Dependence on Charge-Transfer Gap Energy - American Chemical

Article pubs.acs.org/JPCC

Generation and Diffusion of Photocarriers in Molecular Donor− Acceptor Systems: Dependence on Charge-Transfer Gap Energy Jun’ya Tsutsumi,*,† Hiroyuki Matsui,† Toshikazu Yamada,† Reiji Kumai,‡ and Tatsuo Hasegawa*,† †

National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Higashi, Tsukuba 305-8562, Japan Condensed Matter Research Center (CMRC) and Photon Factory, High Energy Accelerator Research Organization (KEK), Institute of Materials Structure Science, Tsukuba 305-0801, Japan

‡

S Supporting Information *

ABSTRACT: Here, we investigated photocarrier generation and diffusion characteristics in molecular-scale donor−acceptor chargetransfer (CT) systems. The photocarrier diffusion characteristics were measured on a series of mixed-stack CT compound crystals by the laser beam-induced current (LBIC) technique where the photocurrent is detected on the crystal surfaces as a function of either the laser illuminated position or the laser-modulation frequency. In the compounds with CT gap energy larger than 0.7 eV, the diffusion length of photocarriers reached larger than 10 μm. The dependence of diffusion length on the electric field and the laser-modulated frequency clearly indicates the direct generation of long-lived photocarriers without forming exciton. In contrast, the photocarrier diffusion was suppressed, and the diffusion length got smaller than 2 μm in the compounds with a gap energy smaller than 0.7 eV. We discuss that the electron−hole recombination becomes dominated when the CT gap energy is as small as the molecular reorganization energy. The results suggest that proper choice of donor−acceptor combination should promote efficient charge separation in organic photovoltaic cells (OPCs).

1. INTRODUCTION Efficient photogeneration of charge carriers in molecular semiconductors has long been the most fundamental issue in the field of organic semiconductors. This subject is receiving growing research attention worldwide as it is associated with recent major developments in the OPCs.1−4 Studies over the past decade have revealed that photocarrier generation in the OPCs can be understood in terms of the following three elementary steps: exciton generation, exciton diffusion, and charge carrier separation.5 It is believed that the first two steps usually occur inside either the donor or acceptor semiconductor layers, whereas the third one occurs efficiently at donor−acceptor hetero interfaces.6,7 These features can be ascribed to the fairly strong excitonic effects characteristic of both small-molecule and polymeric organic semiconductors. Recently, development of highly efficient OPCs with conversion efficiency close to 8% has been successfully achieved by utilizing donor−acceptor-type copolymers composed of alternating donor and acceptor units within the polymer backbones.1,8−12 In the materials, active photon energy range for the OPC operation extends to near-infrared range indicating that the donor−acceptor CT excitation should contribute to the eventual photocarrier generation. However, it is not clear if the electron−hole binding nature in the CT excitons is comparable to that in the Frenkel excitons and also if the excitonic nature is responsible for the efficient photocarrier generations in the OPCs. Nonetheless, further studies on the photocarrier generation mechanism are quite difficult as they © 2012 American Chemical Society

are hindered by the highly disordered structure of the donor− acceptor-type copolymers as associated with the formation of bulk heterojunctions (BHJs). It is known that a series of molecular donor−acceptor CT compounds have molecular scale order of donors and acceptors,13−15 which can be regarded as an model system to study the CT excitation. We have recently succeeded in applying the LBIC technique to analyze the exciton and photocarrier diffusion in CT compound single crystals of dibenzotetrathiafulvalene-7,7,8,8-tetracyanoquinodimethane (DBTTF-TCNQ).16 A finely focused laser beam is directed at a crystal surface, and the generated photocurrent is detected as a function of distance between the position of laser illumination and the semiconductor/electrode interface.17 The spatial decay profile of the photocurrent makes it possible to analyze exciton and photocarrier diffusion. More importantly, it is possible to estimate the diffusion length of excitons and photocarriers directly without assuming any other parameters such as lifetime or mobility, in sharp contrast to the other techniques such as transient absorption,18 impedance spectroscopy,19,20 or photoinduced charge carrier extraction by linearly increasing voltage (photo-CELIV) measurements.21−23 From the LBIC measurements, the diffusion length of CT exciton was estimated at less than 2 μm under low energy excitation (hν = 0.9 eV) just above Received: September 3, 2012 Revised: October 9, 2012 Published: October 16, 2012 23957

dx.doi.org/10.1021/jp308720d | J. Phys. Chem. C 2012, 116, 23957−23964

The Journal of Physical Chemistry C

Article

dimethane (perylene-F4TCNQ), 2-chloro-5-methyl-p-phenylenediamine−2,5-diethyl-7,7,8,8-tetracyanoquinodimethane (ClMePD-Et2TCNQ), 3,3′,5,5′-tetramethylbenzidine−7,7,8,8tetracyanoquinodimethnae (TMB-TCNQ), and tetrathiafulvalene−p-chloranil (TTF-CA). We found that the PVT technique provides thin platelet single crystals with fairly flat surfaces, the quality of which is higher than the conventional cosublimation method.26,27 The crystal structures of perylene-F4TCNQ and TMBTCNQ were examined by synchrotron radiated X-ray diffraction measurement conducted at the BL-8B line of the KEK (High Energy Accelerator Research Organization) Photon Factory.28 The X-rays that we used had energy of 18 keV (wavelength = 0.6885 Å). The monochromated beam was focused at the sample position with beam size of 300 × 300 μm2. The Bragg reflections were detected by a cylindrical imaging-plate diffractometer (Rigaku). For the rate analysis of photocarrier generation and recombination, we calculated intermolecular transfer integrals and reorganization energies for the series of the CT compounds. The intermolecular transfer integrals were calculated by using the extended Hückel model29 on the basis of the crystal structures determined by the X-ray diffraction analysis. We used the crystal structure data reported in the literature for DBTTF-TCNQ,30 PTZ-TCNQ,31 TTF-CA,32 and ClMePD-Et2TCNQ.33 The positions of hydrogen atoms were optimized by molecular orbital calculation (GAUSSIAN 09)34 with the basis set of 6-31G(d) at B3LYP level. The reorganization energies were calculated by the ΔSCF method35 with the basis set of 6-31G(d) at ROB3LYP level. The diffusion characteristics of excitons and photocarriers were examined using the high-spatial-resolution LBIC technique. Figure 2 shows schematic of the device structure

the energy gap (EG = 0.8 eV), which is consistent with exciton diffusion length (∼10 nm) reported for conventional organic semiconductors.24 In contrast, the diffusion length becomes extremely long (20 μm) under high energy excitation (hν ≥ 1.3 eV), which implies that long-lived charge carriers are directly generated by high energy excitation. Such a peculiar feature cannot be found in the case of single component organic semiconductors16 and may be therefore associated with the CT excitation between donors and acceptors in the compounds. In the present article, we report the dependence of photocarrier generation and diffusion characteristics on donor−acceptor combination in single crystals of a series of mixed-stack CT compounds. The study was conducted by the LBIC measurements that include the dependence on applied electric field, laser-modulation frequency, and temperature under high energy excitation. The donor−acceptor combinations were chosen so as to make the CT gap energies from 0.5 to 1.1 eV, and we found a systematic change of the photocarrier generation and diffusion characteristics on the CT gap energy. The compounds with the CT gap energy larger than 0.7 eV exhibited the direct generation and diffusion of long-lived photocarriers, whereas the photocarrier diffusion was suppressed in the compounds with the gap energy smaller than 0.7 eV. We discuss that the photocarrier diffusion is suppressed by electron−hole recombination when the CT gap energy becomes comparable to the molecular reorganization energy. The results suggest that optimum CT gap energy should be present to achieve both efficient electron−hole separation and wide active photon energy range in the OPCs.

2. EXPERIMENTAL SECTION We used the physical vapor-transport (PVT) technique25 under N2 gas flow of 20 mL min−1 at atmospheric pressure to obtain single crystals of CT compounds (Figure 1); dibenzotetrathiafulvalene-7,7,8,8-tetracyanoquinodimethane (DBTTF-TCNQ), phenothiazine−7,7,8,8-tetracyanoquinodimethane (PTZTCNQ), perylene−2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquino-

Figure 2. Schematic of device structure and instrumental setup for LBIC measurements. The abbreviations ND, BE, CL, HM, OL, CS, MS, and CCD correspond to neutral density filter, beam expander, cylindrical lens, half mirror, objective lens, cryostat, motor-driven stage, and CCD camera, respectively.

and the instrument setup for LBIC. We used gold or organic conductors such as DBTTF-F4TCNQ to fabricate a pair of electrodes on the top of the crystal surface at an interelectrode distance of 200−400 μm. For the fabrication of gold electrodes, we used gold paste to prevent thermal damage to the crystal surface. Organic conductors were thermally evaporated under vacuum at around 460 K.36 We used three kinds of cw laser sources for the LBIC measurements.37 The laser light intensity was chopped or modulated by a function generator. The laser beam passed through a cylindrical lens to form a line and was focused on top of the sample crystal by an objective lens close to the diffraction limit. The size of the focused laser beam was about 2 × 30 μm2, estimated using a stripe pattern of aluminum

Figure 1. Molecular structures of CT compounds. 23958



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Figure 3. Crystal structures of CT compounds. The molecules indicated by orange and blue colors correspond to donor and acceptor, respectively. Intermolecular transfer integrals, t, are also shown; tDA between HOMO of donor and LUMO of acceptor, tAA between LUMO of acceptors, and tDD between HOMO of donors.

film on a glass substrate. The laser-illuminated position on the sample surface was scanned along the crystal long axis, that is the stacking axis of donors and acceptors, using a motor-driven stage. The short-circuit photocurrent was amplified and detected as a function of the illuminated position by a combination of a high-speed current preamplifier (FEMTO DHPCA-100) and a lock-in amplifier (NF LI5640). The typical light intensity was 100 mW cm−2, and the scan speed was 10 μm min−1. We also conducted frequency-modulated LBIC measurement while fixing the illuminated position at 10 μm distant from the electrode where the in-phase and out-of-phase photocurrents were detected as a function of the lasermodulation frequency. The photoconduction spectra were measured under applied electric field (0.1−1 kV cm−1) by using a combined grating monochromator and Cassegrain-type microscope. In the measurement of photoconduction spectra the light was illuminated at limited sample surface area between the electrodes (the device structure shown in Figure 2), which enabled us to observe intrinsic photoconduction of the sample materials without the effects of charge separation at metal/ semiconductor interfaces. All the measurements were conducted in an inert N2 atmosphere using an optical microscopy cryostat.

spectra. In part a of Figure 4, the obtained values are plotted as a function of the difference between the oxidation potential of donors and the reduction potential of acceptors, EDox − EAred. As seen, a linear correlation has been obtained between EDox − EAred and the estimated values. We note that the CT absorption peak energy is not linearly correlated with the EDox − EAred, due to the broad feature of the CT absorption. The CT gap energy for TMB-TCNQ was not plotted in part a of Figure 4 due to the low photocurrent signal. We can roughly estimated the gap energy at about 0.6 eV from the extrapolation of (EDox − EAred) value of TMB-TCNQ. 3.2. Photocarrier Diffusion Characteristics by the LBIC Technique. Figure 5 shows the LBIC profiles measured for the single crystals of the CT compounds with a pair of gold electrodes. In the figure, the origin of the abscissa is set at the semiconductor/electrode interface on the left, and only the data at the left electrode side were displayed. The excitation energy (hν = 1.9 or 2.4 eV) was chosen to be large enough to create photocarriers in the compounds. The laser modulation frequency was set at 25 Hz where no phase delay was detected in the photocurrent. As can be seen, the LBIC profiles exhibit maxima on illumination at around the semiconductor/electrode interface and slow decay in the semiconductor region. The decay length is longer than 10 μm in the upper three compounds, whereas the decay length becomes shorter than the spatial resolution limit of the measurement (∼2 μm) in the lower three compounds. The decay length in the former is sufficiently larger than the spatial resolution limit of the measurement (∼2 μm) indicating that the observed decay originates from diffusion of photogenerated exciton or charge carriers. Because the exciton diffusion length is usually quite small, for example, a few tens of nanometers,24 the photocarrier

3. RESULTS AND DISCUSSION 3.1. Fundamental Photoconductive Properties of Donor−Acceptor Systems. Six kinds of the CT compounds used in this study have similar crystal structure where donors and acceptors align alternately along the stacking axes as presented in Figure 3. The photoconduction spectra of the compounds are shown in part c of Figure 4. The CT gap energies were estimated from the onset of the photoconduction 23959



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Figure 6. LBIC curves measured under various electric fields on DBTTF-TCNQ single crystals. The results are shown for both electron diffusion (gold electrodes) and hole diffusion (DBTTFF4TCNQ electrodes). The black lines are measured data, and the red lines are fitting curves based on the 1D diffusion model. The insert shows the diffusion length (L) obtained by the fitting which are plotted as a function of applied electric field (E). The open and the filled circles respectively correspond to the diffusion length estimated at the left and the right electrode sides. The solid lines are fitting curves based on the 1D diffusion model.

Figure 4. (a) CT gap energies (EG) of the CT compounds plotted as a function of difference between oxidation potential of donor (EDox) and reduction potential of acceptor (EAred). The filled circles correspond to the CT gap energies obtained from the onset of photoconduction spectra, whereas the open circles correspond to the gap energies obtained from CT absorption peak. (b) Photocurrent decay lengths (L) in the LBIC profiles plotted as a function of (EDox − EAred) [Figure 5]. (c) Photoconduction spectra measured for the CT compound crystals; a = ClMePD-Et2TCNQ, b = TTF-CA, c = DBTTF-TCNQ, d = PTZ-TCNQ, and e = perylene-F4TCNQ. External quantum efficiency (EQE) is plotted as a function of excitation photon energy.

for the crystal with a pair of DBTTF-F4TCNQ electrodes. In both cases, the electric field was applied so that the electrode on the right side was negatively charged with respect to the left side one. As can be seen, the photocurrent exhibits maxima on illumination at around both the left- and right-hand semiconductor/electrode interfaces. The sign of the photocurrent depended on the type of electrode material. The different signs can be ascribed to electron or hole ejection through the semiconductor/electrode interfaces. The sample with the gold electrodes exhibited negative photocurrent at the left-hand interface and positive photocurrent at the right-hand interface. This corresponds to efficient electron conduction from semiconductor to electrode at both electrodes, indicating that the electrode Fermi level matches the semiconductor conduction band. In contrast, photocurrent of opposite sign was observed for the sample with the DBTTF-F4TCNQ electrodes. This suggests efficient hole conduction, indicating that the electrode Fermi energy matches the semiconductor valence band. These results are consistent with n-type operation observed in DBTTF-TCNQ-based field-effect transistors with gold source and drain electrodes in contrast to p-type operation in the case of DBTTF-F4TCNQ.27,36 The LBIC profiles also exhibit strong dependence of the decay length on the applied electric field. This dependence clearly demonstrates the photocarrier diffusion in the compound instead of the exciton diffusion. For electron diffusion (with the gold electrodes), the photocurrent decay length increases on the left side by applying an electric field, while it decreases on the right side. This dependence reverses for hole diffusion (with the DBTTF-F4TCNQ electrodes). The opposite dependence for electrons and holes provides unambiguous evidence of the drift motion of photogenerated charge carriers in the crystals. Figure 7 shows LBIC profiles measured at various temperatures for the DBTTF-TCNQ single crystal with a pair of gold electrodes. The measurements were conducted at excitation

Figure 5. LBIC profiles measured for six kinds of CT compounds. Only the data measured at the left electrode side are shown.

diffusion is likely cause of the observed slow decay. When the decay lengths are plotted with respect to EDox − EAred (part b of Figure 4), it was found that the decay length decreases drastically at EDox − EAred < 0.3 V (i.e., EG < 0.7 eV). This result indicates that the excited species generated in the small CT gap compounds should have much smaller lifetimes or diffusion coefficients than those in the large CT gap compounds. To confirm the photocarrier diffusion in the large CT gap compounds, we examined dependence of the LBIC profile on the electrode material and the applied electric field. Figure 6 shows the LBIC profiles under various electric fields obtained for the DBTTF-TCNQ single crystals where the He−Ne laser (hν = 2.0 eV) was used as an excitation source. The results were obtained for the crystal with a pair of gold electrodes and 23960



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be derived from eq 2 as a function of the carrier concentration at the electrode position (x = l): J∝D

energy of hν = 1.9 eV. As seen, the LBIC profile exhibits a slower decay curve at lower temperatures, indicating that the diffusion length of electron increases with the decrease of temperature. This feature appears to be due to increased charge carrier mobility at low temperatures reported in the field-effect measurements.38 3.3. Analyses Using a 1D Diffusion Model. Here, we discuss the diffusion characteristics of photocarriers on the basis of the spatial decay profiles in the LBIC. First we consider a 1D diffusion model to simulate the LBIC profiles. Assuming that photocarriers are generated steadily at the laser-illuminated position (x = 0), the continuity equation can be written as39 ∂n n ∂ 2n ∂n = Iδ(x) − + D 2 + μE (1) ∂t τ ∂x ∂x where E is electric field, and n, I, τ, D, and μ are respectively carrier concentration, generation rate, lifetime, diffusion coefficient, and drift mobility. The third and the fourth terms on the right-hand side correspond respectively to diffusion and drift terms. Under a steady-state condition (∂n/∂t = 0) the solution of eq 1 can be derived as

IL02 D

Ld2

+

4L02

⎛ |x | ⎞ exp⎜ − ⎟ ⎝ L⎠

= x=l

⎛ l ⎞ I exp⎜ − ⎟ 2 ⎝ L0 ⎠

(4)

Convoluting the laser spot width to eq 4, the actual results of LBIC measurements can be reproduced as shown by the red line in Figure 6. As a result of fitting, the diffusion lengths under no electric field were estimated to be about 20 μm for the electron diffusion (with the gold electrodes) and 15 μm for the hole diffusion (with the DBTTF-F4TCNQ electrodes). The field dependence of diffusion length is summarized in the inserts of Figure 6. The dependence is roughly reproduced by eq 3, which supports direct photocarrier generation in the DBTTF-TCNQ crystal. The field dependence of electron diffusion is much greater than that of hole diffusion, implying that electron mobility is greater than hole mobility in the crystal. This is consistent with the results of field effect measurements,36 whereas it is contradict to the theoretical calculation.13 We consider that the actual mobility should be affected by a variety of extrinsic carrier traps. 3.4. Frequency Dependent LBIC: Extraction of Diffusion Kinetics. The measurements described in the former sections were carried out at low modulation frequency of 25 Hz, at which the spatial distribution of photocarriers reaches a state of equilibrium due to the balance between photocarrier generation and quenching. In contrast, when the modulation frequency is increased, phase delay of the photocurrent was observed, indicating that the photocarrier distribution is no longer in a state of equilibrium, and that the observed phase delay is ascribable to the finite lifetime and diffusion coefficient of photocarriers. To examine such phase delay, we carried out frequency-dependent LBIC measurements in which the position of laser illumination was fixed at a distance of 10 μm from the semiconductor/electrode interface. The results obtained for the DBTTF-TCNQ single crystals at excitation of hν = 1.9 eV are shown in Figure 8. As seen, both electron and hole diffusion exhibited similar photocurrent relaxation in the high-frequency range: The in-phase photocurrent component falls close to zero, accompanied by a variation in the out-of-phase component. This frequency dependence can be understood in terms of the 1D diffusion

Figure 7. (a) Temperature dependence of LBIC curves measured for the DBTTF-TCNQ single crystal with a pair of gold electrodes. The ordinate is photocurrent normalized by the maximum peak intensity at the semiconductor/electrode interface. The black lines are measured data, and the red lines are fitting curves based on the 1D diffusion model. Only the data measured at the left electrode side are shown. (b) Diffusion length (L) obtained from the LBIC curves plotted as a function of temperature (T).

n=

∂n ∂x

(2)

where L0 is diffusion length under zero-electric field condition expressed by Dτ , and Ld is drift length expressed by μEτ. L denotes the field-dependent diffusion length expressed as L=

L02 +

⎛ Ld ⎞2 Ld ⎜ ⎟ ± ⎝2⎠ 2

(3) Figure 8. Results of frequency-dependent photocurrent measurement at various light intensities for the DBTTF-TCNQ single crystal. Results are shown for both electron diffusion and hole diffusion. The open and the filled circles respectively correspond to in-phase and outof-phase photocurrent. The solid lines are fitting curves based on the 1D diffusion model.

Note that L becomes L0 under zero electric field condition. Eq 2 indicates that the carrier concentration decays exponentially with increasing distance from the position of laser illumination (x = 0). When the electrode is added to the model mentioned above, the current flow J under zero electric field condition can 23961



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model expressed by eq 1 whose photocarrier generation rate I is substituted by I = I0exp(2πif t), where I0, f, and t are respectively the amplitude of photocarrier generation rate, the lasermodulation frequency, and time. The current flow J under zero electric field condition can be derived as a function of the photocarrier concentration at the electrode position (x = l) as J∝D

∂n ∂x

= x=l

I0 ⎛ 1 + 2πifτ ⎞ exp⎜ − l⎟ 2 Dτ ⎝ ⎠

(5)

Using eq 5 allows the frequency dependence of the photocurrent to be fitted fairly well, as shown by the solid curves in Figure 8. For fitting, l was fixed at 10 μm, and I0, D, and τ were used as fitting parameters, delivering diffusion coefficients of 0.02 cm2 s−1 for electrons and 0.01 cm2 s−1 for holes, and lifetimes of 160 μs for electrons and 110 μs for holes. Using the Einstein’s relationship, D = μkBT/e, gives electron mobility of about 1 cm2 V−1 s−1, which is closely consistent with that obtained using field-effect characteristics.27 As illustrated in Figure 8, no difference was observed in the relaxation curves at excitation light intensity of 90−770 mW cm−2, which indicates that the lifetimes are roughly independent of photocarrier concentration. This characteristic implies that the lifetimes are limited by deep trapping rather than bimolecular recombination. It should be noted that the obtained lifetimes were 100 times larger than that of a rubrene single crystal measured by transient absorption technique.40 This may be originated from lack of bimolecular recombination in the case of LBIC measurements because the excitation light intensity of the LBIC measurements is 105 times lower than that of the transient absorption measurement. Low trap density in the high quality DBTTF-TCNQ single crystal could also cause the long photocarrier lifetime. 3.5. Dependence of Carrier Generation Efficiency on Charge-Transfer Gap. In the former sections, it was clarified that the long-lived photocarriers are directly generated in the large CT gap compounds and exhibit long diffusion length larger than 10 μm. In contrast, the decay length of the LBIC profile is quite short in the small CT gap compounds as shown in part a of Figure 9. This indicates that long-lived photocarriers are generated only in the large gap compounds. The photocarrier generation in donor−acceptor systems is often considered by a model of competing charge-transfer processes.41−46 The photoexcitation can undergo a charge transfer between the donor and acceptor molecules, thereby forming a geminate electron−hole pair. The Coulombically bound electron−hole pair can either dissociate into free charge carriers or recombine. The latter two processes are competing each other, where efficient photocarrier generation is expected if the dissociation rate is enough larger than the recombination rate. It is known that the CT rate constant can be estimated in the framework of the Marcus theory, which is widely used for transport calculation under hopping transport approximation.35,47,48 Here, we consider three CT processes shown in the insert of part b of Figure 9; charge recombination (D+ + A− → D + A), electron transfer (A− + A → A + A−), and hole transfer (D+ + D → D + D+). In this model, efficient photocarrier generation is expected if the rate constants of electron and hole transfer are larger than that of charge recombination. On the basis of the Marcus theory, the rate constant of charge recombination is expressed as

Figure 9. (a) Diffusion lengths (L) of the CT compounds plotted as a function of their CT gap energy (EG). (b) Rate constants plotted as a function of the CT gap energy. The filled circles correspond to the rate constants of charge recombination (kr), whereas the open circles are average rate constants between electron transfer (ket) and hole transfer (kht). The solid line is a simulation curve calculated by eq 6 assuming tDA = 140 meV and λr = 0.25 eV. The insert illustrates the schematic of charge recombination (D+ + A− → D + A), electron transfer (A− + A → A + A−), and hole transfer (D+ + D → D + D+) in the CT compound crystal. The molecules indicated by orange and blue colors correspond to donor (D) and acceptor (A), respectively.

kr =

4π 2 h

⎛ (λ − E )2 ⎞ G ⎟ exp⎜ − r 4λrkBT ⎠ 4πλrkBT ⎝ 2 t DA

(6)

where tDA is the intermolecular transfer integral between HOMO of donor and LUMO of acceptor. λr is the reorganization energy associated with the charge recombination reaction and is given by λr = λD+→D+λA−→A where λD+→D and λA−→A are the geometry relaxation energies occurring upon vertical transition from the charged state to the neutral state.43 The rate constant of electron transfer is expressed as ket =

4π 2 h

⎛ λ ⎞ exp⎜ − et ⎟ ⎝ 4kBT ⎠ 4πλetkBT 2 t AA

(7)

where tAA is the intermolecular transfer integral among LUMO of acceptors. λet is the reorganization energy associated with the electron transfer reaction and is given by λet = λA−→A + λA→A−. kht is derived from eq 7 by replacing tAA and λet by tDD and λht, respectively. Table 1 shows the transfer integrals calculated by the extended Hückel model29 and the reorganization energies calculated by the ΔSCF method.35 From the obtained transfer integrals and reorganization energies, kr, ket, and kht were calculated by using eq 6 and eq 7. It should be noted that the largest values of tDA, tDD, and tAA in each compound crystal were used for the calculation because they should give the most effective pass of carrier transport. The results are shown in part b of Figure 9. As seen, kr becomes smaller in large CT gap materials. This feature originates from the exponential dependence of kr on the energy balance between λr and EG as indicated in eq 6: λr is almost constant (0.3 eV) for all the compounds, so that increase of EG above 0.3 eV leads decrease of kr. On the other hand, ket and kht are almost constant with respect to EG, which originates from independence of them on EG as indicated by eq 7. Comparing the magnitude of kr with ket and kht, it is found that kr becomes smaller than ket and kht at EG > 0.7 eV. This result clearly indicates that photocarrier generation preferentially occurs in the large CT gap 23962



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demonstrated that the photocarriers are directly generated in the compounds and exhibit long diffusion lengths more than 10 μm. The readiness to undergo charge carrier separation is in sharp contrast to the strong excitonic effects as is observed in conventional single-component organic semiconductors. It implies that the CT excitation is essential for efficient photocarrier generation. The lifetimes and the diffusion coefficients of photocarriers were respectively estimated at >100 μs and ≥0.01 cm2 s−1 by the frequency dependent photocurrent measurements. In contrast, the diffusion lengths shorter than 2 μm were observed for the compounds with the CT gap energy smaller than 0.7 eV. The dependence of diffusion length on the CT gap energy was interpreted in the framework of the Marcus theory: When the gap energy becomes small and comparable to the molecular reorganization energy, carrier recombination is promoted, resulting in short diffusion length. These results indicate presence of optimum CT gap energy, which allows both efficient charge separation and wide active photon energy range of photovoltaic effect.

Table 1. Intermolecular Transfer Integrals in Each CT Compound Crystal; tDA between HOMO of Donor and LUMO of Acceptor, tAA between LUMO of Acceptors, and tDD between HOMO of Donors; Reorganization Energies Associated with Charge Recombination (λr), Electron Transfer (λet), and Hole Transfer (λht) Are Also Shown; the Shown Transfer Integrals Are the Largest Ones in Each Compound Crystal (See Also Table 2 and Figure 3) tDA/ meV

compound ClMePDEt2TCNQ TMB-TCNQ TTF-CA DBTTF-TCNQ PTZ-TCNQ PeryleneF4TCNQ

tAA/ meV

tDD/meV

λr/eV

λet/ eV

λht/ eV

153.11

8.69

−0.03

0.48

0.27

0.89

191.06 130.13 85.50 129.76 179.63

0.00 −3.98 −1.06 −2.72 1.04

3.91 3.92 −6.55 1.78 −22.84

0.39 0.40 0.25 0.29 0.19

0.25 0.51 0.25 0.25 0.25

0.61 0.28 0.25 0.52 0.14

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compounds because the charge-separation probability should increases rapidly as the charge recombination rate becomes smaller than the electron and hole transfer rates.

ASSOCIATED CONTENT

* Supporting Information S

Crystal structure data of perylene-F4TCNQ and TMB-TCNQ with cif file format. This material is available free of charge via the Internet at http://pubs.acs.org.

4. CONCLUSIONS The elementary photocarrier generation by the CT excitation was investigated in terms of the CT gap energy in single crystals of a series of mixed-stack CT compounds. The LBIC measurements was used to examine the photocarrier generation and diffusion characteristics by detecting photocurrent on the crystal surfaces as a function of the laser illuminated position or the laser-modulation frequency. In the CT compounds with the CT gap energy larger than 0.7 eV, the dependence of decay length of the LBIC profile on applied electric field clearly

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (J.T.), [email protected]. jp (T.H.). Notes

The authors declare no competing financial interest.

Table 2. Symmetry-Equivalent Positions of a Pair of Molecules Which Give tDA, tAA, and tDD Shown in Table 1; Characters in Parentheses Specify the Molecular Type (D, Donor; A, Acceptor) Followed by Its Symmetry Equivalent Position symmetry-equivalent position compound

transfer integral

ClMePD-Et2TCNQ

tDA tDD tAA tDA

TMB-TCNQ

molecule 1

tDD tAA TTF-CA

DBTTF-TCNQ

PTZ-TCNQ

perylene-F4TCNQ

molecule 2

(D) x, y, z x, y, z x, y, z (D) x, −y, z −x, y, −z x, y, z −x, −y, −z x−1, y, z −x, −y, −z (D) x, y, z x, y, z x, y, z (D) x, y, z x, y, z x, y, z (D) x, y, z x, y, z x, y, z (D) −x + 1,−y + 1, −z + 1

tDA tDD tAA tDA tDD tAA tDA tDD tAA tDA

−x + 1, −y + 1, −z + 1 −x + 1, −y + 1, −z + 1 x, y, z − 1

tDD tAA

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(A) x + 1, y, z x − 1, y, z + 1 x, y − 1, z + 1 (A) x − 1, −y, z −x, y, −z x + 0.5, −y + 0.5, z + 0.5 −x + 0.5, y + 0.5, −z + 0.5 x − 1, y, z + 1 −x, −y, −z + 1 (A) x, y, z x, y + 1, z x, y + 1, z (A) x, y, z x, y, z + 1 x, y + 1, z (A) x, y, z x, y + 1, z x, y + 1, z (A) −x + 1, −y + 1, −z + 1 x, y, z − 1 −x + 2, −y + 1, −z + 1 −x + 2, −y + 1, −z + 1 x + 1, y, z − 1



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ACKNOWLEDGMENTS The synchrotron X-ray study was performed with the approval of the Photon Factory Program Advisory Committee (no. 2009S2-003). This work was supported by the New Energy and Industrial Technology Development Organization (NEDO) through its Innovative Solar Cell Program and by the Japan Society for the Promotion of Science (JSPS) through its Funding Program for World-Leading Innovative R&D on Science and Technology (the FIRST Program) and KAKENHI for Young Scientists (B) (24750190).

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