Physical Models for Charge Transfer at Single Crystal Oxide

Mar 5, 2015 - The doping density dependence of photocurrents has been experimentally measured at single crystal rutile TiO2 electrodes sensitized with...
0 downloads 0 Views 3MB Size
Download PDF
Article pubs.acs.org/JPCB

Physical Models for Charge Transfer at Single Crystal Oxide Semiconductor Surfaces as Revealed by the Doping Density Dependence of the Collection Efficiency of Dye Sensitized Photocurrents Kevin J. Watkins,† B. A. Parkinson,*,† and M. T. Spitler*,‡ †

Department of Chemistry and School of Energy Resources, University of Wyoming, Laramie, Wyoming 82071, United States Office of Science, SC 22.13, Department of Energy, Washington, DC 20585, United States

‡

S Supporting Information *

ABSTRACT: The doping density dependence of photocurrents has been experimentally measured at single crystal rutile TiO2 electrodes sensitized with the N3 chromophore and a trimethine dye. As the doping density of the electrodes was varied from 1015 to 1020 cm−3, three different regimes of behavior were observed for the magnitude and shape of the dye sensitized current−voltage curves. Low-doped crystals produced current−voltage curves with a slow rise of photocurrent with potential. At intermediate doping levels, Schottky barrier behavior was observed producing a photocurrent plateau at electrode bias in the depletion region. At highly doped electrodes, tunneling currents played a significant role especially in the recombination processes. These different forms of the current−voltage curves could be fit to an Onsagerbased model for charge collection at a semiconductor electrode. The fitting revealed the role of the various physical parameters that govern photoinduced charge collection in sensitized systems.

■

INTRODUCTION The utilization of single crystal TiO2 as an electrode in the study of dye sensitization has been shown to provide useful insights into the photochemistry and electrochemistry involved in photoinduced charge transfer.1 The crystal substrates offer the researcher the opportunity to construct and characterize simple and controllable model systems that is not available with complex heterogeneous nanocrystalline electrodes. This allows the (photo)electrochemical investigations at well-defined crystallographic faces and charge collection with a defined interfacial electric field through a one-dimensional pathway. AFM imaging of the surface under study establishes the efficacy of the electrode preparation procedure, dye coverage, and the overall surface structure. Such information allows for the correlation of the surface crystalline orientation with aggregate formation of attached dyes and quantum dots.2−4 The crystal electrodes can also be shaped into optical internal reflection elements to allow spectroscopic and flash photolysis studies of the adsorbed dyes.5,6 When quantum dots are used as sensitizers, a well-defined electrode surface removes a host of variables and allows for a more certain claim of the extraction of charge carriers following multiexciton generation.2 In this work, it will be shown how fundamental measurements at sensitized single crystal surfaces can be expanded to illustrate a general model for electron transfer into semiconductor conduction bands, both in the light and in the dark. This will be done through the use of single crystal rutile TiO2 © XXXX American Chemical Society

semiconductor electrodes with doping levels that vary from the near insulating level of ∼1015 cm−3 to the near degenerate density of ∼1020 cm−3. They are sensitized by the ruthenium chromophore N3 and the trimethine thiacyanine dye (G15), sensitizers with contrasting photoexcitation mechanisms. As the doping density of an electrode increases, the bias dependent electric field profile near the electrode surface will change, resulting in changes in the photocurrent voltage curves that provide quantitative insight into the physical processes of diffusion and drift of the electrons in this surface region. The shape of these various current−voltage curves can be explained with a unified physical model that continuously spans the range from low-doped electrodes to highly doped electrodes.7 This mathematically derived Onsager approach describes the diffusion of a charge carrier in an external force field within the semiconductor electrode. The derivation of this model for electron transfer at semiconductor electrodes was made in analogy to a model for charge transfer at the surface of electrodes of molecular crystals.8 However, it long preceded the experimental capability to test it and not until recently did the experimental methods and procedures for electrode preparation Special Issue: John R. Miller and Marshall D. Newton Festschrift Received: November 14, 2014 Revised: March 4, 2015

A

DOI: 10.1021/jp511438j J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B

the oxidation of a reductant in the dark, and will be taken as zero in this work. jinj is the total current in A/cm2 of all injected charge into the electrode from the dye that thermalizes in the interior, which in previous work7,8 has been designated as “b”. kes is the escape velocity in cm/s of electrons from the surface to the bulk, and krec is the recombination velocity in cm/s of electrons with an acceptor at the surface, both in solution and on the surface. ΔΦ is the potential drop from the surface to the bulk of the semiconductor, Nd is the doping density of the semiconductor, and e is the unit electric charge. The term krec designates the recombination velocity, which represents contributions from several reactions. In the dark, it is possible for conduction band electrons to reduce any adventitious molecular oxygen at the surface or to reduce water to hydrogen, although that proceeds slowly at TiO2. Upon illumination, oxidized dye at the surface may be reduced by these electrons, as can be any oxidized form of the regenerator hydroquinone. jisl is the current in the ideal sink limit, that is the current collected in the limit of an infinitely large recombination rate constant krec. Statistically, some charge carriers can diffuse to reach the back contact without ever encountering the surface. This is important for cases where kes is comparable or smaller than krec at large bias potentials or where there is a large thermalization depth for injected charge carriers. jisl only plays a role in this work when the width xo of the Schottky barrier is small, as is the case for highly doped electrodes. It is given by the expression

advance to the point where it was possible for a more thorough experimental examination.9 It was necessary to acquire the ability to prepare TiO2 electrodes with well-defined surfaces that could be characterized through AFM and LEED.9 In addition, the electrode preparation had to be developed that would reproducibly enable high dye coverage where the excited adsorbed dye produced photocurrent with near unity quantum efficiency.10 Lastly, sufficient familiarity and experience had to be acquired in the dye sensitization of these now well characterized and reproducible single crystal electrodes to have confidence in the interpretation of the data.3,11,12 With this background, it is now possible to make a quantitative evaluation of the various aspects of this physical model. The Onsager model expression for the description of the net current flow in A/cm2 over the conduction band of a semiconductor electrode under potential bias is expressed as7 j = jisl +

kes (j + jg − jisl − ek recNd e−ΔΦ / kT ) kes + k rec inj (1)

Equation 1 governs current flow both in the dark and in the light, and for the dye sensitized TiO2 single crystal systems under study here, it describes both the oxidative photocurrent flow at positive bias and the cathodic dark currents at negative bias. This expression has several components, with the pertinent variables being illustrated in Figure 1. jg is the current density from the surface generation of charge, such as

jisl =

∫x

s

x0

B(x′)

∫x

s

x′

eeΦ(x)/ kT dx dx′/

∫x

∞

eeΦ(x)/ kT dx

s

(2)

The term B(x′) describes the distance profile for thermalization of the electrons in the semiconductor, with an overall sum of injected charge being equal to jinj = ∫ xxs0 B(x) dx. Here xs denotes the position of closest approach of the charge carrier to the surface. Through the second term in eq 1, it is seen that the current is governed by the escape velocity kes in cm/s for escape from the surface and the recombination velocity krec in cm/s for electrodes. The branching ratio kes/(kes + krec) then determines the fraction of charge carriers that are collected as anodic current. This is dominant at low doping densities. At intermediate doping densities, the well-known Schottky barrier factor comes into play through the term (jisl − ekrecNde−ΔΦ/kT), where ΔΦ represents the potential difference between the bulk of the semiconductor and xs. Given an injection current density of charge jinj, a back reaction occurs between the concentration of electrons in the semiconductor bulk (Nd) and an acceptor on the surface or near the surface in solution. This acceptor can be the oxidized dye, oxidized forms of the regenerating agent, protons, or any other adventitious species, such as adsorbed oxygen. In the case of the highly doped, 1020 cm−3 electrodes, tunneling of electrons occurs through the Schottky barrier to surface acceptors, with the thinness of the depletion region bringing the ideal sink limit current jisl into consideration. Implicit in eq 1 is the diffusive motion of the electron on the potential profile of the space charge region near the surface. Once the electron from the excited dye is injected into the semiconductor and thermalizes in the interior, it feels the electric field from the bias of the Schottky barrier in competition with a Coulombic attraction from the positive charge from oxidized dye in the surface dye layer. The existence

Figure 1. Schematic diagram for the dye−semiconductor interface illustrating the various aspects of eq 1. A layer of sensitizing dye attached to the surface of the semiconductor can inject charge into the semiconductor with a current density jinj, leaving a positive charge in the dye layer a distance xd from the surface. The injected current jinj thermalizes in energy down to the semiconductor conduction band where it feels the Coulombic potential from the positive charge. These electrons can diffuse to the position of closest approach to the surface xs to recombine with a velocity krec with surface acceptors, or they can escape the Coulomb well with an escape velocity kes into the Schottky potential region, where they may be collected as current after traveling its width x0. This figure shows the potential within the semiconductor to be the sum of the Coulomb and Schottky barrier potentials (solid blue line). jisl cannot be depicted here but can be seen to represent the statistical fraction of the diffusing electrons that never encounter xs as they move around on the potential energy surface and escape at the velocity kes into the interior. Dark cathodic currents in eq 1 occur when electrons in the interior of a semiconductor at the doping density Nd are elevated thermally over the potential barrier ΔΦ to xs to reduce acceptors at the surface. When the Schottky barrier is very thin, a tunneling current jtunnel must be considered. B

DOI: 10.1021/jp511438j J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B of this Coulomb field is evident in Stark effect studies on sensitizing dyes in the surface layer in dye sensitized solar cells,13−15 but in this work, we concern ourselves with the portion of the electric field that extends into the semiconductor. This competition is expected whenever the thermalization distance for the injected charge is shorter than the effective extent of the Coulomb potential well into the solid. Another condition is that the scattering length of the charge carrier within the solid must also be shorter than the length of the Coulomb well. Otherwise, the diffusing charge carrier will pass right over the well before thermalizaton. Both of these conditions are met for electron transport in TiO2. Given the low electron mobility for rutile TiO2 single crystals of 10−3 cm2/(V s),16 the ability to control its doping density and to characterize its surface, and the availability of a pair of well studied sensitizing dyes, it is possible to create experimental conditions for exploration of the various limits of behavior described by eq 1.

from Ivium Technologies, with the data and equivalent circuit being shown in Figure S2 (Supporting Information). A threeelectrode configuration was utilized with a Pt counter electrode and Ag/AgCl reference electrode in 0.1 M HClO 4 (Mallinckrodt, ACS grade) in 18.2 MΩ-cm water, or a AgCl coated silver wire as a pseudoreference electrode in 50 mM tetrabutylammonium hexafluorophosphate (Fluka, electrochemical grade) in acetonitrile (Fischer Scientific, HPLC grade). The AgCl wire was prepared through anodization of a Ag wire in an aqueous chloride solution to create a reliable reference potential for use in acetonitrile. The relative flatband potentials of the variously doped electrodes were assumed to carry over to the dye sensitized electrodes, and the analyses of the photocurrent−voltage data in this work do not bring this into question. Prior to sensitization of the crystal surface, a UV cleaning to remove any adsorbed organic surface films was performed by illumination from an Oriel 150 W Xe lamp run at 3 A of current in a 0.1 M NaClO4 solution with the pH adjusted to 12 using NaOH. Under illumination, a constant bias of 0.7 V vs Ag/ AgCl was applied to the TiO2 electrode for 20 min. Immediately following UV treatment, the crystal was rinsed with 18.2 MΩ-cm water and then ethanol and then immersed in N3 ethanol solution (2 × 10−4 M) or G15 ethanol solution (8 × 10−5 M) for 30 min to ensure full surface coverage.17 The sensitized crystal is then rinsed with neat acetonitrile to remove excess dye and dried with a stream of N2. The dye 2,2′-(diethylcarboxy)-thiacarbocyanine bromide, denoted here as G15, has a reduction potential for the oxidized dye that can be estimated from the redox potentials of similar cyanine dyes to be about +0.97 V vs Ag/AgCl18 and an absorption maximum of about 575 nm, or 2.15 eV when attached to TiO2, placing the thermodynamic potential of the excited dye as the donor, defined as the reduction potential of the oxidized dye to produce the excited state, at −1.18 V vs Ag/ AgCl, in comparison with the corresponding potential for N3 of −0.82.19 The energies of the electron donor levels of the excited states of these two chromophores should not limit the yield of excited state electron transfer to the TiO2, since they are both well negative of the potential of the conduction band edge of rutile. Incident photon current efficiency (IPCE) spectra were measured for the sensitized TiO2 in a three-electrode configuration using a Pt wire counter electrode and the AgCl coated silver wire as a reference electrode. The supporting electrolyte was 50 mM tetrabutylammonium hexafluorophosphate in acetonitrile. The regenerator was 10 mM hydroquinone (Aldrich, 99+%). This electrolyte was degassed with nitrogen and sealed off from ambient air in the electrochemical cell prior to photoelectrochemical measurements. Photocurrent measurements were performed with a potentiostat (Princeton Applied Research Eg&G, 174A) and a lock-in amplifier (Stanford Research, SR830), using a Laser-Driven Light Source (Energetiq Technology, LDLS EQ-99) coupled to a computercontrolled monochromator (Jobin Yvon, H20) as the excitation source. The light source was chopped (Stanford Research System Chopper, SR540) at a frequency of 27 Hz, which was synchronized with the lock-in amplifier. Extensive studies of the time response of the sensitized electrodes to light revealed that this chopping frequency was too fast for only the lowest, 1015/ cm3 doped TiO2 samples. For these low-doped samples, only photocurrent data from constant illumination has been presented and used in this work. For each doping density/

■

EXPERIMENTAL SECTION Rutile (110) TiO2 single crystals were purchased from MaTeck GmbH with a one side mechanical polish. Atomically flat surfaces were obtained by manually polishing using a soft polishing cloth (Allied High Tech Products, Inc.) and 20 nm noncrystalline colloidal silica polishing suspension (Buehler, Inc.), following a figure eight pattern with gentle pressure for about 10 min. After polishing, the crystals were rinsed with a copious amount of 18.2 MΩ-cm Millipore water, immersed into a 10% HF bath for 10 min to remove any colloidal silica, followed by ultrasonication in 18.2 MΩ-cm water for 1 h. The cleaned crystals were then annealed in air at 700 °C for 8 h to produce a terraced surface. Characterization by atomic force microscopy (Cypher AFM by Asylum Research) in air using silicon tips (Asylum Research) with a 42 N/m force constant and 300 kHz resonance frequency revealed uniformly terraced surfaces. Reductive n-type doping of the TiO2 crystals was performed by annealing at high temperature in a vacuum using a rapid thermal annealing furnace (RTA, ULVAC-RIKO, Mila-3000) equipped with a turbo molecular pump (Pfeiffer Vacuum, HiCube). The RTA chamber is pumped down to a pressure of ∼5 × 10−6 mbar before beginning the RTA heating program. To control the doping level, annealing is modified in both temperature and time, ranging from 500−1100 °C and 5−30 min. Qualitative doping levels can be ascertained by noting the color of the crystals, with undoped samples being clear or colorless, lightly doped samples appearing bluish, and highly doped samples being black (see Figure S1, Supporting Information). After doping, the surface is again investigated by AFM to ensure that the atomically flat and terraced surface is preserved. Doped TiO2 crystals were nonpermanently mounted into a home-built Teflon electrochemical cell, where the crystal face is sealed to an O-ring by force of a threaded copper plunger. The face of the crystal was exposed to electrolyte solution, producing a surface area of 0.27 cm2, and an ohmic contact was made at the back of the crystal to the copper plunger using Ga/In eutectic paste. The crystal face was exposed to light through a quartz window in the front of the cell, with a path length through the electrolyte of about 3 mm. Once mounted, standard Mott−Schottky analyses were performed for the purpose of determining the doping density for the reduced crystals. This was done using a CompactStat C

DOI: 10.1021/jp511438j J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B

Figure 2. Representative AFM images of (left to right) prepared atomically flat single crystal (110) rutile TiO2 for clean, N3 sensitized, and G15 sensitized surfaces. Red lines show where the height traces are on the images. Monolayer dye coverage is evident from the underlying terraces still being visible. The spherical shape of N3 dye and the tendency of the flat G15 dye to aggregate is observed in the images.

Figure 3. (a) Spectral IPCE response for N3 sensitized TiO2 electrodes of three different doping densities at a 0.5 V bias vs the Ag/AgCl wire electrode. (b) Corresponding IPCE for G15 sensitized TiO2. The dye structures are shown with their respective spectral responses.

is probed by AFM in the center area that was exposed to dye solution, as well as the outer edges, which were protected from contact with the dye solution through the crystal mounting arrangement. This gives a clean surface providing an internal standard for observing dye coverage by AFM.

dye combination, including unsensitized backgrounds, IPCE measurements were taken at 0.5 V applied bias versus a AgCl wire electrode. This was repeated three times at each bias with time to ensure reproducibility and stability. Current−voltage curves, both DC measurements and coupled with the lock-in amplifier, were measured immediately following the IPCE evaluation. Excitation light from the same LDLS and monochromator combination of the IPCE measurement was used, with the monochromator wavelength set at 532 nm. Current−voltage curves were scanned from positive to negative potentials at 5 mV/s with 1 mV steps after a 10 s equilibration period prior to scanning. For the AFM of sensitized crystals, the same UV cleaning/ sensitizing procedure outlined above is performed. Once sensitized, the crystal is soaked in neat acetonitrile to allow any unbound or weakly bound dye to diffuse from the surface, as well as preventing impurities from the electrolyte from being deposited onto the crystal surface. This same procedure is used prior to measurement of sensitized photocurrents in this work. After removal from the electrochemical cell, the crystal surface

■

RESULTS Representative AFM images of the various TiO2 electrode surfaces are provided in Figure 2 for the case of unsensitized TiO2 and TiO2 with attached N3 and G15 on a stepped surface. The means of their attachment to the TiO2 surface through the carboxylate functions of the dye has been described in previous work.10,17 The image of the surface shows the attached N3 chromophore has a well-defined somewhat hemispherical shape (but broadened due to the tip radius of curvature) and forms a layer on the surface that follows the underlying step structure of the particular (110) TiO2 face. G15, which is a flat dye prone to aggregation, attaches to the TiO2 in a less ordered manner than N3 with a tendency revealed by Figure 2 (right-most) to smooth out the surface structure. D

DOI: 10.1021/jp511438j J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B

sensitized TiO2 over a range of doping densities from 1015 to 1020 cm−3 where it is clearly seen that the IPCE peaks at about 1017 cm−3 and falls to about 10% of the peak value at the extremes of 1015 and 1020 cm−3. In these experiments, and all others described in this work, the electrolyte contained 10 mM hydroquinone solution as a regenerating agent for the dyes. The reduction of hydroquinone over the TiO2 conduction band is kinetically far slower than reduction of traditional one-electron, outer sphere redox agents such as ferrocenium and allows the photocurrent−voltage curves of this work to be measured at far more negative bias potentials. There was no significant difference observed between dark current voltage curves at TiO2 with and without hydroquinone. Current−voltage curves for these two dyes on TiO 2 electrodes doped at levels ranging from 1015 to 1020 cm−3 were recorded both in the dark and with 532 nm illumination. Representative curves are given in Figure 5 for electrodes with doping levels of 2 × 1015, 2 × 1017, and 1 × 1020 cm−3. Curves for other doping densities are given in the Supporting Information (Figure S3). While illuminated at 532 nm, the potential of the sensitized electrodes was swept to negative potentials from 0.5 V vs the Ag/AgCl wire electrode at a rate of 5.0 mV/s. Curves are also shown where the light was chopped by hand as the sweep proceeded. At intermediate doping levels, from 3 × 1016 to 1019 cm−3, a plateau in the photocurrent was observed at positive bias potentials. In contrast, at the lowest doping level, the curves in Figure 5a show that the current continues to rise with increasingly positive bias. The low-sloped increase in current is also observed at more positive bias potentials with the highest doped crystals. Of note with the latter crystals are the relatively high cathodic currents observed in the dark at potentials positive of the flat band potential where a depletion layer exists. It is clear that the depletion

The photocurrent spectra of Figure 3 reflect the spectral response of sensitized TiO2 at three different doping densities for the dyes N3 and G15 at an electrode bias of 0.5 V vs the Ag/AgCl wire electrode. The only significant difference between their photocurrent spectra and solution spectra is a slight increase in the blueshifted aggregate peak for G15 relative to its monomeric maximum at 565 nm. More extensive analyses of the spectral characteristics of these classes of dyes have been reported in previous work.3 In Figure 4, the peak IPCE is shown for

Figure 4. Plot of maximum IPCE for N3 and G15 sensitized TiO2 over a large range of doping densities.

Figure 5. Current−voltage curves for N3 (a−c) and G15 (d−f) sensitized TiO2 electrodes at doping levels of 2 × 1015 (a, d), 2 × 1017 (b, e), and 1 × 1020 cm−3 (c, f). Curves were done in the dark (red), under 80 μW of 532 nm illumination (blue), and chopped by hand as potential was swept (green). E

DOI: 10.1021/jp511438j J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B region is so thin at this doping density that electrons can tunnel through the Schottky barrier to acceptors in solution. From inspection of Figure 5a and d for N3 and G15 at the 1015/cm3 doped electrodes, the difference between the light and dark currents is straightforward to derive with the results depicted in Figure 6a and b. However, the difference is difficult to determine at potentials negative of −0.2 V for the higher doped electrodes because of the very large increase in the dark current background. As a result, a lock-in amplifier measurement was employed to separate the photocurrents from the dark currents where the light was chopped mechanically at a 27 Hz rate, which is slower than the response time of the higher doped electrodes. Examples of the photocurrent−voltage curves obtained with this lock-in approach are provided in Figure 6c−f for N3 and G15 sensitized electrodes doped at 2 × 1017 and 1 × 1020 cm−3. It can be seen that the photocurrent onset for the 2 × 1017 cm−3 electrode is far negative of −0.2 V and actually begins at −0.55 V vs Ag/AgCl wire electrode. This onset is in line with a Mott−Schottky determination of the flatband potential of this electrode in the acetonitrile electrolyte, which was also found to exhibit an intercept at −0.55 V. Lockin measurements for the 2 × 1015 cm−3 doping level are not shown, since they exhibited artifacts in the current−voltage curves which appeared to originate from bulk photoconductivity effects. Additional lock-in measurements were made at the 2 × 1017 cm−3 electrode where the light power was stepped up from 4 μW to 3 mW to 30 mW. The photocurrent curves for N3 that are given in Figure 6c have been normalized to the same plateau level, and are seen to shift to more positive potentials as illumination is increased. At 4 μW, the current shows a plateau positive of −0.2 V, whereas this plateau exists only positive of +0.3 V with the 30 mW illumination. At this illumination intensity, an integration of the photocurrent passed through the surface as the electrode is swept from 0.5 to 0.3 V reveals that an equivalent of 10 monolayers of dye has been photo-oxidized. It can also be regenerator on the surface that is oxidized, since an unquantified amount of hydroquinone is likely coadsorbed on the surface with these dyes.12 For the 3 mW exposure, the charge passed during the entire sweep from +0.5 to −0.2 V is equivalent to little more than a half monolayer of dye. It is evident that the shift of these curves is attributable to a partial or full exhaustion of surface adsorbed regenerator and/or dye. Below a power level of 80 μW, no further shift of the curve is observed. The corresponding experimental results for G15 are given in Figure 6d for 80 μW and 3 mW exposures. Lock-in measurements of sensitized highly doped, 1020 cm−3 electrodes reveal a climb from zero current to plateau shoulders in current much like the intermediate doped samples. This is depicted in Figure 6e and f for both dyes, where the shoulder is observed at about −0.2 V vs reference; however, it is evident that the current continues to rise positive of this potential but at a smaller slope. Such an aspect of the current−voltage curve is not seen with electrodes doped at 1019 cm−3 or lower. The data for the three doping densities used in Figure 6 were selected to illustrate three different regimes of physical behavior contained in eq 1. In the photocurrent−voltage curves for N3 and G15 at 2 × 1015 cm−3 doping, the branching ratio kes/(kes + krec) will be seen to determine the shape of the current−voltage curves. At 2 × 1017 cm−3 doping, the current from the semiconductor bulk over the Schottky barrier potential ΔΦ will control photocurrent−voltage behavior. At very high 1020 cm−3

Figure 6. (a) The difference between dark and light currents of Figure 5a for N3 on 2 × 10 15 cm−3 doped TiO2 given here in red and fit to the several factors of eq 1. This difference has been normalized by the photocurrent observed for the doped electrode at the IPCE maximum in Figure 4. The calculated Schottky barrier (SB, dotted line) factor for xs = 0.2 nm is seen to rise very quickly. The calculated branching ratios (BR, dashed line) kes/(kes + krec) for xs = 0.4 nm and xs = 0.2 nm are found to bracket the photocurrent voltage curve well. The product of the two (SB × BR, solid line) makes only a little change in the curve for xs = 0.2 nm. The calculated curves are absolute predictions from eq 1. (b) The corresponding curves are given for G15. (c) Lock-in measurements of photocurrent−voltage curves for N3 at 2 × 1017 cm−3 doped TiO2 are presented at illumination powers of 4 μW, 3 mW, and 30 mW (red line). Calculations of the SB and BR factors are given for the 4 μW, with the SB and the SB × BR product giving satisfactory fits to the data. As the illumination increases, the kreg factor in eq 5 declines, resulting in a shift in the potential for the calculated SB factor, and a shift depicted here for the overall calculated SB × BR product for selected kreg values of 10−5 and 10−8 s−1 to align with the observed shifts in the photocurrent voltage curves. (d) The corresponding curves are given for G15 with 80 μW and 30 mW illumination. A SB × BR product is given for the 80 μW level but not for the 30 mW where significant photodesorption of the dye has occurred (see text). (e) For 1020 cm−3 highly doped TiO2, the lock-in measurements of the photocurrent−voltage curves (red line) are fit to a weighted sum Jtot of the SB factor and the ideal sink limit factor (Jisl, dashed line) through eq 6 in an illustration of these two aspects of eq 1. (f) The corresponding curves are given for G15.

doping, the space charge layer becomes very thin and it can be shown how the ideal sink limit current jisl can come into play. Beginning with data from the low doped electrodes, eq 1 will be used to analyze the current voltage curves of the 2 × 1015 F

DOI: 10.1021/jp511438j J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B cm−3 doped experiments of Figure 5a and d for N3 and G15. This requires the evaluation of kes, which is defined as7 kes = DeeΦ(xs)/ kT /

∫x

∞

eeΦ(x)/ kT dx

s

Figure 6a for xs = 0.2 and krec = 0.1 cm/s, and xs of 0.4 nm and a krec of 0.9 cm/s. The Schottky factor of eq 1 has a much different behavior. It can be restated through an expression derived from a steady state assumption7 for the concentration of oxidized dye [D+] to be

(3)

where D is the diffusion coefficient in cm2/s and is taken to be 10−3 for rutile16 TiO2 and Φ(xs) is the potential at xs. The potential Φ is the potential felt by an electron at the semiconductor surface and can be approximated by the expression eΦ =

1 (jinj − ek rec Nd e −eΔΦ / kT) =

k reg + k′Nd e−ΔΦ / kT

(5)

k1rec

Here the term is that part of the krec term that represents the recombination of electrons only with the oxidized dye on the surface, since the dark current has been subtracted from the photocurrents through the lock-in technique. It can be expressed as k1rec = k′[D+], where k1rec is the rate constant in cm3/s for reduction of the oxidized dye from the TiO2 conduction band. Assuming a reasonable value of 105/s for the pseudo-first-order rate constant of kreg6 for the regeneration of the oxidized dye by the hydroquinone and a characteristic 10−13 cm3/s rate constant23 for k′ for the reduction of the oxidized N3 at TiO2, taken from the dye sensitized solar cell literature, the potential dependence of the Schottky barrier factor SB of eq 5 was calculated and is given in Figure 6a. The expression in eq 5 assumes a single rate constant k′ and for kreg so there is a quick rise of the Schottky factor from zero to unity, a part of which is depicted in Figure 6a. The consequence is that even a product SB × BR of the branching ratio with the Schottky factor preserves the dominant effect of the branching ratio. However, when considering the photocurrent−voltage data in Figure 6c for the intermediate 2 × 1017 cm−3 doping density, the Schottky barrier factor of eq 1 was found to dominate the branching ratio factor. The branching ratio curve derived from a kes calculation of eq 3 for this doping density is depicted in Figure 6c for N3 and does not describe the data well. If one evaluates the Schottky barrier term using the characteristic 10−13 cm3/s value for k′ discussed in the 2 × 1015 cm−3 doping density calculation, the result is not satisfactory. It is necessary to consider k1rec to encompass a range of rate constants for k′ where k1rec = ∑i k′i , as has been done in the analysis of stretched exponential rate constants for these back reactions in dye sensitized solar cells.14,23,24 In this calculation, a distribution of four differently weighted k′ values was used which has the characteristic mean of 10−13 cm3/s. With this distribution, a Schottky barrier factor curve is calculated and given in Figure 6c for N3 that better matches the experimental data. When the product SB × BR of the Schottky barrier with the branching ratio factor is taken, however, a good approximation of the data is obtained, which is shown in Figure 6c for N3 and through a similar procedure in Figure 6d for G15. Sensitized electrodes with a 1016 cm−3 doping exhibited a behavior intermediate between the 1015 and 1017 cm−3 cases. As a control for this doping density, lock-in measurements of the current−voltage curves for N3 and G15 without the hydroquinone regenerator were made at a very low, 4 μW illumination level. The results were the same as those with the regenerator for the freshly prepared samples, but samples that were allowed to age for up to a day in solution produced curves with a negative curvature to the rising portion of the current voltage curves instead of a linear one. With only the surface structure of the adsorbed dye being expected to evolve with time, this change implies a change in the distribution of recombination rates k′, presumably caused by an evolution of

⎤⎡ ⎤ eNd 1 1 −e ⎡ (x − x0)2 ⎢ ⎥⎢ ⎥+ 2πε0 ⎣ (xd + xs) ⎦⎣ (εsf + εsc) ⎦ 2ϵε0 − eVapp

jinj k reg

(4)

Here ε0 is the permittivity of free space, xd is the distance from the positive hole state on the dye and the TiO2 surface, εsf is the relative permittivity of the surface dye layer, and εsc is the effective relative permittivity of the semiconductor surface region. Vapp is the band bending resulting from the applied potential. In this expression, ϵ represents the commonly known relative permittivity of the semiconductor in the bulk. The first term on the right-hand side of eq 4 is in the form of the Coulombic interaction of opposite charges at an interface between two dielectric media.20 It is an approximation to the real physical situation, and its parameters xs, εsf, and εsc are taken as variables adjusted to fit the data.8,21 The electrostatics of separation of the hole state on the dye from the electron in the semiconductor contain contributions from the Coulombic effects between separated charges and image charge effects, both of which operate within their own time domain. The electrolyte will adjust to screen these electrostatic effects in about a nanosecond, which will usually be longer than the residence time of the electron at the surface, depending upon doping density. However, in the steady state, injection of charge by the dye across the surface can be seen as a discharge of the double layer and an electron diffusing parallel to the surface will feel the potential of nongeminate positive charges as well. For this complicated and highly dynamic physical situation, a (εsf + εsc) of about 15 produced the best fit of the denominator of eq 4 to the data. To calculate the Schottky barrier potential of eq 4, a static relative permitttivity ϵ of 70 was employed. The distance for xd was taken to be 1.0 nm for N322 and 0.5 nm was seen appropriate for G15, given its structure. The fitting of the data worked best with a position of closest approach to the surface xs of 0.2−0.4 nm. The difference between the light and dark current−voltage curves for N3 at the 2 × 1015 cm−3 doped electrode in Figure 5a is given in Figure 6a so that a fit may be made to eq 1. Neglecting jisl and jg, the branching ratio kes/(kes + krec) and the Schottky factor need to be considered. We will show that the Schottky barrier term in eq 1 at this doping density rises far too quickly with potential and reaches a plateau current, which was not observed experimentally for this doping density. It is evident that the branching ratio must play the governing role. Calculating kes for this doping density according to eq 3, a branching ratio BR can be constructed for two different combinations of xs and krec. krec can be estimated from the dark current−voltage curve of Figure 5a using the expression j = krecNde−ΔΦ/kT at the potential onset of cathodic current flow. Values of 0.1−1 cm/s can be derived. BR curves are given in G

DOI: 10.1021/jp511438j J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B Between the Schottky there appear to be the necessary to describe the The relative weighting rearrangement of eq 1:

the dye monolayer surface structures or composition of the attached dye populations with time. Examination of the illumination intensity experiments of Figure 6c for N3 reveals a positive shift of the SB × BR product that is predicted by eq 5. As the high illumination photolytically exhausts the surface adsorbed hydroquinone regenerator, the regeneration rate constant kreg will decline significantly. Inserting an effective kreg of 10−5 and 10−8 s−1 into the Schottky factor from the 4 μW curve in Figure 6c leads to curves in Figure 6c shifted to approximate the onset of the high illumination level curves. There are differences between the model curves and the data, but this may be attributed to changes in the distributions of kreg and k′ constants with the exhaustion of hydroquinone and dye and the production of the resultant acceptor semiquinones on the surface. These shifts move the rising portion of the current−voltage curves into the range where the branching ratio is nearly constant and support the contention that the linear rise of the current with the bias potential is controlled by the Schottky barrier factor of eq 1. In Figure 6d, the corresponding current−voltage data for G15 and the fit of the model is also given. A 30 mW illumination level for G15 is also shown which differs from N3 in showing a long, monotonic rise of the current from zero to the plateau instead of a distinct shift of the entire curve. This is not surprising, since it is known12 that this dye can be desorbed from the surface by the oxidation products of a hydroquinone regenerator (Figure S4, Supporting Information). As a result of this time-dependent change of the surface composition of the dye, no fitting with a SB × BR curve can be made that corresponds to that shown for the 80 μW illumination curve. Moving to an examination of the data for the highly doped 1020 cm−3 TiO2, the lock-in photocurrent measurements presented in Figure 6e and f show a change from the behavior at the 2 × 1017 cm−3 electrodes. As the doping density increases, the IPCE has dropped from its high for 2 × 1017 cm−3 in Figure 4 to a low level at 1020 cm−3. Over this doping range, the crystals themselves become significantly darker to the eye as the doping increases (Figure S1, Supporting Information), being near silver black at 1020 cm−3. Therefore, it is not unreasonable to attribute this drop in IPCE with the increase of doping to energy transfer quenching of the excited state of the dye on the surface by color centers in the underlying TiO2. This behavior at a highly doped electrode would appear to result in an APCE for electron transfer from the excited dye of only about 10%. Another difference between the curves of Figure 6e and f is the continued, linear rise of the photocurrent in the potential region where the plateau is reached at lower doping densities. An explanation was sought through fitting this characteristic curve to eq 1. Adjusting for the higher doping density but retaining the same dye recombination rate distribution, the Schottky barrier factor from the 2 × 1017 cm−3 doping curve of Figure 6c was recalculated and is depicted in Figure 6e. When normalized to the magnitude of the current at +0.7 V, it represents a good approximation up to the shoulder of the curve. At this high doping density, however, the Schottky barrier is very thin, being only about 7 nm thick at 1.0 V band bending, and makes the jisl term of eq 1 assume significance. This jisl term is also depicted in Figure 6e, having been calculated from eq 2. A delta function thermalization profile at 0.4 nm was found to work best for xs equal to 0.2 nm.

Jtot =

barrier and jisl curves in Figure 6e, potential dependent characteristics experimental curve. of these two curves is given in this

k rec kes 1 jisl + (j − k rec Nd e−ΔΦ / kT ) kes + k rec kes + k rec inj (6)

Here the branching ratio kes/(kes + krec) and its complement krec/(kes + krec) determine the relative role of currents from the Schottky barrier and ideal sink limits. The potential dependence of kes can be evaluated through the use of eq 3 for the 1020 cm−3 doping density and its value in the range of −0.2 to +0.6 V is quite high, on the order of 105 cm/s, implying that these experimental conditions may be at the limit of applicability of eq 1. The value of krec is also a function of potential, as has been discussed in the analysis of the data for the 2 × 1015 cm−3 electrodes and as the dark currents for reduction in Figure 5c show, but it is not controlled in these experiments over the entire potential range of Figure 6e. At this high doping density, however, a simple WKB analysis of the tunneling currents from the semiconductor bulk through the Schottky barrier to solution or surface acceptors reveals that these currents can be many orders of magnitude higher than the thermal current over the top of the surface potential barrier. This tunneling current is treated here as an effective increase in the thermal value of krec for this electrode, which in this case can be very high, but still undetermined in this experimental system. For purposes of illustration, if we assume the maximum value of krec of 105 cm/s, that is, 105 times larger than the 0.9 cm/s value used for the 2 × 1015 cm−3 electrodes, and use this in eq 6 with the calculated kes values, we obtain the overall result shown in Figure 6e for N3. The resultant product describes the essential features of the data. A similar calculation is shown in Figure 6f for G15.

■

DISCUSSION The fittings obtained for the current−voltage curves for dye sensitization at the single crystal rutile TiO2 electrodes of Figures 5 and 6 demonstrate that eq 1 can be used to describe the behavior of photoinduced charge transfer over this 5 orders of magnitude range in doping density. The Schottky barrier component of eq 1 dominates the current−voltage behavior over the doping range from 1016 to 1019 cm−3. It is only at the extremes of very low and very high doping that other physical phenomena influence and/or control the shapes and magnitudes of the current−voltage curves. Although a quadratic Schottky potential has been used in eq 1 in this work, the expression of eq 1 is general in application. For any particular potential barrier at a semiconductor interface, which can be multilayer in nature, the appropriate mathematical description of the potential barrier can be used in place of the parabolic potential in the numerical evaluation of eq 4. As in this work, however, the electron mean free path and diffusion constant must be low for a given Onsager distance. As is depicted in Figure 1, the competition for the thermalized injection current jinj between electron recombination and escape to the interior is determined by the relative slopes of the Coulomb and Schottky barrier potentials, that is, by the electric field that the electron feels at its location in the surface region. However, only the Schottky barrier potential H

DOI: 10.1021/jp511438j J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B changes with Nd, as eq 4 shows. The Coulombic potential does not. At a given bias potential for an electrode, therefore, the tendency increases through a greater kes for injected electrons to escape as Nd for the electrode increases. This dependence of kes upon Nd, as given through eqs 3 and 4, means that the potential dependence of the branching ratio krec/(kes + krec) climbs more quickly to unity as Nd increases. A comparison of the BR curves in Figure 6a and c for the doping levels of 2 × 1015 and 2 × 1017 cm−3 confirms this. At a given krec of 1 cm/s, a value of 0.5 for the BR is reached at much lower band bending for the 2 × 1017 cm−3 doped electrodes than for the 2 × 1015 cm−3 doped ones. However, as the SB × BR products in Figure 6c and d show, the BR term is still required to get a good description of the intermediate doping density regime. It is in the low doping range that nanocrystalline electrodes operate in dye sensitized solar cells and the physical principles that govern drift and diffusion in these single crystal systems should be found in nanocrystalline ones as well. One concludes that the BR factor determines the relative amount of charge collection from sensitized injection currents at semiconductor electrodes, much like it is with molecular crystals.8 However, much of this charge collection is reversed by the dark cathodic current which originates in the thermal promotion of electrons from the semiconductor bulk over the Schottky barrier potential to the surface to reduce oxidized dye, expressed in eq 1 as ekrecNde−ΔΦ/kT. Its impact upon the net photocurrent flow is controlled through the Schottky barrier factor (jinj − ek1recNde−eΔΦ/kT), which can be seen to dominate when Nd and krec are high. In the low doped experiments of Figure 6a and b, it is depicted as SB and plays little role, but in the intermediate doping levels of Figure 6c and d, it plays a major part in determining overall photocurrent voltage curves. The SB factor is generally used to interpret current flow at semiconductor electrodes, but it is seen from this work that it provides an incomplete picture at lower doping densities. The ideal sink limit current jisl is a novel concept in semiconductor electrochemistry, and the analysis here has shown that there are regimes, limited in character, where it can assume significance. Through eq 2, one can see that jisl is able to be large when the themalization profile B(x) projects a significant fraction into the interior, which would be the case for thin layers, such as ALD layers on electrode surfaces, or for thin, highly doped semiconductors. Even when jisl is large, eq 6 reveals that its contribution is weighted by the relative size of kes and krec. The two chromophores of this work have distinctly different photochemistry and photophysical character. N3 is a wellknown metal−ligand charge transfer inorganic chromophore where excitation promotes an electron from the metal to a ligand and has an excited state lifetime in the microseconds.19 The G15 carbocyanine dye is excited through a π−π* transition and relaxes within picoseconds through a radiationless decay when in solution, and yet when immobilized on a surface, its lifetime extends to several nanoseconds. Like most planar dyes, G15 will also aggregate on the surface, and this is evident in the IPCE spectral curves of Figure 3b and AFM image of Figure 2c. N3 on the other hand, being roughly spherical in nature, can only form adventitious contact dimers with its neighbors. In spite of this contrast, the current−voltage curves of this work reveal few differences. One is seen in Figure 4 where the higher IPCE for G15 relative to N3 reflects its higher extinction coefficient, ca. 105 M−1 cm−1 versus a third that value. Another is in the comparison of Figure 6c with Figure 6d where the high

illumination exposure of the sensitized surface reveals a distinctly different surface attachment character for the two chromophores, where G15 is photodesorbed by the hydroquinone and N3 is not, as has been previously been reported.12 Last, there is a predicted shift in the current−voltage curves for N3 and G15 owing to the different values for xd used for G15 and N3 in the fitting of eq 1 to the data, where xd is taken to be 1.0 nm for N3 and 0.5 nm for G15. This shift is calculated to be about 70 mV and while not large does appear to be real, because all of the N3 fitting parameters of Figure 6b and d have been carried over as fitting parameters for G15 in Figure 6c and e except for the one change in xd. The resultant shift of the calculated curves reflects the trend of the data. This similar photoelectrochemical behavior observed for distinctly different dyes may imply that the kinetic behavior of charge transfer at these interfaces is controlled by the TiO2. For example, the fits of Figure 6 require the use of a distribution of rate constants k′ for recombination of electrons with the dye and imply the existence of either a collection of different types of reactive dye groups or surface states on the surface. This has been studied spectroscopically at nanocrystalline TiO 2 surfaces.14,23,24 However, in this work, the reaction velocities in the distribution of back reactions are revealed through the measurement of the current−voltage curve instead of through transient absorption spectroscopy. It is unclear from the work with sensitized nanocrystalline electrodes19 whether this stretched exponential is caused by surface trapping in the recombination process or by a real and varying rate for reduction of the oxidized dye that deviates from a Marcus model because of the local surface structure of the attached dye layer. At monolayer coverage of the dye, the concentration of the chromophores is at the molar level, and with adsorbed regenerator, it is not unreasonable to expect the redox chemistry occurring at the surface to be heterogeneous and to deviate from that of the isolated monomeric dye. In contrast to the images of Figure 2b and c, however, highly regular surface structures for squaraine dyes have been observed through AFM at SnS2 surfaces,4 and well-ordered systems such as this offer possibilities to investigate the correlation of dye surface structure with back reaction rates. Another experimental route would be through the study of current−voltage curves for quantum dot (QD) sensitized semiconductors where dyes are absent and the Coulombic attraction of an injected electron with the remaining positive charge is expected to be quite different due to delocalization in the QD.

■

ASSOCIATED CONTENT

S Supporting Information *

Additional figures and experimental details are provided. This material is available free of charge via the Internet at http:// pubs.acs.org.

■

AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors wish to acknowledge the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Biosciences, for financial support through grant DE-FG03-96ER14625. K.J.W. also acknowledges graduate student support from the J. E. Warren I

DOI: 10.1021/jp511438j J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B

(22) Laskova, B.; Zukalova, M.; Kavan, L.; Chou, A.; Liska, P.; Wei, Z.; Bin, L.; Kubat, P.; Ghadiri, E.; Moser, J. E.; et al. Voltage Enhancement in Dye-Sensitized Solar Cell Using (001)-Oriented Anatase TiO2 Nanosheets. J. Solid State Electrochem. 2012, 16, 2993− 3001. (23) Kilså, K.; Mayo, E. I.; Kuciauskas, D.; Villahermosa, R.; Lewis, N. S.; Winkler, J. R.; Gray, H. B. Effects of Bridging Ligands on the Current−Potential Behavior and Interfacial Kinetics of RutheniumSensitized Nanocrystalline TiO2 Photoelectrodes. J. Phys. Chem. A 2003, 107, 3379−3383. (24) Anderson, A. Y.; Barnes, P. R. F.; Durrant, J. R.; O’Regan, B. C. Quantifying Regeneration in Dye-Sensitized Solar Cells. J. Phys. Chem. C 2011, 115, 2439−2447.

Chair of Energy and Environment at the University of Wyoming.

■

REFERENCES

(1) Spitler, M. T.; Parkinson, B. A. Dye Sensitization of Single Crystal Semiconductor Electrodes. Acc. Chem. Res. 2009, 42, 2017−2029. (2) Sambur, J. B.; Novet, T.; Parkinson, B. A. Multiple Exciton Collection in a Sensitized Photovoltaic System. Science 2010, 330, 63− 66. (3) Choi, D.; Rowley, J. G.; Spitler, M.; Parkinson, B. A. Dye Sensitization of Four Low Index TiO2 Single Crystal Photoelectrodes with a Series of Dicarboxylated Cyanine Dyes. Langmuir 2013, 29, 9410−9419. (4) Takeda, N.; Parkinson, B. A. Adsorption Morphology, Light Absorption, and Sensitization Yields for Squaraine Dyes on SnS2 Surfaces. J. Am. Chem. Soc. 2003, 125, 5559−5571. (5) Rowley, J. G.; Parkinson, B. A. Simultaneous Measurement of Absorbance and Quantum Yields for Photocurrent Generation at DyeSensitized Single-Crystal ZnO Electrodes. Langmuir 2013, 29, 13790− 13796. (6) Ryan, M. A.; Fitzgerald, E. C.; Spitler, M. T. Internal Reflection Flash Photolysis Study of the Photochemistry of Eosin at Titania Semiconductor Electrodes. J. Phys. Chem. 1989, 93, 6150−6156. (7) Spitler, M. T. One Dimensional Onsager Model for Dye Sensitized Charge Injection Into Semiconductors. J. Electroanal. Chem. Interfacial Electrochem. 1987, 228, 69−76. (8) Charlé, K.-P.; Willig, F. Generalized One-Dimensional Onsager Model for Charge Carrier Injection Into Insulators. Chem. Phys. Lett. 1978, 57, 253−258. (9) Lu, Y.; Jaeckel, B.; Parkinson, B. A. Preparation and Characterization of Terraced Surfaces of Low-Index Faces of Anatase, Rutile, and Brookite. Langmuir 2006, 22, 4472−4475. (10) Ushiroda, S.; Ruzycki, N.; Lu, Y.; Spitler, M. T.; Parkinson, B. A. Dye Sensitization of the Anatase (101) Crystal Surface by a Series of Dicarboxylated Thiacyanine Dyes. J. Am. Chem. Soc. 2005, 127, 5158− 5168. (11) Lu, Y.; Spitler, M. T.; Parkinson, B. A. Photochronocoulometric Measurement of the Coverage of Surface-Bound Dyes on Titanium Dioxide Crystal Surfaces. J. Phys. Chem. B 2006, 110, 25273−25278. (12) Lu, Y.; Spitler, M. T.; Parkinson, B. A. Regenerator Dependent Photoinduced Desorption of a Dicarboxylated Cyanine Dye From the Surface of Single-Crystal Rutile. Langmuir 2007, 23, 11637−11642. (13) O’Donnell, R. M.; Ardo, S.; Meyer, G. J. Charge-Screening Kinetics at Sensitized TiO 2Interfaces. J. Phys. Chem. Lett. 2013, 4, 2817−2821. (14) Wang, Y.; Wang, X.; Lu, H. P. Probing Single-Molecule Interfacial Geminate Electron−Cation Recombination Dynamics. J. Am. Chem. Soc. 2009, 131, 9020−9025. (15) Ardo, S.; Sun, Y.; Staniszewski, A.; Castellano, F. N.; Meyer, G. J. Stark Effects After Excited-State Interfacial Electron Transfer at Sensitized TiO2 Nanocrystallites. J. Am. Chem. Soc. 2010, 132, 6696− 6709. (16) Bak, T.; Nowotny, M. K.; Sheppard, L. R.; Nowotny, J. Mobility of Electronic Charge Carriers in Titanium Dioxide. J. Phys. Chem. C 2008, 112, 12981−12987. (17) Lu, Y.; Choi, D.-J.; Nelson, J.; Yang, O.-B.; Parkinson, B. A. Adsorption, Desorption, and Sensitization of Low-Index Anatase and Rutile Surfaces by the Ruthenium Complex Dye N3. J. Electrochem. Soc. 2006, 153, 131−137. (18) Ehret, A.; Stuhl, L.; Spitler, M. T. Spectral Sensitization of TiO2 Nanocrystalline Electrodes with Aggregated Cyanine Dyes. J. Phys. Chem. B 2001, 105, 9960−9965. (19) Hagfeldt, A.; Boschloo, G.; Sun, L.; Kloo, L.; Pettersson, H. Dye-Sensitized Solar Cells. Chem. Rev. 2010, 110, 6595−6663. (20) Jackson, J. D. Classical Electrodynamics, 3rd ed.; John Wiley & Sons Inc: New York, 1998. (21) Muntwiler, M.; Yang, Q.; Tisdale, W.; Zhu, X. Y. Coulomb Barrier for Charge Separation at an Organic Semiconductor Interface. Phys. Rev. Lett. 2008, 101, 196403(1)−196403(4). J

DOI: 10.1021/jp511438j J. Phys. Chem. B XXXX, XXX, XXX−XXX