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Electron Transport Patterns in TiO2 Nanocrystalline Films of Dye-Sensitized Solar Cells Po-Tsung Hsiao,† Yung-Liang Tung,‡ and Hsisheng Teng*,†,§ Department of Chemical Engineering, National Cheng Kung UniVersity, Tainan 70101, Taiwan, PhotoVoltaics Technology Center, Industrial Technology Research Institute, Hsinchu 31040, Taiwan, and Center for Micro/ Nano Science and Technology, National Cheng Kung UniVersity, Tainan 70101, Taiwan ReceiVed: January 22, 2010; ReVised Manuscript ReceiVed: February 27, 2010
This study reports synthesis and characterization of nanoparticles for fabricating the TiO2 nanocrystalline films used in dye-sensitized solar cells: phase-pure anatase nanoparticles from a titanate-directed route, and brookite (27%) and rutile (1.2%)-containing anatase nanoparticles from a sol-gel route. After nanoparticlenecking into films, X-ray diffraction pattern simulation shows that the defect density of the anatase (AN) films is less than that of the brookite/rutile-containing anatase (AN-br) films. The defect states in the AN-br films lower the short circuit current and conversion efficiency of the resulting solar cells. Intensity-modulated photocurrent/photovoltage spectroscopic analysis demonstrates electron transport in trap-free and trap-limited diffusion modes and shows that the defects serve as electron trap state to retard electron transport for collection and increase the traveling time prior to recombination. Impedance analysis shows that the trap-free mode extends the electron diffusion length in TiO2 films and its contribution magnitude governs the electron collecting efficiency. Introduction Because of their low lost and high efficiency, dye-sensitized solar cells (DSSCs) are a promising alternative to the conventional silcon-based solar cell.1–8 The electricity generation in DSSCs is based on photoexcitation of the dye sensitizer, which injects electrons into a n-type semiconductor film and leads the hot electrons toward the external circuit. To enhance dye absorption and accessibility to the hole-carrying electrolyte, a mesoporous structure is essential for the semiconductor film.2 However, mesoporous films are of a nanocrystalline nature and contain numerous crystal defects in the grain boundaries. These defects impede electron transport and are harmful to cell performance.9–13 The diffusion of electrons through the nanocrystalline network is several orders of magnitude slower than that in a single crystal.14 Thus, how the crystal structure of nanocrystalline films affects electron transport is an important issue that requires in-depth investigation. To date, titanium oxide (TiO2) is the optimal electron conductor for dye-sensitized solar cells. Several types of sensitizers are capable of conjugating with TiO2.15–17 The morphology, crystallinity, and phase purity of nanostructured TiO2 govern solar cell performance.5,18–20 Anatase, rutile, and brookite are three polymorphs of TiO2. All of these polymorphs consist of TiO6 octahedral units but have different connecting modes.21 Anatase and rutile have tetragonal symmetry, while brookite has an orthorhombic crystalline structure. These polymorphs belong to the I41/amd, P42/mnm, and Pbca space groups, respectively. Compared with rutile and brookite, the anatase crystal structure has more interoctahedron connections, leading to an increased number of pathways to the electrode * To whom correspondence should be addressed: e-mail, hteng@ mail.ncku.edu.tw; fax, 886-6-2344496. † Department of Chemical Engineering, National Cheng Kung University. ‡ Photovoltaics Technology Center, Industrial Technology Research Institute. § Center for Micro/Nano Science and Technology, National Cheng Kung University.
and a faster transport rate.22 However, brookite occurs as a minority phase in most cases of anatase synthesis.23,24 The existence of these minority phases may cause structural distortion when TiO2 nanoparticles are thermally connected into films.25,26 Incident photon-to-current conversion efficiency (IPCE) is a determinant of the efficiency of DSSCs. IPCE is a function of the light absorption efficiency of the dye, the quantum yield of electron injection, and the efficiency of collecting injected electrons at the conducting glass substrate.27 The electron collecting efficiency is associated with electron transport in TiO2 and electrolyte recombination. To achieve a high collecting efficiency, it is necessary to promote the electron transport while minimizing electrolyte recombination.28 Many studies indicate that localized trap states adjacent to the conduction band edge trap electrons, slowing electron transport and increasing the probability of recombination.29–32 These trap states are caused by crystal defects.33,34 In addition, the influence of the trap states on electron transport may vary with their distance from the conducting substrate. This is because the trap occupancy should be higher near the substrate. How the film thickness affects the electron transport behavior is vitally important to elucidating the influence of crystal defects on the efficiency of photon energy conversion efficiency. This study employs Rietveld structural-refinement analysis of the X-ray diffraction results to characterize the crystal defects of TiO2 powders synthesized through two different methods. The defect structures of the powders are correlated with the properties and electron conveying abilities of the resulting TiO2 films. This study investigates the effect of trap states on electron transport behavior in the films of varying thicknesses using intensity modulated photocurrent and photovoltage spectroscopies. Electrochemical impedance spectroscopy reveals the corresponding collecting efficiencies of the films. The resulting solar cell performance and electron transport mechanism in the TiO2 films are interpreted in relation to the crystal structure data. This study demonstrates that the electron transit time in
10.1021/jp1006457 2010 American Chemical Society Published on Web 03/12/2010
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nanocrystallne films governs the cell performance and that the electron lifetime is a minor issue. Experimental Methods This study reports the synthesis of TiO2 powders from titanate-directed and sol-gel methods.25,35 The former synthesized a phase-pure anatase nanoparticle powder designated as AN, while the latter synthesized a brookite/rutile-containing anatase powder designated as AN-br. The detailed procedure for the synthesis of AN and AN-br has been described elsewhere.25,35–37 In brief, the AN TiO2 was prepared 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 an autoclave at 130 °C for 20 h. The resulting white precipitate 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 an AN colloidal solution. To prepare an AN-br suspension, a mixture of 20 mL of titanium isopropoxide (Acros) and 5.4 mL of isopropanol (Aldrich) was dropped slowly into 120 mL of 0.1 N HNO3 under vigorous stirring, and then heated the slurry at 80 °C for 2 h.2 The resulting slurry was diluted with 0.1 N HNO3 to produce 5 wt % TiO2 and then heated in an autoclave at 240 °C for 12 h to obtain the AN-br colloidal solution. To sustain the suspension of the colloids, the TiO2 solutions were mixed with poly(ethylene glycol) (PEG; Fluka, 20000 in molecular weight) to form viscous TiO2 dispersions at a PEG/ TiO2 ratio of 0.4. Each viscous TiO2 dispersion was calcined at 450 °C in air for 30 min prior to structural analysis. To assess the change in the crystalline structure of TiO2 nanoparticles after thermal necking into films, we also subjected the fragments from scraping the TiO2 films to structural analysis. To prepare TiO2 films, viscous solutions were coated on fluorine-doped SnO2 (FTO) conducting glass substrates (TEC 8, Hartford Glass Co.). The TiO2-coated substrates were subsequently calcined at 450 °C for 30 min. This study compares the structures of the calcined TiO2 nanoparticles and films and explores the microstructure of the TiO2 specimens with highresolution transmission electron microscopy (HRTEM; FEI Tecnai G2 F20, Philips). Phase identification was performed with podwer X-ray diffraction (XRD) using a Rigaku RINT2000 diffractometer with Cu KR radiation (λ ) 1.541838 Å) 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 2θ range of 20°-70°. Crystalline structures were refined with the Rietveld technique using the Generalized Structure and Analysis Software (GSAS) package.38–40 Following a previous study, the atomic fraction coordinates were I41/amd for the anatase space group, Pbca for the brookite space group, and P42/mnm for the rutile space group.21 To assemble dye-sensitized solar cells, TiO2 films of varying thicknesses were repetitively coated on the FTO substrates and calcined at 450 °C for 30 min. The thickness of the TiO2 layers was determined with a profilometer (Alpha Step 5000, Tencor). The films (0.5 cm × 0.5 cm) were immersed in an ethanol solution of the ruthenium complex dye cis-di(thiocyanate) bis(2,2′-bipyridyl-4,4′-dicarboxylate)ruthenium(II) (N3, Solaronix) overnight for dye absorption. The concentration of the dye was 3 × 10-4 M. The dyed electrode was rinsed with ethanol, dried, and assembled with a Pt-coated conducting glass using a 60 µm thick thermoplastic frame (SX1170-60, Solaronix). The electrolyte composition was as follows: 0.1 M LiI (Strem Chemicals), 0.05 M I2 (Riedel-de Hae¨n), 0.6 M 1,2dimethyl-3-n-propylimidazolium iodide (Solaronix), and 0.5 M 4-tert-butylpyridine (Aldrich) in acetonitrile (J. T. Baker).
Figure 1. Rietveld refinement plots for AN and AN-br TiO2 specimens: (a) AN TiO2 nanoparticles, (b) AN-br TiO2 nanoparticles, (c) AN TiO2 film, and (d) AN-br TiO2 film. Experimental data and calculated curves are indicated by crosses and continuous lines, respectively. AN TiO2 contains pure phase of anatase and the tick marks correspond to anatase. AN-br TiO2 has three phases: anatase (upper tick marks), rutile (middle tick marks), and brookite (lower tick marks). The difference curve (y(obs) - y(calc)) is displayed near the bottom of the graph.
In the cell performance test, an Oriel 300 W Xe lamp served as a light source in conjunction with an IR filter (Oriel 59044). The AM1.5 Global filter (Oriel 81094) was placed in the light beam to simulate the AM1.5-type solar emission, with an intensity on the cell fixed at 100 mW cm-2. The electron transport properties were measured by intensity modulated photocurrent spectroscopy (IMPS) and intensity modulated photovoltage spectroscopy (IMVS). IMPS and IMVS measurements were carried out using a frequency response analyzer (XPOT, Zahner), which was used to drive a blue light emitting diode (LED, λmax ) 455 nm). The LED provided both the dc and ac components of illumination. The light intensities were modulated ((5%) by modulating the voltage applied to the LED with sinus waves in the frequency range from 0.1 to 1000 Hz for both IMPS and IMVS. The dc light intensity ranged from 0.3 to 15 mW cm-2. The impedance of the cells was measured with a potentiostat equipped with a frequency response analyzer (IM6, Zahner), with the frequency range being 0.05-105 Hz. Bias voltages were set at the open-circuit voltage of the cells with an ac potential amplitude of 10 mV under AM1.5-type solar illumination of 100 mW cm-2. The light source was the same as that in the cell performance test. Results and Discussion Figure 1 shows the XRD patterns of the AN and AN-br nanoparticles and their resulting films. These patterns show that the AN nanoparticles and film are phase-pure anatase, while the AN-br specimens contain the anatase, brookite, and rutile phases. Figure 1 also shows the Rietveld refinement of the XRD patterns, revealing that the AN specimens are 100% anatase and the AN-br have anatase as the principal phase (71.5%),
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TABLE 1: Unit Cell Parameters for AN and AN-br Nanoparticles and Films Obtained from Rietveld Refinementsa,21 TiO2 specimens nanoparticles AN AN-br nanocrystalline films AN AN-br model compound standard anatase a
a (Å)
c (Å)
O s ()c/a) occupancy
Rp/Rwp (%)
3.788 9.505 2.510 3.785 9.476 2.503
0.961 0.963
6.54/9.91 7.20/9.83
3.787 9.504 2.510 3.783 9.481 2.506
0.965 0.913
7.05/10.1 6.86/9.95
3.785 9.513 2.513
1
The data for the standard anatase compound are provided.
brookite as the minority phase (27.3%), and rutile as an impurity phase (1.2%). The criteria and accuracy of the refinement results are described in detail in the Supporting Information. Therefore, the main difference between AN and AN-br TiO2 is the respective absence and presence of brookite in the anatase frameworks. As mentioned above, the anatase framework is favorable for electron transport. The degree of distortion in the anatase phase governs the electron transport rate. Anatase is constructed by tetragonal unit cells and the c/a ratio, the strain factor (s), can be an index for structural distortion, where a and c are the unit cell edge lengths.41,42 Table 1 shows the edge lengths for the different specimens from Rietveld simulations. The strain factor values for the AN and AN-br specimens are ca. 2.510 and 2.503, respectively. The standard anatase unit cell has a strain factor of 2.513 (JCPDS file No. 21-1276). The AN-br specimens have a higher strain factor deviation resulting from the presence of the brookite and rutile phases.25,26 Oxygen occupancy reflects the chemical intactness of a crystalline framework. Table 1 shows that the AN and AN-br nanoparticles have similar oxygen occupancy values. This is because all three TiO2 ploymorphs are composed of TiO6 octahedra. After thermal necking of the AN and AN-br nanoparticles into films, the AN-br film had a lowered oxygen occupancy value while this value remained unchanged for the AN film. The Rietveld simulation revealed that the oxygen occupancy decrease can most likely be attributed to disorder in the crystal lattice.23 Understanding the structural differences of brookite and anatase may reveal how the disorder was created after particle necking. Both the anatase and brookite structures consist of chains of TiO6 octahedra with common edges. A TiO6 octahedron can be described as six Ti-O bond lengths and 12 O-Ti-O bond angles. In an anatase unit cell, the TiO6 structure has a centered symmetry and two symmetrically independent Ti-O bonds of 1.934 Å (four O atoms) and 1.980 Å (two O atoms),43 as Scheme 1 illustrates. In contrast, the TiO6 in brookite is a low symmetric octahedron with six different Ti-O bond lengths ranging from 1.78 to 2.04 Å and 12 O-Ti-O bond angles ranging from 77° to 105°.44 As a result of the disordered TiO6 octahedron, the symmetric anatase TiO6 deforms when connecting with disordered TiO6. In addition, anatase has a crystalline structure with tetragonal symmetry whereas brookite has an orthorhombic crystalline structure with a unit cell. This difference implies a significant lattice mismatch which produces strain in thermally necked crystalline structures.26 As stated above, the existence of brookite causes distortion in the majority phase of anatase crystalline structures. Figure 2 (panels a and b) shows TEM images of the AN and AN-br TiO2 network structures, both of which consist of necked
Figure 2. TEM bright field images of the TiO2 network structure in the (a) AN and (b) AN-br films after calcination at 450 °C for 30 min. The corresponding lattice images are shown in (c) and (d). The square regions in (c) and (d) are magnified to show the crystal distortion (see the insets).
SCHEME 1: The Structure and Arrangement of TiO6 Octahedra in the Anatase and Brookite Unit Cells
crystal grains with diameters of 15-25 nm. The HRTEM images in Figure 2 (panels c and d) show the lattice fringes of the nanocrystalline films and lattice mismatch at the grain bondaries (indicated by arrows in the figures). However, the AN and ANbr networks show a significant difference in their grain interiors. The AN TiO2 (Figure 2c and the inset) has ordered lattice fringes inside the grains, while the AN-br TiO2 (Figure 2d and the inset) shows numerous distorted spots due to lattice mismatch. This confirms a remarkable lattice distortion of the anatase crystal framework in the AN-br TiO2 film. When the anatase TiO2 network is composed of nanoparticles containing secondary crystal phases, the defects are formed not only at grain boundaries but also inside the crystal grains. Because the trapping/detrapping event is a dominant mechanism for electron transport in nanocrystalline TiO2 film,30,31 the defects resulting from lattice distortion may become trap states that impede the electron transport. The AN and AN-br TiO2 films were sensitized with a ruthenium complex dye (N3) and assembled into DSSCs. Figure 3 shows the photocurrent-voltage characteristics of the DSSCs with varying TiO2 film thicknesses under AM1.5-type solar illumination at 100 mW cm-2. The AN cells exhibit a larger
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Figure 3. Photocurrent-voltage characteristics of DSSCs assembled with AN and AN-br TiO2 films of varying thicknesses under AM1.5type solar illumination at 100 mW cm-2.
Figure 5. The IMPS responses of DSSCs assembled with AN and AN-br 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 cm-2 and superimposed 5% ac intensity. As an example, the responses at the high and low fmin frequencies are indicated in the spectrum of the AN cell with a 17 µm film thickness.
Figure 4. The dependence of cell performances on the film thickness of dye-sensitized solar cells with AN and AN-br TiO2 films. The 0.25 cm2 cross area was illuminated under AM1.5 Global spectrum with an IR-off filter and 100 mW cm-2 in intensity.
photocurrent than the AN-br cells, except for the cells with the smallest film thickness (3 µm). Figure 4 summarizes the performance indices of the cells based on the data of Figure 3. Both the open circuit voltage (Voc) and the fill factor decreased as the film thickness increased. In contrast, the short circuit current (Jsc) increased with increasing film thickness to its maximum value and then decreased. As a result of the variation of Voc, Jsc, and fill factor with thickness, the maximum efficiency occurred at a thickness of 17 µm, in which the Jsc was also at its maximum value. This suggests that Jsc governs the cell efficiency even though Voc and the fill factor vary with the thickness. The larger Jsc for AN cells than of AN-br cells, especially for thicker films, may be related to the electron transport dynamics affected by defects in the TiO2 film. Because this study does not use a scattering TiO2 layer to increase light
absorption, the maximum efficiency occurred at an extraordinarily large thickness (17 µm). In addition, using dye sensitizers with high extinction coefficients also effectively reduced the optimal film thickness.45 To identify how the defects in TiO2 films affect electron transport in DSSCs, this study subjected the cells assembled with the AN and AN-br films to IMPS, IMVS, and impedance analysis. The frequency domain of the IMPS technique measures the modulation of photocurrent in response to the modulation of incident light intensity, which is a larger dc illumination intensity superimposing a small sinusoidal perturbation.27,46 During the IMPS measurements, the cells were short-circuited. A typical IMPS plot is characterized by a semicircle feature in the complex plane in the case of a uniform electron diffusion pattern. Figure 5 shows the IMPS responses obtained from AN and AN-br cells with different film thicknesses. Changing the film thickness influenced the shape of the IMPS plots. Both cells exhibited one semicircle feature at a small film thickness of 3 µm. As the film thickness increased, a semicircle appeared at higher frequencies and the plots transformed into a twosemicircle feature. This low-frequency semicircle expanded and became dominant at larger film thicknesses. The frequency at which the minimum IMPS response occurs, fmin, determines the average electron diffusion time (τd) following the equation τd ) (2πfmin)-1.47,48 Two semicircles with different fmin values indicate electron transport with two different diffusion modes.49 Since the short-transit-time (or high-frequency) mode appears for thick films, it must correspond to the transport for electrons induced from the FTO-neighboring position, at which the trap
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a
The AN film, with its minimal degree of lattice mismatch, forms fewer trap and recombination states. Thus, more trap-free and traplimited electrons can be collected in the AN film relative to those in the AN-br film.
Figure 6. (a) Trap-free transit time (solid line) and trap-limited transit time (dash line) over a range of illumination intensities. The AN and AN-br TiO2 films had a thickness of ca. 17 µm. (b) Effect of TiO2 film thickness on the trap-free time (solid line) and trap-limited time (dash line). The transit times for the AN and AN-br TiO2 films were obtained by the fmin of the IMPS plots. The incident dc illumination intensity was 15 mW cm-2.
SCHEME 2: The Photogenerated Electrons with a Long Transit Distance Are Delivered by the Trap-Limited Diffusion Mode, Whereas a Portion of the Electrons Generated near FTO Conducting Glass Are Transported by the Trap-Free Diffusion Mode Because Most the Trap States near FTO Are Occupied
states are filled by the electrons traveling from positions distant from FTO. Therefore, the high-frequency semicircle in the IMPS plot corresponds to the trap-free mode and the low-frequency semicircle to the generally observed trap-limited mode. Scheme 2 summarizes the trap-free and trap-limited electron diffusion patterns in nanocrystalline TiO2 films. The enlarged trap-free semicircle in thicker films results from a greater electron flux that can fill more trap states in the FTO-neighboring region. Figure 6a shows the diffusion time as a function of the incident photon flux in double logarithmic representation. The electron diffusion times for both trap-free and trap-limited modes decrease as the light intensity decreases. This intensity dependence of diffusion time arises from the change in trap occupancy with intensity.50–52 With increasing intensity, deeper trap states are filled and electron trapping/detrapping involves shallower levels, resulting in a shorter diffusion time. The strong photointensity dependence of the trap-free diffusion suggests that this electron transport mode is also affected by shallow traps with
energy levels right below the conduction band level of TiO2. Over a wide range of illumination intensities, the AN cell exhibited a shorter time for both the trap-free and trap-limited diffusion modes than the AN-br cell. This is because the AN TiO2 film has fewer defect states as a result of its less-distorted crystal structure. Therefore, the AN TiO2 film is more effective in electron transport. Figure 6b shows the film thickness dependence of the diffusion times. The trap-limited diffusion times for both TiO2 films increased as the thickness increased, and then leveled off for thicknesses larger than 17 µm. This increasing trend is expected, and the leveling-off indicates that the electrons injected with a long distance from FTO were mostly lost to recombination. In contrast, the trap-free diffusion time decreased slightly with the thickness, indicating that the increased electron flux promoted the occupancy of the trap states near FTO. Scheme 3 demonstrates the influence of crystal distortion on electron transport. Electrons can transport through the interior, boundary, and surface of the necked nanoparticles. Because of its lower trap-state density of the AN film, a larger proportion of the TiO2 film becomes “trap-free” near FTO and a stronger electron diffusion in the trap-free mode appears in the AN film. For electrons introduced with a longer distance from FTO, the diffusion time is governed by the trap states following the traplimited mode. The AN-br film exhibits a higher trapping/ detrapping frequency for electron transportation as a result of the higher density of crystal distortion. The photocurrent due to this diffusion mode decreases with the number of the defect states, which also induces recombination with the electrolyte at the nanoparticle surface.53 Figure 7 shows the IMVS results of the AN and AN-br cells with varying TiO2 film thicknesses. The procedure for the IMVS technique is the same as that for IMPS, except that the cells are open-circuited and this technique measures photovoltage responses instead of photocurrent. The semicircle feature (Figure 7) of the IMVS data presented in a complex plane allows electron lifetime (τn) calculation based on τn ) (2πfmin)-1.47,48 The lifetime of photogenerated electrons in open-circuited cell depends on the recombination rate between the electrons and I3- ions. The one-semicircle feature indicates that the electron transfer behavior for recombination did not vary with the thickness.31 Figure 8a shows the lifetime variation with the photon flux. The decreasing trend in this figure can be attributed to the higher recombination frequency under stronger illumination. Stronger illumination leads to greater photovoltage. Figure 8b shows that lifetime increases along with the film thickness, indicating that the photon flux decreases with the distance from
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Figure 7. The IMVS responses of DSSCs assembled with AN and AN-br TiO2 films of varying thickness under open circuit conditions. A blue light emitting diode (λ ) 455 nm) was used as the modulation light source with dc intensity of 15 mW cm-2 and superimposed 5% ac intensity. As an example, the responses at the fmin frequency is indicated in the spectrum of the AN cell with a 17 µm film thickness.
Figure 8. (a) Electron lifetime over a range of illumination intensities. The AN and AN-br TiO2 films had a thickness of ca. 17 µm. (b) Effect of TiO2 film thickness on the electron lifetime. The lifetimes for the AN and AN-br TiO2 films were obtained by fmin of the IMVS plots. The incident dc illumination intensity was 15 mW cm-2.
FTO, giving longer electron lifetimes. The AN-br cells show longer lifetimes than the AN cells over a range of illumination
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Figure 9. Nyquist impedance plots of DSSCs assembled with AN and AN-br TiO2 films varying thicknesses under AM1.5-type solar illumination at 100 mW cm-2. Bias voltages were set the open-circuit voltage of the cells, with the frequency range being 0.05-105 Hz. The solid lines represent the results simulated using the parameters in Table 2.
intensities and thicknesses. This can be attributed to the higher trap-state density of AN-br, which impedes electron transport for recombining with I3- at the electrolyte/electrode interface.54,55 A short electron transit time and a long lifetime are two characteristics of TiO2 films that give a long electron diffusion length and thus high cell performance. Since the AN cell showed a better performance than the AN-br cell, the IMPS and IMVS results reflect that the short transit time measured at short circuit is an important index of the high performance of the AN cell, while the lifetime obtained at open circuit is not correlated with the cell performance. For understanding the influence of TiO2 crystal structure, the IMPS technique not only reveals how the defects retard electron transport in TiO2 films but also sheds light on the diffusion behavior with respect to the position of electron injection. To further examine the dependence of structural defects on the electron diffusion length and collecting efficiency, this study also subjected the AN and AN-br cells to electrochemical impedance spectroscopy (EIS) analysis. Figure 9 shows the Nyquist impedance spectra for the AN and AN-br cells at the open-circuit potential under 100 mW cm-2 solar illumination. These spectra consist of three arcs situated in high, intermediate, and low frequency regimes. The high- and low-frequency arcs correspond to the charge transfer behavior at the Pt/electrolyte interface and the Nernst impedance of triiodide in the electrolyte, respectively.56–58 The intermediate-frequency arc corresponding to electron motion in the nanocrystalline TiO2 film is the major concern here. This study analyzed the impedance spectra with a reported equivalent-circuit model56,59,60 that interprets the nanocrystalline
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TABLE 2: The Equivalent-Circuit Parameters of DSSCs Assembled with AN and AN-br TiO2 Films of Varying Thicknessesa L (µm) AN cells 3 11 17 21 AN-br cells 3 11 17 21 a
Cµ (µF)
rt (Ω µm-1)
rct (Ω µm)
τd,EIS (ms)
τn,EIS (ms)
ηcc (%)
Ln (µm)
258 830 1100 1580
1.5 0.20 0.16 0.16
68 98 167 162
1.6 2.8 4.6 8.4
8 11 16 19
80 74 71 56
6.7 22 32 32
235 1130 1160 1950
1.6 0.24 0.22 0.20
67 98 179 170
1.8 4.1 8.8 12
8 14 22 22
78 71 65 47
6.4 20 29 29
The values are determined based on the data of Figure 9.
TiO2 film using the transmission line model (see Supporting Information). The solid lines in Figure 9 represent the results simulated with the model. Table 2 shows the chemical capacitance (Cµ), the electron transport resistance (rt), and the interfacial charge recombination resistance (rct) determined from the intermediate-frequency arc. Meanwhile, the average electron lifetime in TiO2 was calculated from the relation τn,EIS ) (2πfmax)-1, where fmax is the frequency at the top of the intermediate-frequency arc.58 The mean electron transit time, τd,EIS can be obtained using the equation
τd,EIS rt ) L2 τn,EIS rct
(1)
where L is the film thickness. Table 2 lists the value of τd,EIS and τn,EIS. The chemical capacitance gives the total density of free electrons in the conduction band and the localized electrons in the trap states.58,61 Table 2 shows that the AN-br films (except for the 3 µm one) had a larger capacitance than the AN films, which agrees well with the preceding argument that the defect sites in the AN-br films act as electron traps. The higher trap density of the AN-br films leads to larger rt and τd,EIS values than those in the AN films. This agrees well with the IMPS results. Table 2 also shows that the rct was slightly larger for the AN-br films due to the trap states deferring charge recombination. As a result, the AN-br films showed a slightly larger τn,EIS than the AN films. The preceding IMVS measurements gave similar results. The AN films with fewer trap states achieved swifter electron transport and recombination. Because the photogenerated electrons diffuse forward and recombine with I3-, the electron collection rate at the FTO substrate is
1 1 1 ) τcc τd,EIS τn,EIS
(2)
where τcc is the time constant for electron collection. Accordingly, the electron collection efficiency (ηcc) can be written as62,63
ηcc )
(
)
τd,EIS 1 1 1 / + )1τcc τcc τn,EIS τn,EIS
(3)
Table 2 shows the calculated ηcc values. For thin films, the ηcc value of the AN cells was slightly larger than that of the AN-br cell (80% vs 78% for 3 µm films). The ηcc difference increased with the film thickness, indicating that the trap states not only retard electron transport but also promote the probability of
losing electrons to recombination. This explains why the Jsc values (Figures 3 and 4) are smaller for the AN-br cells. This study also calculated the electron diffusion length (Ln) according to
Ln ) √Dn,EISτn,EIS
(4)
where Dn,EIS is the electron diffusion coefficient and equal to L2/τd,EIS. Table 2 lists the Ln values, showing that the Ln value increased with the film thickness and then stabilized for L > 17 µm. The Ln increase with L must be attributed to the appearance of the trap-free diffusion mode, because the trap-limited diffusion would give a constant Ln if the trap density did not vary with L. This argument is supported by the IMPS results in Figure 5, in which the trap-free contribution to the photocurrent increases with L. In thick films, the trap-free contribution stabilized (Figure 5 for L > 17 µm) and this also resulted in a stabilized Ln for L > 17 µm. This interpretation demonstrates that the electron diffusion mechanism is not homogeneous throughout the film and trap-free diffusion with the traps fully occupied governs the electron diffusion length in DSSCs. Conclusions This study shows a correlation between the electron diffusion behavior and the trap state density in the TiO2 nanocrystalline films of DSSCs. The trap state density is related to the phase purity of the starting TiO2 anatase nanoparticles. Brookite as the minority phase in most cases of anatase synthesis can result in structural distortion and create defect states during nanoparticle-necking into films. These defect states serve as electron trap states, retarding both the electron transport toward the FTO substrate and electron recombination with the electrolyte. IMPS showed that the electron transport can be characterized by trapfree and trap-limited diffusion modes. The trap-limited mode corresponds to the ordinary trapping-detrapping transport mechanism. The trap-free diffusion mode, with a smaller transit time, corresponds to electron transport through a region with trap states fully filled by electrons. The latter is evident only in films with a considerable thickness, indicating that the FTOneighboring region is likely responsible for electron diffusion in the trap-free mode. IMPS, IMVS, and EIS analyses showed that the magnitude of the trap-free diffusion mode governs the electron diffusion length (or electron collecting efficiency) of TiO2 films. However, the trap-influenced mode is a minor event for diffusion, especially for cells with thick films. Phase-pure anatase TiO2 films that have a low trap density, and thus a large region for trap-free diffusion, can outperform minor phasecontaining TiO2 films in DSSCs.
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