Quantitative Study of Electron Losses in Nanoporous Anatase Using

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J. Phys. Chem. B 2001, 105, 7220-7226

Quantitative Study of Electron Losses in Nanoporous Anatase Using Transient Absorption Spectroscopy Hans van’t Spijker,*,† Brian O’Regan,‡ and Albert Goossens† Laboratory for Inorganic Chemistry, Faculty of Applied Sciences, Delft UniVersity of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands, and Energy Center Netherlands (ECN), Postbus 1, 1755 ZG Petten, The Netherlands ReceiVed: December 31, 2000; In Final Form: April 12, 2001

To elucidate electron migration in dye-sensitized nanoporous anatase TiO2, time-of-flight short-circuit photocurrents and transient absorption spectra between 500 and 2000 nm have been recorded. It is found that electrons in TiO2 dominate the transient absorption between 900 and 1100 nm, whereas at wavelengths longer than 1100 nm absorption by electrons in the SnO2:F substrate prevails. To facilitate a qualitative analysis, the absorption cross-sections of electrons in TiO2 and SnO2:F have been measured. Combining transient absorption and photocurrent response data, the time-resolved recombination loss can be determined. When the excitation density is below 33.5 µJ/cm2, on average less than one electron per nanoparticle is injected. Under this condition the IPCE equals unity. When higher excitation densities are applied, more than one electron per nanoparticle is injected, losses become significant, and the IPCE reduces to 40%. The time evolution of the recombination loss reveals that recombination primarily takes place within a few microseconds.

Introduction Dye-sensitized nanocrystalline solar cells (DSNCs) are able to convert light into electricity with about 10% efficiency.1 A 5-10 µm film of porous nanocrystalline TiO2, grafted with dye molecules, is the active electrode. Platinised glass serves as the counter electrode, and with an I-/I3- nonaqueous redox electrolyte the electrical circuit is closed. These cells acquire considerable technological attention, since inexpensive production seems feasible. From a scientific point of view these cells are intriguing as well, since complex energy and charge transfer processes are involved. One interesting but poorly understood phenomenon is electron transport in porous nanocrystalline TiO2. To study the electron transport mechanism experimentally, intensity-modulated-photocurrent spectroscopy2-4 and transient photocurrent spectroscopy5,6 have been applied. However, these techniques provide only indirect information on the electron transfer mechanism, since only electrons that flow through the external circuit are observed. Better insight into the electron migration mechanism is achieved when photocurrent transients are combined with observations of migrating electrons before they enter the external circuit. This is possible with transient absorption (TA) spectroscopy, by which free and trapped electrons can be observed. So far, TA has been mainly used to study electron injection kinetics7,8 and cation recombination dynamics.9,10 In porous nanocrystalline anatase, which is currently the most studied semiconductor material in DSNCs, trapped electrons give rise to an absorption band peaking around 600 nm, while conduction band electrons absorb mainly at wavelengths >800 nm.11-13 Franco et al.14 combined intensity-modulated photocurrent and absorption spectroscopy and showed that the * Corresponding author. E-mail: Fax: + 31 (0) 15 278 8047. † Delft University of Technology. ‡ Energy Center Netherlands.

[email protected].

absorption response at 940 nm under open and short circuit conditions are similar and attributed the absorption transients to recombination of electrons trapped in surface states with the I3- species in the electrolyte. Our objective is to elucidate fundamental aspects of electron migration in nanoporous TiO2. This is accomplished by measuring simultaneously time-of-flight short circuit photocurrents and transient absorption spectra at wavelengths between 500 and 2000 nm upon pulsed laser excitation. With this combination of techniques, it is possible to trace the electrons right after their injection. We are able to count the electrons and prove that the recombination losses increase significantly when more than one electron per nanoparticle is injected. Furthermore, it is shown that the recombination occurs within a few microseconds after laser pulse. On the basis of these findings a hypothesis concerning electron transport is formulated. Experimental Section Materials. Nanoporous TiO2 films are prepared by doctor blading a colloidal anatase paste (Ti-Nanoxide HT from Solaronix) onto SnO2:F (Libbey Owens Ford 20 Ω/square) glass. The films are fired at 450 °C, cooled to 80 °C, and soaked overnight in 0.3 mM ethanolic RuL2(NCS)2, L ) 2,2′-bipyridyl4,4′-dicarboxylic acid (ruthenium 535 from Solaronix). Prior to applying nanoporous TiO2 films onto quartz substrates, a thin smooth TiO2 layer is deposited by spin-coating 0.2 M ethanolic titanium isopropoxide. Using XRD, the average particle diameter in the film is determined to be 12 ( 1 nm. An anatase colloid, prepared at ECN (Energy Center of the Netherlands) via the standard hydrolysis route1 has been applied as well. The particle diameter of this colloid varies between 10 and 24 nm. If not mentioned otherwise, the results presented in this article are measured on films prepared from the Solaronix paste. The thickness of the nanoporous films varies between 2.0 and 2.3 µm, as determined with a Dektak step profiler. The optically absorbed fraction, corrected for reflection losses, at λ ) 532

10.1021/jp010068g CCC: $20.00 © 2001 American Chemical Society Published on Web 07/06/2001

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Figure 2. Transient absorption and current of dye-sensitized nanoporous TiO2 film (thickness 2.0 µm) in 10 mM KI/1 mM I2, irradiated by 100 µJ/cm2 of 532 nm of a pulsed Nd:YAG laser.

Figure 1. Schematic drawing of the employed transient absorption spectroscopy setup.

nm of these films varies between 0.70 and 0.85 depending on the film thickness. Apparatus. A schematic overview of the employed experimental setup is shown in Figure 1. A freshly prepared dyesensitized film is mounted in a quartz cuvette with an optical path length of 3.5 mm. In this cell a large area platinum counter electrode is placed (18.5 × 45 mm2). A slit is made in the counter electrode to allow transmission of the laser and probe light beams. The cuvette is filled with an electrolyte, mostly 100 mM NaI/2 mM I2 dissolved in acetonitrile (Aldrich 99.93% HPLC grade). By translating the cell vertically, the sample can be irradiated at different spots. Excitation occurs mainly via the SnO2:F substrate side with 532 nm light of a pulsed optical parametric oscillator (Spectra Physics MOPO 710) pumped by the third harmonic of Nd:YAG laser (Spectra Physics QCR). The pulse width is 8 ns wide and the repetition rate is 9 Hz. The unattenuated power density amounts to 20 mJ/cm2. Using gray filters, the excitation intensity is varied between 0.01 and 1 mJ/cm2. The time-of-flight short circuit photocurrent is recorded on a TDS 744 Tektronix digital oscilloscope using a 1 Ω resistor. Simultaneously, transient absorption is recorded at a wavelength between 600 and 2000 nm. The absorption change is defined as -ln(T(t)/T(0)), where T(t) is the transmission at time t. Monochromatic probe light is obtained from a 250 W tungsten halogen lamp (Oriel), quartz lenses, and a Carl Zeiss MM 12 prism monochromator. Visible light is detected by a photomultiplier tube (Hamamatsu R636) or a Si PIN diode (Hamamatsu S5971), while InGaAs photodiodes (Hamamatsu G58531-01, G5125-10) are used for near-infrared detection. The measured

signal is converted by a transimpedance amplifier (FEMTO HCA-200-M-20K-C) and recorded by the oscilloscope. To minimize laser light scattering into the detector, a 532 nm notch filter (Kaiser, Supernotch plus) is used. The instrument response time is 120 ns. The digital oscilloscope is operated in the so-called highresolution mode, which enables measurements with 18 bit resolution. Spectra are obtained by averaging over 50-100 laser shots. In this way absorption changes as small as 10-5 can be detected. Material Handling. At excitation power densities higher than 1 mJ/cm2, the cells degrade within 1000 laser shots, resulting in a significant reduction of the peak current and a faster response time. In addition, the sample starts to bleach at the excited spot. To prevent this degradation, lower excitation densities are used. At an excitation density less than 0.3 mJ/ cm2, the cell can be excited with 10 000 laser shots, without any degradation. In this way, degradation is almost fully suppressed and signals reach a reproducibility to within 10%. Furthermore, a measurement session is completed within 1 day, always using freshly prepared samples. Dissolved oxygen in the electrolyte is removed by bubbling with argon. Since it is known that water in the electrolyte affects the performance of DSNCs,10,15 the water content in the hygroscopic acetonitrile is kept low. Only when the cell under study is mounted is the solvent shortly exposed to ambient air. Contact between the solvent and ambient air is avoided completely by flushing argon above the electrolyte. It appears that these precautions are not necessary as long as a measurement series is performed within 1 day. Addition of 0.5% H2O to the acetonitrile does not affect the cell response, whereas higher concentrations do. Results Figure 2 shows the current response together with TA decay at characteristic wavelengths. The signal decay at 725 nm is assigned to the Ru cation7,16 and is most prominent at times shorter than 1 ms. In contrast, transients at longer wavelengths have a longer lifetime. Above 1500 nm, the TA time response shows an initial growth and peaks at 0.4 ms. It resembles the current transient that peaks at the same moment. The TA response at 1000 nm can reasonably well described by an exponential decay with a time constant of 2 ms. This time constant is almost independent of the excitation density, as is

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Figure 4. Wavelength dependence of the transient absorption of dyesensitized nanoporous TiO2 film (thickness 2.0 µm) in 10 mM KI/1 mM I2, irradiated by 532 nm light of a pulsed Nd:YAG laser at a laser power of 100 µJ/cm2. The time resolution amounts to 10 µs.

Figure 3. Transient absorption spectra and short-circuit photocurrent recorded on dye-sensitized nanoporous TiO2 film (thickness 2.3 µm) in 200 mM NaI/2 mM I2. The film is irradiated by 532 nm light of a pulsed Nd:YAG laser at an excitation density of (a) 33.5 µJ/cm2 and (b) 558 µJ/cm2.

illustrated in Figure 3. The signal amplitude does depend on the intensity; a 16.6-fold increase in intensity yields a 7.6-fold increase of the initial absorption change. In contrast, the lifetime of the time response at 2000 nm shows a clear dependency on the excitation density. At a power of 33.5 µJ/cm2, the 2000 nm TA response shows a nonexponential decay with a half-life of 0.7 ms, whereas at 557 µJ/cm2, the half-life signal has increased to 3.2 ms. Also at this wavelength the change in absorption increases less than proportionally with the excitation density. At an excitation density of 33.5 µJ/cm2 the photocurrent response shows a half-life of 2.8 ms. At an excitation density of 557 µJ/cm2, the half-life is increased to 3.8 ms. The collected charge in Figure 3 increases only a factor of 6.5 at a 16-fold increase of excitation density. Solbrand et al.6 reported on the photocurrent response at different excitation densities as well. They excited 8-12 µm thick dyed nanostructured TiO2 films at 460 nm and showed that the photocurrent response becomes faster with increasing excitation power density between 150 and 1100 µJ/cm2. Furthermore, they show that the collected charge is proportional to the excitation density. We also noted that at excitation densities lower than 60 µJ/cm2, the photocurrent response becomes faster with increasing excitation power density (not shown in this paper), which is in agreement with the observations of Solbrand et al. In the present study, the photocurrent response becomes slower at excitation densities higher than 150 µJ/cm2, which might be due to diffusion limitation of I3- in the electrolyte. Yet, a straightforward comparison with the work of Solbrand et al. is not possible, because of the different experimental conditions. Especially, films employed in this study are only ∼2 µm thick, which is 4-5 times thinner than those studied by Solbrand et al. Accordingly, in our films the laser light is absorbed almost uniformly throughout the film, leading

to a relatively uniform electron generation profile. Hence, the TA and photocurrent transients recorded with front and backside irradiation do not differ significantly. A more detailed study on 2-10 µm thick films under various experimental conditions, such as different electrolyte concentrations, different illumination intensities, and irradiation sides is the subject of a forthcoming paper. The wavelength dependence of the TA spectrum is presented in Figure 4. It shows the well-known bleach of the Ru dye ground state below 600 nm7,9,16 the absorption band by the dye cation between 600 and >900 nm,16,17 and a steady increase at wavelengths longer than 1000 nm. Within 100 µs after laser flash excitation, the intensity of the dye cation band between 600 and 850 nm reduces to 50% of the original value. Knowing that the time resolution of this experiments is about 10 µs, a half-life 900 nm, the TA decay is 2 ms (see Figure 1), which is much longer than the lifetime of the Ru dye cation. Therefore, we conclude that at wavelengths >900 nm the TA contribution of the Ru dye cation is negligible compared to electrons temporarily stored in the dye-sensitized cell. In separate experiments the absence of possible TA contributions of dissolved dye molecules and I-/I3- redox species have been confirmed. Upon exciting 0.3 mM ethanolic RuL2(NCS)2, no significant contribution to the transient absorption at wavelengths larger than 700 nm is observed (∆A < 5 × 10-5 at an excitation density of 1 mJ/cm2). Excitation of the I-/I3electrolyte yields a weak absorption due to creation of I2-.18 It shows a maximum at 750 nm (∆A ) 2 × 10-4 at an excitation density of 1 mJ/cm2) and decreases to ∆A < 5 × 10-5 at 900 nm.19,20 Signals from I2- radicals in higher excited states absorbing at λ < 600 nm and at λ > 900 nm21 are not observed. Since no other contributions to the near-infrared TA spectrum are present, it is clear that TA signals at λ > 900 nm must be attributed to electrons stored either in nanoporous TiO2 or in the SnO2:F substrate. To identify the origin of the near-infrared TA response, the influence of the SnO2:F substrate is investigated. For that purpose dyed TiO2 films on quartz and SnO2:F coated glass have been studied. The TA results are presented in Figure 5.

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Figure 6. Optical absorption cross section of electrons in nanoporous TiO2 and SnO2:F. Figure 5. Absorption change of a dye-sensitized nanoporous TiO2 film (thickness 2.3 µm) on a quartz and SnO2:F substrate in 10 mM KI/1 mM I2, upon 532 nm laser flash excitation of a pulsed Nd:YAG laser at a laser power of 100 µJ/cm2. The presented ∆A is the average absorption change within the first 20 µs after laser flash excitation.

Both cells show a similar TA response between 600 and 1200 nm. The cells with a SnO2:F substrate show a pronounced absorption above 1250 nm, whereas when a quartz substrate is used only weak transient absorption signals are found at λ > 1250 nm. This indicates that the TA in this spectral region is mainly due to electrons temporarily stored in the SnO2:F substrate. This storage of electrons in SnO2:F is a dynamic process reflecting the imbalance between the supply and withdrawal of electrons. The absorption spectrum is similar to that measured by Nu¨tz et al.22 in degenerate SnO2:Sb and has been attributed to free-electron absorption. To check whether the TA response of (trapped) electrons TiO2 depends on the preparation method of the TiO2 colloid, 2 µm nanoporous TiO2 films using the ECN colloid have been studied as well. The TA responses of these films show amplitudes and time responses similar to those using the Solaronix colloid. To allow a quantitative analysis of the electron concentration, the absorption cross sections of electrons in the SnO2:F and in nanoporous TiO2 have been determined. For the measurements of the cross-section in the SnO2:F, a square wave current (with frequencies between 2 and 20 Hz, using currents between (10 and (100 µA) is driven through the cell, consisting of a Pt electrode and SnO2:F substrate in acetonitrile, while monitoring the SnO2:F transmission. A saw-tooth-modulated transmission is observed, following exactly the time dependence of the charge density, accumulated on the SnO2:F glass. During the charging and discharging of the SnO2:F substrate, the potential difference across the acetonitrile did not exceed 0.5 V. Under these conditions, current losses due to electronic transfer reaction with acetonitrile can be neglected. From the observed change in transmission the absorption cross-section is derived. The absorption cross-section is defined by ∆A/Σ, where ∆A is the recorded change in absorption and Σ is the charge density in number of elementary charge carriers/cm2. The absorption cross section of electrons in nanoporous TiO2 is determined potentiostatically. A nanoporous TiO2 film in 0.1 M acetontrilic NaClO4 is negatively polarized, placing a 0.5-2.5 V potential over a Pt electrode and a nanoporous film TiO2 applied on SnO2:F coated glass. Upon discharging the film, the collected charge and the change in absorption are recorded. It is has been reported that at these voltages Na+ intercalation is possible.23 To check whether Na+ intercalation is contributing to the TA spectrum, potentiostatic measurements have been performed by employing

0.1 M acetontrilic TBAClO4. Below 900 nm, the cross sections measured with the NaClO4 salt are ∼1.5 times lower than those measured with TBAClO4. Apparently, some Na+ intercalation may occur. At wavelengths >900 nm, however, the cross sections measured in NaClO4 solution and in TBAClO4 solution are the same. The measured cross sections are presented in Figure 6. The absorption cross section of electrons in TiO2 at 1000 nm is 8.4 × 10-18 cm2, which is close to 7.3 × 10-18 cm2 at 940 nm reported by Franco et al.14 and is in range with other values12,13,24 (between 2.6 × 10-18 (700 nm)13 and 1.3 × 10-17 cm2 (780 nm)12). The latter values correspond to a decadic extinction coefficient of 680 and 3400 mol-1 cm-1, respectively. Discussion Quantitative Determination of Electron Concentration. In previous studies, near-infrared optical absorption of electrons in DSNCs has been detected between 700 and 1100 nm. Tachibana et al.7 report free electron absorption between 700 and 900 nm. Unambiguous assignment of their signals to electrons in TiO2 is problematic, since the dye cations absorb in this wavelength range as well.7 At longer wavelengths, dye cations no longer contribute and the absorption of electrons in TiO2 dominate between 900 and 1100 nm (see Figure 6). The response at 940 nm that Franco et al.14 investigate is indeed attributable to electron transport in TiO2. Hannapel et al.25 detect free electrons at 1100 nm, in agreement with our results. Yet, their findings are not unambiguous, since in the same paper they report on transient response between 500 and 750 nm that is not in agreement with commonly measured spectra.16,25,26 At wavelengths longer than 1300 nm, the absorption of electrons in SnO2:F becomes important (see Figure 6). Ellingson et al. reports a transient absorption signal at 1520 nm but could not draw clear conclusions from their experiments. Certainly, a straightforward analysis of electron injection in TiO2 is hindered by the TA signal of electrons in SnO2:F. To calculate the electron concentration in TiO2 and SnO2:F, the spectra in Figure 3 together with the cross-sections of Figure 6 are combined. In Figure 6 it can be seen that the absorption between 900 and 1100 nm is dominated by electrons in TiO2, whereas between 1200 and 2200 nm the absorption of electrons in the SnO2:F prevails. Therefore, the electron concentrations in TiO2 and SnO2:F can be monitored at 1000 and 2000 nm, respectively. The results are compiled in Table 1. To derive the electron density per nanoparticle, the number of particles per cm2 film must be known. The TiO2 particles have a diameter of 12 nm, the film thickness is 2.3 µm, and the

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TABLE 1: Electron Concentrations in Dye-Sensitized Nanoporous TiO2 Film and SnO2:F Substrate upon 532 nm Laser Flash Excitation of a Pulsed Nd:YAG Laser at Two Different Laser Powersa excitation density (µJ/cm2) photon density (cm-2) no. of absorbed photons (electrons) no. of absorbed photons per nanoparticle collected charge (electrons)

33.5 ( 1 (6.7 ( 0.5) × 1013 (1.34 ( 0.10) × 1013 0.52 ( 0.04 (1.47 ( 0.05) × 1013

557 ( 4 (1.12 ( 0.07) × 1015 (2.23 ( 0.14) × 1014 8.8 ( 0.6 (8.71 ( 0.05) × 1013

transient Absorption signal at 1000 nm cross-section (cm2) electron density (cm-2) no. of electrons in TiO2 no. of electrons per nanoparticle

(4.3 ( 0.3) × 10-4 (8.4 ( 1.0) × 10-18 (5.1 ( 0.6) × 1013 (1.0 ( 0.1) × 1013 0.40 ( 0.05

(3.3 ( 0.1) × 10-3 (8.4 ( 1.0) × 10-18 (3.9 ( 0.4) × 1014 (7.7 ( 0.8) × 1013 3.1 ( 0.3

transient Absorption signal at 2000 nm cross-section (cm2) electron density (cm-2) no. of electrons in SnO2:F

(2.5 ( 0.1) × 10-3 (1.26 ( 0.06) × 10-16 (2.0 ( 0.1) × 1013 (3.9 ( 0.2) × 1012

(8.2 ( 0.1) × 10-3 (1.26 ( 0.06) × 10-16 (6.5 ( 0.5) × 1013 (1.30 ( 0.05) × 1013

a The employed electrolyte is 200 mM NaI/2 mM I , the film thickness 2.3 ( 0.1 µm and the absorbed light fraction amounts to 0.75 ( 0.05. 2 The presented laser powers are corrected for reflection losses and losses due light absorption by the electrolyte.

porosity is assumed to be 50%. Accordingly, 1.27 × 1014 nanoparticles/cm2 are present. The electron density (in electrons/ cm2) in the film is obtained from the TA spectra. Dividing both densities yields the electron density as expressed in a number of electrons per nanoparticle. Note that this number represents an average value over the film thickness. An excitation density of 33.5 µJ/cm2 corresponds to an injection of 0.52 electron per nanoparticle. At this laser power the number of absorbed photons (1.4 × 1013) equals the number of collected electrons (1.4 × 1013), indicating a collection efficiency of unity. From the TA decay extrapolated to t ) 0 the number of electrons per TiO2 nanoparticle is found to be 0.40, which is slightly lower than the number of injected electrons per nanoparticle. At an excitation density of 557 µJ/ cm2, 8.8 electrons per nanoparticle are injected. Now only 3.1 electrons per nanoparticle are derived from the TA response at 1000 nm at t ) 0. The number of collected electrons amounts to 8.7 × 1013, which is 40% of the total injected electrons (2.2 × 1014 electrons). Accordingly, charging a nanoparticle with more than one electron stimulates recombination losses. With less than one electron per nanoparticle, recombination is negligible.27 Electron Recombination Kinetics. Electrons that are injected in nanoporous TiO2 are either transported to the SnO2:F or recombine with I3- in the electrolyte. To calculate the fraction that is lost by recombination, we consider the total charge in the cell. The number of stored electrons at time t is given by the number of electrons injected in TiO2 lowered by the number of collected electrons and the number of electrons lost by recombination: nstore(t) ) ninj - nloss(t) - ncoll(t). The electrons are stored either in TiO2 or in SnO2:F. So we can write

nTiO2(t) + nSnO2(t) ) ninj - nloss(t) - ncoll(t)

(1)

Assuming that all absorbed photons inject an electron into a TiO2 nanoparticle, ninj can be written as AphΦS, where Aph is the absorbed light fraction, Φ is the number of incident photons (in photons/cm2), and S is the illuminated surface (which is 0.2 cm2). The number of collected electrons, ncoll(t), is given by ∫t0I(t) dt/e, I(t) being the current flowing through the cell and e the elementary charge. The number of electrons that are stored in TiO2 and SnO2:F are derived from the recorded TA responses at 1000 and 2000 nm, respectively. Knowing the absorption cross sections of electrons in TiO2 and SnO2:F (see Figure 6), nTiO2(t) can be expressed as ∆A1000(t)S/σ1000 and nSnO2(t) as ∆A2000(t)S/σ2000.

Figure 7. (a) Fraction of electrons in nanoporous TiO2, lost by recombination. The spectra are obtained from the TA and photocurrent spectra of Figure 3. The error bars in the graphs denote the error due to the uncertainties in the cross sections and injected charge. In (b) the fraction, lost in the first 10 ms, is shown.

With the aid of eq 1, the charge lost at time t can be determined for the spectra that are shown in Figure 3. The results are presented in Figure 7, being expressed as fraction of lost charge compared to the injected charge. At low laser powers the lost charge is small for all times. Initially, electrons are injected in the TiO2 film and subsequently they start to flow into the SnO2:F substrate. A photocurrent is generated, peaking at about 0.2 ms after laser flash excitation. At this time, 14% of the total injected charge has been collected and the TA signal of the electrons in TiO2 reduces correspondingly. At longer

Electron Losses in Nanoporous Anatase times, the electrons diffusing from the TiO2-electrolyte interface reach the SnO2:F substrate, without significant recombination loss, as can be seen in Figure 7. At a higher laser power (557 µJ/cm2), corresponding to an injection of 8.8 electrons/nanoparticle, a large fraction (60%) of the injected electrons is lost. This loss occurs within the first few microseconds after the laser flash excitation, as can be seen in Figure 7. The charge loss increases slightly from 56% to 65% between 1 and 10 ms after the pulse. The charge loss at high laser powers may have several causes. First, the electron injection efficiency may be reduced, as has been suggested by Kelly et al.28 Second, the recombination rate of electrons with I3- in the electrolyte may increase, especially at high laser powers when the actual I3- concentration in the pores right after the light pulse will be higher than the 2 mM added in the electrolyte. Third, the back-reaction with Ru dye cations may be stimulated. This possibility is also invoked by Haque et al.,29 who measured the lifetime of the Ru dye cations on TiO2 nanoparticles in inert acetonitrile at varying laser powers and reported that the recombination time of electrons with dye cations decreases drastically when more than one electron per nanoparticle is injected. The origin of this nonlinear dependency is not yet clear. Also, others noted that the dye-sensitized solar cell functions at an average occupancy of about one electron per nanoparticle. Schlichtho¨rl et al.30 and Duffy et al.31 found that the average electron occupancy under illumination is between one and two electrons per nanoparticle. Van der Zanden et al.27 elaborately reported that dyed-nanostructured TiO2 solar cells function at one electron per nanoparticle, despite differences in TiO2 electrode preparation, film thickness, and light intensity. So, the remarkable increase in recombination loss when more than one electron per nanoparticle is injected deserves further attention. A clue may be lain in the average residence time of an electron near the TiO2/electrolyte interface. If one electron is injected in a nanoparticle, it may either reside in the center of a nanoparticle or become trapped in a surface defect. An explanation might be a high defect concentration near the surface, such that band bending would be present.32 Although no experimental evidence is available, if this would be the case, the first injected electron would reside mainly in the center of the nanoparticle. However, when more than one electron is injected, electron-electron repulsion will play a role. A simple electrostatic calculation shows that two electrons at a distance of 5 nm have an interaction energy of 5.8 meV when  ) 50. However, it is unlikely that this high value of  is realistic inside a 12 nm nanocrystal, since the dielectric constant is a macroscopic property. When the presence of the nonpolar electrolyte is accounted for, the dielectric constant may be lowered. When  is between 5 and 10, the interaction increases to 58 and 28.8 meV, respectively, which is significant at room temperature. Accordingly, when two electrons are present in a single nanoparticle, both of them are expected to reside on the surface opposite to each other. Enhanced recombination with I3--and back-reaction to Ru dye cations is the result. But when only one electron is present, it is located most of the time in the center of the particle and does not recombine with I3- or Ru dye cations. It is noted that the recombination loss will be predominant in nanoparticles that contain the highest number of electrons, i.e., in the largest nanoparticles located near the TiO2-SnO2:F interface, where most of the electrons are injected. The observation that injection of more than electron per nanoparticle results in microsecond recombination losses support our previous interpretation of IMPS spectra. Generally, IMPS

J. Phys. Chem. B, Vol. 105, No. 30, 2001 7225 spectra can be correctly modeled using a diffusion model.27,33 Using these models, the fit results of the measured spectra show that electron loss due to recombination can be neglected. This is rather surprising, since the IPCE of the studied cells is usually less than 100%. With the aid of Figure 7 this can be understood. The IMPS measurements are performed at frequencies 100 µs are detected. Our results indicate that the charge loss between 100 µs and 10 ms is negligible, which is in agreement with the IMPS results. Conclusions For the first time, TA spectra have been recorded in a complete dye-sensitized nanostructured solar cell. As a profit, both the TA decay and the generated photocurrent can be recorded simultaneously. Direct insight into the charge-transfer processes relating to the functioning of the solar cell is gained. In Ru-dyed nanoporous TiO2 films, electrons in TiO2 are shown to dominate the transient absorption between 900 and 1100 nm. At longer wavelengths, absorption by electrons in SnO2:F is dominant. At low laser power, i.e., when less than one electron per nanoparticle is injected, almost all the injected photoelectrons are collected. At higher laser powers, when much more than one electron/nanoparticle is injected, the IPCE decreases drastically. It is found that the charge loss manifests in the first few microseconds after laser flash excitation. References and Notes (1) Nazeeruddin, M. K.; Kay, A.; Rodicio, I.; Humphrybaker, R.; Muller, E.; Liska, P.; Vlachopoulos, N.; Gratzel, M. J. Am. Chem. Soc. 1993, 115, 6382. (2) Dloczik, L.; Ileperuma, O.; Lauermann, I.; Peter, L. M.; Ponomarev, E. A.; Redmond, G.; Shaw, N. J.; Uhlendorf, I. J. Phys. Chem. B 1997, 101, 10281. (3) Redmond, G.; O’Keeffe, A.; Burgess, C.; MacHale, C.; Fitzmaurice, D. J. Phys. Chem. 1993, 97, 11081. (4) Cao, F.; Oskam, G.; Meyer, G. J.; Searson, P. C. J. Phys. Chem. 1996, 100, 17021. (5) Solbrand, A.; Lindstrom, H.; Rensmo, H.; Hagfeldt, A.; Lindquist, S. E.; Sodergren, S. J. Phys. Chem. B 1997, 101, 2514. (6) Solbrand, A.; Henningsson, A.; So¨dergren, S.; Lindstro¨m, H.; Hagfeldt, A.; Lindquist, S. E. J. Phys. Chem. B 1999, 103, 1078. (7) Tachibana, Y.; Moser, J. E.; Gratzel, M.; Klug, D. R.; Durrant, J. R. J. Phys. Chem. 1996, 100, 20056. (8) Ellingson, R. J.; Asbury, J. B.; Ferrere, S.; Ghosh, H. N.; Sprague, J. R.; Lian, T.; Nozik, A. J. Z. Phys. Chem.-Int. J. Res. Phys. Chem. Chem. Phys. 1999, 212, 77. (9) Vinodgopal, K.; Hua, X.; Dahlgren, R. L.; Lappin, A. G.; Patterson, L. K.; Kamat, P. V. J. Phys. Chem. 1995, 99, 10883. (10) Pelet, S.; Moser, J. E.; Gratzel, M. J. Phys. Chem. B 2000, 104, 1791. (11) Boschloo, G.; Fitzmaurice, D. J. Phys. Chem. B 1999, 103, 2228. (12) Rothenberger, G.; Fitzmaurice, D.; Gratzel, M. J. Phys. Chem. 1992, 96, 5983. (13) Safrany, A.; Gao, R. M.; Rabani, J. J. Phys. Chem. B 2000, 104, 5848. (14) Franco, G.; Gehring, J.; Peter, L. M.; Ponomarev, E. A.; Uhlendorf, I. J. Phys. Chem. B 1999, 103, 692. (15) Liu, Y.; Hagfeldt, A.; Xiao, X. R.; Lindquist, S. E. Solar Energy Mater. Solar Cells 1998, 55, 267. (16) Moser, J. E.; Noukakis, D.; Bach, U.; Tachibana, Y.; Klug, D. R.; Durrant, J. R.; Humphry-Baker, R.; Gra¨tzel, M. J. Phys. Chem. B 1998, 102, 3649. (17) Trachibana, Y.; Haque, S. A.; Mercer, I. P.; Durrant, J. R.; Klug, D. R. J. Phys. Chem. B 2000, 104, 1198. (18) Fitzmaurice, D. J.; Eschle, M.; Frei, H.; Moser, J. J. Phys. Chem. 1993, 97, 3806. (19) Fitzmaurice, D. J.; Frei, H. Langmuir 1991, 7, 1129. (20) Banin, U.; Ruhman, S. J. Chem. Phys. 1993, 98, 4391-4403. (21) Kliner, D. V.; Alfano, J. C.; Barbara, P. F. J. Chem. Phys. 1993, 98, 5375. (22) Nutz, T.; Zum, F.; Haase, M. J. Chem. Phys. 1999, 110, 12142. (23) Lyon, L. A.; Hupp, J. T. J. Phys. Chem. 1995, 99, 15718-15720.

7226 J. Phys. Chem. B, Vol. 105, No. 30, 2001 (24) Boschloo, G.; Fitzmaurice, D. J. Phys. Chem. B 1999, 103, 78607868. (25) Hannappel, T.; Burfeindt, B.; Storck, W.; Willig, F. J. Phys. Chem. B 1997, 101, 6799. (26) Hannappel, T.; Zimmermann, C.; Meissner, B.; Burfeindt, B.; Storck, W.; Willig, F. J. Phys. Chem. B 1998, 102, 3651. (27) van der Zanden, B.; Goossens, A. J. Phys. Chem. B 2000, 104, 7171. (28) Kelly, C. A.; Farzad, F.; Thompson, D. W.; Stipkala, J. M.; Meyer, G. J. Langmuir 1999, 15, 7047.

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