerene acceptor, with small molecule donors added at low concentration (< 10 mol %). Surprisingly, their efficiencies can be relatively high, despite the limited absorption of the fullerene.29–32 Such low-donorcontent systems have a well-defined morphology, where the donor molecules are homogeneously dispersed in the fullerene matrix.33–35 This presents a very clear advantage for fundamental studies, as the variation of the chemical structure of the small molecule donor does not result in relevant changes of the blend microstructures. Building upon this advantage, lowdonor-content blends have been investigated to correlate macroscopic device properties to molecular parameters, and to understand such correlations on the basis of the underlying dynamic processes.33,36–41 A recent relevant finding is that the CT emission efficiency follows the energy-gap law,39,42 which implies that non-radiative recombination losses become increasingly dominating as the energy of the CT state, ECT, is reduced. In this paper, we address the efficiency of photocurrent generation for a series of devices composed predominantly of C60 (≈ 94 mol %) and small amounts of organic small molecule donors (≈ 6 mol %), with their CT state energies systematically varied. We report a pronounced yet unnoticed decline of all photovoltaic parameters with decreasing ECT. Using a combination of time-delayed collection field (TDCF) and external quantum efficiency measurements (EQE) at different bias voltages, we show that the shape of the JV-characteristics is mainly determined by the bias dependence of photocurrent generation, indicating geminate recombination as the major photocurrent loss in these systems. Importantly, these losses vary strongly among the studied systems, and are most pronounced for the systems with low CT energies (high HOMO offsets). Ultrafast transient absorption spectroscopy (TAS) reveals that blends with lower CT energy suffer from a higher CT decay rate, which we assign to an increased vibronic coupling between the CT and the ground state obeying the energy-gap law for internal conversion.42 As a 4 ACS Paragon Plus Environment

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result, the energy of the CT state is identified as the main parameter determining the efficiency of photocurrent generation in these morphologically well-defined donor-acceptor blends.

RESULTS Device Performance versus Open-Circuit Voltage The devices consist of 50 nm of active layer, sandwiched between ITO/MoO3 and Bphen/Ag electrodes. The donor molecules, co-evaporated with C60, were selected to span a wide range of the ionisation energy, given rise to a significant variation of the CT state energy, between 0.9 and 1.6 eV, when mixed with C60 at 6 mol %.38 Figure 1 shows the JV-curves of several devices and the chemical structures of four selected donors studied in greater detail below. Table S1 summarizes the photovoltaic parameters, hole mobility values and molecular properties of these systems. The absorbance of all blends is very similar to that of a neat C60 layer (Figure S2a) and the C60 emission is efficiently quenched in the blends (Figure S2b), in agreement with a homogenous distribution of the small molecules within the fullerene matrix. Despite the devices absorbing the same number of photons, it is striking that all device parameters, i.e. JSC, VOC and fill factor (FF) are very sensitive to the choice of donor utilized. This indicates that the energetics of the system is determined by the donor:acceptor bulk properties and not to by, e.g., a Schottky barrier between the anode and C60 as has been suggested previously.30 The high sensitivity of the device parameters upon the selection of donor results in a change of the power conversion efficiency (PCE) of almost two orders of magnitude, from ≈ 0.03% to 3% as shown in Figure 1c, where we assemble performance data for a wide range of donor molecules. The photocurrent, however, seems to saturate for most devices at reverse bias, approaching a value close to -5.5 mAcm-2. Since all the solar cells have a similar absorption, we infer that at high reverse bias voltages, CT dissociation and subsequent transport of the carriers to the electrodes is nearly complete and every absorbed photon is converted into a free charge pair.



6 4 2 0

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4P-TPD TAPC Ruberene DMFL-NPD Spiro-MeO-TPD m-MTDATA TPDP

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Rubrene

40

30

m-MTDATA

20 0.0

TPDP

0.2

0.4

0.6

0.8

1.0

Voc [V]

Figure 1. (a) JV-characteristics under simulated AM1.5G illumination (solid curves) and in the dark (dashed lines) for different low-donor-content blends. Details about the used materials can be found in the Supporting Information. (b) Chemical structure of some selected donor molecules. (c) Power conversion efficiency (PCE) as function of the open-circuit voltage (VOC) for a wide range of donor molecules. Highlighted in colour is the performance of the blends with the donors shown in (b). (d) Effective fill factor (FF*, see text) plotted versus VOC. Importantly, a decrease in VOC goes along with a drastic reduction in FF as can be deduced from the JV-curves in Figure 1a. In general, the FF is determined by the voltage dependence of geminate and non-geminate recombination processes,43–47 but it also depends explicitly on the value of VOC.48 Therefore, an effective fill factor, FF*, was calculated by shifting all JV curves so that they all have a VOC of 1 V. The dependence of FF* upon the original (real) VOC is shown in Figure 1d, highlighting the continuous deterioration of the JV-characteristics with decreasing VOC.


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As the Shockley-Queisser limit predicts a FF of ≈ 88% for an ideal solar cell with VOC of 1 V, the FF of all of our devices must be limited by additional, voltage-dependent recombination losses. The close connection between FF* and VOC comes as a surprise since FF summarizes various dynamic processes, namely free charge generation in competition with geminate CT recombination, and free charge extraction competing with non-geminate recombination. Previous work related the FF to non-geminate recombination, putting particular emphasis on the mobilities of electrons and holes.44,47,49–51 Here, we find a modest correlation between FF* and the mobility of the slower holes (Figure S3a), but we also measure very similar FF*’s for devices with m-MTDATA and TPDP despite their three orders of magnitude difference in hole mobility h (Table S1 and Figure S3a)40. Instead, Figure S3b reveals a continuous dependence of FF* on ECT, where high CT energies go along with larger FF*s (Figure S3b). This suggests that the macroscopic device performance is closely linked to the energetics at the donor-acceptor interface, which points to geminate recombination as the major loss mechanism of the poorly performing devices. In light of this evidence, we carried out a detailed investigation of the photocurrent generation mechanisms for four selected blends, guided by their specific values of VOC, FF* and h. The chemical structures of the donor molecules are shown in Figure 1b while Table 1 summarizes the relevant molecular, charge transport and device parameters. In particular, TAPC and rubrene both have high ECT (and VOC’s) while m-MTDATA and TPDP stand out because of their small ECT and their very different h.



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Table 1. Photovoltaic parameters, CT state properties (taken from Ref. 37), and h (taken from Ref. 40) for selected donor:C60 systems (with 6 mol % content of donor). These four systems were chosen because of their distinct differences in ECT, reorganisation energy () and h (see also Table S1). TAPC

Rubrene

m-MTDATA

TPDP

JSC (mAcm-2)

5.30

5.22

1.05

0.81

VOC (V)

0.90

0.90

0.36

0.26

FF (%)

58.5

50.7

32.3

39.6

FF* (%)

59.3

51.8

28.0

29.6

PCE (%)

2.80

2.37

0.12

0.08

ECT (eV)

1.45

1.46

0.95

0.91

 (eV)

0.16

0.08

0.41

0.16

1.57∙10-5

6.61∙10-5

1.08∙10-8

2.42∙10-5

h (cm2V-1s-1)

Photon Energy and Bias Dependence of the External Quantum Efficiency It has been shown that C60 generates free charges with a reasonable efficiency when excited above 2.35 eV, becoming far less efficient at lower photon energies.52–56 This has been attributed to the photogeneration and dissociation of intermolecular C60-C60 CT excitons at high photon energies, while low energy photons excite localized singlet Frenkel excitons. The EQE of a neat C60 device, indeed, depends strongly on photon energy, and this dependence is a function of applied bias (Figure S4). The situation is very different for the four low-donor devices, for which EQE spectra are plotted in Figure 2. Most notably, the bias-dependence is different to that of the neat C60 device and specific to each system, and the significant drop of the EQE below 2.35 eV is largely reduced. We also find that the shape of the EQE spectrum is virtually unaffected by the applied bias, except for the TPDP blend where we observe the growth of a pronounced low energy feature at a more negative bias. These results show that intrinsic charge generation in C60 is of minor importance over the entire spectral range studied here. In other words, irrespective of whether the initially photoexcited species is an intermolecular CT state in neat C60, an


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intramolecular C60 Frenkel exciton or a low energy donor-acceptor CT state, the EQE displays the very same dependence on the internal electric field. A similar situation has been reported for various donor-acceptor blends in the past and assigned to charge generation via low energy donor-acceptor CT states.16,57,58 The poor performing TPDP blend displays a clear and non-trivial effect of the reverse electric bias on the shape of the EQE in the CT absorption range, pointing either to a strongly bound CT state manifold or to optical interference effects in combination with spatially dependent charge generation and/or extraction.

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Figure 2. Photovoltaic EQE spectra for four selected low-donor-content blends. Coloured lines show EQE spectra measured at different bias. The full grey line is the EQE spectrum measured close to the VOC of the respective device, scaled to match the EQE at -2V at high photon energies. Shown with grey dashed lines is the EQE spectrum of neat C60 at -2 V (see Figure SI4). Vertical dotted lines mark the excitation energies in the TDCF experiments described below.



Bias and Photon Energy Dependence of Free Charge Generation Besides depending on the free carrier generation yield, the EQE is also shaped by the efficiency of charge extraction. Charge extraction in turn can be affected by free or trap-assisted carrier recombination, or by the recombination of the photogenerated charges with dark-injected charge. Therefore, time-delayed collection field (TDCF) measurements were performed to assess the efficiency of free charge generation. The details of the method have been discussed in detail elsewhere.59,60 Briefly, a short laser pulse (≈ 4 ns) illuminates the device while holding it at a certain bias, (herein called ‘pre-bias’ Vpre). After a certain delay time after the pulse, the device is taken to a high reverse bias (herein called ‘collection bias’ Vcoll) to extract all mobile charges remaining in the sample. From these data, the external generation efficiency (EGE) is calculated as the ratio of the extracted charges to the photons incident on the device. Great care was taken to prevent non-geminate recombination losses by using a large collection bias of -2.5 V and by setting the laser intensity as low as possible to generate a carrier density typically as little as 1016 cm-3, while maintaining a good signal-to-noise ratio. Figure 3 shows the EGE for the four selected materials as a function of pre-bias, with excitation at 440 nm (2.82 eV). Data for the four studied systems is overlaid onto the JV-curves at reverse bias to directly compare the bias-dependence of charge generation and that of the steady state photocurrent. For the TAPC and rubrene device, which both possess high VOC, EGEs are nearly independent of bias except at around VOC where the internal electric field drops near to zero and non-geminate recombination becomes important. For TPDP, however, the shape of the JV-curve is fully governed by the bias-dependence of the EGE, implying that geminate recombination limits the photocurrent in this system. The situation for m-MTDATA appears to be an intermediate case, where bias-dependent charge generation is accompanied with non-geminate recombination losses resulting from the very low hole mobility of this particular blend. It has recently been proposed that photocurrent generation in low-donor-content blends is determined by the rate at which holes transfer from the donor to the acceptor, through which they are transported to the anode.35 In this picture, devices with a lower VOC (higher HOMO offset) would suffer from a larger barrier for hole transfer. However, three independent 10 ACS Paragon Plus Environment

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observations question the role of hole transfer back to the fullerene in the photocurrent generation of our devices. First, transient mobility measurements on low-donor-content blends of α-sexithiophene (α-6T) with C60 revealed that hole extraction via the fullerene molecules is insignificant in the concentration and bias range studied here.34 Second, an extensive study of space charge limited currents of various low-donor-content layers was fully consistent with predominant hole motion between donor molecules.40 Finally, we find that the EGE from TDCF follows a similar voltage dependence as the steady state JV-characteristics, despite that in TDCF charge is always collected with the same bias (-2.5 V). All these observations point to predominate hole extraction via the donor molecules, and that this process does not impose a major limitation to the device efficiency. Recent simulation work attributed the efficient hole extraction in low-donor-content blends to the formation of percolation pathways extending several tens of nanometers from the anode into the active layer.61

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1.0

Voltage [V] Figure 3. External generation efficiency (EGE) from TDCF measurements, plotted as a function of bias voltage for four selected low-donor-content blends, and compared to the corresponding JVcurves. Excitation was at 440 nm (2.82 eV) with a low fluence of ca. 20 nJ/cm2, generating a carrier density of not more than 1016 cm-3).



Having confirmed that inefficient charge extraction is of subordinate role, we extended our TDCF measurements by exciting the devices at different wavelengths, with the results shown in Figure 4. These measurements were performed to test whether the nature of the primary excited species has an appreciable effect on the free charge generation efficiency. Excitation at 440 nm (above 2.35 eV) primarily produces fullerene CT excitons while Frenkel excitons in C60 are the predominant photoexcited states at 590 (below 2.35 eV).52 Even lower excitation energies will exclusively form donor:acceptor interfacial CT states.38 For all systems, including the poorly performing TPDP-based blend, there is no systematic effect of the excitation energy on the bias dependence of the generation efficiency. This confirms the conclusion from the above biasdependent EQE experiments that photocurrent generation involves a low energy DA-CT state manifold. 1.2

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(d)

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Figure 4. Normalized external generation efficiency (EGE) obtained from TDCF measurements with excitation at different wavelengths. At each excitation photon energy, the excitation fluence was adapted to generate roughly the same carrier density of not more than 1016 cm-3.


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Device Performance versus CT Dissociation Efficiency The above data provide unambiguous evidence that the device performance is limited by geminate recombination and that the photocurrent generation involves a low energy CT state manifold. In this picture, the efficiency of photocurrent generation is governed by the competition between CT dissociation and geminate recombination through the field dependent dissociation probability (escape probability), 𝜂𝑑𝑖𝑠𝑠(𝐸). In general, 𝜂𝑑𝑖𝑠𝑠(𝐸) depends strongly on the details of the dissociation pathway, and hence on the morphology and energetic landscape at the heterojunction and in the bulk phases of the studied systems.62–64 Herein, we benefit from the fact that the active volume of all studied blends consists mostly of C60 to which donor molecules are added at a low concentration. Recent time-resolved measurements on similar lowdonor-content layers revealed electron mobilities of 0.5-1 cm2/Vs, which is orders of magnitude higher than the hole mobilities.34 It is, therefore, reasonable to assume that the CT dissociation pathway is determined by the motion of the electrons. Following this line of arguments, the different blends should differ mainly by the recombination rate of the CT state, 𝑘𝑟, while all parameters describing the dissociation of the CT state should be the same for all blends. We have, therefore, extended our TDCF investigations to three more donors, with the chemical structures and bias dependent EQE spectra shown in Figure S5. Figure 5a displays our complete set of measured external generation efficiencies (with the corresponding JV-curves). The new data confirms the conclusion drawn from the first set of measurements, i.e. that the shape of the JV-curves is largely determined by the bias dependence of charge generation, and that the effect of bias becomes weaker for larger ECT (VOC) systems. The data also shows that the EGE data of most blends saturates at high reverse bias, which we assign to complete dissociation of the photoexcited CT states (𝜂𝑑𝑖𝑠𝑠 = 1). This allowed us to convert the bias dependent EGE data from TDCF into the corresponding field dependence of the dissociation efficiencies, 𝜂𝑑𝑖𝑠𝑠(𝐸), which is shown in Figure 5b with open squares. Here, E = (Vbi-V)/d is the internal electric field, Vbi is the built-in voltage where the photocurrent is zero, and d is the thickness of the blend (see the Supporting Information and Figure S6 for details). Figure 5b also includes the results from additional TDCF measurements on a 100 nm thick blend of C60 with rubrene and TPDP, which is 13 ACS Paragon Plus Environment


the system with the weakest and strongest field dependence of photocurrent generation, respectively. These measurements were performed with an excitation wavelength of 590 nm to penetrate the entire active layer. The resulting 𝜂𝑑𝑖𝑠𝑠(𝐸) is plotted in Figure 5b with full squares. The data from the two different layer thicknesses agree very well, confirming our interpretation that the poorer performing devices suffer indeed from inefficient free charge generation in the bulk of the layer. In view of the limitations of the available analytical models to describe 𝜂𝑑𝑖𝑠𝑠(𝐸), and also the controversies over their applicability,65,66 we decided to analyse our data on the basis of a more realistic simulation model which takes into account the discrete nature of the medium and the presence of energetic disorder. Our simulation method is essentially the same as described in Refs.67,68 and details can be found in the Methods section. In the calculations, we assume an electron mobility 𝜇𝑒 = 0.5 cm2/Vs, a dielectric constant 𝜀 = 4.5, and an energetic disorder of 𝜎 = 0.06 eV; values being typical for C60 fullerene.34,69 We also assume 𝑎 = 1 nm, which is close to the C60 diameter and lies within the range of calculated radii of the lowest energy CT state.70,71 The hole mobility is orders of magnitude lower than the electron mobility in all studied blends, and we use the same value (𝜇ℎ = 10-4 cm2/Vs) for simplicity. Given the large mobility imbalance, 𝜂𝑑𝑖𝑠𝑠 is not depending on the exact choice of 𝜇ℎ. From an independent simulation, we determined 𝐶𝜎 = 0.043.72 Simulations were run to fit the experimental dissociation probabilities 𝜂𝑑𝑖𝑠𝑠(𝐸), by varying only the CT decay rate 𝑘𝑟. The result is plotted as dashed lines in Fig. 5b. Excellent fits were obtained despite the fact that all input parameters except kr were the same for all blends. This confirms our hypothesis that the pathway of CT dissociation is largely independent of the choice of the donor. The obtained values of 𝑘𝑟 are plotted as a function of the Voc in Figure S7. The plot reveals a pronounced dependence of the CT decay dynamics on Voc, where 𝑘𝑟―1 ranges from ca. 100 ps and several nanoseconds, and low Voc (ECT) blends suffer mostly from fast CT recombination.


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(a)

-60

Rubrene TAPC 4P-TPD DMFL-NPD Spiro-MeO-TPD m-MTDATA TPDP

4 2

(b) 100

-40 -20

0

0

-2

20

-4

40

diss [%]

6

J [mAcm-2]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


EGE [%]

Page 15 of 42

Rubrene TAPC 4P-TPD DMFL-NPD Spiro-MeO-TPD m-MTDATA TPDP

10

-6 -2.0

60 -1.5

-1.0

-0.5

0.0

0.5

1.0

106

Voltage [V]

107

108

E [Vm-1]

Figure 5. (a) EGE as function of bias compared to the JV-characteristics under simulated AM1.5G illumination of 50 nm thick low-donor-content solar cells and seven different donors. EGE were determined with TDCF at 440 nm excitation. (b) CT dissociation efficiency 𝜂𝑑𝑖𝑠𝑠 (open squares) as a function of the internal field, deduced from the experimental EGE data in Figure 5(a). Full squares are from TDCF measurements on 100 nm thick layers with 590 nm excitation wavelength. Dashed colored lines show the results of kMC simulations, where the CT decay rate kr was the only fitting parameter.

Charge Carrier Dynamics To directly measure the dynamics of photoexcited species and in particular the fate of CT states and free charges, transient absorption spectroscopy (TAS) was applied to four selected lowdonor-content blends. Experiments were performed with an excitation wavelength of 400 nm (3.1 eV), which excites mainly C60. Figure 6 summarizes the resulting TAS transients for two fluences. We note already here that the overall charge signal decays faster when going from rubrene to TPDP. TAS data contains signal contributions from all the transient species in the sample: excitons, CT states, and spatially separated free charges (SC). In order to retrieve the dynamics of each transient species, we applied the soft modelling technique MCR-ALS 15 ACS Paragon Plus Environment


(multivariate curve resolution by alternating least squares73) to decompose the data into a bilinear model, i.e., pairs of spectra and kinetics for each transient species. TAS data for pristine C60 was used as a spectral mask for the blends, allowing the spectra and kinetics of charges (including both CT states and SCs) to be cleanly isolated without rotational ambiguity (Figure 6a). The spectral assignment of free charges was verified by confirming the C60 anion feature at around 1.2 eV in each case55 and by comparing the spectra to the absorption spectra of FeCl3doped donor solutions (see Figure S8 in the Supporting Information). While the TA spectra of charges do not distinguish CT and SC species, the behaviour of the CT states may be isolated via fluence-dependent measurements. The normalised charge kinetics shown in Figure 6c-f surprisingly reveal a minor fluence dependence on the nanosecond timescale, indicating that a first order recombination process dominates the fate of the photogenerated carriers at this fluence. We argue below that this kinetic scenario stems from the rapid reformation of CT states from free charges through efficient BMR and that it enables the CT lifetime to be recovered from the observed recombination kinetics.


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Figure 6. (a) Spectra of the charge component in each blend, extracted via MCR-ALS. (b) Illustration of the used kinetic model (Equation (1). (c-f) Charge recombination dynamics at different pump fluences (square markers) and the fitting curves from the numerical global fit of Equation (1) (solid lines) for c) TAPC:C60, (d) Rubrene:C60, (e) m-MTDADA:C60, and (f) TPDP:C60, with all fitting parameters listed in Table 2.



We employed a simple rate model74 to describe the competition between CT dissociation and recombination, including CT reformation through the bimolecular recombination of free charge with the encounter coefficient 𝑘𝑒𝑛𝑐 (Figure 6b). 𝑑𝑆𝐶(𝑡) 𝑑𝑡

= 𝑘𝑑𝐶𝑇(𝑡) ― 𝑘𝑒𝑛𝑐𝑆𝐶(𝑡)2

(1a)

𝑑𝐶𝑇(𝑡) 𝑑𝑡

= ―𝑘𝑑𝐶𝑇(𝑡) ―𝑘𝑟𝐶𝑇(𝑡) + 𝑘𝑒𝑛𝑐𝑆𝐶(𝑡)2

(1b)

Here, all recombination to the ground state is via the decay of CT states with the CT recombination rate 𝑘𝑟 as defined above, and 𝑘𝑑 is the zero field CT dissociation rate. We are aware that this rate model oversimplifies the complex process of CT dissociation and reformation via multiple carrier hopping. Nevertheless, this model allows us to reliably assess trends in CT lifetimes without needing to develop a simulation tool capable of assessing the high carrier densities of our measurements, or introducing new parameters that cannot be independently verified. A similar rate model (including also the formation and decay of triplet CT states was successfully employed to model the TAS transients of different donor:fullerene blends over a wide range in fluence.75 Since no analytical solution is found for these non-linear differential equations,76 we performed a numerical global fit of our data in MATLAB using this model with appropriate initial conditions. Because of the nearly complete lack of a fluence-dependence of the TAS traces in Figure 6, an independent determination of the three parameters in Equation (1a,b) was not possible. Unfortunately, results from TAS experiments at lower fluences where BMR dominate the carrier dynamics were very noisy, mainly because of the small thickness of the blend and the low absorption cross section of the fullerene anion. Global fits were, therefore, performed with 𝑘𝑑 and 𝑘𝑒𝑛𝑐 being fixed at selected different values (see the Supporting Information for details). Figure S9 shows the results of such a fitting with Equation (1) where we assumed Langevin-type encounter-limited recombination with 𝜇𝑒 ≫ 𝜇ℎ of 0.5 cm2/Vs34,69 and a dielectric constant of 𝜖𝑟=4.5, yielding 𝑘𝑒𝑛𝑐 = 2 × 10 ―7𝑐𝑚3/𝑠. The fit captures the early temporal decay of the TAS signal, though it deviates from the experimental data at longer delay times. We note that our analysis is rather simple as it does not take into account the molecular details of the blend, energetic disorder and related dispersive effects. Due 18 ACS Paragon Plus Environment

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to these limitations, the parameters 𝑘𝑒𝑛𝑐 and 𝑘𝑑 were modified to obtain a better fitting of the kinetics. For the relatively high value of 𝑘𝑒𝑛𝑐 considered so far, we found that changing 𝑘𝑑 does not improve the quality of the fit and we attribute this to the very rapid bimolecular recombination of SCs to the CT state. Subsequently, we altered the value of 𝑘𝑒𝑛𝑐, and Figure 6 displays fits where such parameter has been reduced to 𝑘𝑒𝑛𝑐 = 2 × 10 ―9𝑐𝑚3/𝑠, now providing a better qualify of the fit. Values for 𝑘𝑟 from these fits are assembled in Table 2. 𝑘𝑟 increases significantly when going from the rubrene blend to the low CT state energy (and low performance) systems, with the corresponding CT decay times decreasing from few nanoseconds to hundreds of picoseconds. At the same time, values for 𝑘𝑟 are smaller than the set value of 𝑘𝑑 = 2.5 × 109 𝑠 ―1 for the TAPC and Rubrene blends, meaning that dissociation is faster than recombination for such blends, whereas the opposite occurs for the m-MTDATA and TPDP blends. This is fully compliant with the interpretation of our EQE and EGE experiments. However, such comparison should be considered with care, as kd simplifies the complex process of CT dissociation as pointed out above. Figure S10 shows how the CT decay times of the different blends vary with different assumptions made for 𝑘𝑒𝑛𝑐 and that, independent of the exact choice of the input parameters, the resulting 𝑘𝑟’s exhibit a similar ten-fold increase when going from rubrene to TDPD.

Table 2. CT decay rates, 𝑘𝑟 , as estimated from the fit of the fluence dependent TAS measurements in Figure 6, with given values for the BMR recombination coefficient, 𝑘𝑒𝑛𝑐, and the zero field dissociation rate, 𝑘𝑑.

Donor

TAPC

Rubrene

m-MTDATA

TPDP

𝒌𝒆𝒏𝒄 [cm-3s-1]

2.0x10-9

2.0x10-9

2.0x10-9

2.0x10-9

𝒌𝒅 [s-1]

2.5x109

2.5x109

2.5x109

2.5x109

𝒌𝒓 [s-1]

0.65x109

0.44x109

3.86x109

2.97x109

1.54

2.27

0.26

0.34

𝟏/𝒌𝒓[ns]



DISCUSSION AND CONCLUSION Our study on low-donor-content organic solar cells reveals a surprising correlation between the VOC and the “quality” of the JV-characteristics as expressed by the parameter FF*. The lower the VOC of the device the stronger is the dependence of photocurrent generation on bias voltage. Our results show unambiguously that the shape of the JV-curves is not governed by the extraction of charges. We presume that the high electron mobility combined with dispersive hole extraction and a small active layer thickness renders it unlikely for a hole to meet an electron before it is extracted. Instead, our data suggest that the JV-characteristics are determined by the field dependence of photocurent generation, i.e. the escape of the electron from the Coulomb barrier of the hole. We also find that photocurrent generation becomes less efficient and more field dependent when decreasing the CT state energy (increasing the HOMO offset), This result is in contrast to the common presumption that photocurrent generation benefits from a large LUMO-LUMO or HOMO-HOMO offset at the donor-acceptor heterojunction (a large Δ𝐸𝐺𝑆 ). Our results, instead, indicate that the performance of our low-donor-content blends does not benefit from excess energy provided by the initially photo-excited states. In agreement with this interpretation, decreasing the incident photon energy in our photocurrent and TDCF experiment has no appreciable effect on the field dependence of photocurrent generation. This suggests that free charge generation proceeds primarily through low energy CT states, similar to “common” bulk heterojunction systems 15–19 as noted above. Notably, despite that all studied blends have a small concentration of molecular donors dispersed into a C60-rich matrix, some systems display a strong effect of the electric field on photocurrent generation while others do not. Apparently, the aggregation of only one component is not sufficient to guarantee efficient charge collection. At the same time, extensive hole delocalisation, e.g. along a conjugated polymer backbone or within molecular aggregate, is not a necessary prerequisite for field-independent photocurrent generation. There is an ongoing 20 ACS Paragon Plus Environment

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debate on the degree of CT delocalization in cases where one of the carriers remains localized. While spectroscopic work revealed a pronounced delocalization of the CT state in low-donorcontent fullerene blends similar to ours,36,37,61 simulation work suggested a strong localization of the electron-hole pair in the lowest energy CT state.70,71 While we acknowledge the general benefit of exciton and charge delocalisation on the device performance, it does not decide the performance-decisive parameter in the studied systems. Instead, our data suggest that the photocurrent characteristics of these low-donor-content blends are dictated by the rate of the CT state decay competing with field-assisted CT dissociation through an incoherent hopping process. This interpretation is conform with recent transient spectroscopy on C60-based blends and bilayer systems, which ascribed the motion of photogenerated charge carriers to hopping in an energetically disordered density of states distribution from the early times on.34,77,78 Our combined steady state – transient study provides conclusive evidence that the rate of the CT decay depends on the CT energy, and that the poor performance of the devices with low VOC is due to the fast non-radiative CT recombination, competing with CT dissociation. It is a common view that the decay of CT states to the ground state in organic donor-acceptor systems occurs primarily through non-radiative decay channels. Recent work proposed that such non-radiative decays are inherent to organic donor-acceptor heterojunctions and that they proceed primarily through internal conversion.39,79. In this limit, the CT decay rate is related to ECT and the vibrational energy ℎ𝜈ν of the dominant/mean high frequency mode via the wellknown energy-gap law:42

[

𝑘r = 𝑘rad + 𝑘nonrad≅𝑘nonrad ∝ exp ―𝐵

],

𝐸CT ― 𝜆 ℎ𝜈ν

(2)

Here is 𝜆 the CT reorganisation energy due to soft (low frequency) modes. The prefactor B in the exponent depends on details of the exact modes involved. Figure 7 plots kr from TAS (Table 2) as function of 𝐸𝐶𝑇 ―𝜆, together with the values of 𝑘𝑟 from the simulation of the TDCF data (Figure 5). Both data sets align with the prediction of the energy gap law according to Equation (2), with ℎ𝜈ν 𝐵

≈ 200 ± 20 𝑚𝑒𝑉. We conclude that blends with low-lying CT states (low VOC) indeed suffer 21 ACS Paragon Plus Environment


from high CT state decay rates, that the rate of this process is determined by non-radiative internal conversion, and that the CT decay kinetics are connected to the CT state energy via the energy-gap law. Notably, the slope of the exponential factor in Equation (2) agrees fairly well with the result from a recent charge recombination study on non-fullerene blends comprising the polymer MEH-PPV and different fluorene-based acceptors.80 This implies a common mechanism determining the CT decay in organic donor-acceptor blends. Recent theoretical and experimental work suggested that the non-radiative decay of CT states involves high frequency carbon-carbon stretching modes of the -conjugated carbon framework, which are intrinsic to all organic semiconducting materials.39

kr [s-1]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1010

1010

109

109

108

108

107 0.4

0.6

0.8

1.0

1.2

1.4

107

ECT -  [eV]

Figure 7. 𝑘𝑟 from the analysis of the TDCF data (open squares) and from the fluence dependent TAS data (stars), plotted as function 𝐸𝐶𝑇 ―𝜆. The dashed line is calculated from Equation (2) with ℎ𝜈ν/𝐵 = 200 𝑚𝑒𝑉. Our findings put particular emphasis on the importance of understanding and reducing the rate of CT state decay in future research on OPV devices. Notably, the 𝑘𝑟’s of our low-donor-content fullerene-based blends are orders of magnitude smaller than the reported decay rate of the C60C60 CT state in neat C60, which was determined to be of the order of 1012 s-1.55 This explains why


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photogeneration in neat C60 is much less efficient than in our low-donor-content blends, particularly at low bias voltage. Neat C60 has a manifold of intramolecular excited states (Frenkel excitons) below the C60-C60 CT state, in contrast to the donor-acceptor blends where the intermolecular CT state is the lowest energy excited state. Importantly, while extensive work has been performed to study and model the process of CT dissociation in donor-acceptor bulk heterojunction blends,7,8,78,81,82 much less is known about the kinetics of the CT decay despite it’s apparent importance in limiting the efficiency of photocurrent generation. This rate should not be confused with the CT state lifetime, as is typically deduced from TAS83,84 or transient photoluminescence measurements.85,86 Such lifetimes comprise contributions from all processes depopulating the CT state (including CT state dissociation). Recently, a rate model similar to the one we are using herein was applied to low fluence TAS measurements on blends of PCBM with different donors and different concentrations.75 This analysis yielded CT decay rates ranging between 2 ― 3 × 109 𝑠 ―1 for a blend with a low bandgap donor polymer and about 7 ― 9 × 108 𝑠 ―1 for PCBM blended with TAPC, in line with our findings. Importantly, the decay rate depended only little on composition, in contrast to the CT dissociation rate, kd, highlighting the local nature of the CT decay process and how its dynamics depends mostly on the molecular structure and energetics of the donor-acceptor heterojunction. Clearly, more work is needed to establish a comprehensive picture of the properties determining the CT decay rate in state-of-the-art bulk heterojunction blends. These blends are known to exhibit a complex morphology, with phases of different compositions, and with the molecular packing and molecular orientation at the heterojunction often being unknown. It has been shown that the microscopic details of the DA heterojunction, in particular the molecular packing and orientation at the heterojunction,64,87,88 and the intermolecular coupling and wave function delocalisation89,90 affect the nature and kinetics of the CT decay process, rendering the investigation and manipulation of the CT decay kinetics an exciting but also challenging topic of OPV research. Irrespective of these details, our work on morphologically well-defined blends proposes a direct energy gap-type link between the efficiency of photocurrent generation and the energy of the relevant CT state. Efforts to increase the VOC of organic DA blends by increasing the CT energy are, therefore, likely to equally improve all other photovoltaic parameters provided 23 ACS Paragon Plus Environment


that charge extraction is efficient. In fact, some novel high-VOC blends with non-fullerene acceptors yielded efficient and bias-independent charge generation despite a nearly zero energy offset at the heterojunction.1,13,91–93


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METHODS Device Fabrication and Photovoltaic Characterization: All layers of the low-donor-content organic solar cells are thermally evaporated at ultra-high vacuum (base pressure < 10-7 mbar) on a glass substrate with a pre-structured ITO contact (Thin Film Devices, USA). For an appropriate hole contact 2 nm of MoO3 (Sigma Aldrich, USA) are deposited followed by the “diluted donor” active layer comprising 50 nm of C60 (CreaPhys GmbH, Germany) doped with 6 mol% of each donor molecule (for more details see Table S1 in Supporting Information). Afterwards, 8 nm of Bathophenanthroline (BPhen from Lumtec, Taiwan), used as electron contact, is evaporated and finished with 100 nm of Al (Kurt J. Lesker, USA). All the organic materials were purified by 2-3 runs of sublimation. The device is defined by the geometrical overlap of the bottom and the top contact and equals either 6.44 mm2 (used for jV and EQE measurements) or 1 mm2 (used for TDCF measurements). To avoid exposure to ambient conditions, the organic part of the device was covered by a small glass substrate, which is glued on top. The samples used for transient absorption measurements comprised the same blends evaporated on top of a glass substrate. At the University of Potsdam, current-voltage (J-V) characterization was carried out under simulated AM1.5G irradiation at 100 mW cm−2 provided by an Oriel 91160 sun simulator calibrated by a NREL certified standard silicon cell. For JV-measurements at the TU Dresden, a Newport Oriel Sol2A solar simulator calibrated by a monocrystalline Si cell (Fraunhofer ISE) was used instead. J-V curves were recorded using a Keithley 2400 source meter.

Bias-dependent External Quantum Efficiency (EQE) measurements: EQEPV measurements were carried out by illumination of the samples using Oriel Corner-stone 74100 monochromator through an optical fiber at wavelengths ranging from 300 – 1200 nm. The light was emitted from a tungsten bulb and chopped by a 2-blade chopper wheel at a frequency of 75 rpm. The electrical current was measured using a lock-in amplifier (Stanford Research Systems SR 830 DSP) and a resistor of 50 Ohm. Varying biases were applied ranging from -2 V to 1 V using Keithley 2400 source meter. Calibration was made using a Newport calibrated Silicon photodiode (Newport



Page 26 of 42

818-UV) for the wavelength range of 300 - 800 nm, and Germanium photodiode (Newport 818IR-L) for longer. TDCF Measurements. An optical pulse train generated by a diode-pumped, Q-switched Nd:YAG laser (NT242, EKSPLA, 500 Hz repetition rate, 3.8 ns pulse duration) was used to excite the sample. In the meantime, the device is held at a constant ‘pre-bias’ set by an Agilent 81150 A pulse generator trough a homebuilt amplifier and then switched to a strong reverse bias ‘collection bias’ after a certain delay time. The current through the device is measured via a grounded 10 Ω resistor in series with the sample and recorded with an Agilent DSO9104H oscilloscope. To compensate for the internal latency of the pulse generator, the laser pulse was delayed by guiding it through an 85 m long silica fiber (LEONI) Monte Carlo simulations: The simulation is carried out on a simple cubic lattice of spacing 𝑎. At the beginning of each simulation run, the lattice sites are assigned random energies drawn from the normal distribution with zero mean and standard deviation 𝜎. We assume that the CT state is represented by a coulombically bound pair of an electron and a hole which occupy neighboring lattice sites. We create such a pair, and then allow both the electron and the hole to perform nearest-neighbor hopping motions for which the transition rates are calculated using the following equation

exp U k BT  k e ,h   e ,h   1

U  0

(3)

U  0

Here, the indices e and h refer to the electron and the hole, respectively,  e,h are the hopping frequency factors, and ∆𝑈 is the potential energy change resulting from an attempted hop, which takes into account the energy of the electron-hole Coulomb interaction, the effect of an applied electric field, and the difference between the random energies assigned to the lattice sites. The hopping frequency factors are related to the charge carrier mobilities by

 e ,h 

1 k BT  e ,h , C ea 2

(4)


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where 𝐶𝜎 is a parameter that characterizes particle diffusion in an energetically disordered system (𝐶𝜎 = 1 in the absence of disorder). The value of 𝐶𝜎 has to be determined from a separate simulation. Whenever the electron and hole occupy neighboring lattice sites, they may not only hop to other sites, but also undergo geminate recombination with the rate constant 𝑘𝑟. At each simulation step, the rates of all possible events are calculated, and it is probabilistically decided which of these events actually occurs. The simulation run is carried out until the electron and hole recombine or get separated by a large distance. By repeating the simulation for ~104 independent runs, we determine the dissociation probability 𝜂𝑑𝑖𝑠𝑠. Transient absorption spectroscopy (TAS). Our transient absorption spectrometer is described in detail in Ref

94

and Ref

95.

It is based on a 3 kHz repetition rate Ti-Sapphire regenerative

amplifier (SpitfirePro, SpectraPhysics) which provides 800 nm fundamental 100 fs laser pulses, which are split into two arms to generate the excitation (pump) and probe pulses. The 400 nm pump pulses are tuned using a parametric amplifier (TOPAS) and the broadband probe is generated by focusing one of the 800 nm arm onto a 3 mm YAG crystal. By chopping every second pulse we measure the transmitted probe pulses through the excited (pump on) and the unexcited (pump off) sample at a particular time delay t with respect to the pump pulse and the TAS signals are calculated as: Δ𝑇 𝑇 (𝜆,𝑡)

=

𝑇𝑝𝑢𝑚𝑝 𝑜𝑛(𝜆,𝑡) ― 𝑇𝑝𝑢𝑚𝑝 𝑜𝑓𝑓(𝜆) 𝑇𝑝𝑢𝑚𝑝 𝑜𝑓𝑓(𝜆)

(5)

The MCR-ALS is based on the following bilinear decomposition: Δ𝑇 𝑇 (𝜆,𝑡)

= 𝐶{𝑜𝑝𝑡}(𝑡) ∙ 𝑆{𝑜𝑝𝑡}(𝜆)𝑇 + 𝐸𝑟𝑟𝑜𝑟

(6)

Where “opt” means that the spectra and charge matrices has been optimized in a least-squares sense. This decomposition was performed under the following constraints: non-negativity for the concentration profiles, non-positivity for PIA signals and using the C60 exciton masks. We find that at very high fluences (higher than the ones presented here) the exciton mask has to be used at a 27 ACS Paragon Plus Environment


matching fluence. At the fluences presented in this work, the exciton spectra at the different fluences are not noticeably different. For the global fitting of Equation (1) the MATLAB function LSQCURVEFIT returns the coefficients that best fit the model to all datasets. The initial conditions for SC and CT were determined such that SC tends to zero at early times (1 ps). This was achieved with 81% of CT and 9% of SC at a 30 ps time delay.

ASSOCIATED CONTENT Supporting Information. Table providing characteristic data of all studied donors and blends, Voc as function of temperature, absorption and PL data of selected blends, effective fill factor versus CT energy and hole mobility, EQE spectra of neat C60 and selected blends for different bias, details about the determining of the efficiency of CT dissociation, absorption spectra of chemically-doped donor molecules, analysis of the TAS spectra and selected fits.

AUTHOR INFORMATION Corresponding Author *[email protected] ORCID: Johannes Benduhn: 0000-0001-5683-9495 Ulrich Hörmann: 0000-0002-2610-3388 Dieter Neher: 0000-0001-6618-8403 Donato Spoltore: 0000-0002-2922-9293 Koen Vandewal: 0000-0001-5471-383X Mariusz Wojcik: 0000-0002-4472-2852 Notes: The authors declare no competing financial interest


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ACKNOWLEDGMENTS We thank Safa Shoaee (U Potsdam), Jenny Nelson (Imperial College London), and Martina Causa and Natalie Banerji (U Bern) for fruitful discussions. This work was funded by the German Ministry of Science and Education (BMBF) within the project UNVEIL (FKZ 13N13719) and the German Research Foundation (DFG) within the collaborative research center 951 “Hybrid Inorganic/Organic Systems for Opto-Electronics (HIOS)”. JMH and SNP acknowledge support from the New Zealand Ministry of Business, Innovation, and Employment, via a Catalyst grant. J. B., D.S. and K.V. were funded by the BMBF through the InnoProfile Projekt “Organische p–i–n Bauelemente 2.2” (03IPT602X). Olaf Zeika (IAPP) is acknowledged for the synthesis of TPDP.



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Page 41 of 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60




TOC Figure

CT energy CT decay rate Current density [mA/cm2]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

6 4 2 0 -2 -4 -6 -1.5

-1.0

-0.5 0.0 Voltage [V]

0.5

1.0


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An Energy-Gap Law for Photocurrent Generation in Fullerene-based

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