Probing Charge Carrier Dynamics in Porphyrin-Based Organic

To improve the power conversion efficiency of solar cells, it is important to understand the underlying relaxation mechanisms of photogenerated charge...
1 downloads 0 Views 1MB Size
Download PDF
Article Cite This: J. Phys. Chem. B XXXX, XXX, XXX-XXX

pubs.acs.org/JPCB

Probing Charge Carrier Dynamics in Porphyrin-Based Organic Semiconductor Thin Films by Time-Resolved THz Spectroscopy Kaoru Ohta,†,‡ Shunrou Tokonami,‡ Kotaro Takahashi,§ Yuto Tamura,§ Hiroko Yamada,*,§ and Keisuke Tominaga*,†,‡ †

Molecular Photoscience Research Center, Kobe University, 1-1 Rokkodai-cho, Nada, Kobe 657-8501, Japan Graduate School of Science, Kobe University, 1-1 Rokkodai-cho, Nada, Kobe 657-8501, Japan § Graduate School of Materials Science, Nara Institute of Science and Technology, 8916-5, Takayama-cho, Ikoma, Nara 630-0192, Japan ‡

S Supporting Information *

ABSTRACT: To improve the power conversion efficiency of solar cells, it is important to understand the underlying relaxation mechanisms of photogenerated charge carriers in organic semiconductors. In this work, we studied the charge carrier dynamics of diketopyrrolopyrrole-linked tetrabenzoporphyrin thin films where the diketopyrrolopyrrole unit has two nbutyl groups, abbreviated as C4-DPP-BP. We used timeresolved terahertz (THz) spectroscopy to track charge carrier dynamics with excitations at 800 and 400 nm. Compared with tetrabenzoporphyrin (BP), the extension of π-electron delocalization to the diketopyrrolopyrrole peripherals leads to an increase in absorption in the near-infrared region. Following the excitation at 800 nm, we found that the transient THz signals in C4-DPP-BP thin films decay with time constants of 0.5 and 9.1 ps, with small residual components. With excitation at 400 nm, we found that the transient THz signals decay with time constants of 0.4 and 7.5 ps. On the basis of the similarity of the decay profiles of the transient THz signals obtained with excitations at 400 and 800 nm, we considered that the decaying components are due to charge carrier recombination and/or trapping at defect sites, which do not depend on the excess energy of the photoexcitation. In contrast to BP, even without an electron acceptor, we observed the finite offset of the transient THz signals at 100 ps, demonstrating the existence of long-lived charge carriers. We also measured the photoconductivity spectra of C4-DPP-BP thin films with the excitation at both 800 and 400 nm. It was found that the spectra can be fitted by the Drude−Smith model. From these results, it was determined that the charge carriers are localized right after photoexcitation. At 0.4 ps, the product of the quantum yield of charge generation and mobility of charge carriers at 400 nm is approximately twice that obtained at 800 nm. We discuss the implications of the excess excitation energy in organic semiconductor-based devices. dye sensitized solar cells,6−8 their application in solutionprocessed bulk heterojunction (BHJ) solar cells is still under development. Tetrabenzoporphrin (BP) is a well-known p-type organic semiconductor that has excellent photophysical properties such as a strong absorption in the visible region and high hole mobility. However, because of the extended π-framework, it exhibits a low solubility in common organic solvents. To overcome this drawback, soluble precursors were synthesized and thermally converted into target molecules.9 By using a soluble precursor of BP, it was demonstrated that BP-based field-effect transistors exhibit comparable performance to

1. INTRODUCTION Organic semiconductors, such as conjugated polymers and small-molecule crystals, are important ingredients for fieldeffect transistors and solar cells.1−3 These materials have great advantages over inorganic-based ones because of the potential for producing cost-effective and flexible devices by using solution processing. For organic photovoltaics, conjugated polymers, such as poly(3-hexylthiophene) (P3HT), are commonly used as electron donors.1,2 Since nature has utilized porphyrin chromophores, such as chlorophylls and bacteriochlorophylls, for light harvesting, porphyrin-based molecules are a natural choice as an artificial counterpart.4,5 These molecules have a number of unique photophysical properties. As is well-known, they show very intense absorptions in the visible region, which are called Soret and Q bands. Even though porphyrins have been frequently used as a photosensitizer for © XXXX American Chemical Society

Received: July 17, 2017 Revised: October 12, 2017 Published: October 12, 2017 A

DOI: 10.1021/acs.jpcb.7b07025 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B pentacene-based ones.10−12 For application in solar cells, Matsuo et al. reported the fabrication of p-i-n organic photovoltaic cells using a BP precursor and silylmethyl[60]fullerene that show a high power conversion efficiency of 5.2%.13 Tamura et al. synthesized a covalently linked BPfullerene (C60) dyad and compared the photovoltaic performance of BP-C60 films with those of a 1:1 blend film of BP and [6,6]-phenyl C61 butyric acid methyl ester (PC61BM) in p-i-n and BHJ devices.14,15 They showed that a p-i-n organic photovoltaic cell consisting of BP, BP-C60, and PC61BM as p-, i-, and n-layers has better power conversion efficiency than the corresponding p-i-n cells having a 1:1 blend film of BP and PC61BM as an i-layer. This study demonstrated that a variety of synthetic strategies are very useful to improve the power conversion efficiency and determine the best material for organic solar cells. To increase the power conversion efficiency of solar cells, it is also important to understand the detailed mechanisms of charge generation, recombination, and charge carrier mobilities of such devices.16,17 Time-resolved terahertz (THz) spectroscopy, i.e., optical pump-THz probe spectroscopy, is known to be a unique technique to quantify the complex-valued conductivity of photogenerated charge carriers in various systems.18−20 In contrast to time-of-flight methods that can monitor long-range charge transport over the micrometer length scale, time-resolved THz spectroscopy is a noninvasive and contact-free method that is intrinsically sensitive to the local charge carrier dynamics with subpicosecond time resolution.18−20 Since the scattering frequency of the charge carriers in semiconductors is typically located in the THz region, THz spectroscopy provides detailed information on both carrier density and mobility for such systems.18−20 So far, time-resolved THz spectroscopy has been used to study the charge carrier dynamics of small-molecule-based organic semiconductors, such as polyacene (pentacene and rubrene) crystals and thin films,21−25 as well as Zn phthalocyanine-C60 films with a layered structure.26−29 However, the charge carrier dynamics of porphyrin-based organic semiconductors has not been examined with time-resolved THz spectroscopy until recently.30 Compared with polymer-based ones, small-molecule-based systems have unique advantages such as the flexibility of varying functional groups and control of the molecular structure. One can also fabricate thin films with a high degree of crystallinity and structural order. In our previous works, we investigated the charge carrier dynamics of BP and BP-based bulk heterojunction (BHJ) thin films using time-resolved THz spectroscopy.30 In both samples, we observed the instantaneous appearance of transient THz signals with an excitation at 400 nm, which are attributed to mobile charge carriers. For BP thin films, the majority of the signal decays to zero with time constants of 0.5 and 6 ps. In the BP-based BHJ films, approximately 10% of the transient THz signal does not decay within 35 ps, indicating the survival of free charge carriers. For a BP:PC61BM BHJ film, the power conversion efficiency is only 0.02%.14 We considered that a slower recombination may be involved in the relaxation process of the charge carriers. There are a couple the reasons why the BP-based BHJ film exhibits a low organic photovoltaic performance. In particular, the extinction coefficients of BP are small near 500−600 nm and at wavelengths longer than 700 nm. To improve performance, Takahashi et al. synthesized a series of diketopyrrolopyrrole (DPP)-linked BPs by changing the length

of the alkyl groups (from n-butyl to n-decyl) on the DPP units.31 Similar to BP, this can be used for the fabrication of organic solar cells. They found that the power conversion efficiency of DPP-BP:PC61BM BHJ cells depends on the length of the alkyl chains on the DPP units. When the chain length is shorter, the power conversion efficiency becomes higher. Furthermore, related studies on BHJ solar cells using DPPlinked zinc porphyrins showed that the power conversion efficiency is over 7%.32−34 These studies clearly showed that DPP-BP-based compounds are promising materials for increasing the power conversion efficiency of porphyrin-based organic photovoltaic cells. In this study, we carried out time-resolved THz measurements for DPP-BP thin films to investigate the charge carrier dynamics. Here, we focused on the intrinsic properties of the charge carrier dynamics of DPP-BP thin films where the DPP unit has two n-butyl groups, as shown in Figure 1. Hereafter,

Figure 1. (a) Molecular structure of diketopyrrolopyrrole-linked tetrabenzoporphyrin (C4-DPP-BP) and (b) absorption spectrum of the C4-DPP-BP thin film.

this molecule is abbreviated as C4-DPP-BP. As mentioned above, the power conversion efficiency of the C4-DPP-BPbased BHJ solar cell is high (5.2%) compared with BP-based ones (0.02%). Therefore, it is very interesting to see whether the charge carrier dynamics in a C4-DPP-BP thin film itself is different from that of BP or not. Excitation wavelength dependence of charge carrier generation has received a lot of attention because excess energy may facilitate exciton dissociation, which is a matter of debate.35−41 We performed the measurements with excitations at 800 and 400 nm to discuss how the different excitation energies affect the charge carrier dynamics and photoconductivity in C4-DPP-BP thin films. In our previous studies of BP thin films, the absorption at 800 nm is too small to measure any transient THz signals.30 Our study provides us with fundamental information to understand the photoinduced dynamics of C4-DPP-BP-based thin films by comparing the experimental results with and without an electron acceptor, especially the process of charge carrier generations. Such studies have been performed for polymer-based thin films,42−45 but not for porphyrin-based ones except our previous study.30 Currently, we are also measuring the charge carrier dynamics of C4-DPP-BP:PC61BM B

DOI: 10.1021/acs.jpcb.7b07025 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B BHJ thin films and found different kinetics of the transient THz signals, which will be reported in another publication.

2. EXPERIMENT The details of our time-resolved THz spectrometer are described in the Supporting Information. Briefly, 800 nm pulses with a duration of ∼100 fs and at a repetition rate of 1 kHz were generated by a Ti:sapphire regenerative amplifier. The generation and detection of THz pulses were based on a so-called femtosecond laser-induced plasma and air-biased coherent detection scheme.46−49 The optical pump pulse was either the fundamental (800 nm) or second harmonic (400 nm) of the regenerative amplifier. The time dependence of the transient conductivity was determined by the change in peak amplitude of the THz waveform as a function of the optical pump-THz probe delay. In this scan mode, the signals reflect the time dependence of the frequency-averaged photoconductivity.20 Transient complex photoconductivity spectra were obtained by scanning the time delays of the optical pump and the THz detection pulses synchronously at a fixed THz probe delay and by performing a Fourier transform of the frequency domain. Details of the synthesis of the thermally convertible precursor of C4-DPP-BP and the fabrication and characterization of the thin films were described elsewhere.31 C4-DPP-BP thin films were fabricated on 0.3 mm thick fused silica substrates. The measurement setup was continuously purged with dry nitrogen to avoid absorption of the THz pulse by water vapor. All measurements were done at room temperature.

Figure 2. (a) Photoinduced change of the THz electric field amplitude in C4-DPP-BP thin films as a function of optical pump/THz probe delay time, measured at the peak of the THz transmission. The excitation fluence was 950 μJ/cm2. (b) Same as part a, except on a longer time scale. The excitation wavelength was 800 nm. Blue solid lines with filled circles and red lines correspond to the experimental results and double-exponential fits convoluted with the instrument response function, respectively.

signals excited at 400 nm. Figure 3 displays the photoinduced change of the peak amplitude of the THz transmission as a

3. RESULTS 3.1. Absorption Spectrum of C4-DPP-BP Thin Films. Figure 1 shows the UV−vis absorption spectrum of the C4DPP-BP thin films. As clearly seen from Figure 1, four different bands were observed in the absorption spectrum, which covers the visible to near-infrared regions. DPP is known to have a πelectron-deficient nature and is frequently used as an acceptor building block in organic photovoltaic materials. On the other hand, porphyrins work as a π-electron donor. Therefore, we can consider that, compared with BP, π-electron delocalization among the porphyrin core and diketopyrrolopyrrole peripherals leads to an increased absorption in the near-infrared region. 3.2. Decay Kinetics of the Transient THz Signals in C4DPP-BP Thin Films. Figure 2 displays the photoinduced change of the peak amplitude of the THz transmission as a function of the optical pump-THz probe delay excited at 800 nm. The THz transient signals rise immediately, which is due to the instantaneous appearance of mobile charge carriers. We considered that the exciton absorption is located in a significantly higher-frequency region than our observed one, as is discussed in the next section. The time profile of the THz transient signals is described by a double exponential decay function with an offset convoluted with the instrument response function. Details of the analysis are described in Supporting Information. The obtained time constants of the fast and slow decaying components of the transient THz signals are 0.5 ± 0.1 and 9.1 ± 1.7 ps, respectively. Small portions of mobile charge carriers exist on a time scale longer than a few tens of picoseconds and are the origin of the offset of the transient THz signals. To study the excitation wavelength dependence on the charge carrier dynamics, we also measured THz transient

Figure 3. (a) Photoinduced change of the THz electric field amplitude in C4-DPP-BP thin films when the sample was excited at 400 nm. The excitation fluence was 620 μJ/cm2. (b) Same as part a, except on a longer time scale.

function of optical pump-THz probe delay. We found that the transient THz signals decay with time constants of 0.4 ± 0.1 and 7.5 ± 2.3 ps, which are similar to those obtained with the excitation at 800 nm. From a comparison of the early transient THz signals obtained with 800 and 400 nm excitations, the contribution of the fast decaying component is larger with excitation at 400 nm. Furthermore, we investigated how the excitation fluence affects the peak amplitude of the transient THz signals. When the sample was excited at 800 nm, we found that the peak amplitude of the signals depends linearly on the excitation C

DOI: 10.1021/acs.jpcb.7b07025 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B fluence, as shown in Figure 4. The excitation fluence dependence of the transient THz signals within a 4 ps time

elementary charge, Z0 is the impedance of free space, F is the excitation fluence in photons per cm2, OD is the absorbance of the sample at the excitation wavelength, and ns is the refractive index of substrate. This quantity does not depend on the depth profile of the excitation beam. Since the reflectivity of the sample at the optical pump wavelength is unknown, the value given by eq 1 represents a lower limit. Figure 5 displays a typical THz electric field transmitted through a sample in the absence of photoexcitation, together

Figure 4. Excitation fluence dependence of photoinduced change of THz electric field of C4-DPP-BP thin films at the peak of the THz transmission. Green filled circles represent the experimental data. The dashed line represents a simple linear fit to the data.

scale is shown in Figure S1 (see the Supporting Information). The temporal profiles of the signals within the 4 ps time scale do not depend on the excitation fluence within our signal-tonoise ratio. On the other hand, it was found that the signals show a sublinear dependence, as shown in Figure S2. In the previous studies of BP thin films using a 400 nm excitation, we observed a sublinear fluence dependence of the transient THz signals and attributed it to exciton−exciton annihilation or the quenching of excitons by holes.30 We considered that this exciton relaxation process occurs at a higher fluence and the yield of the charge carrier generation is suppressed, because this process competes with exciton dissociation.50 However, the transient THz signals of C4DPP-BP thin films with the excitation at 800 nm do not clearly show such a dependence. When the sample was excited at 800 nm, we considered that exciton−exciton annihilation or the quenching of excitons does not occur efficiently. On the other hand, exciton−exciton annihilation or the quenching of excitons by holes leads to the suppression of carrier generation when the sample is excited at 400 nm, which is similar to the behavior of BP thin films.50 Because of the different photon energies (400 and 800 nm), the excitation photon sheet density per unit area at 400 nm is half of that at 800 nm for equal excitation fluences. This means that the small photon sheet density at 400 nm is enough to induce a sublinear dependence of the transient THz signals compared with the response from the 800 nm excitation. 3.3. Transient Photoconductivity Spectra in C4-DPPBP Thin Films. To investigate the nature of mobile charge carriers, we measured the transient complex conductivity spectra excited at 800 and 400 nm. As shown in the previous studies, the complex THz spectrum is sensitive to the transient volume photoconductivity.18−20 However, this quantity depends on the absorption profile of the excitation beam. Rather, we calculated the product of the quantum yield of charge generation and mobility of charge carriers (effective mobility) as follows.42 ϕμ(ω) = −

1 + ns

ΔE(ω) ) E(ω)

−OD

eZ0F(1 − 10

Figure 5. THz electric field transmitted through a C4-DPP-BP film without photoexcitation (blue), and the optically pump-induced differential THz electric field measured at a 0.4 ps time delay (green).

with an optical pump-induced differential field. With the excitation at 800 nm, the amplitude of the photoinduced differential signal is generally less than 1% of the peak transmission of the THz probe pulse. Figure 6 displays the

Figure 6. Transient complex conductivity spectra of C4-DPP-BP thin films measured at (a) 0.4 ps and (b) 1.2 ps. The excitation wavelength was 800 nm, and the excitation fluence was 600 μJ/cm2. Blue (red) open circles are the real (imaginary) parts of the experimental transient conductivity. The corresponding solid lines are fits to the Drude−Smith model, which is given by eq 2.

transient complex conductivity spectra of C4-DPP-BP thin films calculated from eq 1 with the excitation at 800 nm. The real part of the spectra exhibits a positive value that becomes larger at higher frequencies. The imaginary part of the conductivity is negative and approaches zero at lower frequencies, which shows a different feature from what we expect from the classical Drude model.18,19 When excitons dominate the conductivity spectra, the imaginary part of the

(1)

Here, the following abbreviations apply: E(ω) and ΔE(ω) are the transmission and differential transmission spectra of the THz probe pulses obtained by performing a Fourier transform on the corresponding temporal profiles, μ(ω) is the sum of the frequency-dependent electron and hole mobilities, e is the D

DOI: 10.1021/acs.jpcb.7b07025 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B conductivity is negative and passes through zero at zero frequency because of a photoinduced polarizability, while the real part is zero because the exciton absorption is located far from the THz region.43 Therefore, our observed conductivity spectra cannot be explained by the excitons generated by photoexcitation. Instead, the observed spectral feature can be explained by the Drude−Smith model, which is generally used to analyze the conductivity spectra of mobile charge carriers in disordered systems.43,44,50−53 In this model, the frequency dependence of the product of the quantum yield of charge generation and mobility of charge carriers is given as follows.54 ϕμ(ω) = ϕ

ωp2ε0 eNex

⎛ ⎞ τ c ⎜1 + ⎟ ⎝ 1 − iωτ 1 − iωτ ⎠

(2)

Here, the following abbreviations apply: ε0 is the vacuum permittivity, ωp is the plasma frequency, Nex is the excitation density, and τ is the carrier momentum relaxation time. The effect of the disorder is described by the parameter c (between −1 and 0), which is related to the memory effect during the carrier scattering process. As shown previously, for c < 0, carriers tend to undergo backscattering and get localized. On the other hand, eq 2 is equal to the Drude model for c = 0. Since the effective mass of the charge carriers is unknown, we cannot determine the plasma frequency of the charge carriers, so we treat the second factor of the right-hand side of eq 2 simply as a proportional constant. To compare our results with the mobility of other systems, we define the following mobility parameter.

μp =

Figure 7. Transient complex conductivity spectra of C4-DPP-BP thin films measured at (a) 0.4 ps and (b) 1.2 ps. The excitation wavelength was 400 nm, and the excitation fluencies at 0.4 and 1.2 ps were 540 and 620 μJ/cm2, respectively.

at the delay time of 0.4 ps is approximately twice as large as that found with the excitation at 800 nm.

4. DISCUSSION First, we compare the product of the quantum yield of charge generation and mobility parameter, ϕμp, with other systems. In the previous studies using time-resolved THz spectroscopy, Ostroverkhova et al. investigated the transient photoconductive properties of pentacene and its derivatives in both single crystals and thin films.23,24 For pentacene thin films, they showed the transient conductivity spectrum from 0.6 to 2.2 THz. The real part of the conductivity does not depend on the THz frequency, while the imaginary part is nearly zero. The product ϕμ at a zero delay time was estimated to be 0.02 cm2 V−1 s−1 for pentacene films at room temperature.23 Our obtained value of ϕμ in the C4-DPP-BP thin film at 70 cm−1 is comparable to that of pentacene thin films. For a typical semiconducting polymer, P3HT, Ai et al. measured the frequency-dependent complex conductivity by OPTP spectroscopy, upon photoexcitation at 500 nm.43 On the basis of the analysis using the Drude−Smith model, they reported that the mobility parameter, μp, and quantum yield of charge generation are 8 cm2 V−1 s−1 and 24% at 2 ps, respectively. This means that the product ϕμp is equal to 1.9 cm2 V−1 s−1. Cunningham and Hayden reported that the mobility parameter, μp, and quantum yield of charge generation at 1.2 ps are 34 cm2 V−1 s−1 and 1.5%, respectively, with the excitation at 800 nm.44 This means that the product ϕμp is equal to 0.51 cm2 V−1 s−1. Our obtained value of ϕμp is 3 times smaller than that of P3HT reported by Ai et al. and is close to that reported by Cunningham and Hayden.44 It should be noted that the above measurements were performed without electron acceptor. In these measurements, mobile charge carriers were dominant species in the observed THz signals on a time scale of a few picoseconds. On the basis of the results of the transient conductivity measurements, C4-DPP-BP has desirable properties for the charge carrier transport in organic photovoltaic devices in terms of charge generation and carrier mobility. Regarding the decay kinetics of the transient THz signals, we observed similar decaying components of the signals to those

ωp2ε0τ eNex

(3)

In the dc limit, the mobility is given by μdc = μp (1 + c)

(4)

Using the parameters shown above, the product of the quantum yield of charge generation and mobility of charge carriers is given by ϕμ(ω) = ϕμp

⎛ ⎞ 1 c ⎜1 + ⎟ ⎝ 1 − iωτ 1 − iωτ ⎠

(5)

From the analysis of the conductivity spectra, we found that τ and c at 0.4 (1.2) ps are 8.7 ± 1.0 (5.7 ± 1.2) fs and −0.98 ± 0.01 (−0.98 ± 0.01), respectively. At both time delays of 0.4 and 1.2 ps, the parameter c is close to −1. This means that charge carriers are rapidly localized right after the photoexcitation. We also found that the carrier momentum relaxation times are less than 10 fs. The product of the quantum yield of charge generation and mobility parameter, ϕμp, at 0.4 and 1.2 ps are 0.61 ± 0.20 cm2 and 0.69 ± 0.49 cm2 V−1 s−1, respectively. Figure 7 shows the transient complex conductivity spectra measured at 0.4 and 1.2 ps with the excitation at 400 nm. Similar to the excitation at 800 nm, the spectra can be fitted by the Drude−Smith model, and the obtained τ and c parameters at the delay times of 0.4 ps (1.2 ps) are 11 ± 1 fs (9 ± 1 fs) and −0.96 ± 0.01 (−0.96 ± 0.01), respectively. We also found that the values of ϕμp at 0.4 and 1.2 ps are 1.27 ± 0.11 and 1.05 ± 0.13 cm2 V−1 s−1, respectively. Again, similar to the 800 nm excitation, the charge carriers are localized immediately right after the photoexcitation. We also found that the value of ϕμp E

DOI: 10.1021/acs.jpcb.7b07025 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B found in BP thin films. Since the THz signals are proportional to both the population and mobility of the photogenerated charge carriers, there are two possible origins, i.e., a reduction in carrier mobility as charge carriers relax or a recombination and/ or trapping at defect sites of mobile charge carriers. Recent time-resolved THz studies of model photovoltaic systems such as zinc phthalocyanine/C60 and α-sexithiophene/C60 showed that the short-lived decaying components of transient THz signals are due to a decrease of carrier mobility as the carriers thermalize.29 This is supported by the fact that the amplitude of the picosecond decaying component is very small when one excites the electron acceptor (C60) at its absorption edge, and electron transfer occurs from alpha-sexithiophene. However, we still observed a large contribution of the subpicosecond decaying components with the excitation at 800 nm. Therefore, we considered that short-lived components of the transient THz signals are not due mainly to a reduction in carrier mobility. After the photoexcitation, the transient THz signals show up immediately due to the instantaneous appearance of mobile charge carriers. Within a 0.4 ps time scale, charge carriers undergo backscattering because of inhomogeneous crystal structures, and the electron/hole pairs are quickly localized, which leads to efficient charge recombination by Coulombic interactions. Some of the separated mobile charge carriers can travel a long distance, but they slowly decay to the ground state because of the trapping by defect states and/or recombination of the electron/hole pairs. In this case, charge diffusion is necessary to induce such processes. Recently, Ponseca and co-workers showed that the fast decay components of the THz photoconductivity in BHJ conjugated polymer:fullerene blend films result from charge pair annihilation occurring at the high carrier densities.55 From our measurements, we did not observe a clear dependence of the amplitude of the fast decaying components on the excitation fluence within the range of the excitation fluence (see Figure S1). On the other hand, preliminary time-resolved THz measurements of C4-DPP-BP:PC61BM blend films with the excitation at 800 nm showed that the amplitude of the picosecond decaying components does depend on the excitation fluence. As the excitation fluence decreases, the amplitude of the fast decaying components decreases. This observation is similar to that reported by Ponseca and coworkers. We considered that the annihilation of charge pairs is responsible for the fast decaying components in C4-DPPBP:PC61BM blend films at higher excitation fluence. At lower fluence, we considered that the interfacial charge transfer from C4-DPP-BP to PC61BM occurs efficiently before quenching of the charge carriers occurs. This may be the reason why the amplitude of the fast decaying component is small in C4-DPPBP:PC61BM blend films compared with C4-DPP-BP films. At a higher excitation fluence, charge pair annihilation may contribute to the fast decaying components of the transient THz signals even in C4-DPP-BP films. It will be interesting to compare the excitation wavelength dependence of the transient photoconductivity in the other small-molecule organic semiconductors. For pentacene thin films and functionalized pentacene crystals and thin films, Ostroverkhova et al. found that the initial value of ϕμ does not depend on the excitation wavelength in the 400−800 nm region for crystals and the 400−675 nm region for thin films within their experimental error.23 These results are clearly different from ours, even though the values reported by Ostroverkhova et al. are scattered by more than a factor of 2.

Furthermore, Cunningham and Hayden measured the transient conductivity spectra of P3HT with excitation at 400 nm.44 Their obtained value of ϕμp with a delay time of 1 ps is equal to 0.34 cm2 V−1 s−1, which is smaller than that with the excitation at 800 nm. Our observation is in contrast with the results of the previous studies. As mentioned in the introduction, the excitation wavelength dependence of charge carrier generation has gained considerable interest because of the hot exciton dissociation mechanism in organic photovoltaics.35−41 From a comparison of the early transient THz signals for 800 and 400 nm excitations, the contribution of the fast decaying component is larger with the excitation at 400 nm. Furthermore, we clearly observed that the value of ϕμp with the excitation at 400 nm is approximately twice that at 800 nm. This result suggests that either the quantum yield of charge generation or mobility of the charge carriers is initially higher than that excited at 800 nm. It should be noted that the signals show a sublinear dependence (Figure S2). In contrast with that obtained with the excitation at 800 nm, exciton−exciton annihilation or the quenching of excitons by holes leads to the suppression of carrier generation when the sample is excited at 400 nm. This means that the value of ϕμp becomes greater at a lower excitation fluence. Finally, we briefly comment on the crystal structure and local morphology of C4-DPP-BP films and their effect on the charge transport processes. According to the results of two-dimensional grazing-incidence wide-angle X-ray diffraction measurements, Takahashi et al. found that C4-DPP-BP molecules in the neat films are arranged in a face-on geometry.31 This means carrier transport is favorable in the out-of-plane direction. However, n-decyl (C10-)substituted DPP-BP molecules take the edge-on geometry with a high selectivity in neat films. It will be interesting to study how the crystal structure and local morphology affect charge carrier transport by examining the charge carrier dynamics in DPP-BP thin films with different alkyl groups because the THz signals are sensitive to the inplane mobility of the charge carriers. On the other hand, the edge-on orientation is the preferred molecular arrangement regardless of the alkyl-chain length in the blend films with PC61BM. Takahashi et al. also investigated surface morphology of C4-DPP-BP films and its dependence on alkyl-chain length by atomic force microscopy.31 For the C4-DPP-BP:PC61BM film, the grain sizes were found to be approximately 100 nm or smaller, while micrometer-sized grains exist in the case of noctyl (C8-) and C10-DPP-BP:PC61BM thin films. Similar morphologies were also found in the respective neat DPP-BP films. It should be noted that our sample conditions for the above measurements are different from those used for device characterization. For current measurements, we repeated the spin coating and heating of the sample five times to measure transient signals with a good signal-to-noise ratio. In contrast to time-of-flight techniques, time-resolved THz spectroscopy can monitor the carrier mobility over nanometer length scales, and it may not be sensitive to the crystal sizes and grain boundaries, as well as sample preparation conditions. For both measurements excited at 800 and 400 nm, we observed the finite offset of the transient THz signals at 100 ps, demonstrating the existence of the long-lived charge carriers. We expect that this helps to increase the power conversion efficiency (PCE) of C4-DPP-BP-based photovoltaics. Takahashi et al. already measured the photovoltaic properties of C4DPP-BP:PC61BM BHJ solar cells under AM 1.5G illumination at 100 mW/cm2. The results demonstrated that C4-DPPF

DOI: 10.1021/acs.jpcb.7b07025 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B Notes

BP:PC61BM BHJ photovoltaic cells exhibit a good performance (PCE = 5.2%) compared with BP:PC61BM BHJ ones (PCE < 0.1%).14,31 This seems to be correlated with the amount of the finite offset of the transient THz signals of the C4-DPP-BP and BP thin films.

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This research was supported by an Industry-Academia Collaborative R&D program from the Japan Science and Technology Agency. This work was partly supported by Grants-in-Aid for Scientific Research (KAKENHI) JP16H02286 and JP26105004 from the Japan Society for the Promotion of Science (JSPS).

5. CONCLUSION In this study, we measured the charge carrier dynamics of C4DPP-BP thin films at two different excitation wavelengths (800 and 400 nm) using time-resolved THz spectroscopy. We found that the transient signals in C4-DPP-BP thin films decay with time constants of 0.5 ± 0.1 and 9.1 ± 1.7 ps, with small residual components. We considered that the decaying components originate from charge carrier recombination and/or trapping at defect sites. These time scales are similar to those found in BP thin films. Charge pair annihilation may contribute to the fast decaying components in transient THz signals obtained with a high excitation fluence. With the excitation at 400 nm, we found that the transient THz signal decays with time constants of 0.4 and 7.5 ps, which are similar to those acquired with the excitation at 800 nm. We also measured the photoconductivity spectra of C4-DPPBP thin films, which can be fit by the Drude−Smith model. This means that the charge carriers are localized immediately after the photoexcitation. The product of the quantum yield of charge generation and mobility of charge carriers is on the same order of magnitude as that of pentacene films. Interestingly, with the excitation at 400 nm, this value at 0.4 ps is approximately twice that obtained at 800 nm. On the other hand, the charge carrier dynamics with the 400 nm excitation is similar to that measured with the 800 nm excitation. Recent studies suggested that photogenerated charge carriers are transported before complete thermalization occurs.40 Since the mobility of the charge carriers on early time scales is very different from that at later times, information on the charge carrier dynamics right after photoexcitation is very useful to understand the carrier extraction mechanism of the solar cells. Furthermore, we observed the finite offset of the transient THz signals at 100 ps, indicating the existence of long-lived charge carriers. These results are in contrast to those found in BP thin films. This study may help to increase the power conversion efficiency of C4-DPP-BP-based photovoltaic solar cells.

■

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.7b07025. Additional details of the experimental methods, analysis of the time profiles of the THz transient signals, excitation fluence dependence of the transient THz signal with the excitation at 800 nm, and excitation fluence dependence of the peak amplitude of transient THz signal with the excitation at 400 nm (PDF)

■

REFERENCES

(1) Brabec, C. J.; Gowrisanker, S.; Halls, J. J. M; Laird, D.; Jia, S.; Williams, S. P. Polymer-Fullerene Bulk-Heterjunction Solar Cells. Adv. Mater. 2010, 22, 3839−3856. (2) Dou, L.; You, J.; Hong, Z.; Xu, Z.; Li, G.; Street, R. A.; Yang, Y. 25th Anniversary Article: A Decade of Organic/Polymeric Photovoltaic Research. Adv. Mater. 2013, 25, 6642−6671. (3) Walker, B.; Kim, C.; Nguyen, T.-Q. Small Molecule SolutionProcessed Bulk Heterojunction Solar Cells. Chem. Mater. 2011, 23, 470−482. (4) Martinez-Diaz, M. V.; de la Torre, G.; Torres, T. Lighting Porphyrins and Phthalocyanines for Molecular Photovoltaics. Chem. Commun. 2010, 46, 7090−7108. (5) Kesters, J.; Verstappen, P.; Kelchtermans, M.; Lutsen, L.; Vanderzande, D.; Maes, W. Porphyrin-Based Bulk Heterojunction Organic Photovoltaics: The Rise of the Colors of Life. Adv. Energy Mater. 2015, 5, 1500218. (6) Li, L. L.; Diau, E. W. G. Porphyrin-Sensitized Solar Cells. Chem. Soc. Rev. 2013, 42, 291−304. (7) Milot, R. L.; Moore, G. F.; Crabtree, R. H.; Brudvig, G. W.; Schmuttenmaer, C. A. Electron Injection Dynamics from Photoexcited Porphyrin Dyes into SnO2 and TiO2 Nanoparticles. J. Phys. Chem. C 2013, 117, 21662−21670. (8) Nemec, H.; Rochford, J.; Taratula, O.; Galoppini, E.; Kuzel, P.; Polivka, T.; Yartsev, A.; Sundstrom, V. Influence of the ElectronCation Interaction on Electron Mobility in Dye-Sensitized ZnO and TiO2 Nanocrystals: A Study Using Ultrafast Terahertz Spectroscopy. Phys. Rev. Lett. 2010, 104, 197401. (9) Yamada, H.; Okujima, T.; Ono, N. Organic Semiconductors Based on Small Molecules with Thermally or Photochemically Removable Groups. Chem. Commun. 2008, 2957−2974. (10) Aramaki, S.; Sakai, Y.; Ono, N. Solution-Processible Organic Semiconductor for Transistor Applications: Tetrabenzoporphyrin. Appl. Phys. Lett. 2004, 84, 2085−2087. (11) Shea, P. B.; Kanicki, J.; Ono, N. Field-Effect Mobility of Polycrystalline Tetrabenzoporphyrin Thin-Film Transistors. J. Appl. Phys. 2005, 98, 014503. (12) Shea, P. B.; Kanicki, J.; Pattison, L. R.; Petroff, P.; Kawano, M.; Yamada, H.; Ono, N. Solution-Processed Nickel Tetrabenzoporphyrin Thin-Film Transistors. J. Appl. Phys. 2006, 100, 034502. (13) Matsuo, Y.; Sato, Y.; Niinomi, T.; Soga, I.; Tanaka, H.; Nakamura, E. Columnar Structure in Bulk Heterojunction in SolutionProcessable Three-Layered p-i-n Organic Photovoltaic Devices Using Tetrabenzoporphyrin Precursor and Silylmethyl[60]fullerene. J. Am. Chem. Soc. 2009, 131, 16048−16050. (14) Tamura, Y.; Saeki, H.; Hashizume, J.; Okazaki, Y.; Kuzuhara, D.; Suzuki, M.; Aratani, N.; Yamada, N. Direct Comparison of a Covalently-Linked Dyad and a 1:1 mixture of Tetrabenzoporphyrin and Fullerene as Organic Photovoltaic Materials. Chem. Commun. 2014, 50, 10379−10381. (15) Tamura, Y.; Kuzuhara, D.; Suzuki, M.; Hayashi, H.; Aratani, N.; Yamada, H. Fullerene-Linked Tetrabenzoporphyrins for SolutionProcessed Organic Photovoltaics: Flexible vs. Rrigid Linkers. J. Mater. Chem. A 2016, 4, 15333−15342. (16) Clarke, T. M.; Durrant, J. R. Charge Photogeneration in Organic Solar Cells. Chem. Rev. 2010, 110, 6736−6767.

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Hiroko Yamada: 0000-0002-2138-5902 Keisuke Tominaga: 0000-0002-4680-2362 G

DOI: 10.1021/acs.jpcb.7b07025 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B

with Very Low Energy Losses. J. Am. Chem. Soc. 2015, 137, 7282− 7285. (34) Liang, T.; Xiao, L.; Gao, K.; Xu, W.; Peng, X.; Cao, Y. Modifying the Chemical Structure of a Porphyrin Small Molecule with Benzothiophene Groups for the Reproducible Fabrication of High Performance Solar Cells. ACS Appl. Mater. Interfaces 2017, 9, 7131− 7138. (35) Bakulin, A. A.; Rao, A.; Pavelyev, V. G.; van Loosdrecht, P. H.; Pshenichnikov, M. S.; Niedzialek, D.; Cornil, J.; Beljonne, D.; Friend, R. H. The Role of Driving Energy and Delocalized States for Charge Separation in Organic Semiconductors. Science 2012, 335, 1340−1344. (36) Grancini, G.; Maiuri, M.; Fazzi, D.; Petrozza, A.; Egelhaaf, H. J.; Brida, D.; Cerullo, G.; Lanzani, G. Hot Exciton Dissociation in Polymer Solar Cells. Nat. Mater. 2013, 12, 29−33. (37) Jailaubekov, A. E.; Willard, A. P.; Tritsch, J. R.; Chan, W.-L.; Sai, N.; Gearba, R.; Kaake, L. G.; Williams, K. J.; Leung, K.; Rossky, P. J.; Zhu, X.-Y. Hot Charge-Transfer Excitons Set the Time Limit for Charge Separation at Donor/Acceptor Interfaces in Organic Photovoltaics. Nat. Mater. 2013, 12, 66−73. (38) Armin, A.; Zhang, Y.; Burn, P. L.; Meredith, P.; Pivrikas, A. Measuring Internal Quantum Efficiency to Demonstrate Hot Exciton Dissociation. Nat. Mater. 2013, 12, 593. (39) Vandewal, K.; Albrecht, S.; Hoke, E. T.; Graham, K. R.; Widmer, J.; Douglas, J. D.; Schubert, M.; Mateker, W. R.; Bloking, J. T.; Burkhard, G. F.; Sellinger, A.; Frechet, J. M. J.; Amassian, A.; Riede, M. K.; McGehee, M. D.; Neher, M. D.; Salleo, M. D. Efficient Charge Generation by Relaxed Charge-Transfer States at Organic Interfaces. Nat. Mater. 2014, 13, 63−68. (40) Melianas, A.; Etzold, A.; Savenije, T. J.; Laquai, F.; Inganas, O. I.; Kemerink, M. Photo-Generated Carriers Lose Energy During Extraction from Polymer-Fullerene Solar Cells. Nat. Commun. 2015, 6, 8778. (41) Nan, G.; Zhang, X.; Lu, G. Do “Hot” Charge-Transfer Excitons Promote Free Carrier Generation in Organic Photovoltaics? J. Phys. Chem. C 2015, 119, 15028−15035. (42) Nemec, H.; Nienhuys, H. K.; Zhang, F.; Inganas, O.; Yartsev, A.; Sundstrom, V. Charge Carrier Dynamics in Alternating Polyfluorene Copolymer:Fullerene Blends Probed by Terahertz Spectroscopy. J. Phys. Chem. C 2008, 112, 6558−6563. (43) Ai, X.; Beard, M. C.; Knutsen, K. P.; Shaheen, S. E.; Rumbles, G.; Ellingson, R. J. Photoinduced Charge Carrier Generation in a Poly(3-hexylthiophene) and Methanofullerene Bulk Heterojunction Investigated by Time-Resolved Terahertz Spectroscopy. J. Phys. Chem. B 2006, 110, 25462−25471. (44) Cunningham, P. D.; Hayden, L. M. Carrier Dynamics Resulting from Above and Below Gap Excitation of P3HT and P3HT/PCBM Investigated by Optical-Pump Terahertz-Probe Spectroscopy. J. Phys. Chem. C 2008, 112, 7928−7935. (45) Parkinson, P.; Lloyd-Hughes, J.; Johnston, M. B.; Herz, L. M. Efficient Generation of Charges via Below-Gap Photoexcitation of Polymer-Fullerene Blend Films Investigated by Terahertz Spectroscopy. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 78, 115321. (46) Cook, D. J.; Hochstrasser, R. M. Intense Terahertz Pulses by Four-Wave Rectification in Air. Opt. Lett. 2000, 25, 1210−1212. (47) Dai, J.; Liu, J.; Zhang, X.-C. Terahertz Wave Air Photonics: Terahertz Wave Generation and Detection with Laser-Induced Gas Plasma. IEEE J. Sel. Top. Quantum Electron. 2011, 17, 183−190. (48) Karpowicz, N.; Dai, J.; Lu, X.; Chen, Y.; Yamaguchi, M.; Zhao, H.; Zhang, X. − C.; Zhang, L.; Zhang, C.; Price-Gallagher, M.; Fletcher, C.; Mamer, O.; Lesimple, A.; Johnson, K. Coherent Heterodyne Time-Domain Spectrometry Covering the Entire “Terahertz Gap. Appl. Phys. Lett. 2008, 92, 011131. (49) Cooke, D. G.; Krebs, F. C.; Jepsen, P. U. Direct Observation of Sub-100 fs Mobile Charge Generation in a Polymer-Fullerene Film. Phys. Rev. Lett. 2012, 108, 056603. (50) Jin, Z.; Gehrig, D.; Dyer-Smith, C.; Heilweil, E. J.; Laquai, F.; Bonn, M.; Turchinovich, D. Ultrafast Terahertz Photoconductivity of Photovoltaic Polymer−Fullerene Blends: A Comparative Study

(17) Ostroverkhova, O. Organic Optoelectronic Materials: Mechanisms and Applications. Chem. Rev. 2016, 116, 13279−13412. (18) Ulbricht, R.; Hendry, E.; Shan, J.; Heinz, T. F.; Bonn, M. Carrier Dynamics in Semiconductors Studied with Time-Resolved Terahertz Spectroscopy. Rev. Mod. Phys. 2011, 83, 543−586. (19) Jepsen, P. U.; Cooke, D. G.; Koch, M. Terahertz Spectroscopy and Imaging − Modern Techniques and Applications. Laser Photon. Rev. 2011, 5, 124−166. (20) Beard, M. C.; Turner, G. M.; Schmuttenmaer. Transient Photoconductivity in GaAs as Measured by Time-Resolved Terahertz Spectroscopy. C. A. Phys. Rev. B: Condens. Matter Mater. Phys. 2000, 62, 15764−15777. (21) Hegmann, F. A.; Tykwinski, R. R.; Lui, K. P. H.; Bullock, J. E.; Anthony, J. E. Picosecond Transient Photoconductivity in Functionalized Pentacene Molecular Crystals Probed by Terahertz Pulse Spectroscopy. Phys. Rev. Lett. 2002, 89, 227403. (22) Thorsmolle, V. K.; Averitt, R. D.; Chi, X.; Hilton, D. J.; Smith, D. L.; Ramirez, A. P.; Taylor, A. J. Ultrafast Conductivity Dynamics in Pentacene Probed Using Terahertz Spectroscopy. Appl. Phys. Lett. 2004, 84, 891−893. (23) Ostroverkhova, O.; Cooke, D. G.; Shcherbyna, S.; Egerton, R. F.; Hegmann, F. A.; Tykwinski, R. R.; Anthony, J. E. Bandlike Ttransport in Pentacene and Functionalized Pentacene Thin Films Revealed by Subpicosecond Transient Photoconductivity Measurements. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 71, 035204. (24) Ostroverkhova, O.; Shcherbyna, S.; Cooke, D. G.; Egerton, R. F.; Hegmann, F. A.; Tykwinski, R. R.; Parkin, S. R.; Anthony, J. E. Optical and Transient Photoconductive Properties of Pentacene and Functionalized Pentacene Thin Films: Dependence on Film Morphology. J. Appl. Phys. 2005, 98, 033701. (25) Ostroverkhova, O.; Cooke, D. G.; Hegmann, F. A.; Anthony, J. E.; Podzorov, V.; Gershenson, M. E.; Jurchescu, O. D.; Palstra, T. T. M. Ultrafast Carrier Dynamics in Pentacene, Functionalized Pentacene, Tetracene, and Rubrene Single Crystals. Appl. Phys. Lett. 2006, 88, 162101. (26) Esenturk, O.; Melinger, J. S.; Lane, P. A.; Heilweil, E. J. Relative Photon-to-Carrier Efficiencies of Alternating Nanolayers of Zinc Phthalocyanine and C60 Films Assessed by Time-Resolved Terahertz Spectroscopy. J. Phys. Chem. C 2009, 113, 18842−18850. (27) Bartelt, A. F.; Strothkamper, C.; Schindler, W.; Fostiropoulos, K.; Eichberger, R. Morphology Effects on Charge Generation and Recombination Dynamics at ZnPc:C60 Bulk Hetero-Junctions Using Time-Resolved Terahertz Spectroscopy. Appl. Phys. Lett. 2011, 99, 143304. (28) Lane, P. A.; Cunningham, P. D.; Melinger, J. S.; Kushto, G. P.; Esenturk, O.; Heilweil, E. J. Photoexcitation Dynamics in Films of C60 and Zn Phthalocyanine with a Layered Nanostructure. Phys. Rev. Lett. 2012, 108, 077402. (29) Lane, P. A.; Cunningham, P. D.; Melinger, J. S.; Esenturk, O.; Heilweil, E. J. Hot Photocarrier Dynamics in Organic Solar Cells. Nat. Commun. 2015, 6, 7558. (30) Ohta, K.; Hiraoka, S.; Tamura, Y.; Yamada, H.; Tominaga, K. Charge-Carrier Dynamics in Benzoporphyrin Films Investigated by Time-Resolved Terahertz Spectroscopy. Appl. Phys. Lett. 2015, 107, 183302. (31) Takahashi, K.; Kumagai, D.; Yamada, N.; Kuzuhara, D.; Yamaguchi, Y.; Aratani, N.; Koganezawa, T.; Koshika, S.; Yoshimoto, N.; Masuo, S.; Suzuki, M.; Nakayama, K.; Yamada, H. Side-Chain Engineering in a Thermal Precursor Approach toward Efficient Photocurrent Generation with Insoluble Small-Molecule Photoabsorbers. J. Mater. Chem. A 2017, 5, 14003−140011. (32) Qin, H.; Li, L.; Guo, F.; Su, S.; Peng, J.; Cao, Y.; Peng, X. Solution-Processed Bulk Heterojunction Solar Cells Based on a Porphyrin Small Molecule with 7% Power Conversion Efficiency. Energy Environ. Sci. 2014, 7, 1397−1401. (33) Gao, K.; Li, L.; Lai, T.; Xiao, L.; Huang, Y.; Huang, F.; Peng, J.; Cao, Y.; Liu, F.; Russell, T. P.; Janssen, R. A.; Peng, J. Absorbing Porphyrin Small Molecule for High-Performance Organic Solar Cells H

DOI: 10.1021/acs.jpcb.7b07025 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B Correlated with Photovoltaic Device Performance. J. Phys. Chem. Lett. 2014, 5, 3662−3668. (51) Cooke, D. G.; MacDonald, A. N.; Hryciw, A.; Wang, J.; Li, Q.; Meldrum, A.; Hegmann, F. A. Transient Terahertz Conductivity in Photoexcited Silicon Nanocrystal Films. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 73, 193311. (52) Turner, G. M.; Beard, M. C.; Schmuttenmaer, C. A. Carrier Localization and Cooling in Dye-Sensitized Nanocrystalline Titanium Dioxide. J. Phys. Chem. B 2002, 106, 11716−11719. (53) Joyce, H. J.; Boland, J. L.; Davies, C. L.; Baig, S. A.; Johnston, M. B. A Review of the Electrical Properties of Semiconductor Nanowires: Insights Gained from Terahertz Conductivity Spectroscopy. Semicond. Sci. Technol. 2016, 31, 103003. (54) Smith, N. V. Classical Generalization of the Drude Formula for the Optical Conductivity. Phys. Rev. B: Condens. Matter Mater. Phys. 2001, 64, 155106. (55) Ponseca, C. S., Jr.; Yartsev, A.; Wang, E.; Andersson, M. R.; Vithanage, D.; Sundstrom, V. Ultrafast Terahertz Photoconductivity of Bulk Heterojunction Materials Reveals High Carrier Mobility up to Nanosecond Time Scale. J. Am. Chem. Soc. 2012, 134, 11836−11839.

I

DOI: 10.1021/acs.jpcb.7b07025 J. Phys. Chem. B XXXX, XXX, XXX−XXX