Letter pubs.acs.org/JPCL
Coherence and Uncertainty in Nanostructured Organic Photovoltaics Loren G. Kaake,*,† Daniel Moses,† and Alan J. Heeger*,†,‡,§ †
Center for Polymers and Organic Solids, ‡Department of Physics, and §Materials Department University of California, Santa Barbara, California 93106, United States ABSTRACT: The effects of fundamental uncertainty present a compelling rationale for a highly delocalized photoexcitation on ultrafast time scales. This delocalized photoexcitation enables an immediate probability of charge-transfer over distances compatible with the uncertainty principle. We perform transient absorption measurements on organic bulk heterojunction solar cells to investigate charge-transfer dynamics in a variety of materials. A startling generality emerges indicating that the majority of charge carriers are generated at times within the temporal resolution of our instrument (∼100 fs). SECTION: Spectroscopy, Photochemistry, and Excited States
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in a nanostructured material) occur on the same time scale as the lifetime of the coherent wave function, one should expect to find new physics. For example, the highly correlated multiexciton state in oligoacenes was recently observed to participate in the simultaneous transfer of two electrons.14,16 Figure 1 shows the electron-donating molecules and macromolecules that were used in the experiments reported here as well as the substituted fullerenes that were used as the electron-accepting materials. To study the charge-transfer process in organic bulk heterojunction solar cell materials, we use transient absorption spectroscopy. In brief, transient absorption is a two-pulse laser experiment where one pulse, the pump, excites the sample. A second pulse, the probe, arrives at the sample with a variable time delay and detects changes to the spectral profile as a result of the pump pulse. Figure 2 displays changes in the absorption spectrum of the bulk heterojunction samples as a result of illumination by the pump pulse. All spectra share a negative pointing feature at shorter wavelengths and a positive photoinduced absorption at longer wavelengths. The negative features are caused by the photobleaching of the neutral ground state of the electron donors. The positive photoinduced absorptions arise from products of the photoexcitation, often associated with charge carriers or singlet excitons. Stimulated emission signals are often also found in transient absorption spectra and provide a negative contribution spectrally similar to the fluorescence. Ultrafast observations of photoinduced infrared active vibrational (IRAV) modes associated with polaron formation unambiguously established the ultrafast photogeneration of charge carriers in BHJ materials.17 To identify and assign spectral regions that correspond to charge carriers, we compared spectra collected on short time scales (2 ps) with spectra collected on much longer time scales
oherent phenomena are known to influence energy migration processes in light-harvesting biomolecules1−5 and the dynamics of electron solvation6−9 and play an important role in a variety of other phenomena. In organic photovoltaic devices, the role of coherence in the chargegeneration processes is underexplored, despite the fact that coherent phenomena have been observed in solution-phase photon echo measurements of materials widely used in bulk heterojunction blends.10−12 In addition, long-range exciton delocalization was observed via confocal microscopy,13 and a coherent superposition of exciton states is responsible for singlet fission processes.14 These observations require a reexamination of the prevailing organic photovoltaic dogma, which states that light absorption creates (on all time scales >1 fs) a localized exciton that hops randomly and incoherently before encountering an interface at which charge transfer and charge separation occurs.15 We have performed transient absorption measurements on a variety of organic bulk heterojunction nanostructured materials to investigate the photogenerated charge- transfer dynamics. We demonstrate a startling generality that implies that the lifetime of the delocalized coherent state produced on ultrafast time scales is sufficiently long that it plays an important role during the charge- and energy-transfer processes critical to ultrafast charge photogeneration. The spatially extended excited-state wave functions can be understood as originating from fundamental quantum uncertainty. During the light-absorption process, the existence of the photon is uncertain, implying a momentum uncertainty equal to the momentum of the photon. As a result, its position, as well as the position of the photoexcitation it creates, is uncertain, as required by Heisenberg’s famous equation: ΔxΔp ≥ ℏ/2. The length scale imposed by the uncertainty principle is λ/4π, which is greater than 20 nm for visible radiation. Thus, the photoexcitation process generates a delocalized coherent superposition of the eigenfunctions of the Schrodinger equation that describes the nanostructured organic photovoltaic blend. More generally, when phenomena (for example, charge transfer © 2013 American Chemical Society
Received: May 22, 2013 Accepted: June 25, 2013 Published: June 25, 2013 2264
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nm.18 In MEH-PPV:PC70BM samples, exciton absorption is known to result in prominent features centered at 1240 and 730 nm;19 these regions were scrupulously avoided. By coincidence, in each of the bulk heterojunction materials the spectral region from 850 to 900 nm could be integrated to provide information regarding the population of charges within the heterojunction films, as described elsewhere.20,21 These spectral assignments are in agreement with those deduced by other research groups from similar measurements on MEHPPV,19 P3HT,22 and PCDTBT.23 In all bulk heterojunction thin film samples fabricated, the photoinduced absorption signal was integrated (850−900 nm) to provide a measure of the hole population. Because each sample contains a different weight percent of fullerene and because of the known differences in morphology between the materials, one would expect different charge-generation dynamics if the charge transfer were simply the result of random exciton diffusion. Figure 3 shows the normalized intensity of the transient absorption signal associated with carriers produced as a result of
Figure 1. Molecular structures, names, and abbreviations of acceptor and donor compounds used in this study. Figure 3. Transient absorption of bulk heterojunction materials (e.g., P3HT:PC60BM, PCDTBT:PC70BM, etc.). Left: Integrated spectral intensity associated with mobile carriers, normalized to the intensity at 100 fs, and plotted on a linear scale near-zero time delay. Right: Semilog plot of the integrated spectral intensity associated with the slower component of the mobile carrier generation process, normalized to the intensity at 100 fs. Dynamics are representative of the limit of low pump intensity.
charge transfer in a bulk heterojunction film, plotted as a function of time delay between pump and probe pulses. The dynamics display universal behavior, independent of the materials, and correspondingly, independent of the fine details of sample morphology. The data are characterized by a component that rises on a time scale 100 ps), indicative of carrier loss by recombination. In all cases, the maximum value of the charge carrier signal is ∼1.5 times its value at 1 ps. The rapidly rising component of the charge carrier dynamics in Figure 3 is known to arise from ultrafast electron transfer between the electron donor and the fullerene acceptor.24,25 The slower rising dynamics results from the diffusion of excitons to a heterojunction interface where they are split, forming charge carriers: holes on the donor side of the heterojunction and electrons on the acceptor side. The observed longer time scale contribution to the increase in carrier density (∼50 ps) is consistent with typical exciton transport distances ∼10 nm26 and observed length scales in bulk heterojunction materials.27,28
Figure 2. Transient absorption spectra at 2 ps and 1 ms. (a) MEHPPV:PC70BM bulk heterojunction. (b) P3HT:PC60BM bulk heterojunction. (c) PCDTBT:PC70BM bulk heterojunction. (d) p-DTS(PTTh2)2:PC70BM bulk heterojunction.
(1 ms) that are due only to charge-carrier absorption (see Figure 2). For example, in P3HT:PC60BM (Figure 2b), mismatch at 750 nm between 1 ms and 2 ps spectra likely indicates a stimulated emission band that contributes to signal at this wavelength. As a result, the charge carrier signal was extracted by integrating the spectral region 850−900 nm, which largely avoids a large exciton absorption centered near 1200 2265
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The diffusion time scale is consistent with known diffusion constants of excitons in molecular solids.29 These conclusions are further supported by the intensity dependence of the magnitude of the transient absorption signal at 300 fs and 50 ps, shown in Figure 4. Red crosses indicate the
The definite ratio of the amount of charge transferred on ultrafast time scales to the amount of charge transferred following incoherent exciton diffusion is identical to the statement that the probability of charge transfer on short times scales linearly with that at longer times. At the shortest times, the volume probed by a localized exciton approaches zero, meaning that only nearest neighbor interactions are important. If the excited state present on short time scales is delocalized, it can probe a statistically representative volume of material. Such a conclusion ensures a strong correspondence between the probability of charge transfer on short time scales with that following exciton diffusion regardless of the fine details of the film morphology. An alternative means of interpreting the larger effective volume of the initial photoexcitation regarding the chargegeneration dynamics is to invoke long-range electron transfer38 instead of a delocalized initial photoexcitation. This mechanism operates via a tunneling process of the type well known by those who study the conductivity properties of single molecules.39 However, the probability of tunneling over long distances in a nanostructored material in which all states are localized is not large enough to account for the rate and magnitude of ultrafast carrier generation. The existence of an initially delocalized wave function with a finite lifetime is the most straightforward means of understanding the data. The current picture of exciton delocalization focuses on the role of torsional disorder and dynamic reorganization in defining, to some extent, a chromophoric subunit measured in small numbers of monomer units.26,40 However, a number of studies suggest a coherent superposition of chromophoric units determines the spatial extent of the excited state on short time scales.41,42 A general means of understanding excited-state delocalization on short time scales is through fundamental quantum uncertainty; the initial photoexcitation is a coherent superposition of eigenfunctions of the Schrodinger equation, having a spatial distribution of λ/ 4π. The collapse of this initial state is complex, but even in solution, coherence in MEH-PPV has been observed to persist to ∼25 fs,10 and in P3HT to ∼100 fs.11 This implies that a coherent state of sufficient lifetime exists such that it can participate in electron-transfer reactions and the chargeseparation processes. In other words, prior to collapse into the wave function expected for a disordered nanostructured material, electron transfer can occur from phase-separated domains of electron-donating materials (polymers or small molecules) to domains composed of electron-accepting materials (typically substituted fullerenes). This explains the equivalent sampling volumes, along with providing a rationale why the power dependence in the charge-generation dynamics becomes different on long time scales; the system loses coherence. In conclusion, we present transient absorption data that imply the importance of coherent effects in organic solar cells. We observed a generality in the charge-generation dynamics of organic bulk heterojunction materials that is unexpected from the perspective of a highly localized initial photoexcitation. The creation of long-range coherent superposition states is a natural consequence of the Heisenberg uncertainty principle, as applied to the photon absorption process. We expect that phenomena of this type are important not only for organic bulk heterojunction solar cells but also for nanostructured materials in general.
Figure 4. Power dependence of the integrated transient absorption signal associated with the two pathways of mobile carrier generation. (a) MEH-PPV:PC 70 BM, (b) P3HT:PC 60 BM, (c) p-DTS(PTTh2)2:PC70BM, and (d) PCDTBT: PC70BM.
signal level at 300 fs, assigned as the ultrafast charge-transfer yield. This component is linear over two orders of magnitude in pump intensity. Blue crosses indicate the signal level at 50 ps minus that at 300 fs, associated with charge transfer occurring after the diffusion of excitons to a heterojunction. The latter component is strongly nonlinear at pump intensities greater than ∼10 μJ/cm2. This behavior is the result of effects like exciton−exciton annihilation30 and exciton−charge annihilation,31 which destroy diffusing excitons prior to reaching a charge transfer interface. The data in Figure 4 can be used to more precisely determine the ratio between the ultrafast charge-transfer component and charge transfer following exciton diffusion. This can be done by comparing the magnitude of the ultrafast component to that of the exciton diffusion component in the regime where both are linear; the ratio of diffusive carrier generation to ultrafast carrier generation across samples is 0.31 ± 0.02. This is possible only if the photoexcited state, which exists on the shortest time scales, interacts with approximately the same volume of material as the subsequently diffusing excitons; that is, the volume of material sampled by the initial coherent, delocalized photoexcitation is comparable to the volume of material sampled by diffusing excitons prior to reaching a heterojunction interface. Despite observations that fullerenes possess nonzero solubility in several popular semiconducting polymers,32−35 accounting for the charge-transfer dynamics wholly in terms of morphology is implausible given the sample-to-sample variations in fullerene concentration. For example, heterojunctions of p-DTS(PTTh2)2 contain 30% fullerene by weight, while heterojunctions of MEH-PPV are 80% fullerene. Moreover, the correlation between domain purity and high solar cell efficiencies is established by several studies.36,37 2266
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MATERIALS AND METHODS Bulk heterojunction films containing MEH-PPV were prepared by mixing MEH-PPV and PC70BM at a 1:4 (w/w) ratio in chlorobenzene. The concentration was 20 mg of bulk heterojunction materials per milliliter of solution. Samples were spin coated at a speed of 1200 rpm on a 1 × 10 mm sapphire disc prior to annealing at 70 °C for 10 min. Bulk heterojunction films containing P3HT were prepared by mixing P3HT and PC60BM at a 1:0.8 (w/w) ratio in chlorobenzene. The concentration was 15 mg of bulk heterojunction materials per milliliter of solution. Samples were spin-coated at a speed of 2000 rpm on a 1 × 10 mm sapphire disc prior to annealing at 70 °C for 5 min. Bulk heterojunction films containing PCDTBT were prepared by mixing PCDTBT and PC70BM at a 1:4 (w/w) ratio in a cosolvent composed of 1,2-dichlorobenzene and chlorobenzene (3:1) (v/v). The concentration was 7 mg of PCDTBT per milliliter of solution. Samples were spin-coated at a speed of 4000 rpm on a 1 × 10 mm sapphire disc. Bulk heterojunction films containing p-DTS(PTTh2)2 were prepared by mixing p-DTS(PTTh2)2 and PC70BM at a 7:3 (w/ w) ratio in chlorobenzene solution that contained 0.25% diiodooctane (v/v). The concentration was 40 mg of bulk heterojunction materials per milliliter of solution. Samples were spin-coated at a speed of 1700 rpm on a 1 × 10 mm sapphire disc prior to annealing at 70 °C for 10 min. Transient absorption measurements were conducted with a pulsed laser system at a repetition rate of 1 kHz. The laser consists of a titanium sapphire oscillator (Spectra Physics Tsunami) that is pumped with a Nd:VO4 laser (Spectra Physics Millenia). The pulses are fed into a regenerative amplifier (Spectra Physics Spitfire) that is pumped with a high power Nd:YLF laser (Spectra Physics Empower). 790 nm pulses were generated with a pulse width of 100 fs. The pulses were split into pump-and-probe paths. The pump pulse was frequencydoubled to 395 nm and focused onto the sample with a beam diameter of ∼1 mm. The pump pulse was put through a delay stage to achieve time resolution. The probe pulse was focused into a 1 mm sapphire disc to generate the white light continuum used to measure visible and near-IR spectra. The probe pulse was split before reaching the sample to provide a reference path to aid in the correction of intensity fluctuations. The subtraction was aided by careful collimation of the white light probe. In addition, synchronous chopping of the probe enabled the subtraction of an accurate dark count reading, which tends to drift over time. All spectra were manually corrected for the temporal chirp present in the white light continuum. The polarization angle between pump and probe beams was 54 ± 1°. Lastly, spectra were collected with a silicon CCD camera that was calibrated using a series of narrow bandpass filters.
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Center funded by the Office of Basic Energy Sciences of the U.S. Department of Energy (DE-DC0001009). We thank Dr. Yanming Sun and Dr. Wei Lin Leong for help with film preparation (with support from AFOSR (FA9550-11-1-0063)). We thank Prof. David Awschalom, Prof. Daniel Hone, and Sergei Tretiak for important discussions. A.J.H. thanks Michael Frayne for the stimulation of his words regarding the Uncertainty Principle in his play, “Copenhagen”.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected] (L.G.K.), ajhe1@physics. ucsb.edu (A.J.H.). Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Support for these ultrafast studies was provided by the Center for Energy Efficient Materials, an Energy Frontier Research 2267
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