# Analysis of Different Series-Parallel Connection Modules for Dye-Sensitized Solar Cell by Electrochemical Impedance Spectroscopy

Authors: Jung-Chuan Chou; Chin-Hui Huang; Yi-Hung Liao; Yu-Jen Lin; Chia-Ming Chu; Yu-Hsun Nien
Journal: International Journal of Photoenergy
 (2016)

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## Abstract

The internal impedances of different dye-sensitized solar cell (DSSC) models were analyzed by electrochemical impedance spectrometer (EIS) with an equivalent circuit model. The Nyquist plot was built to simulate the redox reaction of internal device at the heterojunction. It was useful to analyze the component structure and promote photovoltaic conversion efficiency of DSSC. The impedance of DSSC was investigated and the externally connected module assembly was constructed utilizing single cells on the scaled-up module. According to the experiment results, the impedance was increased with increasing cells connected in series. On the contrary, the impedance was decreased with increasing cells connected in parallel.


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## Body

## 1. Introduction

Solar energy has become attractive as a promising solution for reducing emissions of greenhouse gases and providing clean energy. For these reasons, the dye-sensitized solar cell (DSSC) has been widely investigated owing to its simple fabrication, low cost, and promising properties [1–3]. Figure 1 displayed working principle diagram of the DSSC. (1) The electrons are injected from the photoexcited dye into titanium dioxide (TiO2) layer when light illuminates the cell; (2) the electrons pass through from TiO2/dye to the transparent conducting oxide and transport into the external circuit; (3) the sensitizer is regenerated by the electrolyte; (4) the electrolyte is regenerated by counter electrode; (5) excited-state decays to ground state; (6) recombination of the injected electrons with the oxidized dye; (7) recombination of the injected electrons with triiodide ions [1].Figure 1
Working principle scheme of the dye-sensitized solar cell [1].In order to enhance the photoelectric conversion efficiency (η) of DSSC, addition of graphene into the P25 TiO2 film enhances the electron transport ability of the photoelectrode [4–6]. Graphene, the 2D carbon nanomaterial, causes widespread concern nowadays, which has drawn extensive attention because it has a high thermal conductivity (about 5000 W/mK), perfect mobility of charge that carries at room temperature (more than 200,000 cm2/Vs), and high specific surface area (about reached 2630 m2/g). Graphene-based hybrid nanomaterials have been widely applied in the photovoltaic devices, photocatalysts, and lithium-ion batteries. Herein, we incorporate the 2D graphene into TiO2 photoelectrode for the improvement of the photovoltaic performances of DSSC [7–13].In this study, we investigate the effects of different series-parallel connection modules on DSSCs. If the DSSC module uses only series connections and no parallel connections, which can obtain easily higher voltage, but a module assembly is impossible to convert electrically because of lower current. Thus, an appropriate level parallel connection in the DSSC module assembly must be fabricated to produce current, composing parallel module assembly with minimum loss that is essential. That is to say, it is important to maintain large internal shunt resistance (RSH) in the module assembly. The current loss is caused by decrease of internal shunt resistance, which can be inhibited by proper series connected [1].


## 2. Materials and Methods

### 2.1. Materials

Graphite powder was purchased from Enerage Inc., Taiwan. Titanium dioxide (TiO2) powder and Ruthenium-535 (N3) were purchased from UniRegion Bio-Tech, Taiwan. The ethanol was purchased from Katayama Chemical, Japan. The Triton X-100 was purchased from PRS Panreac, Spain. The Acetylacetone (AcAc), lithium iodide (LiI), and 4-tert-butylpyridine (TBP) were purchased from Sigma-Aldrich, USA. The iodine (I2) was purchased from Riedel-de Haen, USA. The 1-propyl-2,3-dimethylimidazolium iodide (DMPII) was purchased from Tokyo Chemical, Japan.


### 2.2. Fabrication of Dye-Sensitized Solar Cell

The synthesis of graphene oxide (GO) was reported in our previous paper [14]. The graphene/TiO2 paste consisted of P25 TiO2 powder, deionized water, Triton X-100, acetoacetone (AcAc), and graphene oxide solution, which were mixed by an ultrasonic cleaner for 10 minutes. The graphene/TiO2 paste was coated on fluorine doped SnO2-coated conductive (FTO) glass by spin-coated method. Then the graphene/TiO2 layer was annealed at 550°C for 30 minutes as the working electrode. The working electrode was immersed in 3 × 10−4 M N3 dye solution. Platinum (Pt) layer was deposited for 90 seconds on the FTO-glass substrate as the counter electrode by using radio frequency (R.F.) sputtering system. After that the cell was sealed by Surlyn to form a sandwich structure. And the electrolyte solution consisted of 0.6 M 1-propyl-2,3-dimethylimidazolium iodide (DMPII), 0.5 M lithium iodide (LiI), 0.05 M iodine (I2), and 0.5 M 4-tert-butylpyridine (TBP) in 15 mL 3-methoxypropionitrile (MPN). The active area of working electrode was approximately 0.57 cm2. A module assembly was fabricated with variations module assemblies by copper tape, using 8 DSSCs module assembly and having module areas of 16.32 cm2. Moreover, the total effective area of module assembly was approximately 4.56 cm2.


### 2.3. Characteristic and Photoelectric Properties of Graphene/TiO2 Composite Films

The short circuit current density-open circuit voltage (J-V) curves and photovoltaic characterizations of the DSSCs were carried out by using a Keithley 2400 source meter. A solar light simulator (MFS-PV-Basic-HMT, Taiwan) was used to simulate sunlight under one sun AM1.5 G (100 mW/cm2) illumination provided by a 1000 W Xenon (Xe) lamp. The electrochemical impedance spectroscopy (EIS) measurements were performed using an electrochemical analyzer (BioLogic SP-150, France) with forward bias of 0.70 V in the dark. The impedance spectra were recorded by EC-lab software within the frequency range from 50 mHz to 1 MHz by applying an AC perturbation signal of 10 mV.


## 2.1. Materials

Graphite powder was purchased from Enerage Inc., Taiwan. Titanium dioxide (TiO2) powder and Ruthenium-535 (N3) were purchased from UniRegion Bio-Tech, Taiwan. The ethanol was purchased from Katayama Chemical, Japan. The Triton X-100 was purchased from PRS Panreac, Spain. The Acetylacetone (AcAc), lithium iodide (LiI), and 4-tert-butylpyridine (TBP) were purchased from Sigma-Aldrich, USA. The iodine (I2) was purchased from Riedel-de Haen, USA. The 1-propyl-2,3-dimethylimidazolium iodide (DMPII) was purchased from Tokyo Chemical, Japan.


## 2.2. Fabrication of Dye-Sensitized Solar Cell

The synthesis of graphene oxide (GO) was reported in our previous paper [14]. The graphene/TiO2 paste consisted of P25 TiO2 powder, deionized water, Triton X-100, acetoacetone (AcAc), and graphene oxide solution, which were mixed by an ultrasonic cleaner for 10 minutes. The graphene/TiO2 paste was coated on fluorine doped SnO2-coated conductive (FTO) glass by spin-coated method. Then the graphene/TiO2 layer was annealed at 550°C for 30 minutes as the working electrode. The working electrode was immersed in 3 × 10−4 M N3 dye solution. Platinum (Pt) layer was deposited for 90 seconds on the FTO-glass substrate as the counter electrode by using radio frequency (R.F.) sputtering system. After that the cell was sealed by Surlyn to form a sandwich structure. And the electrolyte solution consisted of 0.6 M 1-propyl-2,3-dimethylimidazolium iodide (DMPII), 0.5 M lithium iodide (LiI), 0.05 M iodine (I2), and 0.5 M 4-tert-butylpyridine (TBP) in 15 mL 3-methoxypropionitrile (MPN). The active area of working electrode was approximately 0.57 cm2. A module assembly was fabricated with variations module assemblies by copper tape, using 8 DSSCs module assembly and having module areas of 16.32 cm2. Moreover, the total effective area of module assembly was approximately 4.56 cm2.


## 2.3. Characteristic and Photoelectric Properties of Graphene/TiO2 Composite Films

The short circuit current density-open circuit voltage (J-V) curves and photovoltaic characterizations of the DSSCs were carried out by using a Keithley 2400 source meter. A solar light simulator (MFS-PV-Basic-HMT, Taiwan) was used to simulate sunlight under one sun AM1.5 G (100 mW/cm2) illumination provided by a 1000 W Xenon (Xe) lamp. The electrochemical impedance spectroscopy (EIS) measurements were performed using an electrochemical analyzer (BioLogic SP-150, France) with forward bias of 0.70 V in the dark. The impedance spectra were recorded by EC-lab software within the frequency range from 50 mHz to 1 MHz by applying an AC perturbation signal of 10 mV.


## 3. Results and Discussion

### 3.1. Characterization of Graphene/TiO2 Composite Film

The photoelectrode of DSSC is composed of graphene/TiO2 composite film. The surface morphology of graphene/TiO2 composite film has been investigated using SEM. Figure 2 showed top-view SEM image of graphene/TiO2 composite film. As shown in Figure 2, graphene/TiO2 composite film had higher specific surface area, which attributed to the lower crystallinity and TiO2 nanoparticles that were attached on the graphene easily [14–16].Figure 2
SEM images of graphene/TiO2 composite film.


### 3.2. Photovoltaic Characterizations of DSSCs

An appropriate level parallel connection in the DSSC module assembly must be fabricated to produce current, composing parallel module assembly with minimum loss that is essential [17, 18]. That is to say, it is important to maintain large internal shunt resistance (RSH) in the module assembly. The current loss is caused by decrease of internal RSH, which can be inhibited by proper series connected [1].Figure3 showed real diagram of DSSC module assemblies. The module assembly was fabricated by 8 DSSCs, and these cells were listed in Table 1. The average Voc, Jsc, FF, and η of these cells were 0.648 V, 14.136 mA/cm2, 37.053%, and 3.008%, respectively.Table 1
Photovoltaic properties of DSSCs.
Sample V o c (V) J s c (mA/cm2) F.F. (%) η (%) 1 0.63 14.96 37.69 3.15 2 0.62 13.96 37.52 2.88 3 0.70 13.05 35.04 2.85 4 0.67 13.75 36.76 3.00 5 0.66 13.92 36.94 3.01 6 0.64 14.45 37.35 3.05 7 0.63 14.52 37.40 3.06 8 0.63 14.48 37.72 3.06 Standard deviation (δ) 0.027 0.592 0.881 0.099 Mean 0.648 14.136 37.053 3.008Figure 3
Real diagram of DSSC module assemblies.


### 3.3. Effect of Different Series-Parallel Connection Modules on Impedance Spectrum

As shown in Figure4(a), the equivalent circuit of DSSC is demonstrated by using EIS. In the equivalent circuit of DSSC, a diode represents the electrical properties of the pn-junction, and a RSH and a constant-current source (IS) are in parallel with the junction, where Q1 and Q2 can be ignored in DC analysis because capacitances are too large, approximately 10 μF/cm2 and 1 mF/cm2, respectively. As shown in Figure 4(b), the equivalent circuit of DSSC can be simplified to Norton’s equivalent circuit theorem by a current source (IS) with series resistance (RS) and RSH in parallel, where the sum of R1, R2, R3, and W4 is expressed as RS. Also, the equivalent circuit of DSSC can be simplified to Thevenin’s equivalent circuit theorem by a voltage source VS with RS and RSH in series, as shown in Figure 4(c). And the sum of RS and RSH is expressed as R, in which the output current (IO) is equal to “(RSH×IS)/R,” but IO is generally similar with IS because RSH is much larger than RS [1].Figure 4
(a) Equivalent circuit of DSSC; simplified equivalent circuit of DSSC by (b) Norton’s equivalent circuit theorem; (c) Thevenin’s equivalent circuit theorem [1].
(a) (b) (c)The internal resistance, the characterization of electron and charge transportation, and diffusion between interfaces were simulated by an RC parallel circuit [19]. The equivalent circuit model was described as follows:(1)R1+R2Q1+R3+W4Q2,where R1 corresponds to the serial resistances of FTO-glass and wires are at the high-frequency region. R2 and Q1 correspond to the resistance and double layer capacitance of the electrolyte/Pt-FTO interface. R3 and Q2 correspond to the resistance and chemical capacitance of the TiO2/electrolyte interface. W4 is the Warburg impedance, which describes the diffusion of I3- in the electrolyte. The symbol Q, also known as constant phase elements (CPE), describes the constant phase element of the capacitance, meaning a nonideal frequency dependent capacitance due to a nonuniform distribution of current by the material heterogeneity [4, 20, 21].As shown in Figures5(a) and 5(b), the cells were connected module assembly in series connection, which was represented as S, two cells in series were denoted as 2S, and so on. In the series-connected models, the impedance was enlarged with increasing module assemblies in series connection, which could be attributed to the longer conductive path for electron. The longer conductive path for electron would easily make the condition of electron recombination happen during the electron transfer from conduction band of TiO2 to I3- in electrolyte. Besides, the result of series connection was beneficial to raise voltage of DSSC, but the current density of DSSC remained unchanged.Figure 5
(a) Cells connected module assembly in series connection; (b) an enlarged view.
(a) (b)On the other hand, Figure6 showed that the module assemblies were fabricated in parallel connection, where parallel connection was represented as P, two cells in parallel were represented as 2P, and so on. In the parallel connected models, the impedance was reduced with increasing module assemblies in parallel connection, which could be attributed to more conductive paths for electron. Besides, the result of parallel connection was beneficial to raise current but the voltage remained unchanged.Figure 6
Cells connected module assembly in parallel connection.In the series-parallel connected models, series connection can maintain large shunt resistance. Figure7(a) showed the series-parallel connected models by composing 2 series connections and 4 parallel connections, where 2 series connections and 4 parallel connections were represented as 2S4P. The total internal shunt resistance was equal to 1/2RSH. Therefore, the number of series connected DSSCs is less than the number of parallel connected DSSCs, in which the total internal shunt resistance is lower than one cell, in spite of the additional parallel connections [1]. On the contrary, Figure 7(b) showed the series-parallel connected models by composing 4 series connections and 2 parallel connections, where 4 series connections and 2 parallel connections were represented as 4S2P. The total internal shunt resistance was equal to 2RSH.Figure 7
Nyquist plots based on different DSSC model assemblies (a) series-parallel module: 2S4P; (b) series-parallel module: 4S2P.
(a) (b)As shown in Figure8(a), the series connected models were composed by 1–4 cells in series connection, the characteristic frequency shifted toward low frequency with increase of series connected cell due to enhancement of shunt resistance. On the other hand, Figure 8(b) showed parallel connected models by composing 1–4 cells, in which the lifetime (τe) did not have significant change, and the characteristic frequency was almost constant because the time constants (τn) were almost the same. Thus, the number of series connected DSSCs was more than the number of parallel connected DSSCs, in which the characteristic peaks were toward low frequency, as shown in Figure 8(c).Figure 8
The Bode phase plots based on different DSSC model assemblies (a) series modules; (b) parallel modules; (c) series-parallel modules.
(a) (b) (c)In Figures9(a)–9(c), the trends of impedances were consistent with Figures 5–7. RS, total series resistance is composed by charge-transfer resistances and Nernst diffusion resistance in DSSC, using conductive substrate with very low sheet resistance, a counter electrode with very large roughness factor (RF), and low R3 to obtain the minimum series resistance theoretically of 0.7 cm2. However, the actual series resistance is much higher [22]. And the EIS results were listed in Table 2.Table 2
Measurement results of EIS based on different DSSC model assemblies.
Models R 1 (Ω) R 2 (Ω) Q 1 (μF) R 3 (Ω) Q 2 (mF) W 4 (Ω) ω m i n (Hz) τ e (ms) τ n (ms) 1 cell 17.05 3.31 39.63 6.29 3.87 2.38 5.87 170.23 24.34 2S 53.62 19.28 18.08 63.64 0.45 12.77 16.38 61.05 28.64 3S 72.64 69.09 15.68 477.41 0.19 38.95 38.10 26.25 90.71 4S 59.06 196.32 6.76 3589.32 0.08 341.15 55.64 17.97 287.15 2P 9.15 1.84 82.78 2.43 5.46 2.06 5.36 186.58 13.27 3P 4.90 1.07 139.66 1.55 8.84 1.16 5.98 167.13 13.70 4P 4.83 0.79 163.41 1.36 10.06 0.98 5.54 180.51 13.68 2S4P 9.42 7.84 91.32 35.96 1.40 2.78 27.13 36.86 50.34 4S2P 35.68 88.98 7.20 3384.19 0.14 442.11 54.75 18.26 473.79Figure 9
Bode impedance plots based on different DSSC model assemblies (a) series modules; (b) parallel modules; (c) series-parallel modules.
(a) (b) (c)Based on Table2, R1 mainly attributed to the sheet resistance of conductive substrate, in which R1 increases in proportion to increasing in the sheet resistance of conductive substrate [21]. In addition, R2 is related to charge-transfer process at the counter electrode, which increases with larger surface area of the counter electrode. In order to decrease R2, RF acts as an index of surface area of the counter electrode, which is defined as the ratio of the total surface area to the active area of the counter electrode [22].


## 3.1. Characterization of Graphene/TiO2 Composite Film

The photoelectrode of DSSC is composed of graphene/TiO2 composite film. The surface morphology of graphene/TiO2 composite film has been investigated using SEM. Figure 2 showed top-view SEM image of graphene/TiO2 composite film. As shown in Figure 2, graphene/TiO2 composite film had higher specific surface area, which attributed to the lower crystallinity and TiO2 nanoparticles that were attached on the graphene easily [14–16].Figure 2
SEM images of graphene/TiO2 composite film.


## 3.2. Photovoltaic Characterizations of DSSCs

An appropriate level parallel connection in the DSSC module assembly must be fabricated to produce current, composing parallel module assembly with minimum loss that is essential [17, 18]. That is to say, it is important to maintain large internal shunt resistance (RSH) in the module assembly. The current loss is caused by decrease of internal RSH, which can be inhibited by proper series connected [1].Figure3 showed real diagram of DSSC module assemblies. The module assembly was fabricated by 8 DSSCs, and these cells were listed in Table 1. The average Voc, Jsc, FF, and η of these cells were 0.648 V, 14.136 mA/cm2, 37.053%, and 3.008%, respectively.Table 1
Photovoltaic properties of DSSCs.
Sample V o c (V) J s c (mA/cm2) F.F. (%) η (%) 1 0.63 14.96 37.69 3.15 2 0.62 13.96 37.52 2.88 3 0.70 13.05 35.04 2.85 4 0.67 13.75 36.76 3.00 5 0.66 13.92 36.94 3.01 6 0.64 14.45 37.35 3.05 7 0.63 14.52 37.40 3.06 8 0.63 14.48 37.72 3.06 Standard deviation (δ) 0.027 0.592 0.881 0.099 Mean 0.648 14.136 37.053 3.008Figure 3
Real diagram of DSSC module assemblies.


## 3.3. Effect of Different Series-Parallel Connection Modules on Impedance Spectrum

As shown in Figure4(a), the equivalent circuit of DSSC is demonstrated by using EIS. In the equivalent circuit of DSSC, a diode represents the electrical properties of the pn-junction, and a RSH and a constant-current source (IS) are in parallel with the junction, where Q1 and Q2 can be ignored in DC analysis because capacitances are too large, approximately 10 μF/cm2 and 1 mF/cm2, respectively. As shown in Figure 4(b), the equivalent circuit of DSSC can be simplified to Norton’s equivalent circuit theorem by a current source (IS) with series resistance (RS) and RSH in parallel, where the sum of R1, R2, R3, and W4 is expressed as RS. Also, the equivalent circuit of DSSC can be simplified to Thevenin’s equivalent circuit theorem by a voltage source VS with RS and RSH in series, as shown in Figure 4(c). And the sum of RS and RSH is expressed as R, in which the output current (IO) is equal to “(RSH×IS)/R,” but IO is generally similar with IS because RSH is much larger than RS [1].Figure 4
(a) Equivalent circuit of DSSC; simplified equivalent circuit of DSSC by (b) Norton’s equivalent circuit theorem; (c) Thevenin’s equivalent circuit theorem [1].
(a) (b) (c)The internal resistance, the characterization of electron and charge transportation, and diffusion between interfaces were simulated by an RC parallel circuit [19]. The equivalent circuit model was described as follows:(1)R1+R2Q1+R3+W4Q2,where R1 corresponds to the serial resistances of FTO-glass and wires are at the high-frequency region. R2 and Q1 correspond to the resistance and double layer capacitance of the electrolyte/Pt-FTO interface. R3 and Q2 correspond to the resistance and chemical capacitance of the TiO2/electrolyte interface. W4 is the Warburg impedance, which describes the diffusion of I3- in the electrolyte. The symbol Q, also known as constant phase elements (CPE), describes the constant phase element of the capacitance, meaning a nonideal frequency dependent capacitance due to a nonuniform distribution of current by the material heterogeneity [4, 20, 21].As shown in Figures5(a) and 5(b), the cells were connected module assembly in series connection, which was represented as S, two cells in series were denoted as 2S, and so on. In the series-connected models, the impedance was enlarged with increasing module assemblies in series connection, which could be attributed to the longer conductive path for electron. The longer conductive path for electron would easily make the condition of electron recombination happen during the electron transfer from conduction band of TiO2 to I3- in electrolyte. Besides, the result of series connection was beneficial to raise voltage of DSSC, but the current density of DSSC remained unchanged.Figure 5
(a) Cells connected module assembly in series connection; (b) an enlarged view.
(a) (b)On the other hand, Figure6 showed that the module assemblies were fabricated in parallel connection, where parallel connection was represented as P, two cells in parallel were represented as 2P, and so on. In the parallel connected models, the impedance was reduced with increasing module assemblies in parallel connection, which could be attributed to more conductive paths for electron. Besides, the result of parallel connection was beneficial to raise current but the voltage remained unchanged.Figure 6
Cells connected module assembly in parallel connection.In the series-parallel connected models, series connection can maintain large shunt resistance. Figure7(a) showed the series-parallel connected models by composing 2 series connections and 4 parallel connections, where 2 series connections and 4 parallel connections were represented as 2S4P. The total internal shunt resistance was equal to 1/2RSH. Therefore, the number of series connected DSSCs is less than the number of parallel connected DSSCs, in which the total internal shunt resistance is lower than one cell, in spite of the additional parallel connections [1]. On the contrary, Figure 7(b) showed the series-parallel connected models by composing 4 series connections and 2 parallel connections, where 4 series connections and 2 parallel connections were represented as 4S2P. The total internal shunt resistance was equal to 2RSH.Figure 7
Nyquist plots based on different DSSC model assemblies (a) series-parallel module: 2S4P; (b) series-parallel module: 4S2P.
(a) (b)As shown in Figure8(a), the series connected models were composed by 1–4 cells in series connection, the characteristic frequency shifted toward low frequency with increase of series connected cell due to enhancement of shunt resistance. On the other hand, Figure 8(b) showed parallel connected models by composing 1–4 cells, in which the lifetime (τe) did not have significant change, and the characteristic frequency was almost constant because the time constants (τn) were almost the same. Thus, the number of series connected DSSCs was more than the number of parallel connected DSSCs, in which the characteristic peaks were toward low frequency, as shown in Figure 8(c).Figure 8
The Bode phase plots based on different DSSC model assemblies (a) series modules; (b) parallel modules; (c) series-parallel modules.
(a) (b) (c)In Figures9(a)–9(c), the trends of impedances were consistent with Figures 5–7. RS, total series resistance is composed by charge-transfer resistances and Nernst diffusion resistance in DSSC, using conductive substrate with very low sheet resistance, a counter electrode with very large roughness factor (RF), and low R3 to obtain the minimum series resistance theoretically of 0.7 cm2. However, the actual series resistance is much higher [22]. And the EIS results were listed in Table 2.Table 2
Measurement results of EIS based on different DSSC model assemblies.
Models R 1 (Ω) R 2 (Ω) Q 1 (μF) R 3 (Ω) Q 2 (mF) W 4 (Ω) ω m i n (Hz) τ e (ms) τ n (ms) 1 cell 17.05 3.31 39.63 6.29 3.87 2.38 5.87 170.23 24.34 2S 53.62 19.28 18.08 63.64 0.45 12.77 16.38 61.05 28.64 3S 72.64 69.09 15.68 477.41 0.19 38.95 38.10 26.25 90.71 4S 59.06 196.32 6.76 3589.32 0.08 341.15 55.64 17.97 287.15 2P 9.15 1.84 82.78 2.43 5.46 2.06 5.36 186.58 13.27 3P 4.90 1.07 139.66 1.55 8.84 1.16 5.98 167.13 13.70 4P 4.83 0.79 163.41 1.36 10.06 0.98 5.54 180.51 13.68 2S4P 9.42 7.84 91.32 35.96 1.40 2.78 27.13 36.86 50.34 4S2P 35.68 88.98 7.20 3384.19 0.14 442.11 54.75 18.26 473.79Figure 9
Bode impedance plots based on different DSSC model assemblies (a) series modules; (b) parallel modules; (c) series-parallel modules.
(a) (b) (c)Based on Table2, R1 mainly attributed to the sheet resistance of conductive substrate, in which R1 increases in proportion to increasing in the sheet resistance of conductive substrate [21]. In addition, R2 is related to charge-transfer process at the counter electrode, which increases with larger surface area of the counter electrode. In order to decrease R2, RF acts as an index of surface area of the counter electrode, which is defined as the ratio of the total surface area to the active area of the counter electrode [22].


## 4. Conclusions

In this study, the internal impedances of different DSSC models were analyzed by electrochemical impedance spectrometer with an equivalent circuit model. It was useful to analyze the component structure and promote photovoltaic properties of DSSC. According to the experiment results, the impedance was increased with increasing cells connected in series. On the contrary, the impedance was decreased with increasing cells connected in parallel. In addition, the cells were composed by 1–4 cells in series connection; the characteristic frequency shifted toward low frequency with increase of series connected cell due to enhancement of shunt resistance. Conversely, the cells were shown parallel connected models by composing 1–4 cells, in which the lifetime did not have significant change, and the characteristic frequency was almost constant because the time constants were almost the same.



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