Nonlinear Density Dependence of Singlet Fission Rate in TetraceneFilmsBo Zhang,† Chunfeng Zhang,*,† Rui Wang,† Zhanao Tan,‡ Yunlong Liu,† Wei Guo,† Xiaoling Zhai,†

Yi Cao,† Xiaoyong Wang,† and Min Xiao*,†,§

†National Laboratory of Solid State Microstructures & School of Physics, Nanjing University, Nanjing 210093, China‡New and Renewable Energy of Beijing Key Laboratory, School of Renewable Energy, North China Electric Power University, Beijing102206, China§Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, United States

*S Supporting Information

ABSTRACT: Singlet fission holds the potential to dramatically improve the efficiency of solarenergy conversion by creating two triplet excitons from one photoexcited singlet exciton inorganic semiconductors. It is generally assumed that the singlet-fission rate is linearlydependent on the exciton density. Here we experimentally show that the rate of singlet fissionhas a nonlinear dependence on the density of photoexcited singlet excitons in tetracene filmswith small crystalline grains. We disentangle the spectrotemporal features of singlet and tripletdynamics from ultrafast spectroscopic data with the algorithm of singular value decomposition.The correlation between their temporal dynamics indicates a superlinear dependence of fissionrate on the density of singlet excitons, which may arise from excitonic interactions.

SECTION: Spectroscopy, Photochemistry, and Excited States

Singlet fission (SF) in organic semiconductors is a spin-allowed process that creates two triplet excitons (2T1) from

one photoexcited singlet exciton (S1).1−7 This process has been

proposed to beat the Shockley−Queisser theoretical limit8 insingle-junction solar cells.9,10 Very recently, its promisingpotential has been evidenced by the rapid development ofSF-sensitized solar cells and photodetectors.11−15 However, theexact physical mechanism for SF, particularly in a prototypicalmaterial of tetracene, is still under intensive debate.3,4,7,16−19

Some new perspectives inspired by recent experiments have putforward interesting concepts such as quantum coherence,20,21

intermolecular interaction,17,22 and electronic coupling,23,24 inaddition to the conventional charge-transfer mechanism.5

The difficulty in elucidating the SF process in tetracene ispartially caused by the endothermic nature (ES1 − 2ET1

<0).1,3,16,18,19,25−29 Thermal activation was originally proposedfor compensating the energy uphill.1,3,27−29 This argument wassupported by an ultrafast transient absorption (TA) study, inwhich Thorsmølle et al. observed a significant temperaturedependence of the triplet signal in tetracene single crystals.3

However, opposite conclusions have been drawn in recentstudies on tetracene films.18,19 In particular, with a similar TAexperiment, Wilson et al. reported that the SF process isactually independent of temperature.19 Recently, coherentelectronic coupling has been considered,18,20 which predicts atemperature-independent process for the initial stage of SF incrystalline tetracene.18 The energy uphill is overcome through a

direct access to an intermediate triplet-pair state by coherentelectronic coupling.18 However, some theoretical and exper-imental works have identified a primary role of charge-transferprocess rather than the contribution from coherent cou-pling.7,24,30

To test these outstanding controversies, we have systemati-cally examined the dynamics of SF process in tetracene filmswith broadband ultrafast TA spectroscopy. In order toaccurately evaluate SF, we extract the spectrotemporal featuresof singlet and triplet excitons from the TA data using thealgorithm of singular value decomposition (SVD).Thecorrelation between the dynamics of singlet and triplet excitonsshows compelling evidence that, instead of a constant value, therate constant for SF is strongly dependent on the singletexciton density in tetracene films with small grain sizes. Weconjecture that in addition to the conventional fission process,photogenerated singlet excitons in tetracene films may undergoanother pathway of SF (the nonlinear part) arising fromexcitonic interaction.The steady-state absorption and emission spectra of a

tetracene sample show clear features of crystalline tetracene(Figure S1, Supporting Information). We first confirm theexistence of SF in the sample with the time-resolved

Received: August 16, 2014Accepted: September 26, 2014Published: September 26, 2014

Letter

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fluorescence (TRFL) spectra. Recently, Burdett and Bardeenhave thoroughly reexamined the quantum beats in the delayedfluorescence of crystalline tetracene,31,32 which has beenregarded as a fingerprint of SF.6,32,33 A typical TRFL trace ofthe sample is shown in Figure 1a. By subtracting the

multiexponential decay component, the oscillations emerge asshown in the inset of Figure 1a. The Fourier transformation ofthe oscillatory components shows three peaks at 1.07, 1.84, and2.95 GHz in the frequency domain (Figure 1b). These valuesare in good agreement with the theoretical prediction of energyseparations between manifolds of the triplet-pair states,32

indicating the presence of triplet pairs generated from SF inthe sample.The exciton dynamics in crystalline tetracene may be

strongly affected by many body interactions such as thesinglet−singlet annihilation (SSA) and triple−triplet annihila-tion (TTA) when the density of excitons is high.16,25 Weconduct power-dependent TA experiments to determine thelinear power regime. The pump−probe traces probed at 2.34eV with different power excitation at 3.1 eV are presented inFigure 2a. No significant power dependence has been observedwith exciton fluence <30 μJ/cm2, which is similar to previousresults.16,25 Nonetheless, the early-stage dynamics in the linearregime is dominated by a component with lifetime <30 ps,which is much faster than that in the literature.3,25 This isprobably caused by the trapping effect in our samples with

small crystalline grains. We characterize the morphology of thefilm by atomic force microscopy. As shown in Figure 2b, thediameters of grains are about ∼100 nm, which is about 5 timessmaller than that in the previous study.4 More trapping centersmay be introduced due to over 2 orders of magnitudeenhancement in surface-to-volume ratio in the sample. It maystrongly affect the exciton dynamics in polyacene materials.2,3

The measured ΔT/T in the 1.3−2.6 eV spectral regionwithin a temporal window of 3 ns monitors the dynamics of theSF process (Figure 3a). The excitation power is set to be ∼5

μJ/cm2 (carrier density, ∼ 2 × 1017 cm−3) in the linear regime.The transient optical response consists of multiple entangledcomponents such as stimulated emission, ground-statebleaching, excited-state absorption, and so on. In tetracene,the transitions of S0 →S1, S1 → Sn and T1 → Tn are responsiblefor the measured TA signal.3,16,19 However, it is challenging toexactly assign the transient features at single wavelengths tospecific transitions. In the current study, the major bands ofphotoinduced bleaching and absorption locate at ∼2.3 eV and∼1.8 eV (Figure 3a), respectively. Their instant build-upprocesses as well as the fast decays at early stage (Figures 3b,c)are the characteristics of singlet excitons.3,19 Nevertheless, thelong-lived tails, with the amplitude ratios much larger than thatexhibited in the TRFL curves, imply that the triplet excitonsmay also make some contributions.The spectrotemporal features for the triplet excitons are

more complicated. In general, triplet excitons are characterizedby long-lived signals of photoinduced absorption. Such featureshave been reported with probe energies at 1.67 eV,3,19 2.53 eV,4

and 2.67 eV16 in different studies, respectively. Here, a similarlong-lived band of photoinduced absorption appears at ∼1.60eV. This component becomes prominent after ∼100 ps andremains largely static in the time scale between 0.1 and 3 ns,which has been regarded as a clear signature of SF in crystallinetetracene.3,19 The build-up process consists of one subpico-second component and one delayed-rising component (Figure3d). Thorsmølle et al. assigned the two components to excitonfission from higher (Sn → 2T1) and lowest singlet states (S1 →2T1), respectively.3 Wilson et al. proposed an alternativeexplanation that the subpicosecond rise is also contributed bysinglet excitons.19

Figure 1. (a) A typical TRFL trace of the tetracene film. The red lineis the curve fitting to multiexponential decay function. Inset shows theoscillations obtained by subtracting the multiexponential decaycomponent in the TRFL trace. (b) The Fourier transform of theextracted oscillations with peaks at 1.07, 1.84, and 2.95 GHz.

Figure 2. (a) Pump−probe traces probed at 2.34 eV with excitation at3.1 eV. The excitation densities range from 5 to 400 μJ/cm2 (∼2 ×1017 cm−3 to ∼1.6 × 1019 cm−3). (b) A typical AFM image (10 × 10μm2) of the tetracene film. Inset shows a magnified image (scale bar:500 nm). The average diameter of the grains is ∼100 nm.

Figure 3. (a) The TA spectra of the tetracene film are shown atdifferent pump−probe delays for photoexcitation at 3.1 eV. (b−d) Thepump−probe traces probed at 2.30, 1.80, and 1.55 eV with the pumpat 3.1 eV, respectively.

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For a better assignment, we employ the established algorithmof SVD34,35 to disentangle the spectrotemporal features ofsinglet and triplet excitons. The detailed description of SVD isavailable in the Supporting Information. This method has beensuccessfully used in extracting both energy- and time-domaininformation from a set of data in several research areas.34−39

Here, we approximately adopt the signals at t ∼ 0.5 ps and t ∼ 3ns as the spectral features to extract the temporal dynamics ofthe singlet and triplet excitons, respectively.40 Such SVDapproach has well reproduced the experimental data ascompared in Figure 4a,b. The reconstructed dynamics of

singlet and triplets are plotted in Figure 4c. The dynamicsprobed at single wavelengths (i.e., 1.6 eV) can be regarded as acombination of the singlet and triplet dynamics, which isfurther confirmed by the excitation-wavelength dependentexperiments (Supporting Information).The dynamics of singlet and triplet population can be

expressed in a set of rate equations as16,19

= − − − +N t t k N t k N t k N t k N td ( )/d ( ) ( ) ( ) ( )S SF S SPS

S SS S2

TT T2

(1)

= − −N t t k N t k N t k N td ( )/d 2 ( ) ( ) ( )T SF S SPT

T TT T2

(2)

where kSF, kSPS , kSS, kSP

T and kTT are the rate constants for SF,spontaneous recombination of singlet excitons (includingspontaneous emission and nonradiative recombination likedefect trapping), SSA, spontaneous recombination of tripletexcitons, and TTA, respectively. Unlike the case of a singlecrystal (Supporting Information), it is difficult to reproduce thecurves recorded from the film with the available rateequations16 or the model used in Wilson’s paper.19

We try to directly connect the fission rate with the dynamicsof singlet excitons. Since spontaneous recombination of tripletexcitons and TTA are very slow, only the process of SF isresponsible for the early-stage dynamics of triplet excitons (t <100 ps), i.e.,

≈N t d k N td ( )/ t 2 ( )T SF S (3)

As deduced in the Supporting Information, the temporaldifferential of triplet density (dNT(t)/dt), i.e., the SF rate, isproportional to the value of NT0 − NT(t) (NT0 is the maximumdensity of triplet excitons) (inset, Figure 5a). We compare itstemporal evolution with the dynamics of singlet excitons in

Figure 5. Surprisingly, the curve of NT0 − NT(t) (i.e., dNT(t)/dt) shows a significant disparity from the linear dependence(NS(t)), but close to the quadratic dependence (NS

2(t)), when t< 10 ps (Figure 5a). This result strongly suggests that, ratherthan being a constant, kSF is actually density dependent, i.e., kSF= kSF0(1 + αNS). That is, the rate of SF is superlinearlydependent on the density of singlet excitons. For a betteranalysis, we rewrite the triplet dynamics in an integration formof

∫ τ τ=N t k N( ) 2 ( ) dt

T0

SF S (4)

The detailed description of the fitting procedure is availablein the Supporting Information. The temporal evolutionbehavior of the triplet exciton population (Figure 5b) can bewell fitted by the superlinear dependence with the parameter ofα ≈ 3kSF0/NS0. Roughly speaking, the triplet populationgenerated from the nonlinear channel is ∼1.5 times of thatfrom the linear channel. Assuming the time constant for linearchannel to be close to the reported value (1/kSF ∼ 100 ps−1),the fractions of singlet excitons that undergo the linear andnonlinear fission processes can be approximately estimated tobe ∼25% and ∼38%, respectively. The overall triplet yield is∼126% in this sample, which is less efficient than the reportedvalue in regular samples.4,16,25,38 This is reasonable consideringthe high density of trapping centers in the films with smallergrain sizes.3

Notably, despite the superlinear dependence is deduced inthe linear power regime as we discussed above, it is also valid in

Figure 4. (a) Experimental data and (b) simulation results with SVDof time-energy matrices for photoinduced transmission change (ΔT/T). (c) The normalized dynamics of singlet and triplet populationsextracted from the experimental data with the SVD method.

Figure 5. (a) The temporal evolutions of NT0 − NT(t), NS(t), andNS(t)

2 recorded at a weak excitation (5 μJ/cm2, ∼ 2 × 1017 cm−3) arecompared with a normalized scale. Inset shows that NT0 − NT(t) isnearly proportional to the value of dNT(t)/dt. (b) The build-up traceof triplet population recorded at the weak excitation (5 μJ/cm2, ∼2 ×1017 cm−3) is compared with the simulations based on linear,quadratic, and superlinear density dependences in the integrationform. The fitting details are available in the Supporting Information.(c−e) The rescaled signals for triplet dynamics under excitation withdensities of 35 μJ/cm2 (∼1.4 × 1018 cm−3), 120 μJ/cm2 (∼4.8 × 1018

cm−3), and 400 μJ/cm2 (∼1.6 × 1019 cm−3), respectively, arecompared with simulations based on linear and superlinear densitydependences.

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the high power regime. As shown in Figures 5c,d, the onset oftriplet dynamics, obtained by eliminating singlet contributionfrom the signal probed at 1.6 eV, can be well produced withexcitation in a high regime with a similar parameter of α whereSSA becomes important. The onset of triplet population ismuch better described by the superlinear than the lineardependence. Nonetheless, further increasing excitation powerleads to a failure of reproducing the experimental data (Figure5e), which is reasonable since eq 3 is no longer valid in thisregime where TTA becomes important at the early stage.The intrinsic physics underlying the superlinear density

dependence of SF rate is yet to be elucidated. In general,second-order rate in population implies a role played by theinteractions between singlet excitons. The process of SSA mayassist the SF in some materials by generating higher energyexcitons.41,42 Nonetheless, SSA has been regarded as a majorchannel that competes against SF in tetracene.16,25 Thepresence of SSA may lead to a fast onset of triplet signal butcause a reduction in the triplet yield.16,32,43 Since the nonlineardensity dependence applies for weak excitation density (5 μJ/cm2, ∼2 × 1017 cm−3), other process different from SSA may beinvolved. To confirm this, we evaluate the excitation-density-dependent fission yield by monitoring the relative density ofdelayed fluorescence. The results are shown and discussed indetail in the Supporting Information (Figure S8). The relativeintensity of delayed fluorescence represents the density ratiobetween singlet excitons from prompt photo excitation andfrom triplet fusion process. The efficiency drop of SF inducedby excitonic annihilation processes (i.e., SSA and TTA) hasbeen observed with a drop in the relative intensity of delayedfluorescence when the excitation density surpasses a value of∼50 μJ/cm2. Under the regime of weak excitation interested inthis work (<50 μJ/cm2), the relative density of delayedfluorescence increases with increasing excitation density, whichqualitatively supports the existence of a nonlinear-density-dependent channel of SF that is different from SSA.In organic crystals, the coupling between excitons and

intermolecular vibrational modes results in coherently emittingmolecules, leading to the superradiant emission.44−47 The rateof superradiant recombination exhibits nonlinearity in a lowdensity regime.48 In crystalline tetracene, these excitations candelocalize over tens of molecules.44,45 These superradiantexcitons, whose transition dipoles interact with light in acollective and coherent fashion,45 may be responsible for the SFwith nonlinear density dependence. Previously, superradiantemission has been observed to be dominant at low temperature,which diminishes with increasing temperature.44,45 Recentexperiments suggest that the exciton delocalization may bealso important at room temperature to explain the SFdynamics16 and weak magnetic coupling between tripletpairs32 in crystalline tetracene. If the fraction of singlet excitonsthat undergo nonlinear fission channel is related to theprobability of exciton encounter, the encounter radius can beroughly estimated to be in the range of 3−10 nm with thestochastic model.49,50 The scale of delocalization for super-radiant excitons is comparable to the encounter radius, whichmay strongly affect the dynamics of SF. Nevertheless, more in-depth research is required to uncover the relation betweensuperradiant excitons and the nonlinear-density-dependent SFin crystalline tetracene. The state-of-art techniques, particularlythe first-principle simulation24 and two-dimensional spectro-scopic survey on quantum coherence,51,52 may provide themost relevant information on this issue.

We also perform control experiments on single crystals andfind that the crystalline quality is important. The value of kSF insingle crystals is close to the general case with linear densitydependence (Supporting Information). This discrepancy can beunderstood if we consider the coexistence of two pathways ofSF in tetracene, i.e., the linear and nonlinear density-dependentparts. Due to the structure imperfections, excitons in organicsemiconductors may be trapped by the localized minima whichstrongly affect the exciton dynamics.2,3 The trapping effect maysignificantly harm the efficiency of SF in polyacene materials.3

The densities of trapping centers induced by structureimperfections (i.e., dislocations and surface states) are muchhigher in films with small grain sizes, which may quench the SFof linear-density-dependent part.3 In this case, tripletpopulation induced by the nonlinear part can be detected. Insingle crystals, the linear part plays a dominant role. Thisscenario also explains the observation in the literature that theamplitude ratios between triplet and singlet signals inpolycrystalline films are much smaller than that in singlecrystals.3,16,25

In summary, we have reported a superliner dependence of SFrate on the density of photoexcited singlet excitons in tetracenefilms with small grain sizes. To elucidate the SF dynamics intetracene films, we employed the SVD algorithm to analyze theultrafast TA data. The nonlinear density-dependent SF impliesa role played by excitonic interactions. Once the understandingof exact mechanism is achieved, it may be considered as a newroute to search for efficient SF sensitizers to improveperformance of solar cells and photodetectors.

■ EXPERIMENTAL METHODS

We prepared the tetracene films with thickness of ∼100 nm byevaporating tetracene powders thermally on precleaned glasssubstrates. The sample quality was characterized by X-raydiffraction and atomic force microscopy. TRFL spectra wererecorded by the technique of time-correlated single-photoncounting with a temporal resolution of ∼50 ps. We utilized acommercial Ti:sapphire regenerative amplifier (Libra, Coher-ent) at 800 nm (1.55 eV) with a repetition rate of 1 kHz andpulse duration of ∼90 fs to carry out the TA experiments. Forbroadband measurements, a second-harmonic light source at3.1 eV was used as the pump beam and an optical parametricamplifier (OperA solo, Coherent) was used to provide a probebeam with tunable wavelength. The relative polarizations of thepump and probe beams were set to be at the magic angle(54.7°). We used balance detection scheme together with alock-in amplifier to measure the fractional change in trans-mission (ΔT/T) with a resolution of ∼10−5. The experimentswere performed with samples in vacuum provided by a cryostat(MicroCryostatHe, Oxford).

■ ASSOCIATED CONTENT

*S Supporting InformationDetailed information concerning experimental procedures, dataanalysis techniques, and extra experimental data. This materialis available free of charge via Internet at http://pubs.acs.org.

■ AUTHOR INFORMATION

Corresponding Authors*E-mail: cfzhang@nju.edu.cn (C.Z.).*E-mail: mxiao@uark.edu (M.X.).

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NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

This work is supported by the National Basic ResearchProgram of China (2013CB932903 and 2012CB921801,MOST), the National Science Foundation of China(91233103, 61108001, 11227406 and 11321063), and thePriority Academic Program Development of Jiangsu HigherEducation Institutions (PAPD). We acknowledge Dr. VitalyPodzorov, Dr. Yuanzhen Chen, and Dr. Jonathan Burdett forproviding valuable information for crystal growth and samplecharacterization.

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The Journal of Physical Chemistry Letters Letter

dx.doi.org/10.1021/jz501736y | J. Phys. Chem. Lett. 2014, 5, 3462−34673467