Modulated Photocurrent Spectroscopy for Determination of Electron and Hole Mobilities in Working Organic Solar Cells

Carrier drift mobility is an important physical constant in the charge transport process of organic solar cells (OSCs). Although time-of-flight and space-charge-limited current techniques have been frequently utilized for mobility measurements, the validity of a new method using modulation photocurrent spectroscopy is discussed in this contribution. The advantages of this method are its applicability to working OSCs with optimized device structures and the simultaneous determination of the electron and hole mobilities. These features make it possible to study the relation between the mobility balance and the solar cell characteristics, such as the power conversion efficiency, using only a single working OSC; hence, it is not necessary to fabricate electron-only and hole-only devices for mobility measurements. After carrying out numerical simulations to examine the validity of this method for mobility determination, the dependence of the mobility balance on the mixing ratio of the electron-donor and –acceptor materials is presented.

can be carried out with a relatively simple experimental setup consisting of a sinusoidally modulated light source and a lock-in amplifier (see Fig. 1) 29 . The MPC technique was originally developed in 1950's as a method to study localized-state distributions in amorphous inorganic [30][31][32][33][34][35] and organic 36 semiconductors, and has been recently applied to BHJ OSCs to investigate charge transport processes such as interface recombination and charge lifetime [37][38][39][40][41][42] . As shown below, the MPC technique can also measure the time period from the photocarrier generation to their arrival to either electrode. However, there is no report that the mobility in organic semiconductors can be determined from the time period (referred to as the transit time hereafter) that is measured with the MPC technique. In this report, we first show the numerical simulations that were carried out to clarify the relation between the transit time and the mobility in the dispersive and non-dispersive conduction modes. The results demonstrate an additional advantage of MPC with respect to the TOF technique, that is, a single analytical method can be used to determine the mobility regardless of the conduction mode. We also present the experimental results from BHJ OSCs based on poly(3-hexylthiopehene-2,5-diyl) (P3HT) and [6,6]-phenyl-C 61 -butyric acid methyl ester (PCBM) including the correlation between the measured mobilities and PCE.

Results
numerical simulations of Mpc measurements. In organic semiconductors, charge transport processes are significantly influenced by localized states. This is evidenced by the dispersive photocurrent transients recorded in TOF measurements [43][44][45] . Such photocurrent transients are simulated by solving the continuity equation considering localized states with an exponential distribution 46,47 . Also, results of the MPC measurements, e.g., the modulation frequency dependence of the photocurrent, can be simulated by the same equations under small-signal sinusoidal photoexcitation 35,48,49 . For the details of the simulations, see the Supplementary Information. An example of the simulated results is shown in Fig. 2(a). In modulation spectroscopy, not only the amplitude of the photocurrent (J) but also its phase delay are important. One way to properly express the modulation frequency (f) dependence of the amplitude and the phase delay is to plot in-phase and out-of-phase components of J as a function of f. The in-phase and out-of-phase components are also referred to as the real and imaginary parts of J, or simply Re[J] and Im[J], respectively. The simple Debye dielectric function tells us that the out-of-phase component has its peak at the frequency (f peak ) that is related to the characteristic relaxation time of a medium 50 . This relaxation time corresponds to the transit time (τ t ) of the photocarriers for BHJ OPVs under a short circuit condition. As shown in the Supplementary Information, τ t is related to f peak as t peak under the assumption that the photocarriers are uniformly excited throughout the BHJ layer. From this assumption, the drift mobility μ is given by t where F is the applied electric field and L is the thickness of the BHJ layer. Throughout this work, we determine τ t and μ with Eqs. (1) and (2). In Fig. 2(b), we also show the transient J simulated with the same set of the physical constants, and the transit time is measured from the time where the slope of the transient J in a double logarithmic plot changes. This way to measure the transit time is frequently used for an analysis of the dispersive transients 43,46,51,52 . We carried out the simulations for a room temperature (T = 300 K) with several characteristic temperatures (T 0 's) of the exponential distribution of the localized states and compared the determined mobilities [see Fig. 2  www.nature.com/scientificreports www.nature.com/scientificreports/ experimental measurements. P3HT and PCBM blends are one of the combinations of the donor and acceptor materials that have been extensively investigated for OSC applications. The electron and hole field-effect mobilities of this combination have been reported to depend on the mixing ratio 13, 14,16 . Solar cell characteristics of the fabricated devices based on this combination are summarized in Table 1 and their current density-voltage characteristics are shown in Fig. S2 in the Supplementary Information. Among the fabricated devices, the best PCE of 3.5% was obtained for the P3HT concentration of 60 wt% and L = 200 ± 10 nm. When the P3HT concentration differs from the optimum value, the fill factor (FF) and the PCE degrade.
We applied the MPC technique to such devices under various bias conditions. The resultant −Im[J]-f characteristics of OSCs with the P3HT concentrations of 50, 60 (the optimum), and 70 wt% are shown in Fig. 3(a-c), respectively. While two peaks are clearly seen in Fig. 3(c), only one peak is observed in Fig. 3(b). In Fig. 3(a), the www.nature.com/scientificreports www.nature.com/scientificreports/ second peak can be found around 300 kHz as a small shoulder. These peaks can be attributed to the transit times of the photocarriers because the peaks shift to the higher frequency side as the applied reverse bias increases and also as L is reduced. The fact that the photocurrent signals are remarkably suppressed at the P3HT concentration of 100 wt% (not shown here) indicates that the peaks observed in Fig. 3(a-c) are due to the photocarriers that are generated at the interface between P3HT and PCBM. In Fig. 3(d), we plot the reciprocal of the transit times obtained from Fig. 3(c) as a function of the effective bias, which is the difference between the applied voltage V and the built-in potential V bi . As expected from Eq. (2), both the shorter and longer transit times are directly proportional to the effective bias. From the slopes, the two mobilities are determined to be 5.7 × 10 −4 and 2.5 × 10 −5 cm 2 V −1 s −1 . All the mobilities determined in this work are summarized in Fig. 4, in which higher and lower mobilities seem to be switched at the 60 wt% P3HT concentration. In a BHJ layer with a low P3HT (PCBM) concentration, insufficient permeation networks for hole (electron) transport are formed and thus result in the degradation of the hole (electron) drift mobility 11,12 . Therefore, the lower and higher mobilities at lower P3HT concentrations can be attributed to holes and electrons, respectively. The highest hole and electron drift mobilities determined are in good agreement with the reported values for P3HT and PCBM neat thin films, respectively, measured with TOF or SCLC techniques 8,14,16,[53][54][55] . From Fig. 4, it is also found that the electron and hole mobilities are well balanced at the optimum (60 wt%) P3HT concentration, where the best PCE is realized. It should be noted that the PCE is dependent not only on the mobility balance but also on other factors, e.g., the absorption spectrum. It is thus expected that the FF has a more straightforward relation with the mobility balance than     www.nature.com/scientificreports www.nature.com/scientificreports/ the PCE. Such a correlation between the FF and the mobility balance is indeed observed experimentally 21,[24][25][26] . Therefore, the best PCE in this work should be mainly attributed to the highest FF.

Discussion
If only one peak is observed in a -Im[J]-f characteristic, it cannot be determined whether the transit times of electrons and holes coincide, or either of them is out of the measurable frequency range. One way to find a missing peak is to compare several -Im[J]-f characteristics for different donor concentrations. The peaks that are completely overlapped at a particular donor concentration would be separated from each other at another concentration, as demonstrated above. This approach also makes it possible to know which mobility is that for electrons. Another way to find a missing peak is to record the -Im[J]-f characteristics at different temperatures. If the activation energies of the donor and acceptor materials are different, the two peaks in the -Im[J]-f characteristic would shift to the lower frequency side with different rates at lower temperatures. An example of the MPC measurements at different temperatures is shown in Fig. 5(a), in which two peaks are recognized at a room temperature but one disappears at lower temperatures. The mobilities determined from the peak frequencies are  www.nature.com/scientificreports www.nature.com/scientificreports/ plotted in Fig. 5(b). Since the measured temperature range is narrow, we assume an Arrhenius-type temperature dependence and fit the following equation to the hole mobilities: where k B is the Boltzmann's constant, μ 0 is the mobility at T = ∞ K, and E a is the activation energy. From the fits, E a is determined to be 154 meV for holes and 144 meV for electrons. The former is consistent with the E a values (124-160 meV) measured on P3HT neat thin films with the SCLC technique 56,57 . The latter value is also between the E a values determined in field-effect transistors based on pure PCBM (112 meV) and a P3HT:PCBM blend with 66 wt% P3HT concentration (160 meV) 58 . Fig. 5(b) shows the possibility that the overlapped -Im[J] peaks can indeed be separated from each other at a different temperature. Another merit of lowering the temperature is that a peak that is above the measurable frequency range at room temperature may be shifted lower within the range at lower temperatures; this means that the measurable range is expanded 49,59 .

conclusions
In conclusion, we have demonstrated that the MPC technique is a powerful tool to determine the carrier drift mobility of BHJ OSCs. Its advantages with respect to other methods, such as TOF and SCLC techniques, are its applicability to a working OSC with an optimum structure and simultaneous determination of electron and hole mobilities. Since no special cells are needed for the mobility determination, the relation between PCE and the mobilities can be investigated. As an example of such an investigation, we demonstrated that a good mobility balance (μ e = μ h = 3.1 × 10 −4 cm 2 V −1 s −1 ) that is achieved by tuning the mixing ratio of P3HT and PCBM results in the best PCE of 3.5% within the OSCs fabricated in this work.

Solar cell fabrication and characterization.
Inverted OSCs with an effective area of 4 mm 2 were fabricated on indium tin oxide (ITO)-coated glass substrates with a 2 mm stripe pattern. The device structure was ITO/ ZnO/P3HT:PCBM (200 ± 10 nm)/MoO 3 (10 nm)/Al (50 nm). The BHJ layer was spin-coated from chlorobenzene solutions containing P3HT and PCBM at a spin-rate of 800 rpm. The mixing ratio of P3HT and PCBM was varied while the concentration of the solutions was kept constant so that the resultant BHJ layer thickness stayed almost the same. The weight ratio of P3HT to the mixed solute was changed from 30 to 80 wt%. All the fabrication procedures were done in a glove box filled with nitrogen gas, and the OSCs were taken from the glove box after the encapsulation. The current density-voltage characteristics were recorded with a source meter under 100 mW/cm 2 AM1.5G irradiation.
Mpc measurements. The MPC measurements were carried out with a home-made setup consisting of a LED with 470 nm emission, a lock-in amplifier, and a transimpedance amplifier. Modulated LED light was irradiated from the ITO side of an OSC. Various biases were applied to an OSC with a DC power supply. During the measurements at lower temperatures, an OSC was set in a vacuum chamber attached to a nitrogen bath, a heater, and a temperature controller. The OSC was maintained in a vacuum of 10 −4 Pa and within a temperature range from 150 to 300 K. numerical simulations. The details of the numerical simulations are described in the Supplementary Information. All the numerical simulations were performed using Microsoft, Visual Studio (C + + ) and NAG, Fortran Builder.