Re-evaluation of Recombination Lossesin Dye-Sensitized Cells: The Failure ofDynamic Relaxation Methods toCorrectly Predict Diffusion Length inNanoporous PhotoelectrodesPiers 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., andDepartment 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 measuredat steady state (LIPCE). Charge collection efficiency calculated using Ln seriously overpredicted photocurrent, while LIPCE correctly predictedphotocurrent. This has implications for optimizing cell design.

Dye-sensitized solar cells (DSSCs) are examples offunctional nanostructures used to form operational devices.Models based on simple physical parameters extrapolatedfrom bulk materials have proved remarkably robust atpredicting many aspects of device performance.1-3 How-ever, there are several areas where these devices displayunusual behavior not predicted by models.4-7 One of theseareas concerns the calculation of electron diffusion length.In this study, we show conclusively that diffusion lengthsderived by Ln ) (τnDn)1/2, the standard equation relating thedynamic electron recombination lifetime (τn) and diffusioncoefficient (Dn), do not accurately predict observed photo-currents. In contrast, diffusion lengths derived from steady-state incident photon-to-electron conversion efficiency (IPCE)measurements do correctly predict the photocurrents.

In DSSCs, transport of electrons through the nanoporoussemiconductor electrode (normally TiO2) is dominated bydiffusion.8 Measurement of the electron diffusion length,L, (defined as the mean distance a photoelectron will travelbefore recombination) is frequently used as a means toassess charge collection efficiency in a DSSC.6,9-24 If L isgreater than the TiO2 layer thickness (d), then we expect

most injected photoelectrons to reach the conducting sub-strate, so that collection losses will be low at short circuit.For example, less than 2% of injected electrons are lost froma d ) 13 µm thick cell sensitized with N719 dye, where L) 50 µm.

Diffusion lengths measured using standard dynamic tech-niques (Ln) on DSSCs indicate Ln J 50 µm under workingconditions, which is around 3 times the typical optimizedcell thickness (d ∼ 13-18 µm24,25), implying no significantcollection losses.2,19,20,22-24,26 Under these conditions, thickerfilms would be expected to pay off since more light couldbe harvested from parts of the spectrum where the cellabsorbs weakly, increasing the photocurrent. Loss in pho-tovoltage associated with increasing d would limit theoptimum film thickness. Consequently, it is surprising thatthere is little discussion of improving the efficiency byincreasing the film thickness found in the literature. Theobservation of long Ln has also focused research efforts onred shifting the light absorption of dyes to increase photo-current.27-30 Red shifting might reduce dye regenerationefficiency, thus increasing recombination and reducing Ln;however, little change in electron collection efficiency isexpected if Ln still exceeds d. In practice, of the manyhundreds of new dyes tested, promising candidates (such asC101 dye used in this study22) are not red shifted but rathervery strongly absorbing relative to the current standard,

* To whom correspondence should be addressed. E-mail: piers.barnes@ic.ac.uk.

† Imperial College London.‡ American University of Beirut.

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N719. These dyes allow the majority of light to be absorbedwithin a thinner film, tacitly implying that electron collectionfrom thicker films limits performance despite the diffusionlength data to the contrary.22-24

Optimized cell thicknesses always appear to be less thanLn measured by dynamic methods. Additionally, there isoften a significant drop in photocurrent when illuminatingcells from the electrolyte-electrode side (EE; see Figure

1c), which is not expected when Ln . d. These observationsare sometimes attributed to problems with the mechanicalintegrity of thick films or optical losses to the platinum andelectrolyte in the case of EE illumination. However, thereappears to be a more fundamental problem with the deter-mination of L using dynamic techniques. Some indicationof this problem was shown previously, where the omissionof the standard TiCl4 surface treatment on dye cells caused

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

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a substantial drop in photocurrent which could not beexplained by transient measurements of Ln.6

Exploration of this inconsistency is the theme of this studyand is relevant to future cell production. Large-scale manu-facture of DSSCs is likely to involve depositing a TiO2 layeron an opaque metal substrate, meaning only EE sideillumination is possible. Assuming a constant injectionefficiency, the majority of the light harvested by the cell willgenerate electrons on the side of the TiO2 layer that is farfrom the collecting electrode, leading to more photocurrentloss than that in a transparent substrate cell illuminated fromthe substrate-electrode (SE) side. Under these circumstances,meaningful measurement of diffusion length is important foroptimizing cell design.

In this Letter, we have addressed the issue by quantifyingtransport losses in specially fabricated cells. These have thickTiO2 layers, strongly absorbing dyes, and different concen-trations of iodine (I2) in the electrolyte to change thephotocurrent lost to recombination at short circuit. We showthat the magnitudes of Ln measurements are too great toexplain the observed photocurrents, despite the values of τn

varying as expected with first-order reaction kinetics. Thephotocurrents can be accurately predicted by diffusionlengths derived from steady-state spectral response measure-ments.

The procedures used to fabricate cells are describedelsewhere,6 and the specific fabrication and experimentalmeasurement details are recorded in the Supporting Informa-tion. Nanoporous films of TiO2 (d ∼ 21 µm) were sensitizedusing dyes called TS4 (Figure 1a and Supporting Informa-tion) and C10122 (Figure 1b). TS4 is a strongly absorbingdye with faster recombination than C101. The cell electrolytecontained 0.6 M tetrabutylamonium iodide in methoxypro-pionitrile. In one set of cells, a standard concentration of0.05 M iodine was used, and in another, 0.2 M iodine wasused to increase the rate of photoelectron recombination. Anadditional set of d ∼ 13 µm cells sensitized with N719 dyewere also made, with the same electrolyte containingconcentrations of 0.05, 0.1, and 0.2 M iodine. For each dyeand electrolyte composition, two cells were made and tested.

The dynamic behavior of DSSCs is frequently explainedusing a simple multiple trapping model.1 This assumes thatphotoelectrons in the conduction band of the nanostructuredTiO2 have a single diffusion coefficient that applies at allplaces and conditions, D0, similar to that of bulk anatase.31

At the surface of a TiO2 nanoparticle, a conducting photo-electron has the opportunity to recombine with chemicalspecies in the surrounding electrolyte. Iodine added to theelectrolyte converts iodide ions to tri-iodide ions accordingto the reaction I2 + I- T I3

-. In the usual case where thereis an excess of iodide ions, the equilibrium constant for thisreaction goes to the right (Keq ≈ 107 in acetonitrile32), suchthat almost all iodine is converted to tri-iodide and [I3

-] ≈[I2]initial. The recombination of electrons with the electrolyteproceeds via transfer to either the I3

- ions or directly withI2.2 The overall rate of loss of photoelectrons is assumed tobe first order for both I3

- and conduction electrons, dn/dt )-knc[I3

-], where k is the recombination rate coefficient, n

is the concentration of electrons in the TiO2, nc theconcentration of conduction band electrons, and t is time. If[I3

-] is approximately constant for a given cell, then thepseudo-first-order lifetime of conduction band electrons isτ0 ) 1/(k[I3

-]).Due to the disordered nature of the nanostructured TiO2/

dye/electrolyte system, charge transport and recombinationare significantly slowed by the capture and release ofelectrons in localized trapping states at energies below theTiO2 conduction band. In fact, under normal operatingconditions, the concentration of trapped electrons, nL,substantially exceeds nc, so that n ) nc + nL ≈ nL. We usedcharge extraction to measure n at varying light intensitiesas a function of both at short-circuit current (jsc) and open-circuit photovoltage (Voc).

In this work, the dynamic electron lifetime, τn, is foundfrom the exponential decay of a small Voc perturbation. Thedynamic electron diffusion coefficient, Dn, is determined bymeasuring the single-exponential tail of a small perturbationphotocurrent decay, τj, with a first-order correction forrecombination by τn at the same n

There are many alternative methods for measuring τn andDn which yield equivalent values such as photovoltage risetimes or frequency domain measurements, IMVS, IMPS, andEIS.1,3,15,19,20,24,33,34

Assuming that the transfer of electrons to and fromlocalized states is fast relative to recombination and transportand that no recombination occurs via trapped electrons, thenτn can be interpreted as τn ) τ0(1 + ∂nL/∂nc).1 Similarly withthe same assumptions (known as the quasistatic approxima-tion), Dn is interpreted as Dn ) D0(1 + ∂nL/∂nc)-1.1 Theseexpressions collapse to τn ≈ τ0�nL/nc and Dn ≈ D0nc/(nL�)if conduction electrons obey Boltzmann statistics and theconcentration of filled trap states is proportional to exp[�qVoc/kBT]; 1/� is sometimes known as the thermodynamicfactor.1,35,36 The electron diffusion length can be written asL ) (D0τ0)1/2. It is thought that L can be determined fromdynamic measurements at matched electron concentrationsby

This is because the bracketed terms in the expressions forDn and τn above cancel, yielding a value Ln in eq 2 whichshould be equivalent to L.

Alternatively, as has been shown previously,6,9,37 L canbe found by analyzing the IPCE measured as a function ofwavelength, which we call η(λ), of a cell illuminated fromthe SE or EE side (see Figure 1c). The key to this analysisis the relationship between the IPCE and L. If sufficientoptical measurements are made, the ratio of η(λ) measuredon opposite sides, ηEE/ηSE, can be described by a function(eq S1, Supporting Information) where the only unknown is

Dn(n) ) d2

2.47[ 1τj(n)

- 1τn(n)] (1)

Ln ) (Dnτn)1/2 (2)

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L.6 We will call the diffusion length evaluated by fitting thisfunction to ηEE/ηSE data LIPCE. If LIPCE is known, then theexpression for η(λ) also has only one unknown parameter,the electron injection efficiency (ηinj), which may also befound by fitting (eqs S2 and S3, Supporting Information).6

Optical measurements allow the light harvesting efficiencyof 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 becalculated from the entire incident spectrum via the electrongeneration profile (eq S10, Supporting Information). Thesecan be used to predict the photocurrent that the cell shouldproduce according to

where q is the charge on an electron and Φ is the total photonflux 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 extinctioncoefficients of the TS4 and C101 dyes relative to N719, theirlarger molecular footprint limits the increase in absorptiononce incorporated within the cell. Also shown are theabsorption coefficients of the electrolytes used in this studywith differing concentrations of iodine. Higher iodineconcentrations decrease the flux of shorter wavelength lightabsorbed by the dye. This effect is more pronounced forillumination from the EE side despite the relatively smallgap between the counterelectrode and film (∼4 µm). Figure1c shows examples of current-voltage curves for SEillumination under light from the solar simulator. The C101cells show higher currents than the TS4 cells, and in bothcases, a reduction in photocurrent is observed when [I2] isincreased from 0.05 to 0.2 M. The photovoltage of the C101cells is a little lower than that of the TS4 cells, which weattribute to a difference in the conduction band positions ofthe two cells relative to the redox potential of the electrolyte,as will be shown below.

Figure 1d indicates the short-circuit photocurrent for thecells measured with both SE and EE side constant illumina-tion from the white LEDs, which were also used to providethe bias light for the IPCE measurements. The LED lightintensity was equivalent to ∼0.24 of the AM1.5 spectrumand was used in the subsequent analysis. The difference inphotocurrent from the AM1.5 and white LED spectra for anequivalent flux of harvested photons in a DSSC wascalculated to be small (see Supporting Information). Figure1d indicates that an increase in [I2] leads to a significant dropin photocurrent in these thick cells; this drop in photocurrentis relatively greater with EE side illumination than that withthe SE side. Corresponding results for the thinner N719 cellsare shown in Figure S1 of the Supporting Information, whichshows less dramatic changes in the current. We now considerthe reasons for the decrease in photocurrent in the TS4 andC101 cells.

Figure 2a shows that n increases exponentially with Voc

for each cell. This characteristic of DSSCs is generallyattributed to an exponential distribution of localized trapping

states below the conduction band edge. The figure alsoindicates that the concentration of electrons in the C101 cellsis a factor of 2-3 times higher than the concentration in theTS4 cells at an equivalent open-circuit voltage. This can beinterpreted as due to the TiO2 conduction band in the TS4cell being ∼80 mV higher than in the C101 cells relative tothe electrolyte redox potential.38 In Figure 2a, there is alsoa shift related to a change in [I2]; this can be partiallyexplained by the change in the electrolyte redox potentialcaused by the increase in [I2] from 0.05 to 0.2 M measuredto be ∼16 mV. Figure 2b shows τn, measured at Voc fordifferent light intensities plotted as a function of n. The C101dye shows around an order of magnitude longer electronlifetimes than the TS4 cells. This may be related todifferences in iodine binding to dye molecules; phenylthio-ether is said to bind ∼10 times more iodine than thiophene,39

and this might increase the availability of recombinationspecies in C101 relative to that in TS4. The plot also showsthat increasing the concentration of iodine in the cell by afactor of 4 reduces the lifetime by a corresponding factor of∼4. This is consistent with a first-order recombinationreaction between electrons and iodine or tri-iodide and isfurther confirmed by measurements on the N719 cells(Supporting Information). The observation is consistent withsome previous measurements40 but not others.41

Charge extracted from the cells operating at short circuitis presented in Figure 2c. There is some variation, which inpart corresponds to the variation in the effective diffusioncoefficient Dn seen in Figure 2d; higher values of Dn resultin shorter residence times of electrons in the film, and thus,less charge will be present for a given light intensity. Thevalues of Dn shown in Figure 2d show that the differencesin the diffusion coefficients between the cells are compara-tively small (up to a factor of about 2 at relatively high

jpred ) qΦηLHηinjηcol (3)

Figure 2. Examples of charge extraction and transient measure-ments 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 electronlifetime against n measured at Voc. (c) n measured at a short circuitplotted against jsc. (d) The effective diffusion coefficient as afunction of n measured at jsc.

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electron concentrations). This can, in part, be explained byincomplete charge extraction but does not contribute to afactor of more than ∼1.2 in the calculation of Ln. Figure 2thus 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 tocalculate LIPCE and ηinj. Wavelength dependence of ηinj wasnot required to achieve good fits to the data. It is clear thatincreasing [I2] modifies the shape of the spectral responseof the thick TS4 and C101 cells (d ∼ 21 µm). In particular,this can be seen for the EE side spectra where the IPCE isreduced at strongly absorbed wavelengths (λ ∼ 540 nm).The change is much less significant for the thinner N719cells (d ∼ 13 µm).

The values of LIPCE derived from fits to ηEE(λ)/ηSE(λ) areshown in Figure 4 compared with values of Ln interpolatedat equivalent charge concentrations. The steady-state LIPCE

values are all less than the cell thickness, consistent withthe photocurrent results (Figure 1f). The transient Ln valuesare 2-3 times greater than LIPCE and are greater than thecell thickness in all cases. For both measurements, there isa significant drop in L as [I2] is increased. A similar trend

was seen for Ln for the N719 cells (Figure S3, SupportingInformation).

Figure 5a shows the calculated collection efficiency as afunction of L for each of the cells using R(λ), d, and theillumination spectrum (eq S10, Supporting Information),confirming the expectation that if L is substantially greaterthan d, then collection losses are small. The plot also showsthat ηcol for EE side illumination is substantially lower thanthat when illuminating from the SE side, particularly whenL < d. In Figure 5b, ηcol calculated for each cell using thevalues of L in Figure 4 is plotted as a function of themeasured photocurrent. It is clear from the Figure 5b thatvalues of ηcol calculated using the LIPCE account for a greatdeal more of the variation in observed jsc than ηcol calculated

Figure 3. Examples of IPCE measurements for cells made with(a) TS4, (b) C101, and (c) N719 dyes and electrolyte containing0.05 M (squares) or 0.2 M (circles) iodine made for SE side (filled)or EE side (open) illumination. Corresponding ratios of IPCEmeasurements are shown in (d), (e), and (f). The lines show thefits used to find LIPCE and ηinj. The measurements used a low-intensity shuttered monochromatic light superimposed on a continu-ous white LED bias light (∼0.24 sun).

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 5. (a) Cell collection efficiency calculated as a function ofdiffusion length using the AM1.5 spectrum, R values shown inFigure 1d, and the cell thicknesses, d, are shown. (b) Collectionefficiencies calculated for each diffusion length measurement shownin Figure 4 plotted against the observed photocurrent. (c) Thecorresponding values of the integrated light harvesting efficiencymeasured for the AM1.5 spectrum and injection efficiency for thecells. (d) The predicted photocurrent calculated using Ln (opensymbols) and LIPCE (filled symbols) plotted against the observedphotocurrent for each cell and illumination direction used in thestudy. The solid line shows the expected 1:1 relationship.

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using Ln. The case for the thinner N719 cells is shown inthe Supporting Information.

Figure 5c shows the variation in light harvesting efficiencyand injection efficiency (from η(λ) fitting) as a function ofthe observed photocurrent. Although there is little variationin the ηLH between the different cells, the injection efficiencyof 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 fitthe data. Values of ηinj derived from the IPCE measurementshave been confirmed with transient photoemission measure-ments.5 Factors controlling ηinj are described elsewhere.5,42

The observed variation in ηinj accounts for only a smallamount of the variation in jsc.

Figure 5d demonstrates the key observation of this study.The product of light harvesting efficiency, injection ef-ficiency, collection efficiency, and the incident photon fluxshould predict the current generated by a cell (eq 3). Figure5d shows that using LIPCE does indeed predict the observedphotocurrent when illuminated by either the SE or EE sides.The photocurrent predicted using a collection efficiencycalculated with Ln clearly overestimates the photocurrent byup 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 wrongby as much as a factor of 3; it is reasonable to ask why. Itseems likely that the error arises from the interpretation ofthe dynamic measurements of τn or Dn rather than measure-ment of n since most of the uncertainty introduced byrecombination losses during charge extraction (at both Voc

and jsc) will cancel out. Although we cannot fully explainthe error, it is in part due to the difference between diffusion/recombination in single-phase semiconductors and analogousprocesses in a nanoporous bulk heterojunction. To accountfor a factor of 2-3 discrepancy in Ln, a 4-9 times differencein the value of either τn or Dn is required, which seems hardto reconcile with the assumptions of the simple multipletrapping model. The slope of the n versus Voc plots in Figure2a yields a value of � ≈ 0.29, and the multiple trappingmodel predicts that the slopes of τn and Dn versus n shouldbe given by 1/� - 1 and 1 - 1/�, respectively; in practice,the measured slopes would be consistent with � values ofapproximately 0.37 and 0.47. This suggests that the influenceof the trap states is partially decoupled from the transientresponses of τn and Dn, which is not predicted by the model.There are other possible errors in the interpretation of thetransients; the derivation of Dn could be influenced by anonuniform generation profile.43 This does not seem likelyto be the root of the problem in this case since the tail of atransient decay should be independent of generation profile.We note that neither Ln nor LIPCE showed the factor of 2drop expected from the 4-fold increase in τn resulting fromthe addition of iodine and that the relative fall in LIPCE wasless than that in Ln. Recent work also indicates that therecombination rate is not only dependent on the electronconcentration but also the light intensity, with the recombi-nation flux being about 2-3 times higher in the light relativeto that in the dark.44 Our previous work also showed that

LIPCE varies with light intensity and hence n.6 This observa-tion implies that either D0 or τ0 is not constant with varyingn or light, such that L is not a characteristic of the cell butmust be thought of as L(n,x). Alternatively, it is reasonableto imagine that the assumptions of the simple transport modelare not sufficient to describe the real cell behavior.

In summary, we find that collection losses calculated usinga transient diffusion length are not useful for quantifyingshort-circuit photocurrent losses in dye-sensitized cells. Wehave previously proposed that transient measurements mightoverestimate the diffusion length. Here, we have proven thisto be the case using cells with thick TiO2 layers and stronglyabsorbing dyes, where recombination was increased byadding more iodine to the electrolyte. On the other hand,we show that photocurrents can be calculated using diffusionlengths derived from IPCE measurements. We have consid-ered a number of possible factors that may contribute to thisdifference. Although collection losses are not large in current“record” cells, it is important to correctly assign photocurrentlosses observed during attempts to improve cells or introducenew geometries for product applications. These observationsshould serve to refocus future research efforts on reducingcharge-transport losses in dye cells which were previouslyassumed to be insignificant.

Acknowledgment. This work is supported by the EPSRCMaterials for Energy (No. EP/E035175/1), SUPERGEN“Excitonic Solar Cells” programes, the European UnionRobust DSC project (No. 212792) and the UniversityResearch Board (URB) at the American University of Beirut(AUB), and the Lebanese National Council for ScientificResearch (LNCSR).

Supporting Information Available: Experimental details,including the synthesis of TS4. The expressions used to findLIPCE, ηinj, ηLH, and ηcol are also presented, including analysisof the influence of the white LED spectrum relative to theAM1.5 spectrum on the results. Results of measurementsand calculations corresponding to Figures 2, 4, and 5 forthe thinner N719 cells are presented. This material isavailable free of charge via the Internet at http://pubs.acs.org.

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