ARTICLE pubs.acs.org/JPCC
Dependence of Dye-Sensitized Solar Cell Impedance on Photoelectrode Thickness James R. Jennings,† Yeru Liu,† Fatemeh Safari-Alamuti,†,‡ and Qing Wang*,† †
Department of Materials Science and Engineering, Faculty of Engineering, NUSNNI-NanoCore, National University of Singapore, Singapore 117576 ‡ Department of Chemical and Biomolecular Engineering, Faculty of Engineering, National University of Singapore, Singapore 117576
bS Supporting Information ABSTRACT: Dye-sensitized solar cells with a wide range of porous TiO2 layer thicknesses (d = 318 μm) have been characterized by impedance spectroscopy. Spectra were analyzed using a well-known equivalent circuit model incorporating a transmission line to obtain the distributed resistance and capacitance parameters characterizing the TiO2 layers. No significant dependence on d was found for any of the distributed parameters, reaffirming the validity of this commonly used model. Other elements in the equivalent circuit model which represent the substrate/electrolyte, cathode/electrolyte, and FTO/TiO2 interfaces are also examined and discussed.
’ INTRODUCTION Over the past decade, the use of impedance spectroscopy (IS) for characterization of porous semiconductor electrodes, particularly those employed in dye- or semiconductor-sensitized solar cells, has become widespread. The impedance response of these electrodes can be derived by solving the continuity equation for carriers in the porous electrode system or equivalently by considering it as a homogeneous transmission line (TL).1 The TL model has been successfully applied to describe the impedance spectra of high efficiency dye- and semiconductor-sensitized solar cells, where the dependence of fitted model parameters on applied bias voltage has yielded important information about carrier transport and recombination.2,3 Despite some concerns being raised about the reliability of parameters obtained from fits to experimental data using this model under certain conditions (specifically when the cathode charge transfer resistance is large or the electron diffusion length is very short), it is generally accepted that the TL model adequately describes the electrode impedance.47 While there is no doubt that equivalent circuit models incorporating a TL impedance are useful, in practice one must take great care when fitting models to experimental data to ensure that the model is correct, not overparameterized, and that the regression does not prematurely terminate at a local minimum of the objective function. These problems can all too easily occur when dealing with impedance data for dye- or semiconductor-sensitized solar cells, where often the transmission line impedance (which is usually of primary interest) is partly or completely obscured by other series and parallel impedances, e.g., the impedances of the cathode/electrolyte and substrate/electrolyte interfaces, respectively. r 2011 American Chemical Society
The influence of the substrate/electrolyte interfacial impedance on the overall electrode impedance has previously been modeled and discussed in detail by Bisquert.8 Fabregat-Santiago et al. have also demonstrated that it is possible to obtain, by fitting, the capacitance of the exposed fluorine-doped tin oxide substrate for the case of a porous TiO2 electrode immersed in a buffered aqueous electrolyte solution, even in a potential regime where the TiO2 exhibits significant conductivity and full TL behavior must be considered.9 While this early work goes a long way toward confirming the validity of common circuit models, the system studied (bare TiO2 in an aqueous electrolyte with no added redox couple) differs appreciably from that in typical dye-sensitized solar cells, and thus further basic studies of the latter system are warranted. An important assumption in the TL model is that the distributed resistance and capacitance parameters are intensive properties that are specific only to a particular material combination, not the electrode thickness. In previous work by others, conductivityvoltage characteristics derived by IS for a few different porous TiO2 electrodes immersed in aqueous electrolyte solution were found to be in approximate agreement.9 However, in this work the electrodes differed in more than just their thickness (porosity, chemical composition, and area also differed), and the electrodes were not used in a typical solar cell configuration. To our knowledge, the dependence of transmission line parameters on porous electrode thickness in complete solar cells has never been deliberately and systematically tested by experiment. One Received: October 10, 2011 Revised: November 20, 2011 Published: November 24, 2011 1556
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The Journal of Physical Chemistry C can argue that such a simple test is important because some relatively recent studies have found that estimates of electron diffusion length obtained using steady-state techniques differ from those obtained by dynamic techniques, such as IS, under certain experimental conditions.10,11 On one occasion, an unexpected dependence of electron diffusion length on electrode thickness was even observed.12 It has since become apparent that the origin for these discrepancies is probably a result of comparing values measured under very different experimental conditions, causing one or more assumptions made in the models used for data analysis to break down.1319 Nevertheless, it still seems prudent to test the validity of the transmission line model by deliberate variation of TiO2 electrode thickness. Variation of the TiO2 layer thickness also forms the basis for a novel way of checking the physical origin of other series and parallel impedances in the equivalent circuit of a complete solar cell, which, if not associated with the bulk TiO2 layer, would not be expected to vary with layer thickness. In the present article, results of the aforementioned tests are presented and discussed. Dye-sensitized solar cells with TiO2 layer thicknesses in the range 318 μm were fabricated, and their impedance response was recorded. Experimental conditions were chosen to ensure almost spatially homogeneous carrier concentrations, as assumed in the derivation of the TL impedance, and data were analyzed using an equivalent circuit model incorporating a TL impedance. Results were generally in keeping with the TL model, with no significant dependence of distributed TL parameters on TiO2 layer thickness being found. Likewise, parameter estimates for other circuit elements in the model did not show any significant dependence on TiO2 layer thickness. It is demonstrated that inclusion of the substrate/electrolyte capacitance in the model is required to obtain good fits at low voltages, especially for the thinner TiO2 layers, and that parameter estimates are of the same order as those obtained in independent experiments. It is also shown that the contact between the FTO substrate and TiO2 blocking layers often has non-negligible impedance, the DC resistance of which can be far larger than the charge transfer resistance at the cathode/electrolyte interface (although still small compared to other series resistances) for typical platinized cathodes contacting tri-iodide/iodide electrolytes.
’ EXPERIMENTAL SECTION Fabrication of DSCs. Fluorine-doped tin oxide coated glass (FTO, Pilkington TEC-15) was cut and then cleaned by sequential sonication in 5% Decon 90 solution, distilled water, and absolute ethanol. When required, compact TiO2 blocking layers were deposited onto the FTO by spray pyrolysis of a 0.2 M solution of titanium(IV)bis(acetoacetonato)di(isopropanoxylate) in ethanol.20,21 The thickness of these compact layers was difficult to accurately control using this deposition method and is estimated to be in the range 20100 nm based on profilometry measurements. Nanocrystalline TiO2 layers of various thicknesses were deposited onto the FTO by successive screen-printing using a TiO2 paste consisting of Degussa P25 TiO2 powder and an ethyl cellulose binder in α-terpinol. The projected area of the TiO2 layers was approximately 0.28 cm2 (circles with 0.6 cm diameter). After screen-printing, the TiO2 electrodes were gradually heated to 450 °C where they were held for 15 min before being heated to 500 °C for a further 15 min. Electrodes were then soaked in a 40 mM solution of TiCl4 in distilled water (prepared by dilution
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of a 2 M stock solution which was prepared at ca. 0 °C) for 30 min at 70 °C before being rinsed, dried, and heated to ca. 500 °C in a hot air stream for 30 min. After cooling to room temperature, the thickness of the TiO2 layers was determined using an Alpha-Step IQ surface profiler (KLA-Tencor). Electrodes were then heated again to ca. 500 °C in a hot air stream for 30 min; once electrodes had cooled to ca. 100 °C they were immersed into an ca. 0.15 mM solution of cis-diisothiocyanato-(2,20 -bipyridyl-4,40 -dicarboxylic acid)-(2,20 -bipyridyl-4,40 -dinonyl) ruthenium(II) (Z-907, Dyesol) in a mixture of acetonitrile and tert-butanol (1:1 volume ratio) and left overnight. Platinized counter electrodes were fabricated on identical pieces of FTO with small holes drilled into one corner. After cleaning, a thin layer of Pt was deposited onto the FTO by thermal decomposition of hexachloroplatinic acid. Dyesensitized TiO2 electrodes were then removed from the sensitizing solution and rinsed thoroughly in neat acetonitrile. Sensitized electrodes were then attached to counter electrodes in a sandwich configuration using a circular gasket with an internal diameter of 0.8 cm made from a hot-melt polymer (Meltonix 1170-25, Solaronix). An electrolyte consisting of 1 M 3-propyl-1-methylimidazolium iodide, 0.1 M I2, 0.5 M N-methylbenzimidazole, and 0.1 M lithium trifluoromethansulfonimide in 3-methoxypropionitrile was introduced into the interelectrode space by vacuum backfilling, and holes were sealed using a small piece of hot-melt polymer and a microscope coverslip. Two different batches of DSCs were fabricated, one with and one without compact TiO2 blocking layers. Within each batch at least two DSCs were fabricated and tested for each TiO2 layer thickness, and results shown are representative of all data collected. Occasionally, cells with very large values of the contact resistance, Rcon,1, were encountered (vide infra). This made reliable determination of parameters such as the electron transport resistance and substrate capacitance problematic, and therefore results obtained for these cells have been omitted. The physical origin of the contact resistance and the occasional lack of reproducibility are discussed at a later stage in this article. To better characterize cell impedances not originating from the nanocrystalline TiO2 layer, a series of cells were fabricated where this layer was omitted. An identical procedure was followed when making these cells, including the application of a blocking layer when required, TiCl4 treatment, and dye sensitization. Symmetrical cells consisting of only platinized electrodes were also fabricated to assist in characterization of the cathode in complete cells. Characterization of DSCs. IS experiments were performed using a potentiostat equipped with a frequency response analyzer (Autolab PGSTAT 302N/FRA2, Ecochemie) and the Nova 1.6 software package. Measurements were performed with cells biased to VOC while under background illumination from a high-power red (λ = 627 nm) light emitting diode (LED, Luxeon). Different background illumination intensities were achieved using neutral density filters mounted in an automated filter wheel system (Newport). The highest intensity used was sufficient to produce a VOC approximately equal to that obtained under AM 1.5, 1 Sun illumination. The optical density (OD) of the filters was varied in steps of approximately 0.5. The voltage perturbation amplitude was 5 mV rms, and the frequency range was 100 kHz to 0.1 Hz. Spectra were fitted using appropriate equivalent circuit models built in the ZView 3.1c complex nonlinear least-squares regression software. Real and imaginary parts of the spectra were simultaneously fitted, and the “calc-modulus” weighting option in the fitting software was used. 1557
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’ RESULTS AND DISCUSSION Figure 1 shows the equivalent circuit model used for fitting IS data obtained for complete DSCs. Most of the model components have been described in detail elsewhere, and only brief definitions will be given here.2 The distributed components describing the transmission line are the electron transport resistance (rt), the charge transfer resistance (rrec), and the electrode capacitance (cμ). The distributed parameters are related to total resistances and capacitances by rt = RtA/d, rrec = RrecAd, and cμ = Cμ/(Ad) where d is the layer thickness and A is the projected area. The units for the distributed parameters rt, rrec, and cμ are then Ω cm, Ω cm3, and F cm3 , respectively. The other standard circuit elements are the series resistance (Rs), the resistances and capacitances of the substrate/electrolyte interface (Rsub and Csub), the substrate/nanoparticle contact (Rcon,2 and Ccon,2), the cathode/ electrolyte interface (Rcath and Ccath), and a Warburg impedance (Zd) representing the diffusion of redox species in the bulk electrolyte layer. Also included in the model is a series-connected, parallel RC circuit representing the contact between the FTO substrate and the TiO2 blocking layer (Rcon,1 and Ccon,1), which was also recently used by Zhu et al. and will be discussed in more detail at a later stage in this article.6 Throughout this article these various interfacial resistances and capacitances will be scaled by the projected electrode area so that their units are Ω cm2 and F cm2, respectively. Given the basic nature of the work presented in this article, it seems appropriate to briefly describe the general approach that was followed to obtain fits to spectra using this model. First, it was assumed that the blocking layer/nanoparticle contact impedance is negligible because the materials are so similar, thus Rcon,2 was set to zero for cells equipped with blocking layers, also making Ccon,2 redundant. For cells without blocking layers, inclusion of Rcon,1 and Ccon,1 obviously cannot be justified, whereas inclusion of Rcon,2 and Ccon,2 probably is justified (note that the positions of these elements are distinguishable due to the presence of Rsub and Csub). All capacitances apart from Csub were replaced with constant phase elements (CPEs). The CPE parameter estimates and corresponding parallel resistances were later used to calculate apparent capacitances with units of farads to aid comparisons between values.7 Fits were usually slightly improved if Csub was also replaced with a CPE; however, this complicates comparison of values between cells if the CPE exponents differ. This is because no simple correction to obtain a capacitance with units of farads (as described in ref 7) is possible if the CPE is in parallel with the transmission line or indeed any other circuit element other than a pure resistor. Distributed TL parameter estimates typically only varied by less than (5% upon replacement of Csub by a CPE, and therefore this point is of minor significance to the main results presented herein. For cells equipped with compact TiO2 blocking layers, it was assumed that Rsub . Rrec at all voltages, and thus Rsub was omitted from the circuit (i.e., Rsub = ∞). Rsub was also omitted from the circuit for cells without blocking layers at high photovoltages, where it is also assumed that Rsub . Rrec, while at lower voltages statistically significant parameter estimates for both Rsub and Rrec generally could not be obtained simultaneously. At this point, a brief note should be made about the statistical significance of fits and parameter estimates. Unfortunately, because weighting of data has been based upon an assumed error structure, interpretation of the approximate standard errors in parameter estimates is difficult.22 Likewise, there is no quantitative
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Figure 1. Generalized equivalent circuit model used to fit impedance spectra for dye-sensitized solar cells.
way to determine whether a fit is adequate or whether the introduction of additional model parameters is justified based upon the improvement of the fit afforded by them. However, the weighted sum-of-squares and parameter error estimates reported by the regression software are still useful in a relative sense, and since they are the only means presently available for comparison of fitting results they were relied upon as guidelines during data analysis. Work aimed at establishing the proper form of the impedance error structure for typical cell/instrument combinations is underway, with the hope that it can be used to perform a more rigorous analysis of impedance data for dye-sensitized solar cells. Typically spectra were fitted in order of descending photovoltage, and it was initially assumed that Rt and Csub were negligible for the highest photovoltage. All other parameters, with the exception of those mentioned above, were allowed to vary freely. After fitting the first spectrum, the Warburg parameters representing the diffusion of redox species in electrolyte were fixed because the associated spectral features become impossible to distinguish at lower photovoltages. For each new fit, parameter estimates from the previous fit were used as initial values. After an initial fit to each spectrum was obtained, it was tested whether inclusion of Rt or Csub could improve the fit. Aside from requiring that the approximate 95% confidence intervals for these parameters did not include 0, Rt was also required to be no more than an order of magnitude smaller than Rcon,1 or Rcon,2, or else it was excluded from the model to avoid potentially unreliable values for Rt.4,5,23 Since very low DC currents flow in cells under the experimental conditions adopted here, Rcath, Ccath, and Zd ought to be almost independent of photovoltage. The values of Rcath and Ccath were therefore fixed to averaged values obtained from symmetrical cells consisting of only platinized electrodes at 0 V DC bias or were omitted from the model altogether. The rationale for this is that the symmetrical cells typically yielded Rcath values of only 0.3 Ω cm2, whereas the resistance associated with the first high-frequency arc in complex plane plots for complete cells (often attributed to the cathode/electrolyte impedance) was typically at least an order of magnitude larger. For this reason it is assumed that the high-frequency arc in complex plane plots mainly arises from the FTO/blocking layer contact impedance, i.e., Rcon,1 and Ccon,1 in Figure 1. For cells without blocking layers, the high-frequency portion of impedance spectra also cannot be explained solely by the cathode/electrolyte interface and is usually better fitted if Rcon,2 and Ccon,2 are included in the circuit. Unlike the cathode/electrolyte parameters, these contact parameters could vary with photovoltage as the quasi-Fermi level in the photoelectrode is expected to shift significantly under illumination at open circuit. Therefore, these parameters were allowed to vary freely during fits provided that their approximate 95% confidence intervals did not include 0.24 1558
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Figure 2. Plots of distributed transport resistance (a), charge transfer resistance (b), electrode capacitance (c), and electron diffusion length (d) versus open-circuit photovoltage for a series of cells with average TiO2 layer thicknesses of 4 (black), 8 (red), 14 (green), 16 (blue), and 18 μm (orange). The filled black points connected by solid lines are data for the 4 μm thick layer which were calculated, incorrectly, by using the thickness of the thickest TiO2 layer. The dashed line in (a) is a fit with a slope of 15.2 V1, while the dashed line in (d) is just a guide to the eye.
Figure 2 shows plots of distributed transmission line parameters (rt, rrec, and cμ) and the small perturbation electron diffusion length (λn) obtained for a series of cells equipped with blocking layers and d in the range 418 μm. Also shown in the plots are data for the thinnest TiO2 layer which have been calculated, incorrectly, using the thickness for the thickest layer, to visually indicate the sensitivity of parameters to the layer thickness. None of the parameters exhibit discernible thickness dependence at any voltage, and the relative magnitude of random variations between cells is small compared to the differences in layer thickness. Even before close examination of the parameter estimates for other circuit elements (e.g., Rcon, Csub, etc.), the results clearly show that the TL model adequately predicts the thickness dependence of the impedance spectra. At the lower end of the range of photovoltages studied, it was essential to include Csub in the equivalent circuit model to obtain acceptable fits. An example fit to a spectrum where inclusion of Csub was required is shown in Figure 3a. Also shown is a simulated curve using the same parameters but with Csub set to 0, together with the best fit that could be obtained without Csub included in the model. In this latter case, estimates for Rrec and Cμ
are similar to those obtained without Csub in the circuit model, but the estimate for Rt is over an order of magnitude smaller and is also 5 times smaller than for the spectrum recorded at the next highest photovoltage, which was fitted well without Csub in the circuit model. Figure 3b shows plots of Csub versus photovoltage for cells with blocking layers and porous TiO2 layers of various thicknesses. The area used for scaling Csub was the internal area of the hot-melt gasket used to seal the cell. As found for the distributed transmission line parameters, no significant dependence of Csub on layer thickness is observed, confirming that it does not arise from the porous TiO2 layer. Also shown are data obtained for a control cell fabricated without the porous TiO2 layer but following an otherwise identical procedure. The dashed line in the plot is the same data multiplied by the fraction of completely exposed substrate in the complete cell, which exists because the hot-melt gaskets used are slightly larger than the porous TiO2 layers. It seems reasonable to expect that the true value of Csub for the complete cell should lie somewhere between the two lines, dependent upon the contact area between the porous TiO2 layer and the substrate. In fact, Csub in complete cells is found to vary 1559
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Figure 3. (a) High-frequency portion of a complex plane plot for a 14 μm thick cell at 0.488 V (black circles) where inclusion of a substrate capacitance in the equivalent circuit model was essential to obtain a good fit (green line; Rt = 2681 Ω, Rct = 46599 Ω, Cμ = 62 μF, Csub = 5 μF, Rcon,1 = 161 Ω, Ccon,1 = 4 μF). Also shown is a simulation using the same parameters with Csub set to 0 (black line) and the best fit which could be obtained without inclusion of Csub in the model (red line; Rt = 101 Ω, Rct = 42853 Ω, Cμ = 64 μF, Csub = 0, Rcon,1 = 1011 Ω, Ccon,1 = 11 μF). (b) Plots of Csub versus photovoltage for cells equipped with compact TiO2 blocking layers and porous TiO2 layer thicknesses of 4 (black), 8 (red), 14 (green), 16 (blue), and 18 μm (orange). (c) Plots of Csub versus photovoltage for cells without compact TiO2 blocking layers and porous TiO2 layer thicknesses of 3 (black) and 5 μm (red). Solid and dashed lines in (b) and (c) represent the upper and lower bounds of Csub expected from measurements made on control cells without porous TiO2 layers.
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from being slightly larger to slightly smaller than in the control cells. Clearly, values are of the correct order of magnitude; however, their voltage dependence is slightly different, and their magnitude at higher photovoltage seems unreasonable. It is not clear at present whether this discrepancy arises because of inaccurate parameter estimates (perhaps caused by an incorrect weighting scheme), sample-to-sample variations in Csub, or a genuine modification of the substrate capacitance, which could plausibly arise in the vicinity of the contact points with the porous TiO2 layer. For comparative purposes, a series of cells without blocking layers were also characterized. Plots of distributed transmission line parameters for these cells can be found in the Supporting Information (Figure S1). Distributed transmission line parameters for these cells do not exhibit any unexpected dependence on layer thickness at sufficiently high photovoltage. However, acceptable fits could not be obtained at photovoltages as low as for cells with blocking layers, especially for thicker photoelectrodes. This is attributed to the effect of recombination via the substrate on the spectra; simulations reveal that even if λn > d, if Rt > Rsub the complex plane plots adopt a distorted shape, and Rt, Rrec, Cμ, and Csub cannot be readily obtained by fitting, even if Rsub is explicitly included in the model (Supporting Information). For the thinnest layers studied here, it is possible that Rt < Rsub, even at low photovoltages, and thus more typical transmission line spectra are obtained from which reliable estimates for Rt, Rrec, Cμ, and Csub can be extracted. Although the meaning of these parameters (especially Rrec) is somewhat ambiguous because Rsub is not included in the present fitting model, the estimates for Rt and Csub still hold some meaning, as can be verified by simulating spectra for finite values of Rsub, followed by fitting the simulated data with a circuit model excluding Rsub. Another observation is that λn values for cells without blocking layers are consistently lower than for cells with blocking layers at matched photovoltage. This can be partly traced to a small band shift between the two batches of cells, as evidenced by cμVOC plots (Figure S2, Supporting Information), and partly to lower rrec for cells without blocking layers (compared at matched cμ to cancel the effect of the band shift).25,26 We attribute this finding to an error in the estimation of rrec at low voltages for cells without blocking layers due to the use of a model which does not explicitly account for recombination via the substrate. Unfortunately, comparisons between λn values at high voltages (where determination of rrec should be more reliable) are also complicated because errors in rt are likely to be larger due to partial overlap between transport and contact spectral features, especially for cells with blocking layers where contact impedances are often larger. Figure 3c shows Csub data obtained for two of the cells without blocking layers and with TiO2 layer thicknesses of 3 and 5 μm, where acceptable fits could be obtained at low voltages. As in Figure 3b, plots showing the expected upper and lower bounds for Csub based upon independent measurements are also shown. In this case, Csub values fall in the expected range at all voltages and are always larger than those obtained for cells with blocking layers, providing further justification for inclusion of the substrate capacitance in the equivalent circuit model. Unfortunately, however, the range of thicknesses where Csub could be obtained by fitting is limited because low enough photovoltages (so that Cμ is sufficiently small and Csub influences the spectrum) usually cannot be reached before it becomes impossible to obtain statistically significant parameter estimates. 1560
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The self-consistency of the results discussed so far implies the circuit models used must at least be adequate for estimating the distributed transmission line parameters, if not also the substrate capacitance. However, the other remaining model parameters, namely Rcon,1 and Ccon,1 (or Rcon,2 and Ccon,2 for cells without blocking layers), ought to be briefly discussed. As indicated by Figures 4a and 4b, no clear correlation of either Rcon,1 or Ccon,1 with layer thickness was observed. However, apparently random sample-to-sample variations were observed, and both parameters are dependent upon photovoltage. Interestingly, spectra for cells without TiO2 blocking layers can be fitted reasonably well even if Rcon,2 and Ccon,2 are fixed to constant values that are obtained in fits near the top of the photovoltage range. Alternatively, if Rcon,2 and Ccon,2 are not fixed during fits, then their 95% confidence intervals often include 0 for photovoltages less than ca. 0.55 V. For this reason, it seems likely that the voltage dependence of the contact parameters found for cells employing blocking layers (i.e., Rcon,1 and Ccon,1) is a real effect and not simply due to unknown errors in parameter estimates. At least for some of the cells studied, it can be stated with good certainty that the increase in Rcon,1 with decreasing photovoltage is not simply a fitting artifact. This is because well-separated, strongly voltage-dependent arcs are observed at high frequency in complex plane plots for some cells; a particularly extreme example of this is shown in Figure 4c. Spectra similar to those shown in Figure 4c gave rise to the data for the 8 μm thick layer (red points in Figures 2, 3b, 4a, and 4b), but such behavior was occasionally observed for other porous TiO2 layer thicknesses. Although the magnitude of Rcon,1 is much larger for the 8 μm sample, the form of its voltage dependence is similar to the other samples, and the voltage and thickness dependencies of all other parameters obtained for this cell are unaffected by whatever causes the large contact resistance. This suggests that the voltage dependence of Rcon,1 in the other samples is a real physical effect. We should note that large contact resistances such as those seen in Figure 4c are not always observed. We have found that the magnitude of the contact resistance depends on the preparation conditions of the blocking layer, with very long deposition times reproducibly leading to larger contact resistances and eventually to decreased fill factors in 1 Sun jV measurements. Unfortunately though, sample-to-sample variations are often large, owing to poor control over the spray pyrolysis procedure used for blocking layer deposition, which presently involves the use of a hand-held aspirator. Provided the deposition time is not too long, cells exhibiting near-identical performance to that obtained for cells without blocking layers can be fabricated while still maintaining greatly suppressed charge transfer via the substrate, as indicated by photovoltage decay transients or by the magnitude of the photovoltage at low illumination intensity.27,28
Figure 4. (a) Plots of contact resistance versus photovoltage for cells equipped with blocking layers (Rcon,1) and average TiO2 layer thicknesses of 4 (black open circles), 8 (red open circles), and 16 μm (blue open circles) and for a typical cell without a blocking layer (Rcon,2; filled black circles). (b) Plots of contact capacitance versus photovoltage for cells with blocking layers (Ccon,1) and porous TiO2 layer thicknesses of 4 (black), 8 (red), and 16 μm (blue open circles) and for a typical cell without a blocking layer (Ccon,2; filled black circles). (c) Typical complex plane plots for a cell with a TiO2 blocking layer exhibiting a particularly high contact resistance. Spectra were recorded at 0.613 V (black), 0.560 V (red), and 0.514 V (green).
’ CONCLUSIONS Dye-sensitized solar cells with porous TiO2 layer thicknesses in the range 318 μm were fabricated and characterized by IS. An equivalent circuit model based upon a transmission line was fitted to the data to obtain the distributed parameters characterizing the TiO2 layers. No significant dependence of distributed resistance and capacitance parameters on TiO2 layer thickness was observed. This result provides a novel reaffirmation of the validity of the transmission line model and demonstrates that meaningful, scalable results can be obtained by fitting spectra acquired for electrodes covering a wide range of thicknesses. 1561
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The Journal of Physical Chemistry C It was necessary to include the capacitance of the substrate/ electrolyte interface in the equivalent circuit model to obtain good fits to all spectra at the lowest photovoltages studied. The capacitances derived from fits were found to be of the same order of magnitude as those expected based upon independent measurements, although for cells equipped with blocking layers they were consistently slightly larger and exhibited different voltage dependence than expected. The arcs occurring at high frequency in complex plane plots could not be solely attributed to the cathode/electrolyte interface for two reasons. First, the associated resistances were too large by at least an order of magnitude (but generally still small compared to other series resistances). Second, the associated resistances and capacitances were voltage dependent in cells equipped with blocking layers, which is not expected for the cathode/electrolyte interface when low DC currents flow during the measurement. If cells did not possess a blocking layer, it was possible to obtain reasonable fits to spectra without inclusion of a voltage-dependent contact resistance, although the contact resistance was still too large to attribute to the cathode/electrolyte interface. The apparent small-perturbation electron diffusion length, λn, was found to be shorter in cells which did not possess a blocking layer. At low photovoltages this is thought to arise from errors in parameter estimates due to use of a model which does not explicitly account for recombination via the substrate. Comparison of λn at higher photovoltages where substrate recombination ought to be negligible is complicated by the fact that estimates for rt may be less reliable, particularly for cells equipped with blocking layers where the contact impedance can be larger than for cells without blocking layers. We plan to address these issues together with a more rigorous and quantitative overall error analysis in a forthcoming publication.
’ ASSOCIATED CONTENT
bS Supporting Information. Plots of distributed transmission line parameters and small perturbation electron diffusion length for cells without blocking layers and with various different porous TiO2 layer thicknesses. Comparison between distributed transmission line parameters for cells with and without blocking layers. Discussion of the influence of recombination via the substrate on spectra obtained at low voltages. This material is available free of charge via the Internet at http://pubs.acs.org.
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’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This work was financially supported by URC grant No. R284000-075-112 and NRF CRP grant No. R-284-000-079-592. We thank Karen Koh Zhen Yu for preparation of the nanocrystalline TiO2 electrodes used in this work. ’ REFERENCES (1) Bisquert, J. J. Phys. Chem. B 2002, 106, 325. (2) Wang, Q.; Ito, S.; Gr€atzel, M.; Fabregat-Santiago, F.; Mora-Sero, I.; Bisquert, J.; Bessho, T.; Imai, H. J. Phys. Chem. B 2006, 110, 25210. (3) Gonzalez-Pedro, V.; Xu, X.; Mora-Sero, I. n.; Bisquert, J. ACS Nano 2010, 4, 5783. 1562
dx.doi.org/10.1021/jp209721c |J. Phys. Chem. C 2012, 116, 1556–1562
