Improvement in light harvesting and device performance of dye sensitized solar cells using electrophoretic deposited hollow TiO2 NPs scattering layer

Improvement in light harvesting and device performance of dye sensitized solar cells using electrophoretic deposited hollow TiO2 NPs scattering layer

Solar Energy Materials & Solar Cells 161 (2017) 255–262 Contents lists available at ScienceDirect Solar Energy Materials & Solar Cells journal homep...

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Solar Energy Materials & Solar Cells 161 (2017) 255–262

Contents lists available at ScienceDirect

Solar Energy Materials & Solar Cells journal homepage: www.elsevier.com/locate/solmat

Improvement in light harvesting and device performance of dye sensitized solar cells using electrophoretic deposited hollow TiO2 NPs scattering layer Rama Krishna Chavaa,b, Woo-Min Leea, Sang-Yeob Oha, Kwang-Un Jeongb, Yeon-Tae Yua,

MARK



a Division of Advanced Materials Engineering and Research Centre for Advanced Materials Development, Chonbuk National University, Jeonju 54896, South Korea b Polymer Materials Fusion Research Center & Department of Polymer-Nano Science and Technology, Chonbuk National University, Jeonju 54896, South Korea

A R T I C L E I N F O

A BS T RAC T

Keywords: Hollow TiO2 Nanoparticles Electrophoretic deposition Dye sensitized solar cells Bi-layer structure Light harvesting

The concept of bi-layer structure in photoanodes is of great importance to prepare highly efficient dye-sensitized solar cells. In this work, Hollow TiO2 (H-TiO2) NPs are successfully produced through the etching of Au NPs in Au@TiO2 core-shell NPs which were synthesized by microwave hydrothermal route. Electrophoretic deposition was utilized to make H-TiO2 NP scattering layer on the top of small sized TiO2 NPs layer. The photoanodes based on H-TiO2 NPs scattering layer showed a photoconversion efficiency of 7.58% which is much higher than that of photoanode without H-TiO2 scattering layer (6.08%). The improved photovoltaic performance is mainly due to relatively light scattering effect, more surface area for effective dye adsorption and increased light harvesting capacity of H-TiO2 NPs in the entire spectral range.

1. Introduction Dye-sensitized solar cells (DSSCs) are a type of photovoltaic devices based on the charge transfer process between dye molecules and an oxide [1–5]. Titania, TiO2 nanoparticles (NPs) are widely used as DSSC photoanode materials which have a high surface area for the uptake of dye molecules, but one of the major drawbacks of these conventional TiO2 NP photoanodes is the negligible light scattering of the films due to the small particle size of TiO2 (20–30 nm), resulting in low light harvesting efficiency [6–8] hence thereby limit the further improvement of PCE. Therefore a bi-layer structure photoanode concept with a light scattering effect by overlaying the submicrometer-sized TiO2 particle layer on TiO2 nanocrystallites underlayer has been proposed [9]. In this bi-layer structured photoanode with a large particle-based top layer working as the light scattering film and a nanoparticle based bottom layer for dye loading is adopted, which could largely enhance the light harvesting efficiency and thus increase the power conversion efficiency [10,11]. Up to now several authors introduced different types of TiO2 particles as light scattering films, for example, Kim et al. [12] introduced nanoporous TiO2 spheres with ultrahigh surface area and well-developed nanopore structure. These 250 nm sized spherical structures provided a fairly good scattering effect with a considerably higher Jsc value due to better contact among the individual spherical structures. Ding et al. [13] specially designed TiO2 microspheres with



large pore size and high porosity provide a high internal surface area for dye adsorption, giving rise to high light harvesting and a photocurrent of 19.21 mA cm−2 and a PCE of 9.98%. Furthermore, TiO2 hollow microspheres [14], shell-in-shell TiO2 hollow spheres [8], hollow/spindle like TiO2 NPs [15], TiO2 microflowers with nanopetals [16], sub-microspheres [17], three-dimensional TiO2 nanohelix array [18], oriented TiO2 nanotubes arrays [19], hierarchical textured TiO2 spheres [20], TiO2 hollow spheres [21] with hierarchical nanostructures are emphasized as promising materials for achieving high efficiency DSSCs in view of their dual function in providing a large surface area, generating effective light scattering and also decrease in the rate of charge recombination. Moreover, recent reports also claimed that the fabrication of bi-layer structured electrodes could improve the photovoltaic efficiency by utilizing the phenomenon of light scattering effect [22–25]. Among these, TiO2 hollow structured materials have received more and more attention owing to their low density, high specific surface areas [26] as potential candidates for electrode materials in photochemical solar cells. It is reported that such TiO2 hollow spheres can trap the incident light for a longer time and bring forth more opportunities for light absorption [27], which can improve the light harvesting efficiency and a fast motion of charge carriers due to the diffractions on the TiO2 hollow spheres and the multiple reflection effect occurring inside the interior cavities of hollow structures, closely

Corresponding author. E-mail address: [email protected] (Y.-T. Yu).

http://dx.doi.org/10.1016/j.solmat.2016.11.037 Received 8 February 2016; Received in revised form 1 November 2016; Accepted 27 November 2016 0927-0248/ © 2016 Published by Elsevier B.V.

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for EPD of H-TiO2 NPs. The suspension for EPD experiments was made by mixing the 15 ml of above synthesized H-TiO2 solution with another 15 ml of ethanol. Then the mixed solution was stirred overnight. The suspension was ultrasonicated for 30 min before EPD experiment and also the pH of the suspension was changed to 13 by using 1 M NaOH. In the electrophoretic deposition procedure, the working electrode (C-TiO2 screen printed FTO substrate with an exposure area 0.1 cm2) and counter electrode (Pt plate with exposed area 2 cm2) were immersed parallel to each other in the suspension, and a voltage of 50 V was applied. The distance between two electrodes was maintained at ~1 cm throughout the experiment. The deposition was carried out for 5, 10 and 15 min at room temperature. After deposition, the substrates were rinsed in ethanol to remove loosely attached H-TiO2 NPs. The films were then dried at 60 °C for 1 h.

packed interpenetrating networks and large internal surface area [28,29]. Moreover, the hollow scattering centers with certain sizes are believed to be more effective to facilitate the electrolyte diffusion than solid ones, resulting in a better DSSC performance [21]. For the fabrication of TiO2 photoanodes in DSSCs usually doctor blading [30], screen printing [31], spray coating [32], spin-coating [33] and electrophoretic deposition (EPD) processes were used so far [34,35]. The coating of viscous TiO2 paste on a FTO glass substrate followed by calcination to remove organic additives results in TiO2 films with loose particle-packing network which can hinders the electron transport. To improve electron percolation in the TiO2 films, EPD which uses no binder and assures intimate contact of deposited particles, represents a potential alternative to the paste-coating methods [36,37]. EPD is a versatile process offering various advantages such as simplicity, need to low cost equipments, short formation time, high reproducibility, ability to deposit even coatings on the substrates with complicated shapes [38]. EPD is a technique that exploits the movement of charged particles in suspension in the presence of an appropriate electric field. This electric field enables the consolidation of said particles into films, cast onto any shaped substrate, or into thick, bulk components. The importance of EPD for the fabrication of DSSCs has been assessed by Chen et al. [39] and Liou et al. [40]. In their work, the photoconversion efficiencies of TiO2 coating obtained by EPD and conventional paste coating methods are compared. It was observed that the EPD films produced a higher packing density than the paste coating ones and therefore higher conversion efficiencies were achieved. In this paper, we investigate the performance of DSSCs with a bilayer structure containing hollow TiO2 NPs (H-TiO2) as a light scattering layer. The H-TiO2 NPs layer was electrophoretically deposited onto a transparent TiO2 nanoparticle layer formed on an F-doped SnO2 (FTO) glass substrate via paste coating. DSSCs based on H-TiO2 photoanodes showed a greater efficiency values due to improved light harvesting capacity. In addition to this, we have also studied the effect of H-TiO2 scattering layer thickness on the performance of DSSCs.

2.3. DSSC fabrication The sheet resistance of FTO used in the present work is ~10 Ω/□ with an average thickness of ~900 nm. Dye sensitization was conducted by immersing H-TiO2 NP films in 0.3 mM N719 Ruthenium dye ethanol solution for one day at room temperature in a sealed beaker. After that, the sensitized films were washed with ethanol and then dried at room temperature for 1 h. For comparison, the electrodes without H-TiO2 NPs scattering layer were also prepared. The counter electrode was prepared by Pt sputtering on pre-drilled FTO glass with holes. The dye-adsorbed TiO2 electrodes were assembled and sealed along with the counter electrode using a 25-μm-thick thermal-plastic Surlyn spacer (SX1170-25, Solaronix) as a spacer to fabricate sandwich-type cells. Finally, the active area of dye-coated TiO2 film was 0.1 cm2. A liquid electrolyte, which contained 0.6 M 1-butyl-3-methylimidazoliumiodide (BMII), 0.1 M guanidiniumthiocyanate(GuSCN), 0.03 M I2, and 0.5 M 4-tertbutylpyridine in acetonitrile–valeronitrile (85:15, vol%) was injected into the gap between two electrodes via a predrilled hole on the counter electrode side. The injection holes were sealed with a transparent tape. The iodide/triiodide couple has a suitable redox potential and provides rapid dye regeneration and slow electron recombination, good solubility, high conductivity, and less light absorption, favorable penetration ability into the mesoporous semiconductor film and long-term stability. Owing to these unique features, the iodide/triiodide couple has been preferred since the beginning of DSSC development [42]. Generally, the recombination occurs both at the interface between the TiO2 and the electrolyte and at the part of the conducting substrate that is exposed to the electrolyte. The latter is usually less important in the case of I−/I3− and can be suppressed by using a compact blocking layer of metal oxide. The recombination can be suppressed by additives in the electrolyte, such as 4-tertbutylpyridine [43] and guanidium thiocyanate (GuSCN) [44]. Both additives give a decreased recombination rate. The most probable mechanism is that these additives adsorb at the TiO2 surface, blocking active reduction sites or preventing approach of I3− to the surface. BMII is a imidazolium-based ionic liquid which are the most commonly used and efficient electrolytes in electrochemical applications and in DSSCs. These electrolytes will give the higher triiodide diffusion coefficients and thus in turn produces higher photocurrents [45].

2. Experimental section 2.1. Synthesis of H-TiO2 NPs H-TiO2 NPs were synthesized by a two-step process of hydrothermal reaction at first Au@TiO2 core–shell NPs [41] and then subsequent KCN reaction for Au etching. In a typical synthesis, 1.2 ml of 0.01 M ascorbic acid was added dropwise into the mixture of HAuCl4 (1 ml, 0.01 M) and Na3Cit (2 ml, 0.01 M) to obtain a reddish brown precursor under magnetic stirring. Such precursor solution was stirred continuously for 15 min, and then 3 ml of 0.04 M TiF4 solution was added. The mixture was subsequently diluted to 30 ml with deionized water and heated in a commercial microwave oven at a temperature of 180 °C for one hour with rigorous stirring. After centrifuging (at 7000 rpm/ 10 min), Au@TiO2 core–shell NPs precipitate was dispersed in 20 ml deionized (DI) water. A 5 ml of 0.01 M KCN solution was added to above Au@TiO2 core– shell NPs solution and stirred for 10 min. After that, pH of the resultant solution was changed to 10.5 by using 0.01 M NaOH solution. The reaction mixture was stirred for 3 h. The resultant white suspension was centrifuged (9500 rpm/15 min) and washed with distilled water. The above synthesis procedure was repeated thirty seven times so as to obtain more H-TiO2 NPs powder and the obtained H-TiO2 NPs content was mixed with 500 ml ethanol to make a stock solution further use in EPD experiments.

2.4. Characterizations The TEM images of as synthesized Au@TiO2 and H-TiO2 NPs were recorded on Hitachi H-7600 transmission electron microscope (TEM) with an accelerating voltage of 100–400 kV. After drying, the deposition patterns and cross-sectional thickness of the TiO2 films were studied by using Field Emission Scanning Electron Microscope (FESEM, Hitachi SU-70). The roughness profiles deposited films were examined by using Atomic Force Microscope (AFM, Bruker Nanoscope V). The Photocurrent–voltage (I-V) characteristics of fabricated DSSCs were measured on McScience K201

2.2. Electrophoretic deposition of H-TiO2 NPs Initially, C-TiO2 NPs paste was screen printed on FTO glass with a thickness of 8.5 µm ( ± 0.5 µm) and dried at 450 °C for one hour. After drying, the FTO substrate with C-TiO2 NPs film was used as electrode 256

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Solar Simulator Lab100 under illumination with power density of AM 1.5 (100 mW/cm2). External quantum efficiency (IPCE) recordings were taken from McScience K3100 spectral IPCE measurement system.

suggesting that the inner Au core was completely removed after KCN etching. The SEM images of as synthesized H-TiO2 spheres also taken and shown in Fig. 2c and d. The dotted arrow lines in Fig. 2d indicate the hollow form of TiO2 nanostructures. These hollow TiO2 nanostructures have a rougher surface due to its special morphology. In addition, it is expected that these hollow TiO2 nanostructures should produce a multi-reflection of incident light in-between of hollow spheres, so as to improve the efficiency of light harvesting. In order to confirm whether the core Au NPs were removed or not, we have taken EDS-elemental mapping/compositional studies on H-TiO2 NPs and are given in Fig. 2e–h. The Fig. 2e is the chosen area of H-TiO2 NPs for mapping and Fig. 2f is the total elemental mapping overlay of TiO2 NPs. Next, the Fig. 2g and h are the individual mapping profiles of O and Ti atoms. To determine the chemical composition details, we have taken the EDS spectrum of H-TiO2 NPs and shown in Fig. 2h. The weight percentages of Ti and O species are 62.85% and 37.15% respectively. From EDS mapping and EDX spectrum it was confirmed that the obtained H-TiO2 NPs consists of only O and Ti atoms and not any other impurities.

3. Results and discussion

3.2. Morphological studies of H-TiO2 films

3.1. Morphological characterization of H-TiO2 NPs

Electrophoretic deposition (EPD) is based on the motion of charged particles in a suspension under the influence of an electric field towards to form a dense, coherent, and homogeneous coating on oppositely charged electrode [46]. A suspension for EPD is an important system which can affect the deposition efficiency, therefore it is better to obtain a well dispersed and stable suspension. Organic solvents are preferable to water since EPD in water is accompanied by the formation of hydrogen (cathode) and oxygen (anode) resulting in bubbles in the deposit which can disturb the forming films [47]. In the present work, for EPD experiments we made a stable and well dispersed suspension (at pH=13) of H-TiO2 in ethanol. The schematic diagram for the deposition of H-TiO2 NPs was shown in Fig. 3. The surface microstructure of as-prepared TiO2 films was analyzed by FE-SEM and shown in Fig. 4. In order to get a compact and uniform

Fig. 1. Schematic diagram for the synthesis of H-TiO2 NPs.

At first, Au@TiO2 core-shell NPs were synthesized by a microwave hydrothermal method at 180 °C for 1 h. After washing the formed coreshell NPs, H-TiO2 NPs were produced by KCN etching of Au NPs at pH=10.5 for 3 h. Experimental details are provided in Section 2.1. The schematic representation for the synthesis of H-TiO2 NPs was given in Fig. 1. Fig. 2 shows the unique morphologies of the as-synthesized H-TiO2 nanostructures. As seen from the TEM and SEM images in the figure, H-TiO2 nanostructures show hollow space left in the middle. The diameters of Au NPs are all in the range of 15–20 nm, and the total HTiO2 spheres have a diameter of 150–200 nm. The TEM images in Fig. 2a and b clearly show a hollow space inside the TiO2 spheres

Fig. 2. TEM images (a, b) and FESEM images (c, d) of H-TiO2 NPs; Chemical composition studies of H-TiO2 NPs: (a) selected area of H-TiO2 NPs for mapping, (b) Total Elemental overlay of H-TiO2 NPs, (C) O mapping, (d) Ti mapping and (e) EDX spectrum of H-TiO2 NPs.

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free and uniform. These types of films are useful for high performance DSSC applications. In addition to these, we have also measured the thickness of obtained films at different deposition times. The Fig. 5b, d and f shows the FE-SEM cross sectional images and the thickness of films were measured as 730 nm, 1.5 µm and 2.3 µm for 5, 10 and 15 min respectively. The film thickness was increased with the deposition times linearly and which was due to the fact that more H-TiO2 NPs are deposited by extending the deposition times. The deposition patterns of H-TiO2 films were also studied by using AFM. Fig. 6 shows the three dimensional surface profiles of as prepared films together with their corresponding roughness values. The surface of C-TiO2 screen printed film in Fig. 6a is characterized by the presence of small grain sized particles since the particle size in C-TiO2 paste is around 20 nm and the corresponding film roughness value was 9.14 nm. The surface morphology of H-TiO2 deposited films are also shown in Fig. 6b–d and these films are characterized by the presence of larger particles since these films contains H-TiO2 NPs of size 150– 200 nm. The roughness values of these deposited films are greatly increased with respect to screen printed C-TiO2 film and are measured as 24.6, 24.0 and 28.8 nm for 5, 10 and 15 min deposited samples respectively. The regions investigated by AFM in Fig. 6b–d with more roughness values are due to the special morphology of H-TiO2 NP which was confirmed from TEM and FESEM images. In addition, we notice that the deposited films are completely free from any cracks and their deposition in a porous medium could be useful for DSSCs. Fig. 3. Schematic diagram for the electrophoretic deposition of H-TiO2 NPs on C-TiO2 coated FTO substrate.

3.3. Photovoltaic performance studies of DSSCs film for DSSC applications, the deposition was carried out at different times 5, 10 and 15 min and their corresponding microscopy images are given in Fig. 4. At all deposition times, we observed complete film and the formed films appeared porous in nature. Fig. 4 also reveals that the deposited H-TiO2 NPs are stable at higher pH values and also after applying a voltage of 50 V. The bird's eye view of deposited films are shown in Fig. 5a, c and e which reveals that the formed films are crack-

Different photoanodes have been prepared with and without a scattering layer to investigate the scattering layer thickness effect of HTiO2 NPs on the photovoltaic performance. The schematic diagram for the device structure was shown in Fig. 7. The J-V characteristics of DSSCs made from C-TiO2 and double layer structured electrodes with H-TiO2 NPs were plotted in Fig. 8a. The distinct photovoltaic behavior of the H-TiO2 NPs is its large short-circuit current (Jsc) values

Fig. 4. The FE-SEM images of electrophoretically deposited H-TiO2 NP films at 50 V under different magnifications: (a–d) 5 min, (e–h) 10 min and (i–l) 15 min.

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Fig. 5. Bird's eye view (a, c, e) and FE-SEM cross sectional images (b, d, f) of electrophoretic deposited H-TiO2 NPs at 5, 10 and 15 min.

Fig. 6. AFM images of the prepared films with their corresponding roughness values (a) C-TiO2 screen printed film, electrophoretic deposited H-TiO2 films for 5 min (b), 10 min (c) and (d) 15 min.

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Table 1 Comparison of short-circuit photocurrent density (Jsc), open circuit photovoltage (Voc), fill factor (FF), overall photoconversion efficiency (η) along with the amount of adsorbed dye N719 for the films with and without H-TiO2 NPs scattering layer. Photoanode

Dye amount 10−7 mol/cm2

VOC Volts

JSC mA cm−2

Fill Factor %

Efficiency η (%)

C-TiO2 H-TiO2 – 5 min H-TiO2 – 10 min H-TiO2 – 15 min

1.09 1.18 1.27 1.69

0.621 0.633 0.638 0.636

14.164 15.330 15.599 17.201

69.13 65.00 69.87 67.29

6.08 6.31 6.95 7.58

light of different wavelengths in the range of visible light [48,49]. Recently few authors revealed that the mesoporous hollow spherical TiO2 can produce a greatly enhanced photocatalytic activity or photoelectric conversion efficiency due to light multi-reflections [50–52]. Similarly, we believed that the improved photocurrent for the H-TiO2 NPs is mainly contributed to by its hollow spherical structure which provides an effective way to enhance light-harvesting efficiency. To understand the major factor responsible for the improved PCE for the H-TiO2 films, the incident photon-to-electron conversion efficiency (IPCE) spectra were measured as a function of the incident-light wavelength, and also this IPCE spectra offer detailed information on the light harvest of the DSSCs. Fig. 8b displays the IPCE spectra for both C-TiO2 and H-TiO2 NPs (10 min deposited sample) based DSSCs. The quantum efficiencies of all cells with N719 dye were maximized at ~550 nm. The dye-loading capacity of each photoelectrode is reflected on the corresponding IPCE in the shorter wavelength region, while the light scattering efficiency can be explained by the IPCE value in the longer wavelength region (600–700 nm). It is observed that the overall IPCE increases considerably by the introduction of a scattering layer, and the H-TiO2 films possess higher IPCE values than the C-TiO2 NP film over the whole spectral range. The maximum quantum efficiency at 550 nm was increased to ~60% for HTiO2 and whereas ~35% only for C-TiO2. These data suggest that a bilayer film structure with H-TiO2 NPs scattering layer deposited on a nanocrystalline C-TiO2 NPs layer remarkably increases the performance of DSSCs. Previously, Nakayama, et al. successfully investigated the performance of a DSSC with a bilayer structure containing αTitania nanotubes (α-TNT) [53]. In this work, authors electrophoretically deposited α-TNT onto a transparent small sized TiO2 NPs film and their photovoltaic properties are studied. The DSSCs based on α-TNT showed a greater Jsc value (14.96 mA/cm2) with a PCE of 7.53% and

Fig. 7. Schematic diagram of DSSC structure.

compared with that of C-TiO2 NPs. This enhanced photocurrent could be attributed to better dye adsorption, due to increased active surface area, or better light-harvesting efficiency, due to the hollow spherical structure. The photoanodes based on C-TiO2 NPs showed a Jsc of 14.16 mA/cm2 with a photoconversion efficiency (PCE) of 6.08% and whereas the photoanodes based on H-TiO2 NPs showed the Jsc values of 15.33, 15.60 and 17.20 mA/cm2 with PCE of 6.31%, 6.95% and 7.58% respectively. In Table 1, photovoltaic properties are compared with the corresponding dye-loading amount of each working electrode. The larger Jsc value for the H-TiO2 NPs is most likely given rise by an enhanced light harvesting due to multiple light reflections and scattering inside of the H-TiO2 NPs. In our recent report, the surface area of both C-TiO2 and H-TiO2 NPs were measured as 82 and 89 m2/g respectively [41]. The adsorbed amounts of N719 dye were determined by measuring the eluted dye concentration from the H-TiO2 structure with UV–Vis absorption spectroscopy. As shown in Table 1, DSSCs based on H-TiO2 photoanodes revealed more dye absorption compared to that of C-TiO2 NPs. The increment in dye absorption was simply proportional to the surface area of the TiO2 NPs. It is confirmed that the enhanced photovoltaic efficiency (η) of the DSSCs fabricated from H-TiO2 NPs is closely related with the larger amounts of anchored dye molecules. The inset in Fig. 8a illustrates the reflecting and scattering of light in a H-TiO2 NP. It is believed that the particles with the different sizes can not only multi-reflect, but also scatter the incident

Fig. 8. (a) I-V characteristics of DSSCs assembled with the C-TiO2 screen printed and bi-layer structure with H-TiO2 films of varying thicknesses, (b) IPCE spectra of DSSCs made from C-TiO2 film and bilayer structure with H-TiO2 NPs.

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also showed a higher IPCE values in the whole spectral range. Similarly, Shao et al. fabricated the DSSCs based on P-25 TiO2 NPs and titania nanorod particles by using EPD method and produced a PCE of 4.35% [54].

[17]

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4. Conclusions In summary, Au@TiO2 core-shell NPs were successfully synthesized by microwave hydrothermal method and then H-TiO2 NPs were produced by selective etching of Au NPs. As confirmed by TEM and EDS elemental/compositional characterizations, Au core was completely removed from Au@TiO2 core-shell NPs. EPD was successfully employed to make H-TiO2 NPs scattering layer with different thicknesses on the top of small sized C-TiO2 NPs film. The DSSCs based on bi-layer structure containing H-TiO2 NPs showed a enhanced PCE of 6.31%, 6.95% and 7.58% at 5, 10 and 15 min deposition times respectively and whereas the alone C-TiO2 film showed only a PCE of 6.08%. The significant improvement in Jsc (or η) values for the DSSCs based on H-TiO2 NPs scattering layer can be ascribed to its higher surface area for adsorbing more dye molecules and superior light scattering capacity for boosting the light-harvesting efficiency which are responsible for the improvement of the power conversion efficiency. In addition, this EPD technique would open a way to produce scattering layers of controllable thickness for high performance DSSC applications.

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This paper was supported by (1) BK21 plus program from the Ministry of Education and Human-Resource Development, (2) National Research Foundation grant funded by the Korea government (MSIP) (BRL No. 2015042417, and 2016R1A2B4014090).

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