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Cite this: Phys. Chem. Chem. Phys., 2014, 16, 7501

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Ultrafast exciton dynamics in dinaphtho[2,3-b:2 0 3 0 -f ]thieno[3,2-b]-thiophene thin films Yuuta Ishino,a Kiyoshi Miyata,a Toshiki Sugimoto,a Kazuya Watanabe,*a Yoshiyasu Matsumoto,a Takafumi Uemurab and Jun Takeyab Ultrafast dynamics of excitons in organic semiconductors is essential for a deep understanding of the working mechanism of plastic opto-electronic devices. In this work, excited state dynamics in dinaphtho[2,3-b:2 0 3 0 -f ]thieno[3,2-b]-thiophene thin films has been studied with femtosecond transient absorption and time-resolved photoluminescence spectroscopy. Upon the excitation with a femtosecond pulse at 400 nm, a broad positive absorption band at 1.5–2.4 eV is observed that contains two components: one decays with a time constant of a few ps and the other with 67  7 ps. Because the decay curve of the latter coincides with that of photoluminescence, the slow decay component is ascribed to the lowest singlet exciton. The former fast decay component is ascribed to mixed states between charge transfer (CT) and Frenkel excitons, because it is accompanied by a feature due to the Stark effect caused by transient charged species: a combination of bleach and positive absorption at hnprobe 4 2.4 eV which looks like derivative modulations of the ground state absorption spectrum.

Received 2nd October 2013, Accepted 27th February 2014

A pronounced polarization dependence is observed for the derivative-like features; this is due to aniso-

DOI: 10.1039/c3cp54157f

changes its shape after the decay of the mixed Frenkel–CT exciton and grows with a pump–probe delay

tropic distributions of the dipole moments formed by the CT excitons. The derivative-like feature time of up to 1 ns due to a thermal effect. The decay rate of the mixed Frenkel–CT exciton strongly

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depends on its density because of exciton–exciton annihilation at high density.

1 Introduction There has been a continuously growing interest in electronic properties and relaxation processes in organic semiconductors.1,2 In aggregates or crystalline forms, the electronic structures of isolated molecules are modified mainly by excitonic interactions.3 In many cases, the excitonic interactions lead to complex eigenstate structures; these transform vibronic progressions in absorption bands of isolated molecules to characteristic Frenkel exciton bands.4–7 Furthermore, configuration interactions with charge transfer (CT) excitons also affect the optical absorption spectra.6,8–10 The fate of primary photoexcited states depends on these interactions. Thus, it is important to understand the electronic structures and the relaxation dynamics of optically excited states for both fundamental science and practical applications to organic solar cells and light emitting diodes. Numerous attempts have been made to understand the ultrafast relaxation dynamics of excited states in organic semiconductors.

a

Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan. E-mail: [email protected]; Fax: +81-75-753-4050; Tel: +81-75-753-4049 b Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5, Kashiwanoha, Kashiwa, Chiba 277-8561, Japan

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Great attention has been recently focused on primary photoinduced dynamics: photoinduced charge separation,11,12 exciton annihilation,13–16 and singlet fission into two triplet excitons.17–20 Mixing of CT states with Frenkel exciton manifolds has been predicted for many organic aggregates and crystals.6,8–10 In addition, there have been ample pieces of experimental evidence for the CT state mixing obtained by electroabsorption spectroscopy.1,21,22 Because the CT states are precursors for photoinduced carrier generation and injection at interfaces, the energy levels and the degree of mixing with a Frenkel manifold are important for understanding the optoelectronic properties. In particular, ultrafast dynamics of the exciton manifolds with the mixed Frenkel–CT character is crucial for understanding the photophysical process. However, few investigations have focused on the relaxation dynamics of the mixed Frenkel–CT states. Recently, crystals and thin films of dinaphtho[2,3-b:2 0 3 0 -f ]thieno[3,2-b]-thiophene (DNTT) (Fig. 1) and its derivatives gather growing attention because of their high hole mobility, superior air stability and easy solution processability.23–28 Hole mobility as high as 8 cm2 V 1 s1 has been reported24 and the origin of the excellent charge transport properties has been a focus of recent research.29,30 Theoretical calculations predict the highest occupied molecular orbital (HOMO)-derived band

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Fig. 1 (a) Chemical structure of DNTT. A red arrow indicates the direction of transition moment of the lowest electronic transition predicted by the TD-DFT calculation (see text for the details). (b) Crystal structure of DNTT. The lattice parameters are a = 618.7, b = 766.2, c = 1620 pm and the angle between the ab plane and the c-axis, b = 92.491.23

width as large as 670 meV, which exceeds the value of pentacene crystals.30 Although the understanding of excited state dynamics is crucial to improving the performance of the material as an optoelectronic device,31 there have been no reports on its primary photophysics. In addition, the CT character of the electronic excited states is expected to be significant in this material due to the predicted high CT integral values.29,30 In this paper, we describe the results of femtosecond transient absorption (TA) as well as picosecond time-resolved photoluminescence (TRPL) of DNTT microcrystalline films. The excitation with a femtosecond pulse at 3.1 eV generates vibronic excitons that are subsequently converted to mixed Frenkel–CT excitons. The CT character of the nascent excited states is evident in TA spectra overlapping with the ground state absorption band. In addition, the decay kinetics of the mixed Frenkel– CT excitons shows a strong annihilation behaviour at high density, while that of the lowest singlet exciton depends only moderately on its density, implying that the wavefunctions of the mixed Frenkel–CT states are more delocalized than those of the lowest singlet excitons.

2 Experimental procedure A DNTT film was evaporated onto a quartz plate under high vacuum conditions at room temperature. The evaporation rate was 0.05 nm s1 and the nominal thickness was estimated to be 200 nm using atomic force microscopy. TA measurements were carried out by using laser pulses (l = 800 nm) with a typical duration of 130 fs provided by a Ti:sapphire regenerative amplifier (Spectra Physics, Spitfire-pro, 1 kHz repetition rate).32 A portion of the output was focused onto a 5 mm quartz-cell filled with distilled water to generate a whitelight continuum with a spectral range from 1.6–2.95 eV; this white-light continuum was used as a probe. The remaining output of the regenerative amplifier was frequency-doubled

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using a b-BaB2O4 crystal to provide a pump pulse (l = 400 nm, 3.1 eV, duration 170 fs). The white-light continuum was split into two: signal and reference. They were fed into a polychromator equipped with a charge-coupled-device (CCD) detector (Andor technology). Simultaneous detection of signal and reference beams allowed the reduction of intensity and spectral fluctuations. Ratio spectra between signal and reference were measured with and without pump irradiation by chopping the pump beam at 2.5 Hz, and TA spectra, DA(l), are obtained by DA(l) = log(I (l)/I0(l)), where I (l) and I0(l) are the ratio spectra with and without pump, respectively. DA(l) is measured as a function of the pump–probe delay, td, by using a stepping stage equipped in the pump beam path. Because the white-light continuum was chirped by dispersive materials in the paths, we corrected the chirp of the probe light by monitoring photocarrier-induced TA spectra of a TiO2 single crystal plate of 1 mm thick placed at the sample position. Polarization dependence of TA spectra was measured by fixing the polarization of pump while setting the probe polarization parallel or perpendicular to the pump. We also used a narrow band detection scheme with a single channel photodiode attached to a bandpass filter at several wavelengths. In this scheme, data processing was done with the combination of a boxcar integrator and an A/D converter. Signals were detected synchronously at a chopped frequency of pump beam at 500 Hz and shot-toshot fluctuations in probe pulse intensity were reduced by taking the ratio with reference signals detected using another photodiode. All measurements were done in air at room temperature. TRPL measurements were done using an optical Kerr gate setup.33 A part of luminescence from the sample induced by a 400 nm pump was collected by a quartz lens and passed through a pair of polarizers. A 2 mm quartz-cell filled with CS2 was placed between the two polarizers, and a portion of the Ti:sapphire output (l = 800 nm) was directed onto the cell as a gate pulse to induce transient birefringence in the CS2 liquid. The two polarizers were set to be crossed with each other, and the transient birefringence in CS2 allowed a part of the luminescence to transmit during a time interval (1.3 ps) determined by a rotational relaxation time of CS2. The timing of the gate was scanned by varying the time delay between the pump and the gate pulses. Spectra of the transmitted luminescence were detected using the polychromator. A time-dependent density functional theory (TD-DFT) was used to estimate electronic transitions of isolated DNTT. A commercial software package (Gaussian09) was used for the calculations using a functional of B3LYP and basis functions of 6-311+g(2df,p).34

3 Results and discussion 3.1

Steady state absorption spectra

Fig. 2(a) shows a steady state absorption and photoluminescence (PL) spectrum of DNTT in o-dichlorobenzene solution.

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Fig. 2 (a) The red thick solid curve is an absorption spectrum of DNTT in a dichlorobenzene solution. The black dots are a fitting result with four Gaussian functions depicted with thin dashed curves. The blue solid curve is a PL spectrum measured with 3.1 eV excitation. Sticks indicate electronic transitions predicted by TD-DFT calculations and their heights are proportional to the predicted oscillator strengths. (b) The red thick solid curve is an absorption spectrum of a DNTT film. The black dotted curve is a fitting result of the absorption spectrum in the range from 2.6 to 3.1 eV with four Gaussian functions depicted with thin dashed curves: G1 (blue), G2 (green), G3 (pink) and G4 (orange). The blue solid curve is a PL spectrum measured with 3.1 eV excitation. The black solid curve is a corrected PL spectrum by eqn (1) and is scaled to the uncorrected spectrum.

Electronic transitions predicted by TD-DFT calculations are also depicted in the figure. The lowest transition at 2.92 eV (A g - Bu) is mainly composed of a transition between the HOMO and the lowest unoccupied molecular orbital (LUMO). The transition dipole is primarily along the long axis of the molecule that is depicted in Fig. 1. The second lowest transition (A g - Bu) was predicted to be at 3.62 eV with a major contribution of HOMO  2 - LUMO. We decomposed the spectrum into four subbands with Gaussian line profiles as plotted in Fig. 2(a). The peak energies of the Gaussian subbands are 3.05, 3.22, 3.40, and 3.53 eV. The lowest three peaks are likely to be vibronic bands of the lowest singlet excited state, because it is reasonable to assign the separation of 0.17–0.18 eV to a vibrational progression of skeleton C–C stretching modes as has been observed in many polyacenes and oligomers.7 A theoretical calculation of the DNTT molecule has predicted C–C stretching modes at around the same energy.30 The PL spectrum shows three peaks with similar separations at 2.94, 2.78 and 2.60 eV, showing an approximate mirror image with 0.1 eV Stokes shift. The relatively intense and narrow line-width feature of the third (3.40 eV) subband in absorption implies overlapping of a contribution of the second excited state that was predicted at 3.62 eV in the calculation. Thus, the absorption structure at higher than 3.4 eV contains the transition to the second lowest singlet excited state. Fig. 2(b) shows a steady state absorption spectrum of a DNTT film. The absorption bands are red shifted and less

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structured in comparison with those in the solution; these features are ascribed to exciton band formation. Fig. 1(b) shows DNTT crystal structure. In DNTT crystals, molecules are almost planar and packed along the ab plane in a herringbone structure.23 The monoclinic unit cell (P21 space group) contains two translationally nonequivalent molecules. The TD-DFT calculation for monomer predicts that the lowest Ag - Bu transition at 2.92 eV (Fig. 2(a)) has a transition dipole primarily along the molecular axis (Fig. 1(a)). These features are close to those in aggregates of oligo-phenylene vinylene (OPV) and oligothiophenes (OT).1,8,35,36 In OPV and OT aggregates, the lowest electronic transition gives two Davydov components due to excitonic couplings mainly in the ab plane: one with strong blue shifted (‘H’ band-like) transition with a moment primarily along the c axis, the other is a weak ‘J’ band-like transition at the red edge of absorption with a moment lying in the ab plane. These originate from in-phase (blue shifted ‘H’ band) and outof phase (red shifted ‘J’ band) combination of the monomer transition dipole between two nonequivalent molecules in the same ab plane of the unit cell. The energy splittings of the two Davydov components are considered to be around 1 eV in many OPV and OT aggregates.37 In addition, several vibronic exciton bands with primarily c polarized transition moment appear between the two Davydov components.37 It is expected that the absorption of DNTT microcrystalline films shares some of these features. We decomposed the absorption spectrum of the DNTT film at 2.6–3.2 eV into four Gaussian components, Gi (i = 1–4), as plotted in Fig. 2(b). The parameters of Gaussian components are tabulated in Table 1. We eliminated the absorption feature monotonically decaying at hn o 2.6 eV in the decomposition, assuming that this is due to a coupling of the excitonic transition to low frequency phonon modes.38 In addition, the region higher than hn = 3.2 eV was eliminated, because the spectral feature is structureless and the unique decomposition into Gaussians is not possible. Here we tentatively assign these bands to clusters of vibronic transitions of excitons with intermolecular CT characters.39 From the analogy with OPV and OT aggregates, the lowest band (G1) is likely to be the ‘J’ band with a transition moment lying in the ab plane. Further discussion on the assignment of other bands is given in the later section (Section 3.6). Because the pump photon energy for the timeresolved measurements (3.1 eV) is B0.4 eV higher than the peak of the G1 band, the excitation takes place to higher vibronic exciton bands originating from the lowest electronic transition of the isolated molecule. A PL spectrum of the DNTT film obtained by excitation at 3.1 eV is also shown in Fig. 2(b). Because the spectral shape is expected to be distorted by self-absorption by the material

Table 1 Parameters for Gaussian fitting of the DNTT film absorption spectrum

Peak (eV) Width (FWHM) (eV)

G1

G2

G3

G4

2.73 0.17

2.81 0.11

2.94 0.15

3.11 0.33

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itself, we corrected the PL spectrum with the following equation,40 ! aðhnÞ   Sc ðhnÞ ¼ 1 þ (1)  Sd ðhnÞ; a hn pump where a(hnpump) and a(hn) are film absorbance at the excitation and detection photon energy, respectively, and Sc(hn) and Sd(hn) are corrected and detected PL spectra, respectively. Eqn (1) is obtained by integrating the PL intensity at a given depth inside the film which is reduced by the self-absorption during the propagation to the surface.40 The corrected spectrum has three vibronic progressions at 2.66, 2.52 and 2.36 eV. While the splitting between the second (0–1) and third (0–2) peaks is 0.16 eV that is consistent with the vibrational progression of C–C stretching modes, the separation between 0–0 and 0–1 peaks (0.14 eV) is relatively small and the 0–0 peak is narrower than the other peaks. This indicates that the origin of 0–0 emission is different from those of 0–1 and 0–2 bands. In theoretical emission spectra of OT and OPV aggregates, the PL spectra were well modeled with an excitonic coupling in two-dimensional square herringbone aggregates and a linear coupling to an intramolecular vibration.41,42 In the model, the emission features are due to the lower Davydov component in absorption bands (‘J’ band) and are composed of a strong 0–0 transition polarized along the b axis and of 0–1, 0–2, 0–n progressions with both b- and ac-polarized transitions.41 The 0–0 emission band possesses a superradiant character: the intensity increases with the number of coherently coupled molecules, N, while intensities of vibronic replicas (0–1, 0–2) are insensitive to N. The 0–0 band can arise only from excitons at the bottom of the band, but 0–1 and 0–2 transitions are contributed by all thermally activated k states, because the momentum conservation can be fulfilled by the ground state phonons. Consequently, vibronic replicas (0–1, 0–2) show temperature dependent peak shifts and broadenings, while 0–0 band shows temperature dependent intensity variation without peak shifts.42 Because the employed model is also applicable to DNTT which possesses a similar crystal structure as those of OT and OPV, these features are likely shared with the PL bands of DNTT film and can be a reason for the relatively narrow bandwidth of the 0–0 band and the smaller splitting between the 0–0 and 0–1 bands. 3.2

TA measurements

Fig. 3 shows TA spectra obtained from a DNTT film. The transient spectra are categorized into four features, A–D: (A) a broad positive absorption band in hnprobe = 1.5–2.4 eV that decays within a few ps; (B) a positive absorption in the similar energy region as feature A that decays within a few hundreds ps; (C) a combination of bleaching and a positive absorption feature apparent in hnprobe 4 2.4 eV for td o 10 ps, which looks like a derivative modulation of the ground state absorption spectrum; and (D) another derivative-like feature in hnprobe 4 2.4 eV that grows for td 4 10 ps and becomes steady at td ^ 1 ns. Spectral differences between those features are clear in Fig. 3(b) in

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Fig. 3 (a) Transient absorption spectra of a DNTT film pumped at 3.1 eV. Delay time, td, is indicated in the figure. Pump fluence was 2.0 mJ cm2. The spectra in 1.5–2.4 eV are magnified by a factor of 5. The black solid curve is the steady state absorption spectrum of the film. Labels A–D indicate features A–D discussed in the text. Pump and probe polarizations were perpendicular to each other. (b) Transient absorption spectra of the DNTT film normalized at 1.6 eV for hnprobe o 2.4 eV and at 2.79 eV for hnprobe 4 2.4 eV. The spectrum in hnprobe 4 2.4 eV at td = 1000 ps is omitted because no detectable signal exists. The black solid curve is a difference spectrum of steady state absorption obtained by subtracting the spectrum at 298 K from that at 333 K. The difference spectrum is normalized at 2.79 eV.

which the normalized TA spectra for selected td are depicted: feature A possesses more pronounced absorption in 1.7–2.3 eV than feature B, and features C and D show a marked spectral difference in 2.5–2.8 eV. Further insights into the transient species are obtained from a probe polarization dependence of TA spectra (Fig. 4). The spectral shape in hnprobe 4 2.4 eV for td o 1 ps (feature C) shows a significant polarization dependence, while other components show less pronounced polarization dependences. Fig. 4 inset shows td dependence of anisotropy at selected photon energy regions, r(t) = (DAJ(t)  D A>(t))/(D AJ(t) + 2D A>(t)), where D AJ(t) and D A>(t) are TA signals with parallel and perpendicular pump–probe geometry, respectively. While the positive TA features (features A and B) show no systematic anisotropy change with delay time (triangles in Fig. 4 inset), it is

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Fig. 4 Probe polarization dependence of TA spectra of a DNTT film pumped at 3.1 eV. Solid curves: probe polarization parallel to the pump polarization. Dotted curves: probe polarization perpendicular to the pump. Delay times are 0.4 ps (red), 1 ps (blue), 8 ps (green) and 50 ps (black). Pump fluence was 3.0 mJ cm2. Inset: r(t) at selected probe photon energy: 1.8–2.2 eV (red triangles), 2.66–2.72 eV (blue open circles) and 2.75–2.80 eV (black filled circles).

notable that r(t) at the two different photon energy regions of feature C show opposite trends: at 2.66–2.72 eV, r(t) reaches higher than 0.1 at td o 1 ps and decays to 0.05 at td = 3 ps, while at 2.75–2.80 eV, r(t) goes negative within td o 1 ps and increases to ca. 0.05 for the later times and remains almost constant to 12 ps. r(t) at 2.66–2.72 eV transiently increases at td 4 4 ps, because D AJ(t) + 2D A>(t) get close to zero at this probe wavelength for td 4 10 ps. The origin of the polarization dependence will be discussed later (Section 3.6). 3.3

Global analysis

We conducted a global analysis of the TA results by obtaining lifetimes and spectral amplitudes with global parallel and sequential fitting routines (Glotaran).43–45 Fig. 5 shows results with a sequential fitting routine, in which a unidirectional, unbranched kinetic scheme is assumed.43 A fitting with three components gives satisfactory results for both polarization. The following superposition of the contributions of different components is assumed:

Fig. 5 Evolution associated spectra (EAS, el) obtained by fitting the TA spectra in Fig. 4 with global sequential routine. A unidirectional, unbranched kinetic scheme with three components is assumed.43 Solid curves are results for probe polarization parallel to the pump, while dotted curves are for probe polarization perpendicular to the pump. The first, second and third components are plotted with red, blue and green curves, respectively. The inset shows time dependent concentrations of the three components with the same color codes. Solid and dotted curves are results for parallel and perpendicular geometries of pump and probe polarizations, respectively. The estimated rate constants of the three components for parallel (perpendicular) pump–probe geometry are 3.03  0.03 (2.57  0.02), 0.177  0.001 (0.147  0.001) and 2.02  103  7  105 (4.23  103  5  105) (ps1), respectively.

where cl and el are concentration and evolution associated spectrum (EAS) of each component, respectively.43 In the sequential fitting routine, a kinetic scheme with unidirectional transformation (1 - 2 - 3) is tested. The three components of EAS, el (hnprobe), are shown in Fig. 5 and the time evolutions of each species (cl(t)) are depicted in the inset. The first component (depicted in red in Fig. 5) with a pronounced polarization dependence represents feature C. Note that the first component contains positive absorption in hnprobe o 2.4 eV, indicating that features A and C have a common origin. The polarization dependence of the spectral shape of feature C is evident in the figure: relative contributions of two negative peaks at 2.69 and 2.79 eV are almost the same for perpendicular polarization, but the former contribution becomes significant for parallel polarization. The third components (depicted in green in Fig. 5) with a derivative-like feature in hnprobe 4 2.4 eV and with a growing contribution with td corresponds to feature D. The second component (depicted in blue in Fig. 5) mainly represents a contribution of feature B. 3.4

TRPL measurements and assignments of features B and D

l¼1

Having categorized the TA features, here we discuss possible assignments of them. A comparison with a fluorescence decay enables the identification of the S1 state. Fig. 6(a) shows TRPL

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3   X   DA td ; hn probe ¼ cl ðtd Þel hn probe ;

(2)

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with a difference spectrum of steady state absorption between 333 and 298 K (Fig. 3(b)): the spectral features including the peak positions and the signs of the signals correspond well to each other. Thus, they are composed of the thermal heating effect and ground state bleaching. In contrast, the feature C shows qualitatively different structures (see td = 0.1 and 1.3 ps in Fig. 3(a) and the first EAS component in Fig. 5); this feature cannot be accounted for by the thermal heating and bleaching. 3.5

The assignments of features A and C

From the global analysis in Section 3.3, it is inferred that features A and C originate in the same transient species. This is confirmed by comparing the decay curves at the representative photon energies of features A and C: in Fig. 7(a), TA decay curves at hnprobe = 2.7 and 2.25 eV, are plotted and they coincide with each other. The bleach recovery at 2.7 eV within td = 3.0 ps cannot be ascribed solely to the ground state recovery, because the difference spectrum between td = 0.1 ps and td = 2.1 ps (Fig. 8(a), dashed curve) does not coincide with the absorption spectrum of the ground state; this rather shows a structure looking like a derivative modulation of the ground state absorption. Transient temperature changes of the sample cannot account for the bleach recovery either,19 because the thermal heating effects are significant in the time domain at td 4 10 ps. Similar TA features which show a combination of bleach and positive absorption have been reported in TA Fig. 6 (a) TRPL spectra of a DNTT film measured with the Kerr gate method. Delay times are indicated in the figure. Pump photon energy was 3.1 eV and the pump fluence was 2.0 mJ cm2. The inset shows a td dependence of the ratio of average counts of TRPL spectra at 2.62–2.65 eV (0–0 band) and 2.47–2.55 eV (0–1 band). (b) Decay of transient absorption probed at 1.58 eV (blue filled circles) and that of photon counts of the TRPL spectra integrated in the region of 2.4–2.7 eV. The pump fluence was 2.0 mJ cm2. The dashed line is least squares fitting of the decay of TRPL intensity with a single exponential function.

spectra obtained with the Kerr gate method. The decay curve of the integrated intensity from 2.4 to 2.7 eV is compared with that of TA at 1.58 eV in Fig. 6(b) in which contributions of features A and B dominate the signal. The two curves coincide well at td 4 10 ps, indicating that feature B in the TA spectra is due to the lowest singlet exciton, S1. The decay time of S1 was estimated to be t = 67  7 ps. The decay characteristics of TA and TRPL are different at td o 10 ps: the TA decay shows a faster decaying component in addition to the decay of S1 with t = 67 ps. This fast component corresponds to feature A. The relative intensity of the 0–0 band to the 0–1 band slightly decreases with td as is depicted in the inset of Fig. 6(a). This is possibly due to the transient heating of the sample which would diminish a coherence length of the exciton:46 i.e., the 0–0 band possess superradiant character which depends on the coherence length while 0–1 band intensity is insensitive to the coherence size.41 Feature D is mainly due to heating of the sample by the excess energy released during the relaxation of transient species.19 This was confirmed by comparing the TA spectra

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Fig. 7 (a) Decay curves of transient absorption at 2.25 eV (open circles) and 2.7 eV (filled circles) with a perpendicular pump–probe geometry. The sign of the signal at hnprobe = 2.7 eV is inverted for comparison and the curves are normalized at their maxima. (b) Time dependent changes of parameters obtained by the fitting of the TA spectra at 2.62 o hnprobe o 2.95 eV with eqn (6): a (filled circles), b1 (open circles), b2 (triangles) and b3 (squares). The coefficient a is plotted after multiplied by 1/10.

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  @sðEÞ 1 Sebastian et al.,22 Ds(E) is dominated by  F  Da  F @E 2 for a transition to a Frenkel exciton. This is because hDmFi is zero for randomly oriented molecules and the second term of eqn (4) is negligible. Instead, Ds(E) for transition to a CT 1 @ 2 sðEÞ exciton is dominated by ðDm  FÞ2 , because Dm is 2 @E 2 very large and then DE(F) E DmF. Therefore, Ds(E) is approximated as,   @sðEÞ 1 1 @ 2 sðEÞ ðDm  FÞ2 : (5) DsðEÞ   F  Da  F þ @E 2 2 @E 2 We fitted the transient features at hnprobe 4 2.4 eV observed at td % 2.2 ps with a linear combination of the first- and second derivatives, and bleaching of the ground state absorption spectrum. Nonlinear least square fittings were carried out for the TA spectra, DA(E), with the following function, DAðEÞ ¼ a  sðEÞ þ

3 X i¼1

Fig. 8 (a) Solid curves are TA spectra in 2.62 o hnprobe o 2.95 eV at td = 0.4 (red), 1.3 (blue) and 2.2 ps (green). Pump fluence was 2.0 mJ cm2. Dotted curves are corresponding fitting results by eqn (6). The thick dashed curve is a difference TA spectrum between td = 0.4 and 2.2 ps. (b) Decomposition of the fitting spectrum at td = 0.4 ps in (a) into each component of eqn (6). The black solid curve is ground state bleaching. Thin solid curves are biqGi(E)/qE, while dashed curves denote ciq2Gi(E)/qE2, in which red open circles are for i = 1, green filled circles are for i = 2, and blue open triangles are for i = 3.

experiments in which charged species are transiently formed, and they have been ascribed to a Stark effect.47–50 Therefore, we attribute feature C to modulations of the ground state absorption band by a Stark effect: when a CT exciton is formed by photoexcitation or by conversion of nascent excited species, its local electric field induces a Stark shift of the ground state absorption bands of its surrounding molecules. The Stark shift of the molecular transition energy is given by,22,51 DE(F) = DmF  12FDaF,

(3)

where Dm and Da are changes in the permanent dipole moment and polarizability of the molecule upon excitation, respectively, and F is the electric field. We expand the field-induced change in the absorption spectrum, Ds(E), in terms of the energy shift DE, DsðEÞ ¼

@sðEÞ 1 @ 2 sðEÞ DE þ ðDEÞ2 ; @E 2 @E 2

(4)

where s(E) is the absorption spectrum of the molecule in the ground state. By substituting eqn (3) into eqn (4), one finds an expression of the field induced spectral change in terms of Dm and Da. According to the early phenomenological treatment by

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bi 

3 @Gi ðEÞ X @ 2 Gi ðEÞ þ ci  ; @E @E 2 i¼1

(6)

where Gi (i = 1,2,3) are Gaussian functions in Fig. 2(b); a, bi, and ci are fitting parameters. Fig. 8(a) shows fitting results for TA spectra with perpendicular pump–probe polarization at td = 0.4, 1.3, and 2.2 ps and Fig. 8(b) shows each component in eqn (6) at td = 0.4 ps. Fig. 7(b) shows the parameters (a, bi, and ci) obtained by the fitting at various delay times. In the fitting, the relative ratios, i.e. ci/bi (i = 1–3), were constrained to be constant for all td: c1/b1 = 0.044, c2/b2 = 0.053, and c3/b3 = 0.0001. Spectra with parallel pump–probe polarization were also fitted well with the same model (not shown) but with different ci/bi (i = 1–3): c1/b1 = 0.077, c2/b2 = 0.032 and negligible contributions of c3 and b3. Because the time evolutions of amplitudes of the parameters bi and hence ci representing the Stark effect coincides with that of feature A (Fig. 7(a)), the species responsible for feature A has to be charged, exerting electric fields onto its surrounding molecules; thus, we assign the species to an admixture state between neutral Frenkel and CT states. The broad spectrum of feature A extending from 1.5 o hnprobe o 2.4 eV is due to absorption from the mixed Frenkel–CT exciton to the higher states. Another possible origin of the derivative-like feature is a many-body effect commonly observed in absorption bands of one-dimensional (1D) excitonic systems such as J-aggregates.52–55 The ‘dispersive’ transient absorption spectra are contributed by a combination of ground state bleaching and blue shifted transient absorption due to a transition from one to twoexciton manifolds.56 In general, the ‘dispersive’ feature deviates from the simple first and second derivatives of the ground state absorption band.57 In addition, as a result of intraband relaxation, the spectral feature changes largely with td (see Fig. 8 and 9 in ref. 58) when a pump pulse induces transitions to highly lying states. The fitting results (Fig. 7(b) and 8(a)), however, show that the derivatives of the ground state absorption band reproduce the TA spectra. In addition, the relative amplitudes of the derivatives are almost independent of td, implying that

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the induced spectral features do not change during the decay. Therefore, we believe that the many-body effect on the derivativelike spectral features is minor in the current three-dimensional excitonic system. This may be due to differences in dimensionality and in the coupling strengths in the current system from those of 1D J-aggregates.

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3.6 Estimation of electric fields exerted by mixed Frenkel–CT states Here we estimate electric field strengths exerted by a mixed Frenkel–CT exciton onto its surrounding molecules by using the parameters estimated in the previous section. Considering that the exerted electric field is nonuniform throughout the crystal, we group the molecules surrounding the Frenkel–CT exciton by the field strength at their centre positions: the group j is the molecules placed in the range of field strength Fj o |F| o Fj + dF. The molecules in the group j are further divided into subgroups labelled by k in which an angle between Dm and F is yj,k. Now Ds(E) in eqn (6) is expressed as,   DsðEÞ X 1 @k0 ðEÞ rj    DaFj 2 d 2 @E j (7) ! X pj; k @ 2 k0 ðEÞ 2 jDmjFj cos yj; k ; þ 2 @E 2 k where rj is the density of molecules of group j; pj,k is the fractional density of the subgroup k; k0(E) is the ground state absorption cross section; and d is the sample thickness. Comparing eqn (7) with eqn (6), we obtain expressions relating the fitting parameters in eqn (6) to the field strength, X rj Fj 2 1 bi   Dai 2 r0 j

where r0 is the density of molecules in the crystal; Dai and Dmi are changes in the polarizability and the dipole moment for the i-th Gaussian component in eqn (6), respectively. We assume P P that @s=@E ¼ r0 d@k0 =@E ¼ @Gi =@E. Note that rj ¼ r0 , so P j

j

i

ðrj Fj 2 =r0 Þ gives an average square of field strength.

Assuming that Da = 3.1  1028 m3 taken from the value estimated in the theoretical study on a tetracene film59 and |Dm| = 24 D estimated from the ion pair distance in the DNTT P crystal (see below), we obtain ðrj Fj 2 =r0 Þ ¼ 4:0  1016 V2 m2 and

PP j

j

ðrj pj;k Fj 2 cos2 yk =r0 Þ ¼ 1:6  1015 V2 m2 from the fit-

k

ting parameters obtained at td = 0.4 ps: b1 = 4.6  103 eV and c1 = 2.1  104 (eV)2. Next, we estimate an actual field strength exerted by the Frenkel–CT exciton. For simplicity, we assume that the field strength can be approximated by that induced by a nearest neighbour ion-pair. Since a recent DFT calculation predicted

7508 | Phys. Chem. Chem. Phys., 2014, 16, 7501--7512

that hole and electron transfer integrals are the largest for the pair indicated by an arrow in the inset of Fig. 9,30 we locate a point dipole with a magnitude of 24 D (=8.1  1029 C m) at the middle of the pair. Then we calculated field strengths exerted by the point dipole at each centre position of molecules surrounding the dipole. Fig. 9 shows a histogram of the field strengths for a super-cell with a size of 11  11  7 unit cells in the directions of a, b, and c crystal axes, respectively. The unit cell that contains the point dipole is located at the centre of the super-cell. The field strength, |F(r)|, is calculated by,   1 3ðp  rÞr FðrÞ ¼  ; (9) p  4per3 r2

(8)

X X rj pj; k Fj 2 cos2 yj;k 1 ci  jDmi j2 ; r0 2 j k

that

Fig. 9 Histogram of the electric field strength exerted by a point dipole placed at the centre of the pair indicated by an arrow in the inset. The inset is a part of the DNTT crystal cut in the ab plane. The field strengths were estimated using eqn (9). See text for the details.

where the relative permittivity of the crystal, e/e0, was assumed to be 3. The largest field strength reaches 1.6  108 V m1. The average of square of the field strength for the 11  11  7 supercell is 2.4  1016 V 2 m2, while that for a 9  9  5 super-cell is 5.1  1016 V 2 m2. These values are in reasonable agreement with the estimated value of square field strength from the spectral fitting, 4.0  1016 V 2 m2. Furthermore, we roughly estimated the degree of mixing between CT and Frenkel states by using the volume of a super-cell; if we assume that the 9  9  5 super-cell contains one CT pair on average, the density of the CT pair is 3.2  1018 cm3 at td = 0.4 ps. Here, we used the lattice constants along a, b and c axes as 6.187, 7.662 and 16.21 Å, respectively.23 The absorbed photon density at a pump pulse fluence of 2 mJ cm2 was estimated to be 1.5  1020 cm3. The decay curves in Fig. 7 imply that the density of the excited state at td = 0.4 ps decreases to about 40% of the initial density. Thus, about 5% of the total density of excitons possesses the CT character. Polarization dependence of the spectral feature C is reflected in the ratio ci/bi (i = 1,2): c1/b1 = 0.077 and 0.044 for parallel and perpendicular polarization, respectively. This indicates that the second term in eqn (7) contributes more largely to

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parallel polarization than to perpendicular polarization of the G1 band. Looking into eqn (8), the polarization dependence is due to the pj,k cos2 yj,k term. Pump excitation generates CT exciton with a preferential direction of ion pairs, and the dipole field, F, exhibits non-isotropic vectorial distribution reflecting the ion-pair distribution. Depending on the relative angles of the transition moment and Dm at probe photon energy, probe polarization variation results in changes in pj,k cos2 yj,k distribution where yj,k is the angle between Dm and F. The opposite trend is found for the peak due to the G2 band: c2/b2 = 0.032 and 0.053 for parallel and perpendicular polarization, respectively: the second term in eqn (7) becomes larger for perpendicular polarization than for parallel polarization. In addition, the striking difference between the two bands manifests itself in the inset of Fig. 4: i.e., r(t) for 2.66–2.72 eV (G1 region) and 2.75–2.80 eV (G2 region) shows opposite trends within td o 1 ps. These indicate that transition dipole moments for G1 and G2 possess a large relative angle and lead to a different selection of the distribution of the pj,k cos2 yj,k term. However, both G1 and G2 are considered to originate in the same transition at 2.92 eV predicted by the DFT calculation (Fig. 2). Thus, one needs to account for the origin of the variation of the transition moment. Here we refer to a theoretical analysis of ground state absorption spectra of OPV and OT aggregates to account for the origin of G1 and G2;37,41 in these materials, the lower energy side of the absorption spectra consists of two kinds of components with nearly orthogonal mutual polarization: one with approximately b polarized transition at the lowest energy which is ascribed to the lower Davydov component and the other is a cluster of bands with moments primarily c polarized which are due to Herzberg–Teller coupling between the lower and the upper Davydov components via phonon modes with asymmetric character. The latter is located at higher energy than the former by ca. 0.65 o0 where o0 is the Frank-Condon active phonon frequency. Because of their structural similarity to DNTT crystals, the emergence of two bands with the same character can also be expected for DNTT thin film.41 Therefore, G1 and G2 with the large relative angle of their transition moments can be understood as the lower Davydov band with an ab plane polarized moment and the vibronic exciton with nearly c polarized moments. The separation of the two peaks is 0.08 eV; 0.47 o0, which is close to the values observed for OPV and OT41 where o0 = 0.17 eV, is the energy separation of the vibronic progression in the DNTT molecule (Fig. 2). As in Fig. 7(b), the time evolutions of parameters bi and ci (i = 1,2,3) almost coincide with each other; this is consistent with the assumption: the Gaussian components are influenced by the Stark effect due to the mixed Frenkel–CT exciton. The nonzero values of b1, b2, c1 and c2 indicate that the G1 and G2 bands are mixed Frenkel-CT states and those states are likely responsible for feature A. The negligible value of c3 implies that the G3 band is characteristic of pure Frenkel exciton. The discrepancy of the decay of the derivative components from that of the ground state bleaching (Fig. 7(b)) indicates that not all of the mixed Frenkel–CT excitons directly decay to the

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electronic ground state. Details of the decay of the mixed Frenkel–CT exciton are discussed in terms of its fluence dependence in the next section. 3.7

Pump fluence dependence

Fig. 10(a) shows the pump fluence dependence of TA decay curves at hnprobe = 1.58 eV, where S1 exciton contributes dominantly for td larger than a few ps. The decay kinetics depend on the fluence moderately; the decay rate is accelerated slightly even at the highest photon density. Thus, the relaxation rate of S1 is insensitive to its density. Fig. 10(b) shows TA decay curves at hnprobe = 2.55 eV for td o 9 ps, where the contribution of the mixed Frenkel–CT state is pronounced. The decay rates increase with fluence markedly contrary to those at hnprobe = 1.58 eV. This indicates that exciton–exciton annihilation becomes an important decay path at higher densities.60–62 It is notable that annihilation occurs in

Fig. 10 Pump fluence dependence of transient absorption decay curve of DNTT film at hnprobe = (a) 1.58 eV and (b) 2.55 eV. The pump–probe polarizations were perpendicular to each other. The pump fluences were 4 mJ cm2 (black open circles), 2 mJ cm2 (blue triangles), 1 mJ cm2 (green filled squares) and 0.2 mJ cm2 (red filled circles). Insets show the same decay curves normalized at their peaks. Note that the regions of the horizontal axis are different for the two figures. Dotted curves in (b) are fitting results by eqn (12) and (13).

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the highly lying mixed Frenkel–CT states, while annihilation of the lowest S1 state does not take place efficiently. A rigorous treatment of exciton annihilation63–65 provides a conversion rate from a two-exciton state, |a2i, to a one-exciton state, |b1i, X  Ca ðn; nÞCb ðnÞ2 kIC : (10) ka2 !b1 ¼ 2 1 n

Here one- and two-exciton manifolds are represented as P P jb1 i ¼ Cb1 ðmÞjmi and ja2 i ¼ Ca1 ðm; nÞjm; ni, respectively, Published on 28 February 2014. Downloaded by Temple University on 25/10/2014 18:36:37.

n

m;n

where m and n are indexes for chromophore sites. This expression implies that the overlap of wavefunctions between an oneexciton and a doubly-excited two-exciton state at a same molecule is an important factor in addition to the internal conversion rate from the doubly-excited state to the first excited state, kIC.63 The marked enhancement of the annihilation rate in the higher mixed Frenkel–CT states indicates that their wavefunctions are delocalized substantially compared to the lowest S1 state. We analyzed the observed decays of the mixed Frenkel–CT states (Fig. 10(b)) using a simple kinetic model, FC + FC - Sn + S0, Sn - FC, FC - S1, S1 - S0.

(11)

In this model, while the mixed Frenkel–CT exciton denoted as FC relaxes into S1 with its intrinsic decay time, a secondorder annihilation pathway between FCs opens at high FC densities. This decay path generates a ground state molecule and a higher exciton state, Sn. Here we assumed that Sn rapidly relaxes into FC. The decay curves were fitted with a solution of the following coupled differential equations that is valid in the limit of incoherent hopping of excitons, d½FC g ¼  kFC ½FC  ½FC2 ; dt 2 d½S1  ¼  kS1 ½S1  þ kFC ½FC; dt

(12)

where [FC] and [S1] stand for the densities of the mixed Frenkel–CT and S1 states, respectively; kFC is the conversion rate constant of FC to S1 at the low density limit; kS1 is the relaxation rate constant of S1 to the ground state; and g is the annihilation rate constant. The TA decay curve, D A(td), is then given by, D A(td) = a[FC] + b[S1],

(13)

where a and b are the absorption coefficients of FC and S1 at the observed wavelength, respectively. We first estimated kFC by fitting the curve at the lowest fluence (0.2 mJ cm2) with a double exponential function, where a slower decay time constant was fixed at 67 ps as estimated for the decay of S1 in Section 3.4. The fitting gave the faster time constant to be 2.0  0.5 ps for the decay of FC. Assuming that the sum of

7510 | Phys. Chem. Chem. Phys., 2014, 16, 7501--7512

Fig. 11 A scheme of ultrafast dynamics in DNTT films. Solid and dashed arrows pointing downwards are radiative and non-radiative decay, respectively.

initial densities of S1 and FC, N0 = [FC]0 + [S1]0, is given by the absorbed photon density in the sample, we fitted globally the curves for pump fluences higher than 1 mJ cm2 with the values of kFC and kS1 given above to obtain the parameters of g, [FC]0, [S1]0, a, and b. As shown in Fig. 10(b), the fitting results based on the kinetic model in eqn (11) reproduced the observed power dependence reasonably well. The estimated value of g is (1.7  0.3)  108 cm3 s1. The values of [S1]0 for all the fluences were less than 2% of N0, indicating that FC is populated by the pump pulse and then S1 is generated by the relaxation of FC. In the case of isotropic diffusion, g is given by16   a0 g ¼ 8pDa0 1 þ pffiffiffiffiffiffiffiffiffiffiffi ; (14) 2pDt where a0 is a critical distance for annihilation and D is a diffusion constant. In the long time limit where the second term is negligibly small, g becomes independent of t: g = 8pDa0. If we use the average value of DNTT crystal lattice constants, 10 Å, as a0 and the estimated value of g, 1.7  108 cm3 s1, the diffusion constant was estimated to be D = g/(8pa0) = 6.8  103 cm2 s1. This gives the nearest neighbour hopping time, a02/6D, to be 0.25 ps. Thus, the approximation of the long time limit is reasonable in the observation time scale. The pronounced annihilation behaviour of FC indicates that energy migration occurs in the highly lying states rather than the lowest S1 state; this is rather an exceptional case.66 The peculiar feature observed in the current study indicates that the mixed Frenkel–CT states in this material have highly delocalized wavefunctions, resulting in rather large hopping integrals of electrons and holes.30

4 Conclusions We carried out transient absorption and time-resolved emission measurements for DNTT thin films pumped by fs laser

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pulses at 400 nm. Fig. 11 shows a schematic diagram of the dynamics deduced from this work. The pump pulses excite to exciton manifolds at 0.6 eV higher than the absorption band edge. Within 0.1 ps, mixed Frenkel–CT exciton is formed, and this mixed exciton decays to S1 exciton by internal conversion as well as to the ground state by the annihilation pathway. S1 exciton decays with a lifetime of 67  7 ps. The mixed Frenkel–CT exciton modulates the ground state absorption spectrum of surrounding molecules. The polarization dependence of the TA spectra indicates anisotropic distributions of dipole moments formed by the CT exciton. The lowest two absorption bands show polarization dependences distinct from each other and this was explained in analogy with OT and OPV aggregates: the lowest band (G1) is the lower Davydov component (‘J’ band) with a transition moment in the ab-plane and the second band (G2) is a vibronic exciton with a transition moment polarized along the c-axis. The mixing of Frenkel exciton with CT states has been invoked by many authors.6,8–10 However, its implication in the observations of ultrafast pump–probe spectroscopy has not been extensively discussed. In this paper, we demonstrated that the derivative-like feature of transient absorption spectra can be a signature of the nascent CT state; this hypothesis was examined by spectral fitting with a model including the Stark effect caused by the excited state with CT character. The employed procedure in this study can be applied to other organic semiconductors and will reveal the CT nature of nascent photoexcited states relevant to photocarrier generation in promising materials for organic electro-optic devises.

Acknowledgements This work was supported by a Grant-in-Aid for Scientific Research (A) from the Japan Society for the Promotion of Sciences (Grant No. 22245001), Grant-in-Aid for Challenging Exploratory Research from Japan Society for the Promotion of Science (Grant No. 24655011), Kyoto University Global COE program, and the program of Network of Joint Research Centre for Advanced Materials and Devices. DNTT material is kindly supplied by Nipponkayaku Co. We thank Mr Shunsuke Tanaka for his help with measurements.

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