ARTICLE pubs.acs.org/JPCC
Structure and Electron-Conducting Ability of TiO2 Films from Electrophoretic Deposition and Paste-Coating for Dye-Sensitized Solar Cells Yong-Jin Liou,† Po-Tsung Hsiao,† Liang-Che Chen,† Yen-Yu Chu,† and Hsisheng Teng*,†,‡ †
Department of Chemical Engineering and Research Center for Energy Technology and Strategy, National Cheng Kung University, Tainan 70101, Taiwan ‡ Center for Micro/Nano Science and Technology, National Cheng Kung University, Tainan 70101, Taiwan
bS Supporting Information ABSTRACT: An electrophoretic deposition (EPD) method, consisting of repetitive short-term depositions with intermediate drying, was developed to prepare nanocrystalline TiO2 films for dye-sensitized solar cells (DSSCs). After calcination, the EPD TiO2 films exhibited a more compact TiO2 network than films derived from the conventional paste-coating (PC) method. X-ray absorption fine structure spectroscopic analysis showed that the EPD films had a higher density of defect states than the PC films because of the higher number of interparticle necking regions created in the EPD films. However, the DSSCs assembled with the EPD films outperformed those with the PC films by 20% in photocurrent and 15% in solar energy conversion efficiency. Intensity-modulated photocurrent spectroscopic analysis showed that the EPD films had a shorter electron transit time than the PC films. Under one-sun illumination on the cells at open-circuit, impedance analysis showed that the EPD films had a constant charge collection efficiency of 95% for thicknesses ranging from 4 to 13 μm, whereas the efficiency of the PC films was not greater than 90% and showed a decreasing trend with increasing film thickness. Concerning the porosity dependence of the electron transport dynamics, the electron diffusivity had much weaker dependence than one would expect from the percolation model with hard spheres. This may result from the fact that interparticle necking causes greater lattice distortion for more compact TiO2 films. The present study demonstrates that an optimized EPD process can construct a nanocrystalline TiO2 architecture with a minimized void fraction to shorten the electron traveling distance and to effectively collect photogenerated charges, even for films with large thicknesses.
’ INTRODUCTION Dye-sensitized solar cells (DSSCs) represent a cost-effective photovoltaic alternative to conventional silicon-based solar cells.18 The cells consist of a dye-sensitized mesoporous n-type semiconductor film filled with an electrolyte and a Pt counter electrode. During illumination of the cells, electrons are injected from the photoexcited dye sensitizer into the conduction band of the semiconductor, from which the electrons pass through the semiconductor film, and are then collected by a transparent conductive oxide (TCO) substrate. To date, TiO2 anatase has been considered to be the optimal choice of semiconductor for DSSCs.9 Because TiO2 films are nanocrystalline and contain crystal defects and grain boundaries that impede electron transport, the framework and crystal structure of the TiO2 film govern the electron transport mechanism and the resulting cell performance. The coating of a viscous TiO2 paste on a TCO glass substrate, followed by calcination to remove organic additives, results in TiO2 films with a loose particle-packing network, which hinders electron transport. To improve electron percolation in the TiO2 films, electrophoretic deposition (EPD), which uses no r 2011 American Chemical Society
binder and assures intimate contact of deposited particles, represents a potential alternative to the paste-coating (PC) method.10,11 In comparison with PC techniques, EPD has the advantages of low cost, short deposition time, and high reproducibility.1214 The binder-free feature of EPD is attractive for preparing TiO2 films on flexible plastic substrates that cannot tolerate hightemperature calcination but can tolerate high-pressure compression.1523 When conducting EPD, particles must be electrically charged to permit film formation in an electrical field and also for stabilization of the suspension. Previous studies have shown that a small iodineacetonewater additive can charge TiO2 nanoparticles in an alcohol solvent via the adsorption of generated protons.12,2224 The lower boiling points of these charging additives enable the fabrication of TiO2 films at relatively low temperatures. We employ this charging process to disperse TiO2 nanoparticles for EPD in the present work. Because a high Received: October 31, 2011 Revised: November 25, 2011 Published: November 25, 2011 25580
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The Journal of Physical Chemistry C evaporation rate of the residual solvent leads to crack formation, we test a multilayer deposition approach to suppress crack formation.20,25 For construction of an electrically connected network for DSSCs, sintering the coated TiO2 films for the necking of nanoparticles is essential. Lattice distortion near the crystal grain boundary appears after sintering for particle necking.26,27 The nanocrystalline framework and thus the TiO6 octahedron arrangement of TiO2 films fabricated by EPD must be different from that of films fabricated by the conventional PC, in which particles are separated by organic additives, resulting in less compact calcined films. Previous studies have elucidated how electron transport in TiO2 films can be influenced by the TiO2 defect-state density, which is closely related to the crystallinity of particles and the film fabrication process.2733 However, the detailed structure and electron-conveying ability of TiO2 films fabricated by EPD have rarely been discussed. With this knowledge, we used both the PC and EPD methods to prepare the mesoporous TiO2 films for DSSCs. The films derived from the two different methods showed obvious differences in surface morphology and network structure. A series of tests showed that the DSSCs assembled with the EPD films outperform those with the PC films in light-to-electricity conversion and showed a higher efficiency in photogenerated charge collection. We employed X-ray diffraction (XRD) and X-ray absorption fine structure spectroscopy to characterize the crystal defects and chemical environments of Ti4+ sites in the TiO2 films. The TiO2 film structure and electron transport analysis demonstrate that the EPD method reduces the tortuosity of the electron diffusion path in TiO2 films and thus enhances the light conversion efficiency.
’ EXPERIMENTAL SECTION The TiO2 nanoparticles for fabricating the PC and EPD films were synthesized from the titanate-directed method described elsewhere.28,29 In brief, we prepared the TiO2 nanoparticles by mixing 3 g of commercially available TiO2 powder (P25, Degussa) with 100 mL of 10 N NaOH (J. T. Baker) and heating the mixture in the autoclave at 130 °C for 20 h. The resulting product was washed with 0.1 N HNO3 (Showa) to achieve pH 1.5. Finally, the low-pH solution was subjected to hydrothermal treatment at 240 °C for 12 h to obtain a TiO2 colloidal solution. To prepare a viscous TiO2 paste for PC, we mixed the TiO2 colloidal solution with poly(ethylene glycol) (PEG; Fluka, 20 000 in molecular weight) at a PEG/TiO2 ratio of 0.4. A TiO2 suspension for EPD was prepared by mixing 3 g of TiO2 with 47 g ethanol and a small amount of acetylacetone (Merck) using magnetic stirring for 24 h. A charging solution was obtained by dissolving 63 mg iodine in a 250 mL ethanol solution containing 10 mL of acetone and 5 mL of deionized water.22,23 Just prior to EPD, the TiO2 suspension was added to the charging solution with subsequent sonication for 15 min in an ice bath. To prepare PC TiO2 films, we blade-coated the viscous TiO2 paste on fluorine-doped SnO2 (FTO) conducting glass substrates (TEC 8, Hartford Glass). The TiO2-coated substrates were subsequently calcined at 450 °C for 30 min. For EPD film preparation, two FTO glass substrates, used as the cathodic substrate and counter electrode, were vertically placed 0.8 cm apart and immersed in the charged TiO2 suspension. The EPD process was conducted at a constant voltage at room temperature. To increase the film thickness while avoiding crack formation,22
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we used a multilayer EPD, consisting of repetitive deposition at 5 V for 60 s with intermediate drying at room temperature. We subjected the films from EPD to sintering at 450 °C for 30 min to obtain the EPD TiO2 films for DSSC assembly. Scanning electron microscopic (SEM) images of the PC and EPD films were obtained using a JEOL JSM-6700F at a beam potential of 10 kV. The specific surface area of the films was measured by N2 adsorption at 196 °C using an adsorption apparatus (Micromeritics, ASAP 2010), with the adsorption data fitted to the Brunauer EmmettTeller equation. The specific pore volume was obtained from the total amount adsorbed at relative pressures near unity. The pore size distribution was analyzed by using the BarrettJoynerHalenda method. To analyze the detailed structure of the TiO2 films, we subjected the fragments scraped from the TiO2 films to structural analysis. The phase identification of the specimens was conducted with powder XRD using a Rigaku RINT2000 with Cu Kα radiation at 40 kV and 40 mA. Data were collected with a step interval of 0.02° and a measuring time of 10 s per point in the 2-theta range of 20°70°. The structural features and chemical environment of the Ti4+ sites on the TiO2 specimens were characterized by X-ray absorption fine structure spectroscopy, including X-ray absorption near-edge structure (XANES) and extended X-ray absorption fine structure (EXAFS). The spectra were measured at room temperature in a transmission mode on the Wiggler beamline of the Taiwan Synchrotron Radiation Research Center. Double-crystal Si(111) was used to monochromatize X-rays from the 1.5 GeV electron storage ring for a current range of 120200 mA. Photon energy was calibrated by characteristic pre-edge peaks in the absorption spectrum of Ti foil (4966 eV). The EXAFS spectra were analyzed using simulation programs UWX-AFS 3.0 and FEFF 7.0 to determine the bond distance and the coordination number of the different shells. Fourier transform (FT) analysis was used on the k3weighted EXAFS oscillation in the range of 2.612 Å1. Each shell fitting was conducted in the R space. To prepare a dye-covered TiO2 film for a DSSC, we immersed a TiO2 film in a 0.5 mM N719 dye (Solaronix) solution in a mixture of acetonitrile and tert-butyl alcohol with a 1/1 volume ratio for 24 h. The thickness of the film (0.4 cm 0.4 cm) was determined by a profilometer (Alpha Step 5000, Tencor). To determine the amount of dye covering each TiO2 film, we placed the sensitized film in a 10 mM KOH solution to desorb the dye and then measured the amount of desorbed dye with absorption spectroscopy (U-4100, Hitachi) at 502.2 nm. The dye-covered electrode was then assembled with a Pt-coated conducting glass using a 60 μm thick sandwich type thermoplastic frame (SX117060, Solaronix). The electrolyte composition for the DSSC was as follows: 0.1 M LiI (Strem), 0.05 M I2 (Riedel-de Ha€en), 0.6 M 1,2-dimethyl-3-n-propylimidazolium iodide (Solaronix), and 0.5 M 4-tert-butylpyridine (Aldrich) in acetonitrile (J. T. Baker). Photovoltaic measurements of the DSSCs employed an AM1.5 solar simulator (sp91160A-4739, Newport), and the intensity of the simulated light was calibrated as 100 mW cm2 using Si solar cell as a reference. The electron transport properties were measured by intensity modulated photocurrent spectroscopy (IMPS). IMPS measurements were carried out by illuminating the cells from the dye-coated TiO2 electrode side and using a frequency response analyzer (XPOT, Zahner), which was used to drive a blue light-emitting diode (LED, λ = 455 nm). The light intensities were modulated ((5%) by modulating the voltage applied to the LED with sinusoidal waves in the frequency range 0.1103 Hz at 25581
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Figure 1. Powder X-ray diffraction (XRD) patterns of the TiO2 fragments from scraping the paste-coating (PC) and electrophoretic deposition (EPD) TiO2 films. The standard diffraction pattern of TiO2 anatase from JCPDS 21-1272 is provided at the bottom of this Figure.
a dc light intensity of 15 mW cm2. We also complemented the IMPS analysis using red light (LED, λ = 625 nm) illumination at a dc light intensity of 13 mW cm2. The electrochemical impedance spectra of the cells were measured with a potentiostat equipped with a frequency response analyzer (IM6, Zahner), over the frequency range 0.1105 Hz. The bias potential was set at the open-circuit with an ac potential amplitude of 10 mV under an AM 1.5 solar illumination of 100 mW cm2.
’ RESULTS AND DISCUSSION Figure 1 shows the powder XRD patterns of the PC and EPD TiO2 fragments obtained by scraping the calcined TiO2 films. The standard pattern of TiO2 anatase from the powder diffraction file of JCPDS (Joint Committee of Powder Diffraction Standards) is shown at the bottom of Figure 1. Because the TiO2 colloids were synthesized along the titanate-directed route, both the PC and EPD TiO2 powders are of phase-pure anatase.26,27,33 Figure 2 shows the top-view SEM images of the PC and EPD TiO2 films. The EPD film exhibits a tightly packed surface morphology, whereas the PC film contains numerous voids because of the space left after the calcination of the PEG binder in the paste. This difference in the arrangement of the TiO2 nanocrystals constituting the mesoporous films may significantly influence the electron transport behavior in the films. For example, the density of defect states resulting from structural mismatch at the crystal grain boundaries would be greater for a more compactly packed film. The electron transport in TiO2 films is closely related to the defect-state density.26,27,33,34 Table 1 shows the surface area and total pore volume of the TiO2 films, and we also listed the porosity (P) of the films calculated from the pore volume.35 The PC and EPD films have similar surface area, whereas the PC films have a larger total pore volume, and therefore a greater porosity value, than the EPD. The smaller porosity of the EPD films reflects a larger number of nearest neighbors for the particles constituting the EPD films. This is in accordance with the SEM inspection (Figure 2). The pore size distribution data (Supporting Information) also show a smaller pore size for the compactly packed EPD film. The similarity in surface area for these two types of films indicates that particle-necking causes negligible surface area loss. However, the necking calcination may result in lattice distortion at the interparticle
Figure 2. Top-view SEM images of the PC TiO2 film (panels a and b) and EPD TiO2 films (panels c and d) with different degrees of magnification.
Table 1. Surface Area, Pore Volume, and Porosity of the TiO2 Films by Paste-Coating (PC) and Electrophoretic Deposition (EPD) Obtained from N2 Adsorption Analysis TiO2 specimen
surface area (m2g1)
pore volume (cm3g1)
porosity, P (%)
PC
77
0.40
61
EPD
79
0.30
54
boundaries and induce defect states. Different numbers of nearest neighbors for the particles may thus cause different degrees of lattice distortion in the resulting films. We subjected the chemical environment of the Ti4+ cations in the TiO2 films to analysis with X-ray absorption fine structure spectroscopy in an attempt to determine the defect-state density. Figure 3a shows the Ti K-edge XANES patterns of the EPD and PC TiO2 fragments scraped from the films. The coordination number (CN) of the first shell TiO determines the position and intensity of the pre-edge feature. The pre-edge region (Figure 3b,c) shows obvious peaks labeled as A1, A3, and B. An additional peak labeled A2 is present as a weak shoulder on the low-energy side of the A3 peak. The A1, A2, and A3 features in the pre-edge correspond to the dipole transitions of the Ti core electrons to 4p orbitals hybridized with crystal split Ti 3d orbitals on neighboring Ti atoms. The B feature corresponds to the transition to Ti 4p hybridized with neighboring Ti 4s, O 2p, or both.36 The four-, five-, and six-fold coordinated Ti4+ can be distinguished by the A3 peaks at 4969.5, 4970.5, and 4971.5 ( 0.2 eV, respectively.3739 Both the PC and EPD films had an A3 position of 4971.7 eV, indicating an almost six-fold coordination of Ti4+ ions in these two specimens. However, the EPD film shows a higher intensity of pre-edge peaks and a smaller edge jump. This suggests a smaller CN for EPD.3941 Furthermore, structural distortion generally leads to an increase in the intensity of the B peak and the intensity ratio of A2/A3, which both serve as sensitive probes for the degree of distortion in the TiO6 octahedron.42,43 We decomposed the pre-edge spectra using Gaussian fitting, and 25582
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Figure 4. Fourier transformed k3χ(k) EXAFS spectra of the PC and EPD TiO2 powders from scraping the films. The dashed line curves denote the best fitting of the spectra in the range of 13.5 Å.
Table 2. Coordination Number (CN) and Bond Distance (R) of the Ti4+ Sites in the TiO2 Films by Paste-Coating (PC) and Electrophoretic Deposition (EPD) Obtained from EXAFS Analysis TiO2 specimen PC EPD anatase
Figure 3. (a) Ti K-edge XANES spectra of the PC and EPD TiO2 powders from scraping the films. The pre-edge features of the XANES spectra: (b) PC and (c) EDP. The dashed lines in panels b and c indicate the Gaussian-fitting curve that is composed of individual peaks A1, A2, A3, and B.
Figure 3b,c shows the individual peaks from the simulation (dashed lines). The B peak intensities for the PC and EPD films were 0.25 and 0.29, respectively, and the intensity ratios of A2/A3 were 0.33 and 0.41. The EPD film had higher values of both B peak intensity and A2/A3 ratio, indicating a higher degree of structural distortion in the EPD film. The EXAFS is derived from the scattering of neighboring atoms and provides quantitative coordination information on the target ions. Figure 4 shows the FTs of the k3χ(k) EXAFS for the PC and EPD TiO2 films with a radial distance ranging from 1 to 3.5 Å. The spectra in the Figure have been corrected for phase shifts. Table 2 summarizes the CN and the bond distance (R) of the first and second shells (TiO and TiTi) obtained by FEFF simulation. The data for the standard TiO2 anatase are also shown in the Table for comparison. The CNs of both the PC and EPD films were smaller than those of the standard anatase
shell
CN
R (Å)
σ2 (Å2)
TiO
5.68
1.97
0.007
TiTi
3.44
3.06
0.003
TiO
5.44
1.97
0.004
TiTi
3.18
3.06
0.004
TiO
6.00
1.96
0.008
TiTi
4.00
3.07
0.005
because of the nanocrystalline feature of the films. Because the XANES analysis revealed six-fold coordinated Ti4+ with O2 for both films, the lowered CNs may mainly result from structural distortion, rather than oxygen vacancy. The EPD film resulted in smaller CNs than the PC for both TiO and TiTi, justifying the conclusion from the XANES analysis that the crystal lattice of the EPD film is more disordered than that of the PC. These two films were constructed from the same colloidal TiO2 nanoparticles. This suggests that thermal necking between nanoparticles has created this difference in CNs. The tightly packed configuration of the EDP film (Figure 2c,d), in which the TiO2 nanoparticles have a large number of nearest neighbors, must have encountered a high degree of interparticle lattice interference during calcination and enhanced the structural distortion near the crystal grain boundaries.44,45 The PC and EPD TiO2 films were sensitized with a ruthenium complex dye (N719) and assembled into DSSCs. Figure 5 shows the photocurrent—voltage characteristics of the DSSCs with varying TiO2 film thicknesses under AM 1.5 solar illumination at 100 mW cm2. The EPD cells exhibited a larger photocurrent than the PC cells for each film thickness. It could be argued that the amounts of dye covering the EPD and PC films were different. Figure 6 shows the amounts of the dye loaded onto the EPD and PC films. For films of 7.513 μm thick, the EPD films have ∼11% more dye loading than the PC films, whereas the former films exhibit 2335% more in photocurrent. The difference in the amount of dye-loading may affect the photocurrent performance, but this alone cannot account for the great difference between the photocurrents exhibited by these two types of films. Figure 7 summarizes the cell performance indices 25583
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Figure 5. Photocurrentvoltage characteristics of DSSCs assembled with the PC and EPD TiO2 films of varying thicknesses under AM 1.5 solar illumination at 100 mW cm2.
Figure 6. Dependence of dye loading on the TiO2 film thickness of DSSCs assembled with the PC and EPD films.
based on the data of Figure 5. Both the open circuit voltage (Voc) and the fill factor decreased with film thickness. In contrast, the short circuit current (Jsc) increased with increasing film thickness to its maximum value and then decreased. Because of the variation of Voc, Jsc, and fill factor with thickness, the maximum efficiency occurred at a thickness of 13 μm, at which the Jsc was also maximized. This suggests that photocurrent governs the cell efficiency, even though Voc and the fill factor vary with thickness. The larger photocurrent and thus the larger efficiency of the EPD cells relative to those of the PC cells may be related to the electron transport dynamics, influenced by defects in the TiO2 film. In previous studies, we showed the significant influence of defect-state density on electron transport in TiO2 films.26,27,33 This study subjected the cells assembled with the PC and EPD films to IMPS and impedance analysis. The IMPS technique measured the response of the photocurrent to the modulations in incident light intensity, which is a constant dc illumination intensity superimposed with a small sinusoidal perturbation.46 Figure 8 shows the IMPS responses of the PC and EPD cells for different film thicknesses under blue light irradiation (λ = 455 nm). Both the EPD and PC cells exhibited a semicircular feature in the complex plane at a small film thickness (4 μm). A semicircle appeared at higher frequencies for the cells with a larger film thickness, and the IMPS plots were characterized by two overlapping semicircles.
Figure 7. Dependence of cell performances on the film thickness of DSSCs assembled with the PC and EPD films under AM 1.5 solar illumination at 100 mW cm2.
This high-frequency semicircle expanded and became dominant at larger film thicknesses. Our previous work indicated that the two-semicircle IMPS response reflects two different diffusion modes for electron transport.26 van de Lagemaat and Frank indicated the presence of nonthermalized (hot) electrons accounting for the high-frequency (swift-transit) response.47 Halme et al. employed the standard diffusion model to simulate the IMPS response and explained the appearance of two time constants with two distinct transport lengths,48 the faster component corresponding to direct diffusion to the collector and the slower to diffusion to the opposite direction with subsequent reflection for collection. Nissfolk et al. also used a simple diffusion model to predict 25584
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Figure 9. Effect of TiO2 film thickness on the faster-component transit time (dash line) and slower-component transit time (solid time) based on the blue light IMPS analysis. The transit times for the PC and EPD films were obtained by the fmin of the blue light IMPS plots. The incident dc illumination intensity was 15 mW cm2.
Figure 8. IMPS responses of DSSCs assembled with the PC and EPD TiO2 films of varying thicknesses under short circuit conditions. A blue light-emitting diode (λ = 455 nm) was used as the modulation light source with dc intensity of 15 mW cm2 and superimposed 5% ac intensity. As an example, the responses at the high and low fmin frequencies are indicated in the spectrum of the EPD cell with a 10 μm film thickness.
the shape of the photocurrent transients.49 The frequency at which the minimum IMPS response occurs, fmin, gives the average transit time (τd) of electrons from photogenerated injection to collection by the conducting glass, following the equation τd = (2πfmin)1.50,51 Figure 9 summarizes the electron transit times of the faster and slower components for different thicknesses. The faster-component time constant of the thicker films is smaller than the time constant of the thinner films that exhibit only one constant. This observation may indicate that the simple diffusion model alone cannot explain the fast transit process observed in the thicker films. The shorter transit time (of both the faster and slower components) for the EPD film reflects the difference in transport behavior of the PC and EPD films and explains the higher photocurrents of the EPD cells (Figures 5 and 7). However, the EPD films have a larger defect-state density than the PC films and are expected to have a longer electron transit time.26 This apparent contradiction may be associated with the network arrangement of the TiO2 nanoparticles constituting the films. The appearance of two time constants in the IMPS response for thicker films may be associated with the use of strongly absorbing blue light because the photoinduced charges would be mainly generated on the illuminated side of the TiO2 film. We have also conducted IMPS measurements using a red light diode (λ = 625 nm). Because red light is weakly absorbed by the dye,
Figure 10. Schematic showing the difference in electron transport pattern of DSSCs assembled with the PC and EPD TiO2 films.
charges are generated uniformly throughout the film. The redlight IMPS results (Supporting Information) show that the faster transit pattern diminished, especially for the EPD films that contain more trap states. The distribution of electron injection intensity over the film thickness affects the electron traveling pattern.47,48 Similar to the results using blue light, the EPD films exhibited a shorter transit time than the PC films under red light irradiation (Supporting Information). Figure 10 shows a schematic to elucidate the difference in the electron diffusion path of the films. The EPD film consists of 25585
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closely packed TiO2 nanoparticles and gives a shorter average path length before collection for photogenerated electrons. The PC film is composed of loosely packed TiO2 nanoparticles, leading to various directions of electron diffusion. We may express the effective diffusion coefficient per unit cross section of a porous film, Deff, as52 Dθ ð1Þ Deff ¼ T D is the electron diffusion coefficient of solid-phase TiO2 with a certain defect-state density, θ is the solid-phase fraction of the film, and T is a tortuosity factor that allows the direction of diffusion to be varied. The EPD films had a smaller D value than the PC film because of its higher defect-state density. Nevertheless, the large θ and smaller T values result in a greater Deff for the EPD film relative to that of the PC film. This schematic interpretation demonstrates that both the defect-state density and architectural design must be considered when fabricating an electron-conducting film for DSSCs. In addition to eq 1, percolation theory that correlates the electrontransport dynamics with film network geometry was employed for the DSSC system.35,53,54 We will discuss the present work using percolation theory later. Defect states in TiO2 films impede electron transport and increase the transit time and also impede electron recombination with I3 at the electrolyte/electrode interface.55,56 To explore the electron recombination kinetics and the influence of defect state density, we subjected the PC and EPD cells to further electrochemical impedance spectroscopy (EIS) analysis.57,58 Figure 11a shows the Nyquist impedance spectra of the PC and EPD cells with varying TiO2 film thicknesses at the opencircuit voltage under 100 mW cm2 of solar illumination. In general, the impedance spectra of DSSCs comprise three arcs that are associated with the charge transfer at the Pt/electrolyte interface (high frequencies), the electron motion in the TiO2 mesoporous film (middle frequencies), and the Nerstian diffusion of I3 in the electrolyte (low frequencies).5961 The impedance spectra were simulated and interpreted using an equivalent circuit (Figure 11b) corresponding to the transmission line model.6265 The elements of the circuit relating to TiO2 film are the electron transport resistance, Rt (= rtL), the interfacial charge recombination resistance, Rct (= rct/L), and the chemical capacitance produced by the accumulation of electrons in the TiO2 film, Cμ (= cμL), where L is the TiO2 film thickness. The solid lines in Figure 11a represent the results of the simulation. This study is concerned with the elements of the circuit relating to the TiO2 film. Table 3 shows the values of cμ, rt, and rct obtained from the simulation. Meanwhile, the mean lifetime of the electrons in TiO2 was calculated from the relationship τn,EIS = rct cμ. The mean electron transit time, τd,EIS, can be determined from the equation τd,EIS = rt cμ L2. Table 3 lists the values of τn,EIS and τd,EIS. After taking the porosity effect on cμ into account, the EPD films had larger chemical capacitance values than the PC films (except the films of 17 nm). The more compact EPD films had smaller rt for electron transport. This is in agreement with the results of IMPS measurements, which showed shorter transit times for the EPD films. The rct values are similar for the PC and EPD films because the films are composed of the same nanoparticles. These values of cμ and rct together contributed to the longer lifetimes (τn,EIS) for the EPD films shown in Table 3. The transit time determined from τd,EIS = rt cμ L2 shows a smaller value for the EPD films. Because the EPD films have larger cμ values, the smaller τd,EIS for the EPD films is primarily due to the much smaller rt values.
Figure 11. (a) Nyquist impedance plots of DSSCs assembled with the PC and EPD TiO2 films of varying thicknesses under AM 1.5 solar illumination at 100 mW cm2, with the ac frequency ranging from 0.1 to 105 Hz at the open-circuit voltage of the cells. The solid lines represent the results simulated using the parameters in Table 2. (b) General equivalent circuit of DSSCs. Rs is the sheet resistance of the conducting glass. rt, rct, and cμ correspond to the electron transport resistance, interfacial charge-transfer resistance, and chemical capacitance in the TiO2 film. RPt and CPt are the charge-transfer resistance and capacitance at the Pt/electrolyte interface, respectively, and ZN is the Nernst impedance.
With the EIS analysis, we also calculated the electron diffusion coefficient (De) of the TiO2 films following De = L2/τd,EIS = (rt cμ)1 and listed the De values in Table 3. By correlating the De and P data with a power-law relationship: De µ |P Pc|β, where Pc is the critical porosity (0.76, according to ref 35) and β is the power-law exponent, the TiO2 films of 413 μm thick show a β value of 1.2 to 2.3, which in most cases is lower than the conductive exponent for a 3D percolation model (β = 2). This is somewhat in agreement with the study by Frank et al.,35 who anticipated that the nanoparticles in the TiO2 film reorganize to maintain interparticle contact and therefore lower the influence of porosity on the diffusivity. In the present work, the XANES and EXAFS analyses have disclosed the fact that the TiO2 nanoparticles are not hard spheres that are premised by percolation theory. The distortion degree of TiO2 lattice increases with the TiO2 particle density of the porous films. The crystalline lattice disorder in the high-density film impedes the electron transport and therefore lowers the effect of density on electron diffusion coefficient. This explains why the TiO2 films showed a β value smaller than 2 that accounts for 3D conductive percolation. 25586
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Table 3. EquivalentCircuit Parameters of DSSCs Assembled with the PC and EPD TiO2 Films of Varying Thicknesses and the Electron Diffusion Coefficient in the TiO2 Filmsa L (μm)
cμ (μF μm1)
rt (Ω μm1)
4
53.8
0.92
155
7.5 10
56.7 66.0
0.40 0.30
208 217
11.8 14.3
13
80.8
0.26
265
17
55.1
0.28
354
rct (Ω μm)
τn,EIS (ms)
τd,EIS (ms)
De (cm2 s1)
8.33
0.79
2.0 104
1.3 2.1
4.4 104 5.1 104
21.4
3.6
4.8 104
19.5
4.5
6.5 104
PC Cells
EPD Cells
a
4
87.8
0.36
117
11.4
0.51
3.2 104
7.5
79.5
0.16
187
14.9
0.72
7.9 104
10
97.7
0.10
224
21.9
0.98
10 104
13
91.5
0.09
290
26.5
1.4
12 104
17
56.3
0.10
306
17.2
1.6
17 104
Values are determined based on the data of Figure 11.
where τcc is the time constant for electron collection and 1/τcc corresponds to the electron collection rate at the FTO substrate and is equal to (1/τd,EIS 1/τn,EIS). Figure 12a shows the film thickness dependence of the electron collection efficiency. The values of the EPD films are larger than those of the PC films, explaining the larger Jsc of the EPD films. Moreover, the ηcc of the EPD films remain as high as 95% for film thicknesses up to 13 μm, whereas the ηcc of the PC films, with a value of 90% at 4 μm, show a decreasing trend with the film thickness. This indicates that the high compactness and thus small-tortuosity feature of the EPD film facilitates effective electron collection when introduced even at a distance of more than 10 μm from the FTO. The electron diffusion length (Ln) is an alternative index of electron transport effectiveness.66,67 Figure 12b shows the film thickness dependence of Ln values, which were calculated according to rffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rct ð3Þ Ln ¼ De τn, EIS ¼ rt
Figure 12. Dependence of (a) charge collection efficiency (ηcc) and (b) effective diffusion length (Ln) on the film thickness for DSSCs assembled with the PC and EPD TiO2 films.
For a quantitative comparison of the effectiveness of the PC and EPD films in electron conveying, we neglected the effect of light absorption profile and approximately estimated the charge collection efficiency (ηcc) using the equation
ηcc ¼
1 τcc 1 1 þ τcc τn, EIS
! ¼ 1
τd, EIS rt ¼ 1 L2 τn, EIS rct
ð2Þ
Light absorption in the film is stronger for positions closer to the FTO substrate; therefore, the mean absorbed photon number per unit thickness is larger for thinner films. This makes Voc larger for thinner films (Figure 7) and therefore the Ln value of a cell dependent on the film thickness.68,69 As expected, the Ln values were larger for the EPD films. Equation 3 explicitly shows that the rt value governs Ln if identical TiO2 nanoparticles, of similar rct, are used to constitute the films. Because of the small rt values, the Ln values of the EPD films were four times the film thickness, ranging from 4 to 13 μm. The important implication is that the packing pattern of TiO2 nanoparticles may critically affect the rt value and thereby the cell performance. However, it should be noted that any electronic property changes associated with the film-structural difference may also influence electron transport in the TiO2 films. This should be a subject of additional research.
’ CONCLUSIONS The present study demonstrates that TiO2 films obtained from EPD with subsequent calcination can serve as an efficient conducting medium for photogenerated electrons in DSSCs. The EPD produces a closely packed network of TiO2 nanoparticles, whereas the conventional PC deposition results in a large 25587
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The Journal of Physical Chemistry C void fraction and less interparticle contact for the TiO2 film. After thermal necking, the EPD films had a smaller tortuosity factor for electron diffusion than the conventional PC films. The EPD film exhibited a smaller Ti4+ coordination number, corresponding to a higher density of defect states due to a higher degree of interparticle necking. However, the DSSCs assembled with the EPD films exhibited a higher photocurrent and light conversion efficiency than those with the PC films. On the basis of IMPS analysis, the EPD films exhibited smaller electron transit times in both the slower and faster diffusion components than the PC films because the former had a smaller void fraction and thus a tortuous electron path. Impedance analysis showed that the EPD films had a charge collection efficiency of 95% for thicknesses ranging from 4 to 13 μm, whereas the efficiency of the PC films was 90% at a thickness of 4 μm and decreased to 83% at 13 μm. The effective electron diffusion length for the EPD films remained more than four times the thickness of the TiO2 films even at a film thickness of 13 μm. By applying the percolation concept to the electron transport dynamics, the electron diffusivity varied with the porosity much weaker than the percolation model with hard spheres would expect. Interparticle necking with calcination resulted in greater lattice distortion for more compact TiO2 films, and this may cause the weaker porosity dependence of the electron transport rate. The comparison of the EPD and PC films explicitly elucidates both the network geometry and crystalline lattice governing the electron transport pattern in TiO2 films. This provides a useful insight for the development of effective nanocrystalline TiO2 films by minimizing the distance of electron travel between injection from the dye and collection by the FTO substrate.
’ ASSOCIATED CONTENT
bS
Supporting Information. The pore size distribution of the PC and EPD TiO2 films, the red-light IMPS responses of DSSCs assembled with the PC and EPD TiO2 films, and the electron transit times in TiO2 films determined from the red-light IMPS. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Fax: 886-6-2344496.
’ ACKNOWLEDGMENT This research is supported by the National Science Council of Taiwan (98-2221-E-006-110-MY3, 99-2622-E-006-010-CC2, 100-3113-E-006-001, 100-3113-E-006-012, 100-3113-E-007008, and 98-2221-E-006-112-MY2), the Bureau of Energy, Ministry of Economic Affairs, Taiwan (101-D0204-2). We thank Dr. Jyh-Fu Lee of the Taiwan Synchrotron Radiation Research Center for the help with the conduction of the X-ray absorption experiments. ’ REFERENCES (1) O’Regan, B.; Gr€atzel, M. Nature 1991, 353, 737. (2) Longo, C.; De Paoli, M. A. J. Braz. Chem. Soc. 2003, 14, 889. (3) Gr€atzel, M. J. Photochem. Photobiol., A 2004, 164, 3.
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