Re-evaluation of Recombination Losses in Dye-Sensitized Cells: The

NANO LETTERS

Re-evaluation of Recombination Losses in Dye-Sensitized Cells: The Failure of Dynamic Relaxation Methods to Correctly Predict Diffusion Length in Nanoporous Photoelectrodes

2009 Vol. 9, No. 10 3532-3538

Piers R. F. Barnes,*,† Lingxuan Liu,† Xiaoe Li,† Assaf Y. Anderson,† Hawraa Kisserwan,‡ Tarek H. Ghaddar,‡ James R. Durrant,† and Brian C. O’Regan† Department of Chemistry, Imperial College London, London SW7 2AZ, U.K., and Department of Chemistry, American UniVersity of Beirut, Beirut, 11-0236 Lebanon Received June 2, 2009

ABSTRACT Photocurrents generated by thick, strongly absorbing, dye-sensitized cells were reduced when the electrolyte iodine concentration was increased. Electron diffusion lengths measured using common transient techniques (Ln) were at least two times higher than diffusion lengths measured at steady state (LIPCE). Charge collection efficiency calculated using Ln seriously overpredicted photocurrent, while LIPCE correctly predicted photocurrent. This has implications for optimizing cell design.

Dye-sensitized solar cells (DSSCs) are examples of functional nanostructures used to form operational devices. Models based on simple physical parameters extrapolated from bulk materials have proved remarkably robust at predicting many aspects of device performance.1-3 However, there are several areas where these devices display unusual behavior not predicted by models.4-7 One of these areas concerns the calculation of electron diffusion length. In this study, we show conclusively that diffusion lengths derived by Ln ) (τnDn)1/2, the standard equation relating the dynamic electron recombination lifetime (τn) and diffusion coefficient (Dn), do not accurately predict observed photocurrents. In contrast, diffusion lengths derived from steadystate incident photon-to-electron conversion efficiency (IPCE) measurements do correctly predict the photocurrents. In DSSCs, transport of electrons through the nanoporous semiconductor electrode (normally TiO2) is dominated by diffusion.8 Measurement of the electron diffusion length, L, (defined as the mean distance a photoelectron will travel before recombination) is frequently used as a means to assess charge collection efficiency in a DSSC.6,9-24 If L is greater than the TiO2 layer thickness (d), then we expect * To whom correspondence should be addressed. E-mail: piers.barnes@ ic.ac.uk. † Imperial College London. ‡ American University of Beirut. 10.1021/nl901753k CCC: $40.75 Published on Web 07/31/2009

 2009 American Chemical Society

most injected photoelectrons to reach the conducting substrate, so that collection losses will be low at short circuit. For example, less than 2% of injected electrons are lost from a d ) 13 µm thick cell sensitized with N719 dye, where L ) 50 µm. Diffusion lengths measured using standard dynamic techniques (Ln) on DSSCs indicate Ln J 50 µm under working conditions, which is around 3 times the typical optimized cell thickness (d ∼ 13-18 µm24,25), implying no significant collection losses.2,19,20,22-24,26 Under these conditions, thicker films would be expected to pay off since more light could be harvested from parts of the spectrum where the cell absorbs weakly, increasing the photocurrent. Loss in photovoltage associated with increasing d would limit the optimum film thickness. Consequently, it is surprising that there is little discussion of improving the efficiency by increasing the film thickness found in the literature. The observation of long Ln has also focused research efforts on red shifting the light absorption of dyes to increase photocurrent.27-30 Red shifting might reduce dye regeneration efficiency, thus increasing recombination and reducing Ln; however, little change in electron collection efficiency is expected if Ln still exceeds d. In practice, of the many hundreds of new dyes tested, promising candidates (such as C101 dye used in this study22) are not red shifted but rather very strongly absorbing relative to the current standard,

Figure 1. The chemical structure of the (a) TS4 dye and (b) the C101 dye. (c) Schematic of a dye-sensitized cell, indicating illumination from the substrate-electrode side (SE) or the electrolyte-electrode side (EE). (d) Examples of absorption coefficients for the materials used in the cells. (e) Examples of photocurrent voltage characteristics for TS4 (d ∼ 20.6 µm) and C101 (d ∼ 20.8 µm) cells with different electrolyte [I2] (illuminated from the SE side with a Xe lamp simulated AM1.5 spectrum). (f) The dependence of the short-circuit photocurrent on the iodine concentration and illumination side (SE and EE) for the TS4 and C101 cells. Photocurrent measured with white LEDs with an intensity equivalent to ∼0.24 sun for consistency with the bias light used during IPCE measurements.

N719. These dyes allow the majority of light to be absorbed within a thinner film, tacitly implying that electron collection from thicker films limits performance despite the diffusion length data to the contrary.22-24 Optimized cell thicknesses always appear to be less than Ln measured by dynamic methods. Additionally, there is often a significant drop in photocurrent when illuminating cells from the electrolyte-electrode side (EE; see Figure Nano Lett., Vol. 9, No. 10, 2009

1c), which is not expected when Ln . d. These observations are sometimes attributed to problems with the mechanical integrity of thick films or optical losses to the platinum and electrolyte in the case of EE illumination. However, there appears to be a more fundamental problem with the determination of L using dynamic techniques. Some indication of this problem was shown previously, where the omission of the standard TiCl4 surface treatment on dye cells caused 3533

a substantial drop in photocurrent which could not be explained by transient measurements of Ln.6 Exploration of this inconsistency is the theme of this study and is relevant to future cell production. Large-scale manufacture of DSSCs is likely to involve depositing a TiO2 layer on an opaque metal substrate, meaning only EE side illumination is possible. Assuming a constant injection efficiency, the majority of the light harvested by the cell will generate electrons on the side of the TiO2 layer that is far from the collecting electrode, leading to more photocurrent loss than that in a transparent substrate cell illuminated from the substrate-electrode (SE) side. Under these circumstances, meaningful measurement of diffusion length is important for optimizing cell design. In this Letter, we have addressed the issue by quantifying transport losses in specially fabricated cells. These have thick TiO2 layers, strongly absorbing dyes, and different concentrations of iodine (I2) in the electrolyte to change the photocurrent lost to recombination at short circuit. We show that the magnitudes of Ln measurements are too great to explain the observed photocurrents, despite the values of τn varying as expected with first-order reaction kinetics. The photocurrents can be accurately predicted by diffusion lengths derived from steady-state spectral response measurements. The procedures used to fabricate cells are described elsewhere,6 and the specific fabrication and experimental measurement details are recorded in the Supporting Information. Nanoporous films of TiO2 (d ∼ 21 µm) were sensitized using dyes called TS4 (Figure 1a and Supporting Information) and C10122 (Figure 1b). TS4 is a strongly absorbing dye with faster recombination than C101. The cell electrolyte contained 0.6 M tetrabutylamonium iodide in methoxypropionitrile. In one set of cells, a standard concentration of 0.05 M iodine was used, and in another, 0.2 M iodine was used to increase the rate of photoelectron recombination. An additional set of d ∼ 13 µm cells sensitized with N719 dye were also made, with the same electrolyte containing concentrations of 0.05, 0.1, and 0.2 M iodine. For each dye and electrolyte composition, two cells were made and tested. The dynamic behavior of DSSCs is frequently explained using a simple multiple trapping model.1 This assumes that photoelectrons in the conduction band of the nanostructured TiO2 have a single diffusion coefficient that applies at all places and conditions, D0, similar to that of bulk anatase.31 At the surface of a TiO2 nanoparticle, a conducting photoelectron has the opportunity to recombine with chemical species in the surrounding electrolyte. Iodine added to the electrolyte converts iodide ions to tri-iodide ions according to the reaction I2 + I- T I3-. In the usual case where there is an excess of iodide ions, the equilibrium constant for this reaction goes to the right (Keq ≈ 107 in acetonitrile32), such that almost all iodine is converted to tri-iodide and [I3-] ≈ [I2]initial. The recombination of electrons with the electrolyte proceeds via transfer to either the I3- ions or directly with I2.2 The overall rate of loss of photoelectrons is assumed to be first order for both I3- and conduction electrons, dn/dt ) -knc[I3-], where k is the recombination rate coefficient, n 3534

is the concentration of electrons in the TiO2, nc the concentration of conduction band electrons, and t is time. If [I3-] is approximately constant for a given cell, then the pseudo-first-order lifetime of conduction band electrons is τ0 ) 1/(k[I3-]). Due to the disordered nature of the nanostructured TiO2/ dye/electrolyte system, charge transport and recombination are significantly slowed by the capture and release of electrons in localized trapping states at energies below the TiO2 conduction band. In fact, under normal operating conditions, the concentration of trapped electrons, nL, substantially exceeds nc, so that n ) nc + nL ≈ nL. We used charge extraction to measure n at varying light intensities as a function of both at short-circuit current (jsc) and opencircuit photovoltage (Voc). In this work, the dynamic electron lifetime, τn, is found from the exponential decay of a small Voc perturbation. The dynamic electron diffusion coefficient, Dn, is determined by measuring the single-exponential tail of a small perturbation photocurrent decay, τj, with a first-order correction for recombination by τn at the same n Dn(n) )

[

1 1 d2 2.47 τj(n) τn(n)

]

(1)

There are many alternative methods for measuring τn and Dn which yield equivalent values such as photovoltage rise times or frequency domain measurements, IMVS, IMPS, and EIS.1,3,15,19,20,24,33,34 Assuming that the transfer of electrons to and from localized states is fast relative to recombination and transport and that no recombination occurs via trapped electrons, then τn can be interpreted as τn ) τ0(1 + ∂nL/∂nc).1 Similarly with the same assumptions (known as the quasistatic approximation), Dn is interpreted as Dn ) D0(1 + ∂nL/∂nc)-1.1 These expressions collapse to τn ≈ τ0βnL/nc and Dn ≈ D0nc/(nLβ) if conduction electrons obey Boltzmann statistics and the concentration of filled trap states is proportional to exp[βqVoc/ kBT]; 1/β is sometimes known as the thermodynamic factor.1,35,36 The electron diffusion length can be written as L ) (D0τ0)1/2. It is thought that L can be determined from dynamic measurements at matched electron concentrations by Ln ) (Dnτn)1/2

(2)

This is because the bracketed terms in the expressions for Dn and τn above cancel, yielding a value Ln in eq 2 which should be equivalent to L. Alternatively, as has been shown previously,6,9,37 L can be found by analyzing the IPCE measured as a function of wavelength, which we call η(λ), of a cell illuminated from the SE or EE side (see Figure 1c). The key to this analysis is the relationship between the IPCE and L. If sufficient optical measurements are made, the ratio of η(λ) measured on opposite sides, ηEE/ηSE, can be described by a function (eq S1, Supporting Information) where the only unknown is Nano Lett., Vol. 9, No. 10, 2009

L.6 We will call the diffusion length evaluated by fitting this function to ηEE/ηSE data LIPCE. If LIPCE is known, then the expression for η(λ) also has only one unknown parameter, the electron injection efficiency (ηinj), which may also be found by fitting (eqs S2 and S3, Supporting Information).6 Optical measurements allow the light harvesting efficiency of the device to be calculated for the incident light spectrum, ηLH (eq S6, Supporting Information). Correspondingly, knowledge of L allows the collection efficiency, ηcol, to be calculated from the entire incident spectrum via the electron generation profile (eq S10, Supporting Information). These can be used to predict the photocurrent that the cell should produce according to jpred ) qΦηLHηinjηcol

(3)

where q is the charge on an electron and Φ is the total photon flux in the incident spectrum (eq S7, Supporting Information). The absorption coefficients of the dye adsorbed to the TiO2 are shown in Figure 1d. Despite much higher extinction coefficients of the TS4 and C101 dyes relative to N719, their larger molecular footprint limits the increase in absorption once incorporated within the cell. Also shown are the absorption coefficients of the electrolytes used in this study with differing concentrations of iodine. Higher iodine concentrations decrease the flux of shorter wavelength light absorbed by the dye. This effect is more pronounced for illumination from the EE side despite the relatively small gap between the counterelectrode and film (∼4 µm). Figure 1c shows examples of current-voltage curves for SE illumination under light from the solar simulator. The C101 cells show higher currents than the TS4 cells, and in both cases, a reduction in photocurrent is observed when [I2] is increased from 0.05 to 0.2 M. The photovoltage of the C101 cells is a little lower than that of the TS4 cells, which we attribute to a difference in the conduction band positions of the two cells relative to the redox potential of the electrolyte, as will be shown below. Figure 1d indicates the short-circuit photocurrent for the cells measured with both SE and EE side constant illumination from the white LEDs, which were also used to provide the bias light for the IPCE measurements. The LED light intensity was equivalent to ∼0.24 of the AM1.5 spectrum and was used in the subsequent analysis. The difference in photocurrent from the AM1.5 and white LED spectra for an equivalent flux of harvested photons in a DSSC was calculated to be small (see Supporting Information). Figure 1d indicates that an increase in [I2] leads to a significant drop in photocurrent in these thick cells; this drop in photocurrent is relatively greater with EE side illumination than that with the SE side. Corresponding results for the thinner N719 cells are shown in Figure S1 of the Supporting Information, which shows less dramatic changes in the current. We now consider the reasons for the decrease in photocurrent in the TS4 and C101 cells. Figure 2a shows that n increases exponentially with Voc for each cell. This characteristic of DSSCs is generally attributed to an exponential distribution of localized trapping Nano Lett., Vol. 9, No. 10, 2009

Figure 2. Examples of charge extraction and transient measurements for the TS4 and C101 cells with [I2] ) 0.05 and 0.2 M. (a) Charge concentration, n, as a function of Voc. (b) Effective electron lifetime against n measured at Voc. (c) n measured at a short circuit plotted against jsc. (d) The effective diffusion coefficient as a function of n measured at jsc.

states below the conduction band edge. The figure also indicates that the concentration of electrons in the C101 cells is a factor of 2-3 times higher than the concentration in the TS4 cells at an equivalent open-circuit voltage. This can be interpreted as due to the TiO2 conduction band in the TS4 cell being ∼80 mV higher than in the C101 cells relative to the electrolyte redox potential.38 In Figure 2a, there is also a shift related to a change in [I2]; this can be partially explained by the change in the electrolyte redox potential caused by the increase in [I2] from 0.05 to 0.2 M measured to be ∼16 mV. Figure 2b shows τn, measured at Voc for different light intensities plotted as a function of n. The C101 dye shows around an order of magnitude longer electron lifetimes than the TS4 cells. This may be related to differences in iodine binding to dye molecules; phenylthioether is said to bind ∼10 times more iodine than thiophene,39 and this might increase the availability of recombination species in C101 relative to that in TS4. The plot also shows that increasing the concentration of iodine in the cell by a factor of 4 reduces the lifetime by a corresponding factor of ∼4. This is consistent with a first-order recombination reaction between electrons and iodine or tri-iodide and is further confirmed by measurements on the N719 cells (Supporting Information). The observation is consistent with some previous measurements40 but not others.41 Charge extracted from the cells operating at short circuit is presented in Figure 2c. There is some variation, which in part corresponds to the variation in the effective diffusion coefficient Dn seen in Figure 2d; higher values of Dn result in shorter residence times of electrons in the film, and thus, less charge will be present for a given light intensity. The values of Dn shown in Figure 2d show that the differences in the diffusion coefficients between the cells are comparatively small (up to a factor of about 2 at relatively high 3535

Figure 4. (a) LIPCE and Ln as a function of iodine concentration. (b) LIPCE as a function of iodine concentration expanded for clarity. The cell thicknesses (d) are also indicated.

Figure 3. Examples of IPCE measurements for cells made with (a) TS4, (b) C101, and (c) N719 dyes and electrolyte containing 0.05 M (squares) or 0.2 M (circles) iodine made for SE side (filled) or EE side (open) illumination. Corresponding ratios of IPCE measurements are shown in (d), (e), and (f). The lines show the fits used to find LIPCE and ηinj. The measurements used a lowintensity shuttered monochromatic light superimposed on a continuous white LED bias light (∼0.24 sun).

electron concentrations). This can, in part, be explained by incomplete charge extraction but does not contribute to a factor of more than ∼1.2 in the calculation of Ln. Figure 2 thus contains all values required to find Ln(n) using eq 2, and the calculated values will be presented in Figure 4. Figure 3 shows examples of the IPCE data used to calculate LIPCE and ηinj. Wavelength dependence of ηinj was not required to achieve good fits to the data. It is clear that increasing [I2] modifies the shape of the spectral response of the thick TS4 and C101 cells (d ∼ 21 µm). In particular, this can be seen for the EE side spectra where the IPCE is reduced at strongly absorbed wavelengths (λ ∼ 540 nm). The change is much less significant for the thinner N719 cells (d ∼ 13 µm). The values of LIPCE derived from fits to ηEE(λ)/ηSE(λ) are shown in Figure 4 compared with values of Ln interpolated at equivalent charge concentrations. The steady-state LIPCE values are all less than the cell thickness, consistent with the photocurrent results (Figure 1f). The transient Ln values are 2-3 times greater than LIPCE and are greater than the cell thickness in all cases. For both measurements, there is a significant drop in L as [I2] is increased. A similar trend 3536

Figure 5. (a) Cell collection efficiency calculated as a function of diffusion length using the AM1.5 spectrum, R values shown in Figure 1d, and the cell thicknesses, d, are shown. (b) Collection efficiencies calculated for each diffusion length measurement shown in Figure 4 plotted against the observed photocurrent. (c) The corresponding values of the integrated light harvesting efficiency measured for the AM1.5 spectrum and injection efficiency for the cells. (d) The predicted photocurrent calculated using Ln (open symbols) and LIPCE (filled symbols) plotted against the observed photocurrent for each cell and illumination direction used in the study. The solid line shows the expected 1:1 relationship.

was seen for Ln for the N719 cells (Figure S3, Supporting Information). Figure 5a shows the calculated collection efficiency as a function of L for each of the cells using R(λ), d, and the illumination spectrum (eq S10, Supporting Information), confirming the expectation that if L is substantially greater than d, then collection losses are small. The plot also shows that ηcol for EE side illumination is substantially lower than that when illuminating from the SE side, particularly when L < d. In Figure 5b, ηcol calculated for each cell using the values of L in Figure 4 is plotted as a function of the measured photocurrent. It is clear from the Figure 5b that values of ηcol calculated using the LIPCE account for a great deal more of the variation in observed jsc than ηcol calculated Nano Lett., Vol. 9, No. 10, 2009

using Ln. The case for the thinner N719 cells is shown in the Supporting Information. Figure 5c shows the variation in light harvesting efficiency and injection efficiency (from η(λ) fitting) as a function of the observed photocurrent. Although there is little variation in the ηLH between the different cells, the injection efficiency of the C101 cells is around 18% higher than the TS4; however, no significant dependence on [I2] was observed, and as noted earlier, no dependence of λ was required to fit the data. Values of ηinj derived from the IPCE measurements have been confirmed with transient photoemission measurements.5 Factors controlling ηinj are described elsewhere.5,42 The observed variation in ηinj accounts for only a small amount of the variation in jsc. Figure 5d demonstrates the key observation of this study. The product of light harvesting efficiency, injection efficiency, collection efficiency, and the incident photon flux should predict the current generated by a cell (eq 3). Figure 5d shows that using LIPCE does indeed predict the observed photocurrent when illuminated by either the SE or EE sides. The photocurrent predicted using a collection efficiency calculated with Ln clearly overestimates the photocurrent by up to a factor of 2. The discrepancy originates because Ln predicts low collection losses (Figure 5b). Since LIPCE correctly predicts jsc, it appears that Ln is wrong by as much as a factor of 3; it is reasonable to ask why. It seems likely that the error arises from the interpretation of the dynamic measurements of τn or Dn rather than measurement of n since most of the uncertainty introduced by recombination losses during charge extraction (at both Voc and jsc) will cancel out. Although we cannot fully explain the error, it is in part due to the difference between diffusion/ recombination in single-phase semiconductors and analogous processes in a nanoporous bulk heterojunction. To account for a factor of 2-3 discrepancy in Ln, a 4-9 times difference in the value of either τn or Dn is required, which seems hard to reconcile with the assumptions of the simple multiple trapping model. The slope of the n versus Voc plots in Figure 2a yields a value of β ≈ 0.29, and the multiple trapping model predicts that the slopes of τn and Dn versus n should be given by 1/β - 1 and 1 - 1/β, respectively; in practice, the measured slopes would be consistent with β values of approximately 0.37 and 0.47. This suggests that the influence of the trap states is partially decoupled from the transient responses of τn and Dn, which is not predicted by the model. There are other possible errors in the interpretation of the transients; the derivation of Dn could be influenced by a nonuniform generation profile.43 This does not seem likely to be the root of the problem in this case since the tail of a transient decay should be independent of generation profile. We note that neither Ln nor LIPCE showed the factor of 2 drop expected from the 4-fold increase in τn resulting from the addition of iodine and that the relative fall in LIPCE was less than that in Ln. Recent work also indicates that the recombination rate is not only dependent on the electron concentration but also the light intensity, with the recombination flux being about 2-3 times higher in the light relative to that in the dark.44 Our previous work also showed that Nano Lett., Vol. 9, No. 10, 2009

LIPCE varies with light intensity and hence n.6 This observation implies that either D0 or τ0 is not constant with varying n or light, such that L is not a characteristic of the cell but must be thought of as L(n,x). Alternatively, it is reasonable to imagine that the assumptions of the simple transport model are not sufficient to describe the real cell behavior. In summary, we find that collection losses calculated using a transient diffusion length are not useful for quantifying short-circuit photocurrent losses in dye-sensitized cells. We have previously proposed that transient measurements might overestimate the diffusion length. Here, we have proven this to be the case using cells with thick TiO2 layers and strongly absorbing dyes, where recombination was increased by adding more iodine to the electrolyte. On the other hand, we show that photocurrents can be calculated using diffusion lengths derived from IPCE measurements. We have considered a number of possible factors that may contribute to this difference. Although collection losses are not large in current “record” cells, it is important to correctly assign photocurrent losses observed during attempts to improve cells or introduce new geometries for product applications. These observations should serve to refocus future research efforts on reducing charge-transport losses in dye cells which were previously assumed to be insignificant. Acknowledgment. This work is supported by the EPSRC Materials for Energy (No. EP/E035175/1), SUPERGEN “Excitonic Solar Cells” programes, the European Union Robust DSC project (No. 212792) and the University Research Board (URB) at the American University of Beirut (AUB), and the Lebanese National Council for Scientific Research (LNCSR). Supporting Information Available: Experimental details, including the synthesis of TS4. The expressions used to find LIPCE, ηinj, ηLH, and ηcol are also presented, including analysis of the influence of the white LED spectrum relative to the AM1.5 spectrum on the results. Results of measurements and calculations corresponding to Figures 2, 4, and 5 for the thinner N719 cells are presented. This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Bisquert, J.; Vikhrenko, V. S. J. Phys. Chem. B 2004, 108 (7), 2313– 2322. (2) Peter, L. M. J. Phys. Chem. C 2007, 111 (18), 6601–6612. (3) de Jongh, P. E.; Vanmaekelbergh, D. Phys. ReV. Lett. 1996, 77 (16), 3427–3430. (4) Splan, K. E.; Massari, A. M.; Hupp, J. T. J. Phys. Chem. B 2004, 108 (13), 4111–4115. (5) Dor, S.; Grinis, L.; Ruhle, S.; Zaban, A. J. Phys. Chem. C 2009, 113 (5), 2022–2027. (6) (a) Barnes, P. R. F.; Anderson, A. Y.; Koops, S. E.; Durrant, J. R.; O’Regan, B. C. J. Phys. Chem. C 2009, 113 (3), 1126–1136. (b) Barnes, P. R. F.; Anderson, A. Y.; Koops, S. E.; Durrant, J. R.; O’Regan, B. C. J. Phys. Chem. C 2009, 113 (28), 12615. (7) Kopidakis, N.; Benkstein, K. D.; van de Lagemaat, J.; Frank, A. J.; Yuan, Q.; Schiff, E. A. Phys. ReV. B 2006, 73 (4), 7. (8) O’Regan, B.; Moser, J.; Anderson, M.; Gratzel, M. J. Phys. Chem. 1990, 94 (24), 8720–8726. (9) Halme, J.; Boschloo, G.; Hagfeldt, A.; Lund, P. J. Phys. Chem. C 2008, 112 (14), 5623–5637. (10) Ahn, K. S.; Kang, M. S.; Lee, J. W.; Kang, Y. S. J. Appl. Phys. 2007, 101 (8), 084312. 3537

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