8916
J. Phys. Chem. B 2000, 104, 8916-8919
Investigation of the Kinetics of the Back Reaction of Electrons with Tri-Iodide in Dye-Sensitized Nanocrystalline Photovoltaic Cells N. W. Duffy, L. M. Peter,* R. M. G. Rajapakse,† and K. G. U. Wijayantha Department of Chemistry, UniVersity of Bath, Bath BA2 7AY, United Kingdom ReceiVed: March 29, 2000; In Final Form: August 1, 2000
A novel technique has been developed to study the kinetics of the back reaction of electrons with I3- in dye-sensitized nanocrystalline cells. A solid-state switched operational amplifier feedback circuit controlling the cell is used to alternate open-circuit and short-circuit conditions. In the experiment, electrons are injected by the photoexcited dye during illumination at open circuit, and then the subsequent decay of the opencircuit photovoltage in the dark is recorded up to a given time, at which the cell is short-circuited abruptly. The electron charge extracted at short circuit is measured by a current amplifier and integrator device. The kinetics of electron decay at open circuit has been studied by varying the delay between interrupting the illumination and short-circuiting the cell. Analysis of the time dependence of the electron density has established that the decay process is second-order in the total electron concentration. This is consistent with a mechanism involving the formation of I2-• as an intermediate. The pseudo-second-order rate constant for the reaction of electrons with tri-iodide was found to be 1.9 × 10-17 cm3 s -1 for [I3-] ) 0.05 M at 24 °C.
Introduction
Experimental Section
Dye-sensitized nanocrystalline photovoltaic cells have achieved solar conversion efficiencies comparable with those of polycrystalline thin-film solid-state devices,1-4 but it is not clear what factors ultimately limit their performance. The cells differ in several respects from conventional solid-state photovoltaic devices. The light-harvesting dye is adsorbed on the high surface area of the nanocrystalline oxide, and the porous electrode is permeated by an electrolyte that contains I- and I3-. Following electron injection, regeneration of the dye from its oxidized state is achieved by electron capture from I-. Electron transport in the nanocrystalline oxide is strongly influenced by trapping/ detrapping, and the injected electrons are collected at the substrate by dispersive diffusion.5-11 Electrons may back react with I3- before they reach the substrate, limiting the efficiency of the device. This “recombination” reaction had been treated as a first-order process analogous to the recombination of minority carriers in a conventional p-n junction.12,13 However recent work has indicated that this approach may be an oversimplification. The electron lifetime, τn, determined by small-amplitude photovoltage measurements using modulated9,14,15 and pulsed16 illumination, is found to depend on illumination intensity. It has been proposed that this is because the rate of reaction of electrons with I3- is second-order in electron density.14,15 The objective of the present work was to develop a more direct approach for studying the kinetics of the electron/I3- reaction by following the decay of the total electron concentration at open circuit. The results show that the rate of the back reaction of electrons with I3- is second-order in total electron concentration. Although this conclusion has been reached by an indirect route,15 the measurements reported in this letter represent the first direct determination of the kinetics of the back reaction.
DSN cells were fabricated using sol-gel films prepared via the techniques developed by Nazeeruddin et al.2 Conductive glass substrates (Libby Owens Ford, 10 Ω/sq F-doped SnO2) were cleaned by overnight immersion in a solution of KOH in 2-propanol, rinsed with de-ionized water, and dried in an air stream. Using a glass rod and adhesive tape spacers, we spread the TiO2 colloid over the substrate. The plate was dried in air for a few minutes and then fired at 450 °C for 30 min, resulting in an almost transparent film. The active area of the cell was 0.25 cm2, and the thickness of the TiO2 layer, as determined by scanning electron microscopy, was 18 µm. The freshly prepared film was immersed overnight in a 3 × 10-4 M solution of cis-di(thiocyanato)-N,N-bis(2,2′-bipyridyldicarboxylate)ruthenium(II) (Solaronix) in dry ethanol for dye absorption. After dye absorption, the electrode was dried and stored under argon. A sandwich cell was prepared with a second conductive glass coated with sputter-deposited Pt, and the plates were sealed together with transparent polyethylene (PE) hot melt film. The electrolyte was introduced through holes drilled in the counter electrode, and these were sealed subsequently with microscope cover plates and PE hot melt film. The electrolyte was composed of 0.85 M methylhexylimidazolium iodide (MHImI), 0.05 M iodine, 0.1 M LiI, and 0.2 M 4-tert-butylpyridine in acetonitrile. Analytical-grade iodine (BDH), acetonitrile (Aldrich), and 4-tertbutylpyridine (Aldrich) were used without further purification. The IPCE measured at 470 nm was 0.65. All measurements were performed in a screened dark box, and care was taken to eliminate stray light. The cell was illuminated from the substrate side with a blue-light-emitting diode (λmax, 470 nm; maximum output, 2 mW). The LED was placed close to the cell so that the spot size had a diameter of about 8 mm (the dimensions of the active cell area were 5 mm × 5 mm). The diode was driven by a pulse generator that allowed synchronization of the illumination pulse with the switching of the cell between open and short circuits. The cell was controlled using an electronic circuit developed for potentiostatic/galvanostatic measurements.17,18 This operational ampli-
* Corresponding author. Tel: 01225 826502. Fax: 01225 826815. E-mail:
[email protected]. † On leave from the Department of Chemistry, University of Peradeniya, Peradeniya, Sri Lanka.
10.1021/jp001185z CCC: $19.00 © 2000 American Chemical Society Published on Web 08/30/2000
Letters fier-based instrument contains a fast VMOS switch that changes the controlled variable from the potential (potentiostatic mode) to the current (galvanostatic mode) and back in a sequence controlled by external trigger signals. This sequence is termed PGP (potentiostatic-galvanostatic-potentiostatic). The measurement sequence was as follows. The initial potentiostatic state was 0 V in the dark (i.e., short circuit). The cell was then switched to the galvanostatic mode (zero current), and the LED was switched on for 550 ms. The increase in the photovoltage toward its photostationary value was recorded. The LED was then switched off, and the decay of the photovoltage was recorded. The circuit was switched back to the potentiostatic mode (0 V, i.e., short circuit) at different points along the photovoltage decay curve by varying the delay between switching off the LED and re-establishing the potentiostatic control. When the cell went from open circuit to short circuit, a current pulse was observed as electrons in the film were extracted. The output of the potentiostat current amplifier was integrated using an operational amplifier integrator. The integration time was 3 s. Longer integration times were not used because the residual currents from the cell were smaller than the offset drift of the current amplifier (i.e., less than ∼10 nA). The drift was minimized by carrying out measurements in a temperaturecontrolled room at 24 °C. The system was calibrated and zeroed accurately by replacing the cell with a 1 µF capacitor. The offset current in the G mode was manifest by the ramping of the voltage output at a rate given by dV/dt ) ioffset/C, where C ) 10-6 F. The offset current was adjusted until the ramp rate was less than 10 mV s-1, which corresponds to a residual current of less than 10 nA. The analogue integrator connected to the current amplifier output was also zeroed accurately to eliminate the drift. The voltage and charge outputs were interfaced via a Hitachi VC-6265 digital storage oscilloscope and an IEEE interface to a PC. This allowed accurate determination of the relationship between photovoltage, extracted charge, and time. Intensity-modulated photovoltage measurements (IMVS) were carried out using a blue-light-emitting diode (λmax ) 470 nm) driven by a Solartron 1250 frequency response analyzer. The LED provided both the dc and ac components of the illumination. The ac component of the current to the LED generated a small modulation superimposed on the dc light intensity. The intensity incident on the DSN cell was adjusted by the insertion of calibrated neutral density filters (Schott). The dc light intensity was measured using a calibrated silicon diode (traceable to NBS). Photovoltages were measured using a high-impedance low-noise battery-operated preamplifier (Stanford SR560; input impedance, 108 Ω). Since measurements were made down to very low light intensities, special precautions were needed to eliminate electrical noise. Measurements were performed in an earthed Faraday box, and computer equipment was shielded to prevent interference. Results and Discussion Figure 1 illustrates the time dependence of the photovoltage for an incident photon flux of 1.4 × 1016 cm-2 (3.9 mW cm-2). When the LED was switched on, the photovoltage quickly attained a steady-state value close to 700 mV. When the LED was switched off, the photovoltage decayed at open circuit over a period of seconds. The decay curve was found to be very reproducible. The experiment was repeated, and the decay curve was interrupted after different delay times, td, by switching the cell to short circuit. These points can be identified on the trace in Figure 1 by the vertical lines where the voltage falls to zero.
J. Phys. Chem. B, Vol. 104, No. 38, 2000 8917
Figure 1. Time-dependent photovoltage decay curves for a DSN cell illuminated from the substrate side for 550 ms at 470 nm (3.9 mW cm-2). The vertical lines indicate the points at which the cell was shortcircuited after a delay time td to extract the remaining charge.
Figure 2. Charge-extraction transients for the DSN cell obtained upon switching to the potentiostatic mode after different delay times during the photovoltage decay in the dark.
When the cell is switched from the G mode (open circuit) to the P mode (short circuit) during the photovoltage decay, a current transient is observed. The quantity of interest is the amount of excess charge that is extracted, and this was found by integrating the current transients. Figure 2 illustrates a family of charge transients for different td’s. The charge extracted during the first 3 s at short circuit was used in the subsequent analysis of the kinetics of the back reaction. Since the transit time for electrons to reach the substrate under short-circuit conditions depends on the electron quasi-Fermi level (i.e., on the trap occupancy), the integration period of 3 s places a limit on the photovoltage range over which reliable charge data can be obtained. A further limitation to the present method arises from the fact that the electron diffusion length decreases as the electron density falls. When the diffusion length becomes smaller than the film thickness, some fraction of the electrons will back-react before they reach the substrate. This will lead to underestimation of the charge at long times. Figure 3 shows how the extracted charge varies with delay time. The charge per unit volume has been calculated by considering the illuminated area (0.25 cm2) and the film thickness (18 µm). By switching to the P mode immediately after the interruption of the illumination, we found the total excess electron charge in the cell under photostationary conditions to be 5 × 10-2 C cm-3 at an incident photon flux of 1.4 × 1016 cm-2. In principle, this value should be corrected for the charge associated with the change in electron density on the tin oxide substrate that occurs when the cell voltage changes from the open-circuit value to zero. Since an order of magnitude estimate suggests that the correction is less than 10%, it has been neglected in the present analysis. The steady-state charge in the film corresponds to an electron density of 3 × 1017 cm-3. If an average particle size of 20 nm and a packing fraction of
8918 J. Phys. Chem. B, Vol. 104, No. 38, 2000
Letters
Figure 3. Extracted photocharge as a function of delay time td for the DSN cell.
Figure 4. (a) Second-order plot of charge extraction for t ) 0-2 s demonstrating that the back reaction is second-order in electron density. (b) Second-order plot of charge extraction for t ) 0-5 s and corresponding decay of the photovoltage. The deviation from the second-order plot at longer times is attributed to retention and back reaction of electrons in deep traps, leading to the underestimation of the electron density.
50% are assumed, the average electron occupancy should be close to 2 per particle. At the open circuit, the decay of the total electron concentration in the film is determined by the rate of the reaction
I3- + 2e f 3I-
(1)
In the simplest case where the reaction follows first-order kinetics, the decay in electron concentration should be exponential. If, on the other hand, the reaction is second-order in electron density, the decay should be hyperbolic, and a plot of 1/Q(t) vs t should be linear. In both cases, this conclusion only holds if the rate constants are independent of the mean electron energy (i.e., of the electron quasi-Fermi level, nEF). Figure 4a shows that a second-order plot of 1/Q(t) vs t is linear from t ) 0 s to t ) 2 s. The slope of the plot gives the second-order rate constant k ) 6.5 × 104 C-1 cm2 s-1. To
Figure 5. Comparison of τn values measured by IMVS (open circles) with the behavior calculated from the second-order rate constant derived from charge-extraction measurements (line). Second-order kinetics gives rise to an inverse square root dependence of τn on the photon flux (or short-circuit current), provided that the IPCE is constant. This corresponds to the slope of -0.5 in the log-log plot observed experimentally.
convert the rate constant to conventional units (cm3 s-1), it is necessary to note that the thickness of the TiO2 film was 18 µm. The second-order rate constant is found to be 1.9 × 10-17 cm3 s-1, which is equivalent to 1.1 × 104 dm3 mol-1 s-1. Figure 4b shows that the second-order plot exhibits a positive deviation at times longer than 3 s. The plot shows that the decay of the photovoltage has lowered the electron quasi-Fermi level so far that a significant fraction of the remaining electrons is located in deep traps. In this case, the transit time for these remaining electrons to reach the substrate will significantly exceed the integration time of 3 s. This conclusion has been confirmed by an analysis of the density of states function for electron traps derived from the PGP measurements (details will be presented elsewhere).19 In addition, the diffusion length will become smaller than the film thickness so that not all the electrons will reach the substrate.14 As a consequence of these two effects, the measurement of the extracted charge after longer delay times will underestimate the total electron charge in the device. The back reaction has also been studied using small-amplitude photovoltage measurements. Intensity-modulated photovoltage (IMVS) measurements were made on the same cell, and the electron lifetime was determined from the angular frequency of the minimum in the semicircular IMVS response.15,20 In the IMVS measurements, a small sinusoidal intensity modulation is superimposed on a much larger dc illumination level using a light-emitting diode. The lifetime for the second-order case under these conditions can be derived by the expansion and linearization of the response for small perturbations. In this small-amplitude limit, τn is given by
τn ) 1/(2kn)
(2)
(the factor of 2 was omitted in error in ref 14). Equation 2 allows τn to be calculated as a function of n using the value of k measured in the PGP measurements. Since the steady-state electron density at the open circuit is expected to vary with the square root of the intensity for second-order electron decay,14 τn should decrease with the inverse square root of the shortcircuit photocurrent (assuming that the IPCE is constant). The calculated variation of τn with illumination intensity (shortcircuit photocurrent) is compared in Figure 5 with values determined experimentally using IMVS. It is clear that the electron lifetime values determined by IMVS correspond closely to the values calculated from the second-order rate constant using eq 2. The slope of the IMVS plot is slightly higher than
Letters
J. Phys. Chem. B, Vol. 104, No. 38, 2000 8919
the value of -0.5 expected for second-order kinetics, and this may indicate that electron occupancy exerts a weak but measurable effect on the rate constant for electron transfer. The observation that the rate of the back reaction is secondorder in electron concentration can be interpreted using the reaction scheme
I3- H I2 + I-
(3)
I2 + e H I2-•
(4)
Conclusions
followed by either ket
I2-• + e 98 2I-
(5)
or kdisp
2I2-• 98 I3- + I-
(6)
We assume that all electrons are available to react with the species in solution even if they are trapped. This means that the majority of trapped electrons must be located in surface states. Furthermore, it is assumed that K2 and ket are independent of the electron occupancy (i.e., the electrochemical potential of electrons). If reaction 5 is the rate-determining step and reaction 4 is in equilibrium (equilibrium constant K2), the rate of electron decay will be given by
[I3-]n2 dn ) -ketK1K2 dt [I ]
The intensity dependence of the small-amplitude electron lifetime is attributed to the fact that the back reaction of electrons with I3- is second-order in electron concentration. The values of τn determined experimentally by intensity-modulated photovoltage spectroscopy agree well with the values calculated from the second-order rate constant for the back reaction derived from the decay of the total electron concentration at open circuit in the dark. The charge extraction method is now being used to study the back-reaction kinetics in dye-sensitized nanocrystalline cells using other oxides such as ZnO.23 Acknowledgment. This work has been supported by the U.K. Engineering and Physical Science Research Council, the Royal Society, and the Leverhulme Trust. The authors thank Ingo Uhlendorf (INAP, Gelsenkirchen) and Robert Potter (Johnson Matthey Technology Centre) for supplying materials. The authors thank the referee for drawing their attention to the influence of substrate charge in the measurements. References and Notes
(7)
If reaction 6 is the rate-determining step and reaction 4 is in equilibrium, the rate of electron decay will be given by
[I3-]2n2 dn ) -2kdispK12K22 - 2 dt [I ]
10-7 mol dm-3 for reaction 4 in acetonitrile.22 Using the experimental value of k ) 1.1 × 104 dm3 mol-1 s-1, we find that the equilibrium constant K2 ) 1.6 × 105 mol-1 dm3 for reaction 4. If, on the other hand, the main route involves two electron-transfer steps (reactions 3 and 4), the product ketK2 will be 2.1 × 1012 dm6 mol-2 s-1 (ket is a homogeneous secondorder rate constant).
(8)
Here, K1 is the equilibrium constant for the dissociation of I3-, K2 is the equilibrium constant for the formation of I2•-, ket is the homogeneous electron-transfer rate constant for step 5, and kdisp is the rate constant for the disproportionation of I2-• in step 6 (the factor 2 was inadvertently switched between eqs 7 and 8 in ref 14). Both pathways (eqs 5 and 6) would explain the observed second-order dependence of the back reaction on electron concentration. To distinguish between the two, it is necessary to determine the reaction order with respect to the tri-iodide/iodide concentration ratio at constant electron concentration. This is difficult to do by photovoltage measurements, since the redox Fermi level depends on the tri-iodide/iodide ratio. However, it should be possible to use the PGP method to determine the pseudo-second-order rate constant for a range of concentration ratios. Work is in progress to fabricate a series of cells for these measurements. In principle, the second-order dependence of the rate of decay of electrons on electron density could arise from first-order kinetics with K2 and ket depending on electron concentration (i.e., on the electron quasi-Fermi level). However, it seems improbable that this mechanism would give such a good fit to a second-order plot. If the disproportionation route is dominant, an order of magnitude value of the equilibrium constant K2 for reaction 3 can be obtained using the value of kdisp ) 8 × 109 dm3 mol-1 s-1 reported by Grossweiner and Matheson21 for aqueous solution and the reported equilibrium constant K1 )
(1) O’Regan, B.; Gra¨tzel, M. Nature 1991, 353, 737. (2) Nazeeruddin, M. K.; Kay, A.; Rodicio, I.; Humphrybaker, R.; Muller, E.; Liska, P.; Vlachopoulos, N.; Gra¨tzel, M. J. Am. Chem. Soc. 1993, 115, 6382. (3) Hanke, K. P. Z. Phys. Chem. 199, 212, 1. (4) Gra¨tzel, M.; Brooks, K.; McEvoy, A. J. AdV. Sci. Technol. 1999, 577. (5) Cao, F.; Oskam, G.; Meyer, G. J.; Searson, P. C. J. Phys. Chem. 1996, 100, 17021. (6) Solbrand, A.; Henningsson, A.; So¨dergren, S.; Lindstrom, H.; Hagfeldt, A.; Lindquist, S. E. J. Phys. Chem. B 1999, 103, 1078. (7) 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. (8) Zaban, A.; Meier, A.; Gregg, B. A. J. Phys. Chem. B 1997, 101, 7985. (9) Peter, L. M.; Wijayantha, K. G. U. Electrochem. Commun. 1999, 1, 576. (10) Schlichtho¨rl, G.; Park, N. G.; Frank, A. J. Z. Phys. Chem. 1999, 212, 45. (11) Nelson, J. Phys. ReV. B 1999, 59, 15374. (12) So¨dergren, S.; Hagfeldt, A.; Olsson, J.; Lindquist, S. E. J. Phys. Chem. 1994, 98, 5552. (13) Liu, Y.; Hagfeldt, A.; Xiao, X. R.; Lindquist, S. E. Sol. Energy Mater. Sol. Cells 1998, 55, 267. (14) Fisher, A. C.; Peter, L. M.; Ponomarev, E. A.; Walker, A. B.; Wijayantha, K. G. U. J. Phys. Chem. B 2000, 104, 949. (15) Schlichtho¨rl, G.; Huang, S. Y.; Sprague, J.; Frank, A. J. J. Phys. Chem. B 1997, 101, 8141. (16) Duffy, N. W.; Peter, L. M.; Wijayantha, K. G. U. Electrochem. Commun. 2000, 2, 262. (17) Bruckenstein, S.; Miller, B. J. Electrochem. Soc. 1970, 117, 1040. (18) Hills, G. J.; Peter, L. M.; Scharifker, B. R.; Pereira, M. I. D. J. Electroanal. Chem. 1981, 124, 247. (19) Duffy, N. W.; Peter, L. M.; Rajapakse, R. M. G.; Walker, A. B.; Wijayantha, K. G. U. Manuscript in preparation. (20) Peter, L. M.; Vanmaekelbergh, D. In AdVances in Electrochemical Science and Engineering; Alkire, D. M., Kolb, D., Eds.; VCH Wiley: New York, 1999; Vol. 6, p 77. (21) Grossweiner L. I.; Matheson, M. S. J. Phys. Chem. 1957, 61, 1089. (22) Nelson, I. V.; Iwamoto, R. T. J. Electroanal. Chem. 1964, 7, 218. (23) Duffy, N. W.; Peter, L. M.; Rajapakse, R. M. G.; Wijayantha, K. G. U. Manuscript in preparation.
