Efficiency Limitations in Dye-Sensitized Solar Cells Caused by

ARTICLE pubs.acs.org/JPCC

Efficiency Limitations in Dye-Sensitized Solar Cells Caused by Inefficient Sensitizer Regeneration James R. Jennings, Yeru Liu, and Qing Wang* Department of Materials Science and Engineering, Faculty of Engineering, NUSNNI-NanoCore, National University of Singapore, Singapore 117576

bS Supporting Information ABSTRACT: It is widely believed that the prototypical ruthenium dyes N719 and Z907 are regenerated by iodide with near unity quantum yield following photo-oxidation in dye-sensitized solar cells (DSCs). However, the incident photon-to-current efficiency (IPCE) of DSCs using these dyes decreases with increasing forward bias, limiting power conversion efficiency (η) compared to the hypothetical constant-IPCE case. This phenomenon could arise due to incomplete regeneration, but despite the important implications for cell efficiency, it has received little attention. DSCs employing electrolytes with different iodide concentrations and the Z907 sensitizer have been characterized using complementary photoelectrochemical techniques to test whether the decrease in IPCE is caused by inefficient regeneration. The results strongly suggest that this is the case, even for abnormally high iodide concentrations, where η is reduced by as much as 30% by the effect. Similar results are obtained with the N719 sensitizer. Interestingly, the predicted reduction in photovoltage is partially offset by a change in the electrostatic potential drop across the Helmholtz layer at the TiO2
electroyte interface, which has an estimated microscopic areal capacitance in the range 2.3
9.3 μF cm
2. These findings suggest that it will be important to carefully consider sensitizer regeneration kinetics and interfacial electric fields to further improve the efficiency of DSCs.

’ INTRODUCTION Dye-sensitized nanocrystalline solar cells (DSCs)1,2 continue to receive a great deal of attention as a potential rival to conventional silicon-based photovoltaics.3 DSCs invariably consist of a nanocrystalline metal oxide film, usually TiO2, onto which a transition metal complex or metal-free organic sensitizer is attached.4
6 The dye-sensitized oxide layer is contacted by a redox electrolyte which fills the pores of the nanocrystalline film and shuttles charge to and from a platinized cathode.7 The redox couple is almost always I3
/I
,8 although in recent years several other very promising alternatives have been investigated.9
13 In operation, photoexcitation of the sensitizer results in injection of electrons into the TiO2.14 Injected electrons then diffuse toward a pseudo-ohmic back contact made from fluorine-doped SnO2,15,16 probably by a multiple trapping or hopping mechanism,17
19 where they are collected and flow through an external circuit to the cathode. The average distance electrons can travel in the TiO2 before undesirable recombination with acceptor species is known as the electron diffusion length (Ln), which can be used to predict the electron collection efficiency, ηcol (Supporting Information).20
24 Following injection, the sensitizer is left oxidized and must be rereduced by redox species before recombination with electrons in the TiO2 occurs, a crucial step normally referred to as sensitizer regeneration. Scheme 1 shows the key chemical and physical processes occurring in an operating DSC, together with kinetic and thermodynamic r 2011 American Chemical Society

information. Definitions of selected chemical and physical parameters can be found in Table 1. Based mainly upon results from ex-situ transient absorption experiments, it is usually assumed that regeneration of the prototypical ruthenium dyes ruthenium(II) cis-diisothiocyanato-bis(2,20 -bipyridyl-4,40 -dicarboxylato) (N719) and ruthenium(II) cis-diisothiocyanato-(2,2 0 -bipyridyl-4,4 0 -dicarboxylic acid)(2,20 -bipyridyl-4,40 -dinonyl) (Z907) by iodide is fast enough not to significantly influence the performance of DSCs.25
30 Indeed, for most DSCs regeneration must proceed with near unity quantum yield at short circuit because incident photon-to-current efficiencies (IPCEs) of near unity are frequently observed, from which the short-circuit photocurrent density (jsc) under AM 1.5 1 Sun illumination can be predicted with reasonable accuracy. However, it is not necessarily the case that regeneration is efficient at other points on the current
voltage (j
V) characteristic, such as open-circuit or the maximum power point. Here, the electron concentration in the TiO2 can be several times larger than that at short circuit,31,32 especially close to the substrate where the majority of light absorption usually occurs, and this could increase the probability of undesirable electron transfer to the oxidized sensitizer (S+). It is in fact well-known that the light j
V characteristics of DSCs cannot usually be predicted from the sum of the dark Received: June 6, 2011 Revised: June 23, 2011 Published: June 27, 2011 15109

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j
V and the short-circuit photocurrent (jsc).33
35 This phenomenon could be explained by invoking significant recombination with S+, but despite the important implications for cell efficiency, it has received relatively little attention. In a recent study, Barnes et al. examined differences between dark and light j
V curves of DSCs.36,37 Making extensive use of numerical methods to solve systems of nonlinear partial differential equations, they found that non-negligible recombination with S +, together with local changes in electrolyte concentrations due to current flow, could explain their data. We have recently found that differences between IPCE spectra, measured near open circuit with illumination incident on opposite sides of the sensitized TiO2 layer, imply that electrons can be efficiently collected from throughout the entire layer,

yet at the same time, the IPCE for both illumination directions decreases once a certain open-circuit photovoltage (V OC ) is reached. 23 We have shown that under steady-state conditions a decrease in regeneration efficiency (ηreg ) could cause such an effect and would be indistinguishable from a decrease in electron injection efficiency (η inj). We should note here that part of this decrease in IPCE arises due to the finite series resistance of real DSCs (Supporting Information), although this cannot account for all of the observed decrease. The objective of the present work was to test the hypothesis that the decrease in IPCE with increasing forward bias is caused by inefficient regeneration. Central to our approach is measurement of the differential IPCE (ηIPCE) which can be defined as

Scheme 1. Key Processes Occurring in Operating DSCs: Kinetics, Thermodynamics, and Quantum Efficienciesa

dJn ¼ ηIPCE ¼ ηlh ηinj ηreg ηcol dI

a

Energies are approximate and do not represent any one specific system. Desirable kinetic processes are shown in green and undesirable processes in red. Symbols representing the quantum efficiency of a process are indicated in blue, while thermodynamic information is given in black.

ð1Þ

where Jn is the electron flux; I is the incident photon flux; and ηlh is the light harvesting efficiency. Unlike the more conventional large-perturbation IPCE defined as Jn/I, which is usually measured at short circuit, ηIPCE can be measured under all operating conditions, including at the maximum power point or open circuit. To determine whether changes in ηIPCE with operating conditions can be attributed to changes in ηreg, a series of DSCs were fabricated where regeneration rate was controlled by deliberately varying electrolyte iodide concentration. DSCs were then characterized in detail using a range of widely available photoelectrochemical techniques, and data were interpreted with the aid of simple analytical expressions derived from continuity equations. The results of the study strongly suggest that the decrease in IPCE across the j
V characteristic is caused by inefficient regeneration, which can reduce overall power conversion efficiency by up to 30%.

Table 1. Definitions of Chemical and Physical Parameters Used to Characterize DSCs parameter (unit)
3

definition a

n (cm ) [S+] (M)

TiO2 electron concentration oxidized sensitizer concentration

[I
] (M)

electrolyte iodide concentration

k1 (cm
3(1
γ1) s
1)

pseudofirst-order rate constant for electron transfer to electrolyte speciesb

k2 (cm
3(1
γ2) M
1 s
1)

rate constant for electron transfer to oxidized sensitizer speciesb


γ3
1

k3 (M

s )

rate constant for sensitizer regeneration by iodide

γ1,2,3

reaction orders in n or [I
] for the above reactionsb

ηcol

electron collection efficiency

ηinj ηlh

electron injection efficiency light harvesting efficiency

ηreg

sensitizer regeneration efficiency

ENHE (eV)

energy of the normal hydrogen electrode

Ec (eV)

energy of the TiO2 conduction band minimum

nEF

TiO2 electron quasi-Fermi level

(eV)

EF,redox (eV)

electrolyte redox Fermi level

Vcell (V)

measured/applied cell voltage

Vcorr (V)

cell voltage corrected for ohmic losses and overpotentials due to TiO2 electron transport, electrolyte mass transport, and charge transfer at the cathode

a nc is the free electron concentration, and ntot is the total electron concentration, including trapped electrons. b k1,2 and γ1,2 are used for reaction rates quantified using nc, while k0 1,2 and γ0 1,2 are used for reactions rates quantified using ntot.

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provided by a Newport class A solar simulator, or illumination was provided by a red LED of sufficient intensity to produce ca. 40% of the short-circuit photocurrent obtained under 1 Sun illumination. ηIPCE for λ = 627 nm was measured at each light intensity and bias voltage or VOC by modulating the intensity of the red LED by (2.5% and recording the change in photocurrent. Different background illumination intensities were achieved using neutral density filters mounted in an automated filter wheel system (Newport).

’ RESULTS AND DISCUSSION Apparent Discrepancy between Dark and Light j
V Characteristics. Figure 1 shows the dark and light (AM 1.5, 1 Sun) Figure 1. Typical dark (black) and light (red) j
V characteristics for a DSC employing the N719 sensitizer. Solid lines represent measured j
Vcell data, and dash-dot lines represent j
Vcorr data, where the voltage scale has been corrected for various ohmic drops and overpotentials (Scheme 1). Also shown is a prediction using jlight(Vcorr) = jmax + jdark(Vcorr) (blue line); note the gross overestimation of cell efficiency.

’ EXPERIMENTAL SECTION Details of DSCs Used in This Work. Several batches of DSCs were fabricated following the procedure outlined in the Supporting Information. In one batch, DSCs were equipped with compact TiO2 blocking layers,38,39 did not possess a light scattering layer, and used the Z907 sensitizer. Electrolytes were 2.10 M Li+ and 0.10 M I2 in 3-methoxypropionitrile (3-MPN) with varying concentrations of I
(0.40, 0.83, 1.25, 1.68, and 2.10 M) and ClO4
(1.70, 1.28, 0.85, 0.43, and 0 M). Due to the very high equilibrium constant for the formation of I3
from I
and I2 (pK =
8.2 in propionitrile),40 we assume throughout this article that electrolytes are 0.10 M in I3
and (x
0.10) M in I
, where x = 0.40, 0.83, etc., with very low concentrations of free I2. Two DSCs were fabricated for each [I
], and unless otherwise stated data for each [I
] were pooled together for analysis. DSCs of higher efficiency were also fabricated, without compact TiO2 blocking layers, but with light scattering layers, using the N719 sensitizer. Electrolytes used for these DSCs consisted of 0.6 M PMII, 0.03 M I2, 0.1 M guanidinium thiocyanate, and 0.5 M 4-tert-butylpyridine in a mixture of acetonitrile and valeronitrile (85:15 volume ratio). Characterization of DSCs. Absorbance spectra of bare and dye-sensitized TiO2 layers filled with electrolyte, complete DSCs, and FTO substrates coated with blocking layers were measured using a UV
vis
NIR spectrometer (SolidSpec-3700, Shimadzu). The average absorption coefficient of Z907 sensitized TiO2 layers at λ = 627 nm was estimated from absorbance measurements. ηIPCE, VOC, and impedance spectroscopy (IS) measurements were performed using a potentiostat equipped with a frequency response analyzer (Autolab PGSTAT 302N/ FRA2, Ecochemie) and the Nova 1.6 software package. ηIPCE and IS measurements were performed with cells biased close to VOC under background illumination from a high-power red (λ = 627 nm) light emitting diode (LED, Luxeon). IS spectra were also measured at various different bias voltages in the dark or with cells under constant background illumination. Either simulated AM 1.5 1 Sun illumination was used, which was

j
V characteristics of a DSC employing the N719 sensitizer. The j data are plotted versus two different voltages, Vcell and Vcorr (Scheme 1). The former is the applied cell voltage, while the latter is the cell voltage corrected for ohmic drops, transport overpotentials, and charge transfer overpotentials. These voltage losses were all estimated from IS measurements made in parallel with the j
V measurements.41 The true, measured external efficiency of this cell is 6.6%. After correction for ohmic drop across only the cell series resistance, it increases to 8.1%, which is a reasonable estimate of the internal cell efficiency. Further correction for mass transport and charge transfer overpotentials only yields a slightly increased efficiency of 8.4%. Also shown in Figure 1 is a prediction of the light j
V characteristic assuming identical charge transfer mechanisms under illumination and in the dark, i.e., jlight(Vcorr) = jmax + jdark(Vcorr), where jmax is the saturation photocurrent. Interestingly, the predicted efficiency is an impressive 10.2%, which would represent a significant improvement if it could be realized experimentally. To determine the cause of this intriguing phenomenon, a range of simple experiments have been performed using a series of DSCs that constitute a model system, specifically designed to test whether or not the reduction in photocurrent along the j
V is caused by a decrease in ηreg. The experiments were performed using DSCs identical in construction to cells exhibiting conversion efficiencies of up to 8.0%, except that nonstandard electrolytes and the Z907 sensitizer (chosen for its superior stability compared with N719) were used. Basic Characterization of the Model System: TiO2 Capacitance, Conductivity, and Evidence for Band-Edge Unpinning. To obtain ηreg from ηIPCE, knowledge about the energy of the TiO2 conduction band edge (EC) is required since it partly determines ηinj, another contributor to ηIPCE. Figures 2a and 2b show the TiO2 capacitance (Cmeas) and conductivity (σ), respectively, as a function of the quasi-Fermi level of electrons in the TiO2 (nEF) for DSCs employing electrolytes with varying [I
]. Here, nEF has been calculated according to qVOC = nEF
EF,redox where EF,redox was measured by potentiometry for each electrolyte (Supporting Information). Plots of Cmeas or σ versus nEF are all in reasonably close coincidence, with small shifts along the nEF axis of at most 0.05 eV that are uncorrelated with [I
]. Both Cmeas and σ are known to be determined by the difference between nEF and the TiO2 conduction band edge (EC),42 thus the coincidence between plots is good evidence that EC is the same for all cells at each nEF. It is also known that EC determines ηinj;43 therefore, it is reasonable to conclude that ηinj is also the same for all cells, at least for any given nEF. Essentially identical results to those shown in Figure 2 were also obtained from 15111

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Figure 2. (a) Dependence of Cmeas on nEF for cells with electrolytes containing varying [I
]. (b) Dependence of σ on nEF for the same cells. The legend is as follows: black, 0.3 M I
; red, 0.73 M I
; green, 1.15 M I
; yellow, 1.58 M I
; blue, 2 M I
. The inset of (a) shows a fit of eq 2 to data for a DSC with a 2 M I
electrolyte. The dashed red line in (b) is an exponential fit with a forced slope of 17 decades per eV.

measurements made in the dark, where nEF was calculated from Vcorr (Supporting Information). The semilogarithmic Cmeas
nEF plots in Figure 2a are obviously curved. There are several literature examples of this curvature in either capacitance
voltage or charge
voltage plots,36,44,45 although it is not usually discussed in detail. It is reasonable to suggest that the curvature may be caused by the semiconductor bands unpinning due to charging of the Helmholtz capacitance.46 Assuming the measured capacitance arises from the series connection of a constant Helmholtz capacitance and the TiO2 chemical capacitance,42 the following expression can be derived (Supporting Information)
 qΔQ kB T CH Cmeas ln þ n E F ¼ n E F, 0
CH β CH
Cmeas

ð2Þ

where ΔQ is the excess charge in the electrode relative to thermal equilibrium and can be calculated by numerical integration of Cmeas
nEF data; CH is the Helmoholtz layer capacitance; β is an empirical parameter describing the broadening of the density of localized states (DOLS) in the TiO2; and nEF,0 is a constant. As illustrated by the inset in Figure 2a, the data can be fitted reasonably well by eq 2, with fitting parameters in the ranges CH = (5.0∼7.9)  10
4 F, (nEF,0
ENHE) = 0.47∼0.35 eV, and β = 0.40∼0.51. The surface roughness factor for the TiO2 layers used in this study is estimated from BET measurements to be 763, from which a microscopic areal Helmholtz capacitance in the range 2.3
3.7 μF cm
2 is obtained. This is small compared to typical CH values obtained for metal electrodes (10
100 μF cm
2) or degenerate metal oxides such as F:SnO2 (8
15 μF cm
2).39,47,48 However, values of CH reported for nondegenerate semiconductor electrodes are typically far smaller, in the range 1
3 μF cm
2.46 Cappel et al. have recently inferred a microscopic areal Helmholtz capacitance for dye-sensitized TiO2 of 4 or 6 μF cm
2, depending on the dye used, based upon the influence of a Stark effect on photoinduced absorption spectra.49 The lower of these two estimates agrees well with our values, and as will be explained later in this article, we obtain from an independent experiment a higher value of 9.3 μF cm
2.

Figure 3. Dependence of Rct,dark on σ for cells with various [I
]. Data from two cells per [I
] are shown. Dashed lines are fits to Rct,dark. The inset shows the dependence of a (µ 1/k1) on [I
] for γ1 = 1. The solid line is a linear fit (corresponding to electron transfer to I2 being rate determining), and the dashed line is a power law fit with a forced exponent of 0.5 (corresponding to electron transfer to I• being rate determining). The legend is as follows: black, 0.3 M I
; red, 0.73 M I
; green, 1.15 M I
; yellow, 1.58 M I
; blue 2 M I
.

Semilogarithmic plots of σ versus nEF are also obviously curved for high values of σ, but for σ < 10
5 S cm
1 data for all cells are reasonably well described with an “ideal” slope of close to 17 V
1, broadly consistent with conduction band transport.41 For σ > 10
4 S cm
1, the data must be viewed with some caution as these values are derived from IS spectra where fitted electron transport resistances (Rt) were equal to or smaller than the cathode charge transfer resistance.50,51 However, even for σ < 10
4 S cm
1, where Rt derived from fitting IS spectra is believed to be very reliable, a slight curvature can still be observed, lending support to the explanation that the band edge becomes unpinned at high nEF. It is worth noting at this point that uncertainty in σ for high nEF does not affect fitting Cmeas, which can be accurately obtained even when σ is very high. Assuming the band edge unpinning explanation to be correct, the maximum potential drop across the Helmholtz layer is found to be ca. 0.1 V at the highest nEF studied. It is possible that this could cause a decrease in ηinj, the extent of which will depend on 15112

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Figure 4. Dependence of Ln on nEF for cells with electrolytes containing various [I
]. Data are shown for measurements made under constant illumination intensity (closed points), in the dark (open points), and near open circuit (solid lines). The dashed line indicates the TiO2 layer thickness. The legend is as follows: black, 0.3 M I
; red, 0.73 M I
; green, 1.15 M I
; yellow, 1.58 M I
; blue, 2 M I
.

exactly where the excited state of the dye is localized within the interfacial double layer region.52,53 However, Koops et al. have shown experimentally that ηinj only decreases by up to 8% for forward bias voltages several hundreds of millivolts larger than VOC obtained under 1 Sun illumination.43 We have also found that DSCs employing the Z907 dye without Li+ in the electrolyte can deliver as much as 80% of the photocurrent produced by cells with 1 M Li+ in the electrolyte.54 We estimate that for Li+-free cells EC is at least 0.22 eV higher than that in cells with 1 M Li+ electrolytes. Therefore, ηinj is not expected to decrease by more than 20% in the present case. This conclusion will prove to be essential for deconvoluting ηreg from ηIPCE, as will be demonstrated later in this article. Electron Transfer from TiO2 to Electrolyte Acceptor Species in the Dark. To unambiguously attribute changes in ηIPCE to changes in ηreg, knowledge of electron transfer from the TiO2 to the electrolyte acceptor species is required since it could also influence ηIPCE. Figure 3 shows double logarithmic plots of the TiO2 charge transfer resistance measured in the dark (Rct,dark) versus σ. In principle, σ is linearly proportional to free electron concentration (nc) for an n-type semiconductor; thus, using this approach we can determine fundamental information about the dark charge transfer reaction. The data in Figure 3 can be fitted by Rct,dark = aσ
γ1, where a is proportional to the inverse of the pseudofirst-order rate constant (1/k1) for the dark electron transfer from TiO2 to the electrolyte, and γ1 is the reaction order in nc for this reaction (Supporting Information). For all cells, γ1 is found to be in the range 1.02
1.15 with a mean value of 1.09, consistent with previous observations that for DSCs containing a high Li+ concentration and the Z907 dye γ1 is close to 1.23,54 The inset of Figure 3 shows a plot of the prefactor a, with γ1 fixed to 1. It is clear that a significantly increases with [I
], which is a strong indication that I3
is not the main electron acceptor present in the electrolyte since the change in [I3
] caused by varying [I
] should be entirely negligible. It should be noted that these data appear to be consistent with comments made by other authors in a recent publication.36 A number of possible reaction

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schemes for the overall reduction of I3
by TiO2 electrons have been proposed in the literature, in which electron transfer to I2•
, I•, and I2 have all been considered.33,55 The value of γ1 obtained here obviously rules out schemes which are overall second order in nc. This includes schemes where electron transfer to I2•
is rate determining or where the reaction I2 + e
T I2•
is in equilibrium, with the disproportionation of I2•
being rate determining. The value of γ1 is then also consistent with recent reports that reduction of I2•
by electrons in bare TiO2 cannot compete with the disproportionation reaction.30,56 One charge transfer scheme which is first order in nc involves formation of I• by dissociative chemisorption of I2, with subsequent electron transfer to I• being rate determining. However, in this scheme a should vary with [I
]0.5, which does not fit the data well (dashed line in the inset of Figure 3), especially for low [I
] where error estimates are small. If instead electron transfer to I2 was rate determining, a linear dependence of a on [I
] is expected, and in fact the data are fitted reasonably well with a straight line which passes through the origin. Interestingly, Lobato et al. have estimated that the pre-exponential factor in the Arrhenius expression for k1 is many orders of magnitude lower than expected if I3
was the electron acceptor but consistent with I2 being the electron acceptor57 and thus in agreement with our results. Dependence of Electron Diffusion Length on Operating Conditions. Knowledge of Ln combined with optical measurements can be used to estimate ηcol (Supporting Information), an important determinant of ηIPCE. Figure 4 shows Ln obtained from IS (Ln = d(Rct/Rt)1/2, where d is the TiO2 layer thickness),21,41 plotted as a function of nEF, and for clarity, only one plot per [I
] is shown. Data are shown for measurements made under three sets of conditions: at various bias voltages in the dark, under illumination of various intensities at open circuit, and at various bias voltages under illumination of a single intensity (sufficient to produce 40% of the short-circuit photocurrent obtained under 1 Sun illumination). For data obtained in the dark or at open circuit, the model used to fit the IS spectra is valid, and Ln values should strictly correspond to the smallperturbation electron diffusion length.21 In most cases, data obtained in the dark and at open-circuit coincide quite closely. There is an obvious trend of increasing Ln with increasing [I
], which has its origin in the very significant increase of Rct with increasing [I
]. Despite the variation with [I
], Ln in the dark or at open circuit is longer than two times the film thickness for all values of nEF. Consequently, internal charge collection efficiencies (i.e., the probability of photogenerated electrons reaching the contact) under these measurement conditions are high, descending to a minimum of 0.92 for [I
] = 0.3 M, and practically unity for all other concentrations. Ln data for very high nEF are not shown in Figure 4 as there is significant uncertainty in the reliability of Rt obtained from IS under these conditions. In these cases, a minimum Ln can still be calculated if it is assumed that the reason for the absence of well-defined transport features in the IS spectrum is that Rt has become too small to measure. However, at these high cell voltages the resistance of the electrolyte-filled TiO2 layer, RTL,59 can become comparable to the external series resistance (i.e., the sum of the FTO, cathode, and electrolyte resistances). This leads to recombination competing with extraction of electrons through the external resistances and causes attenuation in ηIPCE, despite the fact that Ln is longer than the TiO2 layer thickness. Provided that the external series resistance 15113

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Figure 5. (a) Dependence of ηIPCE/ηcol (λ = 627 nm) on ntot for cells with electrolytes containing various [I
]. The legend is as follows: black, 0.3 M I
; red, 0.73 M I
; green, 1.15 M I
; yellow, 1.58 M I
; blue, 2 M I
. Also shown are fits using eq 3 (solid lines, single recombination pathway) or eq 4 (dashed lines, two recombination pathways), and for clarity only fits for [I
] = 0.3, 0.725, and 2 M are shown. The inset shows the same data with a linear ntot scale, together with fits obtained using eq 4 for all [I
]. (b) Dependence of fitted k3[I
]γ3/k02 values on [I
] obtained from fits using eq 3 (black points, left y-axis) and dependence of fitted k3[I
]γ3/k02,a (red points, right y-axis) on [I
] obtained from fits using eq 4.

and RTL are known (as in the present case), these additional “extraction losses” can be accounted for when calculating ηcol (Supporting Information). Another way of understanding this attenuation in ηIPCE is that it arises from uncompensated iR drop across the series resistance during the ηIPCE measurements. Under intense illumination of constant intensity and varying bias voltage, a significant decrease in Ln is observed as nEF decreases and large photocurrents (up to ca. 6 mA cm
2) flow in the cell. As nEF increases and photocurrents flowing in the cell reduce, Ln increases, approaching values found at open circuit or in the dark. When large currents are flowing in the cell, the assumption of spatial homogeneity which is made in the derivation of the transmission line impedance is not valid.58,59 However, spectra can usually be fitted reasonably well by the model, and it seems reasonable to assume that the fitted parameters represent some form of weighted average of the distributed transmission line parameters. Therefore, the decrease in Ln relative to open circuit or the dark could be interpreted in one of two ways: either the model used for fitting the IS data becomes invalid, or as recently suggested,22,36,60 an accumulation of electron acceptors in the pores of the TiO2, required to drive diffusive mass transport in the electrolyte, causes Ln to decrease. Regardless of the origin of the decrease in Ln when large photocurrents flow, Ln obtained in the dark or at open circuit is almost certainly a meaningful parameter and, together with RTL and the cell series resistance, can be used to predict ηcol under open-circuit conditions during ηIPCE measurements. Dependence of ηreg on [I
] and TiO2 Electron Concentration. Figure 5a shows plots of ηIPCE/ηcol (λ = 627 nm) versus total TiO2 electron concentration, ntot. Measurements were performed with cells biased near open circuit, and ntot was calculated by numerical integration of Cmeas
nEF data (Supporting Information). The quantity ηIPCE/ηcol can be thought of as the effective differential photogeneration efficiency, i.e., ηlhηinjηreg. In principle, all of these parameters could be differential quantities if they are dependent upon illumination intensity. However, it is reasonable to assume almost constant ηinj for all cells studied here, and it is also reasonable to assume constant ηlh since cells only differ in the [I
]:[ClO4
] ratio (Supporting Information). Therefore, any changes in ηIPCE/ηcol

with [I
] or ntot should reflect changes in ηreg in the present case. Assuming the rate-determining steps for regeneration and recombination are first order in [S+], it can be shown that ηIPCE/ ηcol is given by (Supporting Information) ηlh ηinj k3 ½I
γ3 ηIPCE ¼ ηlh ηinj ηreg ¼ 0 0 γ ηcol k3 ½I
γ3 þ k2 ntot2

ð3Þ

where k3 is the rate constant for regeneration; γ3 is the reaction order in [I
]; k02 is the apparent rate constant for recombination of electrons with S+; and γ02 is the reaction order in ntot (γ02 is related to the reaction order in nc by γ2 = γ02β). To test eq 3, global fits to the data were performed with the product ηlhηinj fixed to the saturation value of ηIPCE measured at short circuit using low intensity illumination for [I
] = 2 M, where it can be assumed that ηcolηreg ≈ 1. The quantity k3[I
]γ3/ k02 was allowed to vary freely for each [I
], while γ02 was allowed to vary but was common to all data sets. Data for [I
] = 1.15
2 M can be fitted well using eq 3 (solid blue line in Figure 5a), but data for [I
] = 0.3
0.725 M cannot be fitted well at low ntot (solid black and red lines in Figure 5a). However, for ntot greater than ca. 2  1017 cm
3, data for all [I
] are adequately described by eq 3, and a trend of increasing ηIPCE/ηcol with increasing [I
] is found all the way up to [I
] = 2 M, which can be discerned more easily for [I
] = 1.15
2 M when data are plotted using a linear ntot scale (inset of Figure 5a). Satisfactory fits for low ntot and [I
] still cannot be obtained even if ηinjηlh is allowed to vary freely; allowing ηlh to vary is also inconsistent with the fact that the absorbance of all cells at 627 nm is found to be almost identical (Supporting Information), and changes in ηinj at such low ntot seem very unlikely. Interestingly, the data can be fitted well over the entire ntot range by allowing for a second recombination reaction with S+ (dashed lines in Figure 5a), the rate of which is also dependent upon ntot, only with a different rate constant and reaction order, so that eq 3 becomes ηIPCE ¼ ηcol 15114

ηlh ηinj k3 ½I
γ3 γ

0

γ

0

k3 ½I
γ3 þ k2, a ntot2, a þ k2, b ntot2, b 0

0

ð4Þ

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The Journal of Physical Chemistry C At this stage no clear physical justification for this reaction scheme is forthcoming, thus eq 4 should be regarded as empirical. However, it is easy to imagine that the rate constants and reaction orders for recombination of trapped electrons and free electrons could be different, in much the same way as recombination with electrolyte species can be modeled by allowing for recombination from both the conduction band and surface states.54,61,62 Figure 5b shows plots of k3[I
]γ3/k02 (black points, eq 3) and k3[I
]γ3/k02,a (red points, eq 4) versus [I
] (the ratio k3[I
]γ3/ 0 k02,b is not plotted since it is simply related to k3[I
0 ]γ3/k 2,a by a 36 3(γ2,b
γ2,a0 ) 0 0 ). Both constant factor of k2,b/k2,a = 9.2  10 cm data sets are fitted reasonably well with a straight line passing through the origin suggesting that, regardless of the recombination scheme used, the order of the regeneration reaction in [I
] is 1, in agreement with results recently reported by Anderson et al.63 Taking γ3 = 1, the ratio k3/k02 can also be obtained. Taking the literature value of k3 = 105 M
1 s
1 for regeneration k02 = 2.1  of Z907 by0 iodide in 3-MPN,27 we obtain
1
37 3γ2,a0
1 0 2 s , k = 2.7  10 cm s , and k02,b = 10
17 cm3γ 2,a 0 2.5 cm3γ2,b s
1. The reaction order with respect to ntot obtained using the simple model, γ02, is 1.2, and the reaction orders obtained from the more complex model are γ02,a = 2.1 and γ02,b = 0.21. There is a spread of corresponding free electron reaction orders (γ2 or γ2,a and γ2,b, for the simple or complex model, respectively) due to the spread of β values obtained in Cmeas
nEF fits (β = 0.40
0.51). For the simple model γ2 = 0.48
0.61, while for the more complex empirical model γ2,a = 0.84
1.1 (this is the reaction order applicable to higher ntot) and γ2,b = 0.08
0.11 (this is the reaction order applicable to lower ntot). These latter two reaction orders appear to be consistent with recent results of Katoh et al., who studied recombination of injected electrons with S+ using transient absorption spectroscopy.64 They found that recombination half times decreased linearly with excitation fluence for high enough fluence, which, neglecting trapping effects, is consistent with γ2 = 1. However, for lower fluence recombination, half times scaled with fluence raised to the power
0.3, broadly consistent with the lower reaction order found here at low ntot. Observation of the predicted dependence of ηIPCE on [I
] and ntot is strong evidence that ηIPCE/ηcol decreases as nEF increases because of inefficient regeneration. However, a possible criticism of the approach used here is that there is no “direct” spectroscopic observation of S+. Time-resolved or steady-state measurement of [S+] in complete, functional DSCs is experimentally very challenging owing to the tiny concentrations involved. Even if accurate measurements can be made, interpretation of data can be significantly complicated by the non-negligible absorbance of electrons in the TiO2, I2•
, and, for time-resolved measurements, the unknown influence of electron trapping. For these reasons, such spectroscopic measurements have not been attempted here, although it should be noted that significant progress in making and interpreting these difficult measurements has recently been made by other authors.63,65 Since in the present case S+ is not directly observed, we cannot straightforwardly rule out the possibility that ηIPCE may decrease due to recombination of electrons with a shortlived intermediate or product produced by the regeneration process. For some purposes, such as predicting the j
V characteristic, this distinction is not actually useful, and arguably the regeneration reaction is not entirely complete until any short-lived products have reacted to form I3
. The

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Figure 6. Dependence of Rct on Cmeas in the dark (Rct,dark, open points) and under illumination at open circuit (Rct,light, closed points) for cells with electrolytes containing 0.3 M I
(black), 0.73 M I
(red), and 2 M I
(blue). The inset shows the dependence of ηreg on Cmeas predicted from Rct,dark/Rct,light using eq 7 (solid lines) or estimated from ηIPCE measurements (points).

possible intermediates/products in the regeneration process are I•, I2•
, and perhaps complexes of I
and S+. Recombination of electrons with the latter can still be considered as recombination with S+, and it is very unlikely that I• is produced as its formation is thermodynamically disfavored.66 I2•
is known to be produced, but this species disproportionates very rapidly. Rowley et al. have found no evidence for a reaction between I2•
and TiO2 electrons,67 even for electron concentrations over 100 times higher than those relevant to normal cell operation. The rate of disproportionation of I2•
also scales with the square of [I2•
], which will partially or completely compensate for the increase in electron concentration as light intensity is increased; this is not the case for the rate of reaction between S+ and [I
], which scales linearly with [S+]. Furthermore, a dependence of ηIPCE on [I
] would not be expected if recombination with I2•
caused the decrease in ηIPCE (although if I• were formed then a dependence of ηIPCE on [I
] can be envisioned). We therefore conclude that S+ is by far the most likely additional electron acceptor present under illumination that causes ηIPCE to decrease. One might also suggest that the observed decrease in ηIPCE with increasing photovoltage is caused by a voltage-dependent rate constant for electron extraction at the FTO
TiO2 contact.34,68
70 However, there is evidence in the literature which suggests the FTO
TiO2 contact is pseudo-ohmic, possibly because any barrier at the contact during operation is thin enough for electrons to tunnel through.15,16 We also note that the so-called “junction model” does not obviously predict the dependence of ηIPCE on [I
] and ntot found here. Interfacial Charge Transfer Resistance under Illumination and in the Dark. Another important test of the hypothesis, that ηIPCE decreases as a result of inefficient regeneration, does in fact exist. It can be shown from continuity equations for electrons and S+ that the interfacial charge transfer resistance, Rct, should decrease under illumination compared to in the dark, as a result of recombination with S+ (Supporting Information). Neglecting changes in electrolyte composition between the dark and open 15115

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Figure 7. (a) Dependence of nEF on generation rate assuming constant ηreg (red points, calculated using eq 8) or assuming ηlhηinjηreg = ηIPCE/ηcol (blue, calculated using eq 9) for a cell with an electrolyte containing 2 M I
. (b) Measured dependence of nEF on generation rate assuming ηlhηinjηreg = ηIPCE (closed points, eq 9). Also shown are simulations using eq 10 for CH . Cmeas (black line), for CH obtained from fits of eq 2 to Cmeas
nEF data (blue dashed line), and for CH = 1.4 mF. The dotted red line shows the variation of qΔVH with Geff, calculated using the later CH value.

circuit, Rct measured under illumination is given by


Rct, light ¼

q2 dAk

γ1 1 neqm ðγ1

E
EF, redox kT exp
γ1 n F kB T þ γ2 ð1
ηreg ÞÞ



ð5Þ while in the dark it is given by
 kT n E F
EF, redox Rct, dark ¼ 2 exp
γ1 γ1 kB T γ1 q dAk1 neqm

ð6Þ

where A is the projected area of the TiO2 layer and neqm is the dark equilibrium concentration of free electrons. Interestingly, the ratio of these charge transfer resistances at the same nEF yields an expression only containing γ1, γ2, and ηreg, which upon rearrangement yields ! γ1 Rct, dark ηreg ¼ 1 þ 1
ð7Þ γ2 Rct, light Figure 6 shows plots of Rct versus Cmeas obtained under illumination at open circuit or in the dark for 0.3, 0.73, and 2 M I
. Here, Cmeas is used for comparison of light and dark data (as opposed to nEF or σ as implied by eqs 5 and 6) as it is believed to be the most accurate indicator of nEF for the dark data, which would require complicated iR drop corrections. It also allows comparison of Rct values at very high nEF, where σ data become unreliable. The exact relationship between Rct and Cmeas is unimportant for the following analysis; all that is required is that each Cmeas corresponds to a unique value of nEF, an assumption which is supported by Figure 2a and also by the good agreement between Cmeas
nEF data obtained in the dark and under illumination (Supporting Information). It is clear from Figure 6 that, as predicted, Rct does significantly decrease under illumination at high Cmeas. The inset in Figure 6 shows plots of ηreg calculated from Rct,light and Rct,dark data using eq 7 assuming γ1 = γ2 = 1, a simplification based on the values of these parameters obtained in the preceding analyses. To perform this calculation, Rct values at matched Cmeas were obtained by linear interpolation of Rct
Cmeas data in logarithmic form. For

comparison, plots of ηreg versus Cmeas obtained from ηIPCE data using eq 3 are also shown. The plots are not in exact quantitative agreement, but the expected trend in ηreg with both [I
] and Cmeas is obviously present. It is possible the disagreement arises because either γ1 or γ2 is not equal to unity, or perhaps a more complex recombination mechanism needs to be considered in the derivation of eqs 5
7. It could be argued that the apparent decrease in ηreg predicted from Rct,light and Rct,dark actually reflects a decrease in k1 in the dark due to the depletion of I3
and I2 in the pores of the TiO2 when dark currents flow. However, the low currents flowing during the measurements suggest that this effect should be relatively small in the present case, although it will surely add some distortion to ηreg calculated using eq 7. Taking the diffusion coefficient of I3
to be 1.3  10
6 cm2 s
1 (an average value determined by fitting the low-frequency Warburg impedance for these cells), a maximum decrease in I3
concentration of 7% is estimated at the highest Cmeas value plotted in Figure 6. This concentration change would correspond to an increase in Rct,dark of 7%, assuming a charge transfer reaction first order in I3
(note that, if electron transfer to I2 is rate determining, a first-order dependence on I3
will also be observed). Another possible explanation for the difference between Rct,
light and Rct,dark is that the concentration of I3 in the cell is higher under illumination due to charge accumulation in the TiO2. The redox chemistry of this system requires that an additional I3
ion is produced for every two excess electrons in the TiO2. Using this logic, the increase in I3
concentration calculated from ntot data is at most 1% of the equilibrium concentration; therefore, even the combined effect of opposite shifts in I3
concentration away from the equilibrium value can only explain 8% of the drop in Rct,light relative to Rct,dark at the highest Cmeas. For lower values of Cmeas, the predicted changes in I3
concentration due to charge accumulation or current flow rapidly become negligible and cannot explain the still significant differences which exist between Rct,light and Rct,dark. Dependence of nEF on Illumination Intensity at Open Circuit: The Combined Effects of Inefficient Regeneration and Band Edge Unpinning. Figure 7a shows plots of nEF versus 15116

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Figure 8. (a) Dependence of ηIPCE/ηcol on VOC (solid lines) and iR-corrected bias voltage (Vcorr, points) for a cell with a 2 M I
electrolyte. Measurements made as a function of bias voltage were performed with cells under background illumination provided by a red LED which was of intensity sufficient to produce 40% of the 1 Sun jsc. (b) j
Vcorr characteristics for a DSC containing 2.1 M LiI and 0.1 M I2 in the electrolyte under illumination (blue points) and in the dark (solid black line). Also shown are simulations using jdark(V) + jsc (long dashed black line) and jdark(V) + jscηreg,0(V) (short dashed blue line). The red points represent the maximum power points.

effective photogeneration rate, Geff, calculated in one of two ways. For the first calculation the following relation is used Geff , 0 ¼

I0 ηlh ηinj I0 ηIPCE, max ¼ d d

ð8Þ

where Geff,0 is the generation rate assuming a constant ηreg of unity; I0 is the measured incident photon flux; and ηIPCE,max is a constant which is fixed to the highest value of ηIPCE measured (where ηcolηreg ≈ 1). For the second calculation of Geff, the following relation is used Z 1 I0 η =η dI ð9Þ Geff ¼ d 0 IPCE col which is evaluated by numerical integration of the data. Plots of nEF versus log(Geff,0) appear to be reasonably linear over a wide range, as is frequently observed for DSCs employing a compact TiO2 blocking layer. The most obvious interpretation of this, without the additional information we have at hand, is that ηreg, k1, and γ1 are all constant. However, since ηIPCE/ηcol decreases as nEF increases, a fact that is very likely to be caused by a decrease in ηreg, it is surprising that plots of nEF versus log(Geff,0) are almost linear. Obviously then, if nEF is plotted versus Geff instead (i.e., Geff,0 corrected for the decrease in ηreg), the plot is slightly curved at high nEF. This somewhat surprising result is entirely consistent with the curvature observed in plots of Cmeas or σ versus nEF (Figures 2a and 2b), if it is assumed that the cause of the curvature is band-edge unpinning. This explanation can be tested more quantitatively by predicting the nEF
Geff curve using the expression nEF

¼ EF, redox

0

Gef f þ kB T ln@ γ1 k1 neqm

!1=γ1

1 qΔQ þ 1A
CH

ð10Þ

1 and γ1 can be obtained from Rct,dark Here, the product k1nγeqm measurements made at low bias voltage, where we assume the band edge is pinned and errors arising from current flow (i.e., iR drop correction and changes in [I3
]) are negligible. These

parameters can also be obtained from nEF
Geff or Rct,light
nEF plots for sufficiently low intensities, and usually parameters obtained by all methods are in reasonable agreement. Geff is calculated using eq 9, and the band edge shift, qΔQ/CH, at each Geff is calculated taking the CH value obtained from fitting eq 2 to
nEF
Cmeas data. Figure 7b shows experimental data (2 M I electrolyte) and the results of this simulation, with and without inclusion of the qΔQ/CH term in eq 10. The simulated curve including the qΔQ/CH term (which is calculated using no free parameters) does not fit the data perfectly. However, it does capture the curvature of the plot at high nEF, which the simulation excluding the qΔQ/CH term cannot reproduce. It is not particularly surprising that the curves do not agree exactly because eq 2 does not perfectly describe the Cmeas
nEF data, which may arise because the underlying variation of the TiO2 chemical capacitance is not perfectly exponential. If instead CH is used as a fitting parameter, very satisfactory agreement between the simulated curve and the data is obtained for CH = 2  10
3 F (microscopic areal capacitance of 9.3 μF cm
2), around 2.5 times the value obtained from fitting eq 2 to Cmeas
nEF data for this cell, and physically very reasonable. Note that this approach does not require any assumptions about the variation of the internal TiO2 capacitance with nEF and is applicable regardless of the physical origin of the TiO2 capacitance. The value of CH obtained using this approach is broadly consistent with estimates made by Cappel et al. in a recent PIA study,49 and it is worth noting that O’Regan and Durrant have suggested the TiO2 band edges may become unpinned in DSCs, based upon measurements of activation energies for electron transport and recombination.71 It would appear then that all data obtained for these cells are consistent with the explanation that the decrease in ηIPCE/ηcol with increasing electron concentration (and thus VOC) is caused by a decrease in ηreg. Therefore, it must be expected that ηreg will also decrease as electrons accumulate with increasing bias along the j
V characteristic. Influence of Inefficient Sensitizer Regeneration on Overall Power Conversion Efficiency. Figure 8a shows plots of ηIPCE/ηcol versus either Vcorr or VOC, for 0.3, 0.725, and 2 M I
. The measurements made as a function of Vcorr were performed 15117

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The Journal of Physical Chemistry C with cells under background illumination which produced ca. 40% of the 1 Sun jsc. There is a degree of ambiguity in the results obtained from these experiments when large photocurrents are flowing because spatially homogeneous conditions are necessarily not achieved. However, it is reasonable to assume that Vcorr (which includes a correction for nEF gradients due to transport in the TiO2 layer; Scheme 1) is a good indicator of the average quasi-Fermi level of electrons in the TiO272 and therefore of the average electron concentration. In support of this assumption, plots of ηIPCE/ηcol versus Vcorr are in close agreement with plots versus VOC. The data shown in Figure 8a, combined with the fact that a reduction in ηreg causes the decrease in ηIPCE/ηcol at open circuit, can be viewed as good evidence that the decrease in ηIPCE/ηcol along the j
V curve, relative to short circuit, is caused almost entirely by increased recombination with S+. Since ηIPCE and ηcol are differential quantities, they cannot be used directly to predict the j
V characteristic, which requires the overall (i.e., integrated) effective photogeneration efficiency at each Vcorr. However, in the present case ηIPCE/ηcol is known over a wide range of I and ntot for open-circuit conditions, and Geff can be calculated for each I using eq 9. Although in this case the integration is performed with respect to I, the results are in principle applicable for constant I and varying Vcorr or ntot since ηreg is not actually directly dependent upon I, only upon ntot (cf. eq 3). This result arises due to the reasonable assumption that the regeneration and recombination rates are of the same order in [S+], so that this quantity does not appear in the branching ratio. Figure 8b shows light and dark j
Vcorr characteristics for a DSC with a 2 M I
electrolyte, together with two simulations. The first simulation is calculated in the same manner as for Figure 1, i.e., j(Vcorr) = jdark(Vcorr) + jsc. The second simulation is calculated using j(Vcorr) = jdark(Vcorr) + (ηreg,0  jsc), where ηreg,0 is the integrated regeneration efficiency, defined as Geff/I0 (cf. eq 9). The first simulation, which neglects the decrease in ηreg,0 along the j
Vcorr characteristic, grossly overestimates the efficiency of this DSC by ca. 30%, whereas the second simulation accurately predicts the efficiency, as well as most of the j
Vcorr characteristic. This result clearly demonstrates that the efficiency of this cell is significantly limited by inefficient regeneration, despite the abnormally high I
concentration (2 M) and the presence of Li+ ions, which are often thought to result in an increased rate of sensitizer regeneration.26 Collection losses could also lower jsc if the electron diffusion length is shorter than the film thickness. As recently suggested by others,36,60 and implied by the Ln data in Figure 4, these collection losses may be larger than expected based on dark or open-circuit measurements, due to current flow changing the concentrations of electron acceptors in the pores of the TiO2. However, current flow always decreases upon increasing forward bias from short circuit toward open circuit, so any reduction in ηcol caused by this effect must also lessen with increasing bias. It is also frequently observed that DSCs (without an unusually high Li+ concentration) exhibit γ1 < 1. This leads to Ln increasing with forward bias and thus, if it has any effect at all (i.e., if Ln is short to begin with), cannot cause a decrease in ηIPCE along the j
V characteristic. Obviously some caution must be exercised when applying these findings to efficiency-optimized DSCs, which employ different electrolyte compositions and in some cases different dye molecules. However, to date the most efficient DSCs are based on the I3
/I
redox couple and ruthenium bipyridyl dyes; therefore, the basic operating principles of these cells are probably similar to those of the cells studied here. It is also

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worth remembering that we have observed similar efficiency limitations in all DSCs we have studied, an example of which was presented in Figure 1. This is particularly surprising since an efficiency-optimized, nonviscous acetonitrile electrolyte is used in conjunction with the N719 sensitizer. This raises the important question of whether or not the efficiency of current “champion cells” is also limited by sensitizer regeneration to any significant extent.

’ CONCLUSIONS The IPCE of DSCs is often found to decrease with increasing forward bias voltage. A detailed characterization of DSCs employing the Z907 sensitizer with various [I
] has revealed that a significant fraction of the decrease in IPCE is likely to be caused by a reduction in ηreg. An important conclusion is that ηreg can be less than unity at the maximum power point, even if it is close to unity at short circuit and even for cells with very high I
and Li+ concentrations. Similar effects are also observed in DSCs employing the N719 sensitizer with an efficiency-optimized electrolyte, and it is reasonable to expect that these conclusions may apply to other systems. Therefore, it could still be beneficial to DSC performance to significantly increase the rate constant for sensitizer regeneration, even if ex-situ transient absorption measurements suggest otherwise. The new methodology presented here should prove useful in assessing the improvement, or otherwise, in efficiency brought about by improved regeneration when utilizing alternatives to the I3
/I
redox mediator, such as CoII/III bipyridyl complexes10 and ferrocene/ferrocenium.73 These results also challenge the commonly held view that fill factor and VOC are solely determined by recombination with electrolyte species. VOC and ηIPCE/ηcol measurements made in parallel imply that the band edges of TiO2 can become partially unpinned at relatively weak illumination intensities in the electrolytes used here. Further evidence in support of this explanation is found in σ and Cmeas data derived from IS experiments, and the microscopic areal Helmholtz capacitance for nanocrystalline TiO2 in the electrolytes used here is estimated to be 2.3
9.3 μF cm
2. Taking the results presented here together with results from quite different and independent experiments already present in the literature, it must now be considered that there is overwhelming evidence for the band edges of nanocrystalline TiO2 in DSCs becoming unpinned under normal operating conditions. This effect has serious implications for the interpretation of cell parameters (e.g., Cmeas) which are measured as a function of cell voltage and must be adequately accounted for in the theoretical modeling of DSCs. The only integer reaction order in nc consistent with our data for recombination of electrons with electrolyte acceptor species and S+ at sufficiently high nc is 1. The order in [I
] for the sensitizer regeneration reaction is also found to be 1. Another interesting finding is that the apparent rate constant for the dark TiO2-to-electrolyte electron transfer reaction decreases as [I
] is increased, suggesting that a species other than I3
is the main electron acceptor. Our data are most consistent with the ratedetermining step in this reaction being electron transfer to I2, which is consistent with all relevant recent literature. ’ ASSOCIATED CONTENT

bS

Supporting Information. DSC fabrication procedure. Equivalent circuit used to fit IS spectra. Electrolyte redox potentials.

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The Journal of Physical Chemistry C Comparison between Cmeas and σ data obtained from dark and open-circuit IS measurements. Absorbance spectra of complete DSCs with various electrolyte [I
]:[ClO4
] ratios. Justification of the measurement conditions used. Discussion of the effect of the cell series resistance on ηIPCE measurements and prediction of ηcol. Derivation of all equations used. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This work was financially supported by NUS startup grant No. R-284-000-064-133, URC grant No. R-284-000-068-112, and NRF CRP grant No. R-284-000-079-592. We thank Karen Koh Zhen Yu for providing the P25 TiO2 paste used for fabrication of the DSCs used in this work. ’ REFERENCES (1) Oregan, B.; Gr€atzel, M. Nature 1991, 353, 737. (2) Gr€atzel, M. Acc. Chem. Res. 2009, 42, 1788. (3) Green, M. A.; Emery, K.; Hishikawa, Y.; Warta, W. Prog. Photovoltaics 2010, 18, 346. (4) Nazeeruddin, M. K.; Gr€atzel, M. In Photofunctional Transition Metals Complexes; Springer-Verlag: Berlin, 2007; Vol. 123, p 113. (5) Mishra, A.; Fischer, M. K. R.; Bauerle, P. Angew. Chem., Int. Ed. 2009, 48, 2474. (6) Nazeeruddin, M. K.; Zakeeruddin, S. M.; Lagref, J. J.; Liska, P.; Comte, P.; Barolo, C.; Viscardi, G.; Schenk, K.; Gr€atzel, M. Coord. Chem. Rev. 2004, 248, 1317. (7) Papageorgiou, N. Coord. Chem. Rev. 2004, 248, 1421. (8) Boschloo, G.; Hagfeldt, A. Acc. Chem. Res. 2009, 42, 1819. (9) Tian, H. N.; Jiang, X. A.; Yu, Z.; Kloo, L.; Hagfeldt, A.; Sun, L. C. Angew. Chem., Int. Ed. 2010, 49, 7328. (10) Feldt, S. M.; Gibson, E. A.; Gabrielsson, E.; Sun, L.; Boschloo, G.; Hagfeldt, A. J. Am. Chem. Soc. 2010, 132, 16714. (11) Wang, M. K.; Chamberland, N.; Breau, L.; Moser, J. E.; Humphry-Baker, R.; Marsan, B.; Zakeeruddin, S. M.; Gr€atzel, M. Nat. Chem. 2010, 2, 385. (12) Li, D. M.; Li, H.; Luo, Y. H.; Li, K. X.; Meng, Q. B.; Armand, M.; Chen, L. Q. Adv. Funct. Mater. 2010, 20, 3358. (13) Liu, Y.; Jennings, J. R.; Parameswaran, M.; Wang, Q. Energy Environ. Sci. 2011, 4, 564. (14) Watson, D. F.; Meyer, G. J. Annu. Rev. Phys. Chem. 2005, 56, 119. (15) Pichot, F.; Gregg, B. A. J. Phys. Chem. B 2000, 104, 6. (16) Gregg, B. A. In Molecules as Components of Electronic Devices; 2003; Vol. 844, p 243. (17) Peter, L. Acc. Chem. Res. 2009, 42, 1839. (18) Bisquert, J. Phys. Chem. Chem. Phys. 2008, 10, 3175. (19) Cao, F.; Oskam, G.; Meyer, G. J.; Searson, P. C. J. Phys. Chem. 1996, 100, 17021. (20) Halme, J.; Boschloo, G.; Hagfeldt, A.; Lund, P. J. Phys. Chem. C 2008, 112, 5623. (21) Bisquert, J.; Mora-Sero, I. n. J. Phys. Chem. Lett. 2009, 1, 450. (22) Barnes, P. R. F.; O’Regan, B. C. J. Phys. Chem. C 2010, 114, 19134. (23) Jennings, J. R.; Li, F.; Wang, Q. J. Phys. Chem. C 2010, 114, 14665. (24) Sodergren, S.; Hagfeldt, A.; Olsson, J.; Lindquist, S. E. J. Phys. Chem. 1994, 98, 5552. (25) Haque, S. A.; Tachibana, Y.; Willis, R. L.; Moser, J. E.; Gr€atzel, M.; Klug, D. R.; Durrant, J. R. J. Phys. Chem. B 2000, 104, 538. (26) Pelet, S.; Moser, J. E.; Gr€atzel, M. J. Phys. Chem. B 2000, 104, 1791.

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