Nowadays, photovoltaic performances of organic photovoltaic cells (OPVs) have been drastically improved by optimizing molecular structures of donor polymers and device architectures     . The red-shifted absorption band of p- type polymer in combination with the bulk heterojunction structure leads to photovoltaic performance higher than 10%. In addition, nanoscale morphology of donor-accepter blend layer is also an important parameter to determine the carrier recombination probability under irradiation of the solar light, which closely correlates with the photovoltaic performance    . Because photocurrent generation requires efficient exciton dissociation at the donor-acceptor interface and most of photo excited excitons are deactivated without the donor/ acceptor interface. The optical absorption length is almost same compared to the organic active layer thickness ranging from 80 to 200 nm, but the exciton diffusion length of normal organic semiconductors is shorter. To solve this problem, bulk heterojunction architecture has been used for a long time due to the large interface area between donor-acceptor materials.
In parallel to the synthesis of new polymers, molecular stacking in the active layer, and optimized device structures, evaluation methods of carrier dynamics in OPVs have been developed by many researchers     . Several cha- racterization techniques as carrier mobility of organic materials   , energy level at the interfaces   , and transient absorption spectroscopy   have been investigated to understand carrier dynamics in the OPVs. Impedance spectroscopy is an important tool to discuss carrier dynamics including carrier mobility and density through the equivalent circuit of the device. In this method, the impedance of the device is obtained from the phase difference between the input sinusoidal voltage and the response current. By analyzing the measurement results in a wide frequency range (10−3 to 106 Hz), it is possible to separate and observe components having various relaxation times contributing to the impedance in the device. In addition, it is one of the features that can measure an actual device because it is a non-destructive measurement method that can be applied to various electronic devices. Especially, one simple interpretation of impedance measurement is that resistance and capacitance components of each layer and each interface can be discriminated from the equivalent circuit   . Garcia-Belmonte et al. studied the influence of bias voltage on the depletion layer capacitance and the minority carrier (electron), and evaluated electron mobility and the electron lifetime by fitting the equivalent circuit  . The revers bias capacitance generally exhibits Mott-Schottky-like behavior due to the formation of a Schottky junction (band bending) at organic/metal interface in conventional OPVs. In addition, Leever et al. evaluated the electron density and the electron lifetime of OPV as a function of applied voltage by the equivalent circuit with charge transfer resistance and the capacitance of bulk layer and the donor-acceptor interface  .
Recently, we demonstrated that an improved photovoltaic performance of ITO/MoOx/organic active layer/LiF/Al device drastically by using the annealed- MoOx layer at 160˚C  . By evaluating the angle-dependent X-ray photoelectron spectroscopy, oxygen vacancies in MoOx can be recovered by the annealing process, and this fact causes the efficient carrier injection at the MoOx/organic interface. Since the MoOx layer has been often used as a hole transport layer of the normal OPV device architecture, several researches on the surface of MoOx layer have been reported. However, detailed mechanism of efficient carrier transport at the interface of MoOx/organic layer is unclear, and further investigation has been required.
In this study, we applied the impedance spectroscopy to bulk heterojunction OPV with the MoOx layer, which was annealed at 160˚C in the inert condition to reduce surface defects. The resistance and capacitance components in the organic layer can be evaluated using the equivalent circuit. In addition, the relaxation time and electron lifetime of diffusion were evaluated to understand the mechanism of improved photovoltaic performance.
Poly[4,8-bis(5-(2-ethylhexyl)thiophen-2-yl)benzo[1,2-b;4,5-b’]dithiophene-2,6-di-yl-alt-(4-(2-ethylhexyl)-3-fluorothieno[3,4-b]thiophene-)-2-carboxylate-2-6-diyl)] (PTB7-Th) and [6,6]-phenyl-C71-butyric acid methyl ester (PC71BM, puri- ty: >99.0%) were purchased from 1-Material Inc. and Solene BV, respectively. MoOx powder was purchased from Kojundo Chemical Laboratory. These materials were used without further purification.
2.2. OPV Fabrication
We fabricated OPV by following procedure. An indium tin oxide (ITO) anode with the thickness of 150 nm was first patterned on a glass substrate by chemical etching process, and was sequentially treated with acetone, isopropyl alcohol, and pure water using the ultrasonic cleaner. The substrate was then cleaned using the UV ozone cleaner for 20 min. A MoOx layer, used as a hole transport layer, was then thermally evaporated on the ITO layer, controlling the thickness as 40 nm. Then, the sample was annealed at 160˚C for 5 min under a nitrogen atmosphere to avoid the unexpected oxidation by air (called as device A). For comparison, a reference device was also fabricated using the same process without the annealing step of MoOx layer (called as device B). In this research, PTB7- Th: PC71BM was used as an active layer. PTB7-Th and PC71BM were co-dis- solved in chlorobenzene at a concentration of 20 mg/ml in a weight ratio of 1: 1.5. After adding 1,8-diiodooctane (3 vol%) in the resulting solution  , the PTB7-Th: PC71BM layer was spin-coated at 2000 rpm for 1 min, and measured thickness was 100 nm. Finally, the LiF (0.5 nm)/Al (80 nm) electrode, with an active area of 8 mm2, was thermally deposited in a vacuum deposition chamber.
The current density-voltage (J-V) characteristics under irradiation with AM1.5G, 100 mW/cm2 simulated solar light and external quantum efficiency (EQE) spectra were measured by the spectral response measurement system (Bunkou Keiki, CEP-25BX). The frequency response of impedance was measured using the impedance analyzer (Iwatsu, PSM1735).
3. Results and Discussion
Figure 1(a) and Figure 1(b) show current density-voltage characteristics and EQE spectra of devices A (with annealing for MoOx) and B (without annealing for MoOx), respectively. As clearly shown in these results, higher photocurrent and increased EQEs of all the wavelength region from 300 to 900 nm were observed when the MoOx layer was annealed at 160˚C for 5 min. These results correspond to the increased short circuit current density (Jsc) by a factor of 2.44 shown in Table 1. Calculated photo conversion efficacies (PCEs) of devices A and B were 5.65% and 2.05%, respectively. In addition, PCE, Jsc, open circuit voltage (Voc) and fill factor (FF) of devices A and B are summarized in Table 1. Especially Jsc was improved by the thermal annealing for the MoOx, leading to higher PCE. This trend confirms our previous paper stating that the annealing of MoOx is effective for improving photovoltaic performance of OPV  . In this previous paper, we conclude that it is the cause of the improvement of the OPV characteristics that oxygen defects that can be electron traps on the surface of MoOx are filled by the annealing. In addition, this effect was equally confirmed at a temperature of 160˚C to 200˚C and a time of 5 to 30 min (data not shown). The condition of 160˚C for 5 min is a reasonable choice in terms of high compatibility with other processes such as the annealing of P3HT: PCBM  
Figure 1. (a) Current density-voltage characteristics under irradiating AM1.5 solar light and (b) EQE spectra of OPVs fabricated with (device A) and without (device B) annealing process after depositing MoOx layer, respectively.
Table 1. Photovoltaic characteristics of devices A and B, which were fabricated with and without annealing for MoOx layer.
which are representative materials used as photoactive layer and use of a film substrate.
Figure 2(a) displays the cole-cole plot of devices A (with annealing) and B (without annealing) by the electrical impedance measurement. The bias and AC voltages for the measurement were set as 0 and 100 mV, respectively. In addition, measurements were taken in the dark. Impedance spectroscopy is generally performed in the dark, however, when discussing the origin of VOC, there is a possibility that it is necessary to perform measurement under light irradiation, the electronic state at the interface changed due to the movement of photo carriers. It can be seen that the cole-cole plots for both devices showed almost same single semicircle shape except for the radius, and the radius was reduced after the annealing process for MoOx layer. By assuming a single semicircle, fitting curves matched the impedance spectra well in the whole measurement frequency region from 0.1 Hz to 1 MHz. The radius of semi-circle corresponds to the resistance component of PTB7-Th: PC71BM layer  . Calculated resistance components of PTB7-Th: PC71BM layers in devices A and B were 6.5 and 17 MΩ, respectively. This result indicates that the resistance component of PTB7-Th: PC71BM layer was reduced after annealing for the MoOx layer. The spin-coating conditions of PTB7-Th: PC71BM layers for both devices were completely same in our experiment, and molecular orientation of PTB7-Th is same for both devices since the annealing was performed before spin-coating of PTB7-Th: PC71BM layer. Therefore, the carrier mobility of PTB7-Th: PC71BM was not affected by the annealing process of MoOx. These facts indicate that the reduced resistance is originated due to the carrier injection at the MoOx/PTB7-Th: PC71BM interface. Our previous paper demonstrated that surface defects of MoOx, which are caused by the oxygen vacancy of MoOx, were reduced by the annealing process  . An efficient carrier injection at the interface of MoOx/PTB7-Th: PC71BM layer can be realized for the device A.
We also evaluated the carrier transport resistance components as a function of
Figure 2. (a) Impedance cole-cole plots of OPVs, which were fabricated with (device A, blue circle) and without (device B, red triangle) annealing process of MoOx layer. The amplitude of sine wave and bias voltages were 0.1 and 0 V, respectively. The blue and red linesare fitting curvesof samples A and B, respectively; (b) Resistance components of PTB7-Th: PC71BM layers, which were calculated from the impedance cole-cope plot, by changing the bias voltage ranging from 0 to 5 V.
DC bias voltage from impedance measurement. Figure 2(b) shows the relationship between the resistance and the bias voltage ranging from 0 to 5 V for devices A and B, respectively. Such type of impedance pattern belongs to an ordinary response, in which carrier transport is determined by diffusion-recombination between nano-absorbing contacts  . In addition, injected minority carriers (i.e. electrons) from the Al electrode can diffuse within the PTB7-Th: PC71BM active layer and the impedance model consist of an equivalent circuit as shown in Figure 3  . It contains distributed resistors rt, which stand for the electron transport, the distributed capacitance Cn, and recombination resistance rrec accounting for the electron recombination processes. The rrec continuously decreased with increasing bias voltage for both cases of devices A and B due to the carrier injection by applying DC bias voltage. The electron recombination resistances were reduced by the thermal annealing for all the DC voltage conditions. It implies that the carrier injection efficiency at the MoOx/PTB7-Th: PC71BM was improved by the thermal annealing of MoOx layer. The photovoltaic performance of the device A is improved after the thermal annealing of MoOx  .
Since both electron recombination resistance and distributed capacitance are known as important parameters to affect the carrier injection/transport at the interface and inside the organic active layer, we then evaluated the modulus cole-cole plot to investigate the capacitance component of PTB7-Th: PC71BM layer for both devices. Figure 4(a) shows the typical modulus Cole-Cole plots of
Figure 3. An equivalent circuit of the diffusion-recombination mechanism used for fit- ting analysis in this study.
Figure 4. (a) Modulus cole-cole plots of OPVs, with (blue circle) and without (red triangle) the annealing process of MoOx layer; (b) Capacitance components of PTB7-Th: PC71BM layers calculated from the impedance cole-cope plot.
OPVs when the bias voltage was set at 0 V. The measurement frequency range was from 0.1 Hz to 1 MHz, therefore, only the part of semicircle was observed as clearly shown in Figure 4(a). However, the measured modulus cole-cole plot could be fitted as the semicircle by using the Debye relaxation model in the whole measuring frequencies  . The radius of modules cole-cole plot, corresponding to the distributed capacitance component (Cn) of PTB7-Th: PC71BM layer in Figure 3, increased from 0.040 nF to 0.068 nF after annealing the MoOx layer. This result indicates that only the capacitance component of PTB7-Th: PC71BM layer increased when the MoOx layer was thermally annealed at 160˚C, and was opposite trend of electron recombination resistance component in Figure 2. However, the annealing effect of electron recombination resistance was larger than that of capacitance component, and the reduced electron recombi- nation resistance affects the carrier transport from the PTB7-Th: PC71BM layer to the MoOx layer.
The red triangle and blue circle correspond to devices fabricated without and with thermal annealing process of MoOx layer.
A relaxation time (τ) is also an important parameter to determine the carrier dynamics of OPV. It can be calculated from the frequency of measurement (fm) at which the impedance value becomes maximum as
Figure 5 shows the imaginary part of impedance (Z") as a function of frequency of applied sine wave voltage for different forward bias condition. The peak frequency was drastically shifted toward higher frequency side from 6 Hz (0 V) to 167 kHz (5 V) in device A (a) and from 1 Hz (0 V) to 29 kHz (5 V) in device B (b), respectively. It means that the relaxation time was also reduced. The influence of DC bias voltage on the relaxation time of devices A and B is shown in Figure 6. The relaxation time of OPV decreased with increasing the DC bias voltage. The relaxation time of device A was 153 ms, and was reduced down to 27 ms by annealing the MoOx layer (device A) when the DC bias voltage was not applied for the measurement. The small relaxation time corresponds to the efficient carrier transport in the PTB7-Th: PC71BM layer. Therefore, this re-
Figure 5. Relationship between imaginary part of impedance (Im Z") and frequency for (a) device A (with annealing) and (b) device B (without annealing).
Figure 6. Relaxation time as a function of DC bias voltage for devices A and B, respectively.
sult indicates that the photo generated carriers are efficiently transported forward from the active layer to the electrode, resulting in higher photovoltaic performance. This fact is in good agreement with the device performance shown in Figure 1.
The impedance model mainly contains electron recombination time (τn), which can be calculated by means of the relation 
where rrec and Cn are the electron recombination resistance and the distributed capacitance in Figure 3, respectively. Figure 7 shows the relationship between the electron recombination time and the DC bias voltage. The electron recombination time was reduced by annealing of the MoOx layer. It corresponds to reduced losses due to the electron-hole recombination in the PTB7-Th: PC71BM layer, although the surface recombination route cannot be excluded. Therefore, based on these experimental results more efficient carrier dissociation takes place in the device A.
We fabricated normal OPV with PTB7-Th: PC71BM photoactive layer and MoOx hole transport layer and investigated the mechanism of improved photo conversion efficiency through impedance spectroscopy. By evaluating the electrical and modulus cole-cole plots, the electron recombination time was calculated from the electron recombination resistance and the distributed capacitance. The electron recombination time decreased by the annealing process for the MoOx layer, leading to the efficient carrier dissociation in the PTB7-Th: PC71BM layer. In addition, the relaxation time was estimated from the imaginary part of impedance as a function of measuring wavelength. The relaxation time decreased also by the annealing process. Therefore, these facts indicate that the photo-induced carriers were efficiently extracted from the PTB7-Th: PC71BM layer, resulting in the higher PCE. In the future, this nondestructive evaluation method can be applied to in-line evaluation by improving measurement accuracy and speed, thereby contributing to improvement of OPV productivity and reliability.
Figure 7. Electron recombination times of devices A and B as a function of DC bias voltage.
The authors gratefully acknowledge the support from the JSPS KAKENHI pro- ject (No. 26420267).