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Correlations between Photovoltaic Characteristics, Adsorption Number, and Regeneration Kinetics in Dye-Sensitized Solar Cells Revealed by Scanning Photocurrent Microscopy Masaaki Mitsui, Yuya Kawano, Kyosuke Mori, and Naoto Wakabayashi Langmuir, Just Accepted Manuscript • Publication Date (Web): 11 Jun 2015 Downloaded from http://pubs.acs.org on June 12, 2015

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Correlations between Photovoltaic Characteristics, Adsorption Number, and Regeneration Kinetics in Dye-Sensitized Solar Cells Revealed by Scanning Photocurrent Microscopy Masaaki Mitsui,1* Yuya Kawano,2 Kyosuke Mori,1 Naoto Wakabayashi1 1

Department of Chemistry, College of Science, Rikkyo University, 3-34-1, Nishiikebukuro,

Toshima-ku, Tokyo, 171-8501, Japan. 2

Department of Chemistry, Graduate School of Science, Shizuoka University, 836 Ohya, Suruga-

ku, Shizuoka 422-8529, Japan.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]

ACS Paragon Plus Environment

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ABSTRACT

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Newly developed simultaneous scanning photocurrent and luminescence

microscopy was applied to ruthenium-based dye-sensitized solar cells (DSCs) comprising a cover glass photoanode with a 100-nm-thick TiO2 layer. Using this, we have investigated the lateral variations of several parameters of these DSCs under short-circuit conditions. Simultaneous measurement of photocurrent and luminescence images for the same area of the DSC demonstrated submicrometric lateral resolution of our photocurrent microscopy, which is approximately 10-fold better than the resolution of photocurrent microscopy used in past studies. The photovoltaic parameters, such as short-circuit current density, open-circuit voltage, and charge-collection efficiency, were thus evaluated for local (or submicrometric) regions of the DSCs. Furthermore, the photocurrent saturation behavior of the DSCs was examined as a function of the excitation rate and analyzed on the basis of a three-state kinetic model. This protocol allowed for quantification of the dye adsorption number and dye regeneration rate constant for any local area of the DSCs. Consequently, the correlations between the dye adsorption number, photovoltaic parameters, and regeneration rate constant, which are difficult to address through examination of the entire cell, were revealed by the “zoom-in” approach utilizing this high-resolution photocurrent microscopy.


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1. INTRODUCTION

Dye-sensitized solar cells (DSCs) continue to arouse tremendous interest as prospective alternatives to conventional solar cells because of their low fabrication cost and relatively high energy conversion

efficiency.1–4

DSCs

are composed

of dye-adsorbed

mesoporous

semiconductor films and redox electrolyte (most commonly a combination of TiO2 and I−/I3−), which are sandwiched between two transparent electrodes. Photoelectric conversion in DSCs proceeds by photooxidation of the adsorbed dye molecules, which separate charge carriers by injecting photoexcited electrons into the conduction band of the semiconducting electrode, followed by reduction of the photooxidized dyes (referred herein as S+) by redox couples in the electrolyte (i.e., dye regeneration). It is well known that these crucial processes occur at significantly heterogeneous semiconductor/dye/electrolyte interfaces, which are accompanied by a variety of adsorption densities, binding modes, and aggregation formation of adsorbed dye molecules.3–7 Furthermore, concentration gradients and nonuniform adsorption of electrolyte compositions across the semiconductor surface can also be formed under short-circuit operation.8 These facts suggest lateral nonuniformity of photovoltaic characteristics and interfacial photoconversion kinetics in DSCs. Scanning photocurrent microscopy (SPCM or laser beam induced current technique) is a spatially resolved characterization technique that has long been used for research of semiconductor and photovoltaic devices.9−11 In recent times, this technique has also been applied to DSCs.5,11–14 and quantum dot sensitized photoelectrode systems.15 Photocurrent imaging has been utilized to examine nonuniform distribution of photocurrents in DSCs,5 dye photostability,


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reasons for dye degradation,12,13 and

two-dimensional

dye

coverage.7 More recently, the electron diffusion length in a nanoporous TiO2 layer of a DSC was directly estimated using the SPCM technique.16,17 Previously, SPCM measurements have been implemented with relatively low spatial resolutions (several µm) as

Figure 1. Schematic of the SPCM setup equipped with an oil-immersion objective lens. Ru(bpy)2(dcbpy)2+ dyesensitized solar cell device with a TiO2/ITO-coated cover glass photoelectrode, dedicated to submicrometric SPCM measurements.

a “dry” objective lens is used, which has a low numerical aperture (i.e., N.A. < 1). In this study, ruthenium-based dyesensitized solar cells having a cover glass photoanode were fabricated, allowing us to analyze the DSC devices using an oil-immersion objective lens (N.A. > 1), as depicted in Figure 1. This setup dramatically improved the spatial resolution of SPCM by a factor of 10, compared with previous work. Consequently, the photovoltaic characteristics, such as short-circuit current density (Jsc) and open-circuit voltage (Voc), for a submicrometric area of the DSCs were evaluated. Furthermore, the excitation rate dependence of the photocurrent, quantitatively derived dye adsorption number (N), and dye regeneration rate constant (kreg) were determined within a local area of the DSCs. Such evaluation for a number of local positions in the DSC samples revealed correlations between these parameters. 2. EXPERIMENTAL SECTION


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2.1.

Cell Fabrication. All solvents (analytical grade) used in this study were purchased from

Wako Pure Chemical Industries and used without further purification. DSCs for SPCM measurements were prepared as follows. The titanium dioxide (TiO2) thin films were prepared by spin coating (3000 rpm for 60 s) one drop of Ti-Nanoxide HT-L/SC paste, containing approximately 3 wt% of 8–10 nm TiO2 anatase particles (Solaronix), onto thoroughly cleaned indium tin oxide (ITO)-coated cover glasses, 10 Ω/□ (Matsunami), and sintering at 250 °C for 30 min. This TiO2 paste was used to produce a highly transparent scaffolding thin film approximately 100 nm thick (roughly 2 × 1013 nanoparticles/cm2), as measured by atomic force microscopy (SPM-9700, Shimadzu), and suppress light scattering effects upon tightly focused light illumination. Such a thin film shortens the electron diffusion length in TiO2 and is thereby expected to increase the collection efficiency of photoinjected electrons (ηcc), because of the reduction of recombination probability of injected electrons with oxidized dye molecules and/or oxidized redox species. Furthermore, the cover glass TiO2 electrode allows for the use an oilimmersion objective lens with a high N.A., as shown in Figure 1. The obtained TiO2 films were carefully shaped to 5 × 5 mm2 and sonicated for 20 min in ethanol. The films were then soaked in

low

concentration

dying

solutions

of

cis-bis(2,2′-bipyridine)-(4,4′-dicarboxy-2,2′-

bipyridine)ruthenium(II), abbreviated as Ru(bpy)2(dcbpy)2+, (Solaronix, see Figure 1) and kept at room temperature for 1 d. Although this ruthenium dye does not exhibit excellent photovoltaic performance,18,19 it was selected because of its relatively high photoluminescent yield and photochemical stability.20 These properties enable us to implement simultaneous photocurrent and luminescence measurements. Then, the sensitized films were repeatedly rinsed and sonicated in acetonitrile to remove the loosely bound dye molecules. The platinized counter electrode was obtained by spreading a Pt-based solution (Platisol T/SP, Solaronix) on a conductive glass sheet


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(fluorine doped tin oxide) of 15 × 40 mm2 and heating at 450 °C for 30 min. To construct a complete solar cell, the counter electrode was assembled with a thermal adhesive film (Meltonix 1170-25PF, Solaronix) that served as a spacer and sealing element. The commercial iodide-based redox electrolytes were obtained from Solaronix (Iodolyte Z-50) and contained the I−/I3− redox couple ([I−] = 1 M, [I2] = 50 mM), ionic liquid, N-alkylbenzimidazole, and guanidinium thiocyanate in 3-methoxypropionitrile solution. In the fabrication of DSCs with different I− concentrations, we used three homemade electrolytes having 0.4, 0.6, and 1.1 M 1-propyl-3methyl imidazolium iodide (PMII). All contained 0.3 M benzimidazole, 0.05 M guanidinium thiocyanate, and 50 mM iodine in 3-methoxypropionitrile. For 0.6 and 0.4 M samples, we replaced

PMII

with

1-propyl-3-methylimidazolium-bis(trifluoromethylsulfonyl)imide

(PMITFSI) to maintain a constant PMI+ concentration. To estimate the amount of Ru(bpy)2(dcbpy)2+ adsorbed on TiO2, a 5 cm2 dye-adsorbed TiO2 film was fabricated by spin coating the same TiO2 paste on an ITO-coated glass sheet (25 × 80 mm2). The amount of desorbed dye was determined from the absorbance at 441 nm, recorded on a UV-Vis spectrometer (Lambda 650, Perkin-Elmer), where dye molecules were completely detached from the film by dipping it in 10 mL of 0.1 M aqueous NaOH for 10 min. 2.2.

Photocurrent and Luminescence Measurements. Simultaneous photocurrent and

luminescence microscopy measurements were performed on a homemade laser scanning optical microscope. A detailed description of the laser scanning method and optical setup of our microscope have recently been published elsewhere.21 The excitation light was provided by a 441 nm pulsed diode laser (PLP10-044C, Hamamatsu Photonics) operating at 100 MHz and a pulse width of approximately 70 ps full-width at half-maximum (FWHM). The circularly polarized light, which allows for excitation of all in-plane dye orientations of the molecular


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transition dipole moment, was focused on a DSC from the TiO2-electrode side using an oilimmersion objective lens (100×, N.A. = 1.4, Olympus) to form a diffraction-limited spot size in the electrode plane. It must be emphasized that this laser spot size is approximately an order of magnitude smaller than that in past studies using the light beam induced current technique,5,7,9–17 which allows us to perform higher spatial resolution photocurrent measurements of the DSCs. As shown in Figure 1, photocurrent measurements of the DSCs were conducted at short-circuit using a picoammeter (6487, Keithley Instruments). Fluorescence photons from the DSC samples were collected through the same objective, filtered using a 75 µm diameter pinhole for rejection of out-of-focus background, and directed onto an avalanche photodiode detector (APD; SPCMAQR-14, Perkin-Elmer). The signals from the APD were sent to a time-correlated single photon counting (TC-SPC) card (TimeHarp 200, PicoQuant) in the time-tagged and time-resolved mode. Data acquisition was performed using SymPhoTime v5.2.4 (PicoQuant) software. Initially, we measured current density versus voltage (J–V) curves and the excitation rate dependence of the photocurrent under wide illumination of the excitation laser through a shadow mask (i.e., light-exposed volume of approximately 0.2 cm2 × 100 nm). Then, such measurements were conducted under local (or submicrometric) illumination conditions, where a volume of approximately 1.37 × 10−9 cm2 × 100 nm of cells were exposed to the excitation laser light. In the SPCM measurements, photocurrent and luminescence images of the sample were simultaneously acquired by raster scanning of the laser focal spot. Then, an electronic shutter was used to block the excitation laser light. After the laser focus was moved to the position of interest, the shutter was reopened at the start time of data acquisition. We measured the excitation rate dependence of photocurrent by changing the laser intensity stepwise from high intensity to low intensity. At each laser intensity, a photocurrent time trace was recorded for 60 s.


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This procedure was adopted for both wide and local illumination measurements. After this series of measurements was completed, J–V curves were recorded by scanning the applied voltage from −0.2 to 0.2 V under dark (unilluminated) and light (illuminated) conditions. The imaging and positioning process, as well as the J–V measurements, homemade

were

LabView

controlled programs.

by The

abovementioned SPCM measurements were performed for 30–100 local positions in each cell to construct histograms and correlation plots of photovoltaic multiparameters. All measurements were conducted at room temperature.

3. RESULTS and DISCUSSION It is well known that the photocurrent response of DSCs is relatively slow, with typical time constants on the order of milliseconds to seconds depending on light intensity, and the photocurrent signal does not immediately appear/disappear. Therefore, a methodology for correcting this effect on

Figure 2. (a) Photocurrent time traces of a Ru(bpy)2(dcbpy)2+-DSC obtained under wide illumination (89 µW/cm2) and local illumination (13.4 kW/cm2) with a 441 nm laser light. The photocurrent integration time was 167 and 1.67 ms, respectively. (b) Photocurrent and (c) luminescence images simultaneously recorded for the same area in a Ru(bpy)2(dcbpy)2+-DSC. The intensity profiles along the dashed line in b and c exhibit a diffraction-limited width (FWHM) of 209 nm and 182 nm, respectively, for the unintentional nanostructure that exists in the DSC. Scale bar: 1 µm.

the photocurrent image has been developed by Navas el al.11,14 However, as can be seen


8

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in Figure 2a, the DSC fabricated in this study exhibits very fast photocurrent responses of less than 1 ms for both the charge and discharge processes under local (or submicrometric) light illumination conditions. A previous study has shown that the photocurrent response becomes progressively faster as the light intensity increases, where a rise time of 8 ms was observed at 4 mW/cm2.22 In our SPCM measurements, much higher light intensities (1–10 kW/cm2) were applied to a submicrometric area of the cell so that high electron densities in the TiO2 film could be locally and transiently produced. This perhaps allows for high electron mobility in the TiO2 film, as the electron diffusion coefficient is strongly dependent on trap occupancy (i.e., quasiFermi level for electrons) in the film.3,23,24 As will be discussed later, approximately 100% of injected electrons generated by local illumination will reach the back contact and flow to the external circuit (i.e., charge-collection efficiency, ηcc ≈ 1). Because of the fast response of the present cells, the photocurrent image was obtained without any corrections, as displayed in Figure 2b. The luminescence image simultaneously recorded for the same area is also shown in Figure 2c. The studied DSCs possess a very thin TiO2 layer of approximately 100 nm thick to suppress light-scattering effects, which may deteriorate the lateral resolution of the photocurrent image. The axial length (in the z direction) of the diffraction-limited focal volume is estimated to be approximately 500 nm, which is much larger than the thickness of the TiO2 film used. Thus, all dyes residing in the z direction of the focal volume are exposed to the incident light. As shown in Figure 2b, the intensity profile exhibits a FWHM of 209 ± 18 nm, which is slightly worse than the Abbe diffraction-limited lateral resolution of 158 nm. Therefore, the effective light-exposed area and volume at local illumination are estimated to be 1.37 × 10−9 cm2 and 1.37 × 10−14 cm3, respectively. In Figure 2c, the corresponding luminescence profile obtained with the confocal optical arrangement displays a comparable FWHM of 182 ± 20 nm, ensuring negligible


9

light

intensity.

The

observed

nanostructure in Figure 2b and c is likely because of increased local thickness of the TiO2 film, allowing for increased adsorption

1.0

(a) Jlight 0.5

−0.1

0.2

Jdark 0.0

cm2

area

of

the

Ru(bpy)2(dcbpy) - DSC with a 441 nm laser beam, whereas typical J–V curves obtained by the photoexcitation of a

200

0.05

0.10

22

(b)

150

Jlight 100

−0.05

50

Figure 3b. From these, we derived values for the short-circuit current density and the open-circuit voltage. The corrected current were

calculated

by

subtracting the dark current density (Jdark) from the light current density (Jlight), i.e., Jcor = Jlight − Jdark. They were plotted against the

0.00

0.05

0.10

Voltage / V

Jdark

0 0.00

0.05

0.10

Voltage / V

submicrometric region of the photoactive layer (i.e., 1.37 × 10−9 cm2) are shown in

20

18

-0.05

(Jcor)

0.00

Voltage / V

2+

densities

0.1

0.0

Voltage / V

−0.05

Figure 3a shows J–V curves measured by a

0.10

0.05

and/or uptake of dye.

illuminating

0.15

Jcor / Acm− 2

applied

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Jcor / µAcm− 2

light-scattering effects within the range of

Current density / Acm−2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Current density / µAcm− 2

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Figure 3. Current density versus voltage (J–V) curves under dark (dashed line) and light (solid line) conditions, recorded for a 2+ Ru(bpy)2(dcbpy) -DSC at (a) wide illumination with a 441 nm laser light with an intensity of 56 µW/cm2 and (b) local illumination (12.8 kW/cm2). Insets in a) and b) show corrected photocurrent density (Jcor) obtained by subtracting dark current density (Jdark) from light current density (Jlight). Dashed lines in the insets indicate the saturation value of Jcor.

applied voltage and are displayed as insets in Figure 3a and b. In both cases, the photocurrent densities increased with the applied negative voltage and became nearly constant below −0.05 V and −0.08 V. If charge-collection efficiency of the DSC device is unity, in principle, the


10

should

not

increase

by

0.8

(a)

η cc

photocurrent

increase in Jcor indicates that there is a slight loss of injected electrons. The value

(c)

20

1

2

kex /

value of Jcor at 0 V by the saturation value 25

of Jcor in a region of negative voltage.

illumination

respectively. efficiency

The

depends

on

the

excitation

intensity (Pex), as the electron concentration in TiO2 influences the recombination efficiency

of

injected

oxidized

dyes

and/or

electrons oxidized

with redox

species at the TiO2/electrolyte interface.26 To verify this effect, the dependence of ηcc on the excitation rate constant (kex) was examined

under

wide

and

local

illumination conditions, each example of which is depicted in Figure 4a and b. The kex value was calculated by the equation

2

4

6

8

10

kex / 105 s-1

(f)

10 0 20

40

60

Time / s

(g)

S*

kinj

conditions,

charge-collection

0

50 100 Occurrence

kex

local

0

(e)

values of 0.74 and 0.98 for ηcc under wide and

4

10

10-3 s-1

20

0

From the data given in Figure 3, we derived

3

(d) 20

30

Photocurrent / nA

of ηcc can be estimated by dividing the

(b)

0.9 30

40

0

1.0

Photocurrent / nA

applying a negative voltage. Thus, the

Photocurrent / nA

0.6

0

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η cc

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kS*

S+ kS+ = krg[I−] + kcr[e−]

S0 Figure 4. (a, b) Charge collection efficiency (ηcc) and (c, d) short-circuit photocurrent (I) as a function of the excitation rate (kex) under wide and local illumination conditions, respectively. The solid lines represent the best fits of the I−kex plots. (e) Photocurrent time trace (integration time 16.7 ms) recorded under local illumination at a light intensity of 12.8 kW/cm2 (kex = 1.4 × 106 s−1), along with (f) the corresponding histogram. (g) Schematic of a three-state model comprising the electronic ground state (S0), first excited state (S*), and oxidized state (S+) of the adsorbed dye. The sensitizer dye is photoexcited with an excitation rate of kex, followed by ultrafast electron injection (kinj) into the conduction band of TiO2. The formed dye cation (S+) is re-reduced by the redox species (kreg[I−]) and/or charge recombination with the injected electrons in TiO2 (kcr[e−]).


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given below:

k ex =

Pex σλ , hc λ

(1)

where Pex is the excitation laser intensity in Wcm−2, σλ is the absorption cross-section at the excitation wavelength (λ), c is the light velocity, and h is the Planck constant. The value of σ441 = 5.0 × 10−17 cm2 for Ru(bpy)2(dcbpy)2+ in acetonitrile was used in the calculation of kex. Under wide illumination conditions, ηcc became nearly constant in the region of kex > 1 × 10−3 s−1 (Figure 4a). More remarkably, the value of ηcc under local illumination was independent of kex and almost reached unity (> 0.95), as can be seen in Figure 4b. This is because the use of a very thin layer of TiO2 (approximately 100 nm thick) allows the photoinjected electrons to approach much closer to the back contact, compared with conventional DSCs whose film thicknesses are typically 5–10 µm.1–4 Both the short-circuit and high light intensity conditions applied in this study enhance the diffusion of injected electrons in the film.23,24 This is consistent with the fast photocurrent response of the present cells (< 1 ms), as mentioned above. Furthermore, the electrolyte used contains guanidinium cations, which are known to suppress charge recombination efficiency.27 Consequently, almost all injected electrons can rapidly reach the contact without recombination loss. Figure 4c and d show the dependence of the short-circuit photocurrent (hereafter referred to as I) on kex, which were obtained under wide and local illumination conditions, respectively. As illustrated in Figure 4e, the photocurrent time traces were measured for 60 s at each laser intensity. The average photocurrent values determined from Gaussian fits (e.g., Figure 4f) are plotted against kex in Figure 4c and d. In the applied range of kex, we did not observe any decline


12

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in the photocurrent over ten minutes, indicating that there is no photodegradation of the chemisorbed dyes, even at light intensities exceeding 10 kW/cm2. In contrast, the emission intensity rapidly decreased even though it was under much weaker light illumination (data not shown). This indicates that luminescent Ru(bpy)2(dcbpy)2+ molecules are readily photobleached and do not contribute to the photocurrent generation. Such “bad dyes,” which either do not undergo electron injection or inject photoexcited electrons at a very slow rate, have also been found in Ru(bpy)2(dcbpy)2+-sensitized mesoporous TiO2 films and are attributed to the unbound dye that is trapped within the pores of the film.20 As is evident in Figure 4c, the photocurrent under wide illumination linearly increases with increasing kex. This linearity indicates that the photocurrent is not dominated by diffusion of iodide or triiodide ions in the electrolyte.28 Conversely, the I−kex plot obtained under local illumination (Figure 4d) shows nonlinear behavior. Under these conditions, photooxidized dyes can be formed at a considerably high density within the extremely small focal volume of 1.37 × 10−14 cm3. This most likely decreases the local concentration of I− in the light-exposed space of the TiO2 film. Thus, local I− depletion may be a source of photocurrent saturation under local illumination. However, photocurrent saturation is mainly because of the fact that the excitation rate constant becomes comparable to the decay rate constant of the oxidized dyes (kS+), which will be discussed later. To analyze theses dependencies, we herein propose a simple three-state model of the electronic ground state (S0), excited singlet state (S*), and photooxidized state (S+) of the dye, as depicted in Figure 4g. For Ru(bpy)2(dcbpy)2+, a significant proportion of the electron injections occur from the unrelaxed, vibrationally hot, and singlet metal-to-ligand charge transfer states (S* or 1MLCT) within 100 fs.20 The electron injections from the triplet state (T* or 3MLCT) formed via ultrafast intersystem crossing (ISC) also contribute to the


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electron injection efficiency (Φinj). However, the ISC from 1MLCT to 3MLCT (kisc) and subsequent electron injection (3kinj) are much faster (subpicosecond) than deexcitation from the S* state (kS*) and reduction of S+ (kS+).20 Thus, electron injection can be seemingly regarded as occurring from one electronic excited state. Indeed, a four-state model of S0, S*, T*, and S+ under 1kinj, kisc, 3kinj >> kS*, kS+ conditions rendered the same result as the threestate model (S0, S*, and S+) with 1kinj >> kS*, kS+. We also assumed that dye regeneration is first order in the concentration of S+. This is because self-exchange hole-transfer along the monolayer of Ru-polypyridyl sensitizers was observed on a micro- to millisecond timescale under most conditions,29 which is much slower than the timescale of the dye regeneration process (typically 10−8–10−6 s).3,8 Considering the aforementioned assumptions, the kinetic equations of the three-state model are expressed by the following equations: dN S0 dt

= − kex N S0 + kS* N S* + kS+ N S + ,

(2)

dN S* = k ex N S0 − ( kS* + kinj ) N S* , dt

dNS+ dt

= − kS+ NS+ + kinjNS* ,

(3)

(4)

where NS0, NS*, and NS+ represent the number of molecules in the S0, S*, and S+ states, respectively, kS+ is the sum of the rate constant for dye regeneration (kreg[I−]) and the recombination rate constant between S+ and injected electrons (kcr[e−]): kS+ = kreg[I−] + kcr[e−].

(5)


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In this equation, the order of the reaction was set to be 1 in iodide.8 The number of adsorbed dye molecules per light-exposed volume (denoted as N) corresponds to the sum of the number of molecules in the S0, S*, and S+ states under steady-state approximation as follows: N = N S0 + N S* + N S + .

(6)

Because of the mesoporous structure of the TiO2 film, the transition dipole moments of adsorbed dyes should be randomly oriented in the projected plane of the circularly polarized electric vector. Therefore, the photocurrent is given by the following equation:

I=

3 1 e kinj NS* ηcc , 5

(7)

where e is the elementary charge. The coefficient of 3/5 corresponds to the orientational averaging of adsorbed dyes with random orientation.30 By solving equations 2–4 and 6 with the reasonable assumption that 1kinj >> kS* and 1kinj >> kS+, I is derived as follows:

I =

3 kex eNηcc . 5 1 + kex kS+

(8)

Under wide illumination conditions, kex is approximately 10−3 s−1, which is much smaller than other rate constants. In this case, it is conceivable that all the molecules are in the S0 state (i.e., N = NS0) when photoexcited, and thus the photocurrent (I) should show a linear dependence against kex as follows:

I =

3 eNΦ injηcc kex . 5

(9)


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Here we further assume 100% electron injection (i.e., Φinj = 1) of Ru(bpy)2(dcbpy)2+ into TiO2. This is because the electron injection rate constants from the singlet and triplet MLCT states (1kinj and 3kinj, respectively) are known to exceed 1012 s−1, which is approximately 106 larger than the decay rate constant of the excited state lifetime in the absence of injection.20 Furthermore, luminescent dyes, which are apparently minor constituents, should make almost no contribution to photocurrent generation. Therefore, eq 9 is expressed as follows:

I =

3 eNηcc kex . 5

(10)

Under wide illumination (Figure 4c), the portion of the I−kex plot, where ηcc is constant, is fitted by eq 10, yielding N = 1.7 × 1014, which corresponds to 145 µmol/cm3, based on the volume of wide illumination. Five DSC samples were similarly analyzed, resulting in adsorption densities that fell within the range of 110–160 µmol/cm3, which is in accordance with 138 µmol/cm3, determined by the dye desorption experiment (see Experimental section for details). This agreement corroborates the validity of the analysis mentioned above. Conversely, under local illumination of the same cell, the best fit of the I−kex plot (Figure 4d) was obtained by eq 8, with N = 6.6 × 105 molecules (80 µmol/cm3, based on the experimentally estimated irradiated volume of 1.37 × 10−9 cm2 × 100 nm) and kS+ = 8.6 × 105 s−1. Figure 5a shows the histogram of N obtained for 118 different local positions in the DSC sample in Figure 4. The mean value of N determined from a Gaussian fit of the histogram was (1.1 ± 0.6) × 106 molecules, which corresponds to 132 µmol/cm3. Comparable dye adsorption densities obtained under wide and local illumination conditions indicated that the present photocurrent saturation analysis provides a reliable estimate for N in a submicrometric area of the DSCs.


16

and

1

kinj >> kS+ ≈ kex, N/2

molecules should remain in the +

NS+

oxidized state (S ), i.e.,

=

N/2, while the other half are in the S0 state, i.e., NS0 = N/2. The average

value

approximately

of

N

30

which

105 dye cations are formed within the light-exposed volume of 1.37 × 10−17 L. At an iodide 1.0

(b)

20 10

80

(c)

40

1.0

106,

of

(a)

is

means that approximately 5 ×

concentration

occurrence

approximation with 1kinj >> kS*

Voc / mV

steady-state

M,

ηcc

Under

(d) Normalized occurrence

0.9 12

kS+ / 105 s− 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Jsc / Acm− 2 Normalized

Page 17 of 27

(e)

(f)

8 4 0.0

0.5

1.0

1.5

2.0

approximately 8 × 10 iodide

N / 106

ions reside in the same volume,

Figure 5. (a) The number of adsorbed dyes per lightexposed surface area (N), (b) short-circuit current density (Jsc), (c) open-circuit voltage (Voc), (d) charge-collection efficiency (ηcc), and (e) decay rate constant of oxidized dye (kS+) as a function of N.

6

which is 16 times larger than that of S+ estimated above. It has

been

reported

that

photocurrent saturation was not observed at a 10:1 ratio of I− to adsorbed dye, but was observed at a 1:1 ratio.8 Hence, we considered that the observed photocurrent saturation is mainly caused by the comparability of kex to kS+ under local illumination conditions. As can be seen in Figure 5b and c, the short-circuit current density and open-circuit voltage


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increase almost linearly as N increases. We also found that there was a positive correlation (correlation coefficient: r = +0.82) between Jsc and Voc (Figure S1, Supporting Information). Since Voc is determined by the difference between the electron quasi-Fermi level in the TiO2 film under illumination and the redox electrolyte level in the dark, higher electron density (i.e., higher Jsc) raises the quasi-Fermi level in TiO2, resulting in an improved Voc. Under local illumination, short-circuit photocurrent density was extremely large (i.e., several tens of A/cm2), while the net photocurrent was only 1–100 nA (e.g., Figure 4d). However, the values of Voc are very small (50–100 mV) compared to the reported values for Ru(bpy)2(dcbpy)2+-DSCs (approximately 500 mV).19 The most probable explanation is that the virtual photocurrent density rapidly declines within the timescale of photocurrent measurements in the J–V curve experiment (approximately 180 ms), because of rapid electron diffusion in the TiO2 film, as mentioned above. The resultant small photocurrent density results in very small Voc. In Figure 5d, the values of ηcc for any local position were almost unity (ηcc = 0.9–1.0), indicating the negligible contribution of the charge recombination process under local illumination conditions. Thus, the second term in eq 5 can be ignored; that is, kS+ = kreg[I−].

(11)

Since the regeneration efficiency (Φreg) is defined as follows

Φ reg =

k reg [ I - ] k cr [e - ] + k reg [ I - ]

,

(12)


18

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it was found that Φreg almost reaches unity under local illumination conditions (i.e., Φreg ~1). The data exemplified in Figure 5 were obtained for the DSCs where a commercially available electrolyte (Iodolyte Z-50) containing 1.0 M iodide was used. Therefore, the rate constant of kS+ is directly related to that of dye regeneration (kreg). The plot of kS+ against N is illustrated in Figure 5e. The histogram of kS+ in Figure 5f yields the average value of kS+ as 7.7 × 105 M−1s−1, which is thus regarded as that of kreg. It is necessary to corroborate the proportionality in eq 11; therefore, the same analyses were performed by varying the I− concentration from 0.4 to 1.1 M in the DSC electrolytes. The DSC sample with [I−] = 0.1 M was also examined, but the photocurrent was found to be independent of the excitation rate. This can be ascribed to the effect of I− shortage;8 at [I−] = 0.1 M, the ratio of I− to S+ reaches approximately 1:1.

3

(a)

obtained through multipoint analysis of the

N / 106

In Figure 6, the average values of N and kS+,

DSCs with [I−] = 0.4, 0.6, and 1.1 M

plotted against [I−]. As is evident in Figure 6a, N does not depend on [I−] and comparable values were obtained for these cells, whereas kS+ clearly exhibits a linear

2 1 0

(Figure S2, Supporting Information), are

10 kS+ / 105 s−1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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(b)

5 0.4

value of (7.5 ± 0.7) × 105 M−1s−1 for kreg. This value shows good agreement with the

0.8

1.0

1.2

-

[I ] / M

dependence against [I−] (Figure 6b). The slope of the linear fit of the data gave a

0.6

Figure 6. Plots of (a) N versus [I−] and (b) kS+ versus [I−]. The data obtained are for DSCs using homemade electrolytes containing 0.4, 0.6, and 1.1 M iodide. The solid line shows the linear least squares fit of the data in (b).


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estimated value of kreg (or kS+) for the DSC using commercially available electrolyte ([I−] = 1.0 M), as mentioned above. Although no literature values of kreg for complete Ru(bpy)2(dcbpy)2+-DSC device samples have been reported, the kreg for Ru(bpy)2(dcbpy)2+ adsorbed on SnO2 film substrates immersed in an acetonitrile solution of LiI was reported to be 1.2 × 1010 M−1s−1,31 which was determined by monitoring the recovery of photobleached molecules in the ground state absorption of the dye under a large pulse energy of 5 mJcm−2pulse−1. Surprisingly, this was approximately 104 times larger than the kreg value obtained in this study. However, as indicated by O’Regan et al.,8 the charge recombination apparently increases the regeneration rate constants, particularly under high excitation intensities, as it is impossible to correctly separate the effects of regeneration and charge recombination on transient absorption decays. Correlating transient absorbance decays with short-circuit current density and electron concentration, they have succeeded in providing a reliable estimate of kreg for Ru complex dye (N719)-sensitized solar cells. It was determined to be 7.8 × 105 M−1s−1 in the 3-methoxypropionitrile electrolyte, whose composition was nearly identical to that of the electrolyte used in this study. Since both N719 and Ru(bpy)2(dcbpy)2+ have sufficiently large driving forces (−∆G0 > 0.7 eV) for the regeneration of iodide,19,28 comparable kreg values for Ru(bpy)2(dcbpy)2+ and N719 are considered reasonable. However, large differences in the light-illumination conditions are noted. The kreg value of N719 was evaluated for full cells under a normal operating condition (i.e., bias illumination of 0.1 or 1 sun),8 whereas in the present study, the local and monochromatic light excitation with high photon densities (1−10 kW/cm2) was applied without bias illumination. Thus, the aforementioned agreement implies that the dye regeneration kinetics is being probed under conditions that are similar to their normal operating conditions. However, a slight influence of


20

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local I− depletion upon the regeneration kinetics appears to emerge under local illumination conditions, as mentioned below. Finally, it is worth noting that no correlations were found for Jsc versus kS+ or Voc versus kS+ (Figure S3, Supporting Information); however, reproducible, weak negative correlations (r ~ −0.7) were found between kS+ and N (see Figure 5e and Figure S2). Since the charge recombination process can be ignored over the observed range of N (i.e., ηcc ~ 1), this correlation indicates that dye regeneration more rapidly occurs with a decrease in the dye adsorption density. A plausible explanation is that the magnitude of intermolecular interactions between the adsorbed dyes (i.e., polarization energy) become weaker as the dye adsorption density decreases, causing gradual, small, downward energy shifts of the HOMO levels of adsorbed dyes from the vacuum level.32 However, the adsorbed Ru(bpy)2(dcbpy)2+ dye possesses a sufficiently large driving force for regeneration; thus, this effect is considered to be negligible. Therefore, this weak correlation implies that the local depletion of I− in the pores may slightly contribute to photocurrent saturation, as lower formation density of S+ can ease I− depletion, leading to an increase in kS+.

4. CONCLUSIONS In conclusion, we have developed a new SPCM setup for high-resolution local analysis of DSCs and demonstrated further potential of photocurrent microscopy. The analysis of the photocurrent saturation phenomenon induced by local light illumination with ultrahigh photon density revealed a new method to enable quantification of dye adsorption number and regeneration kinetics for submicrometric areas in DSCs. The advantage of this method is that the decay rate of oxidized dyes can be evaluated without charge recombination loss. Implementation of such evaluation for many local positions in DSCs allows for disclosure of statistical distribution and


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Page 22 of 27

inhomogeneity of the dye regeneration kinetics. As a consequence, correlations between multiparameters such as dye adsorption number and regeneration rate constant were revealed for the first time. Hence, the “zoom-in” approach reported herein is useful to scrutinize microscopic aspects of photoelectric conversion kinetics in DSCs. Finally, a potential future direction of our SPCM experiment is the simultaneous photocurrent and luminescence measurement of a single adsorbed dye molecule in DSC device environments, which would bring new molecular-level aspects of heterogeneity in interfacial charge transfer dynamics under the DSC device environment.

ASSOCIATED CONTENT

Supporting Information Correlation plots of Jsc versus Voc, Jsc versus kS+ and Voc versus kS+, which are the same data shown in Figure 5. Histograms of N and kS+ and correlation plots of N versus kS+ obtained from DSC samples with [I−] = 0.4, 0.6, and 1.1 M. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION

Corresponding Author *E-mail [email protected]

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS


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This work is supported by Grants-in-Aid for Scientific Research (C), No. 24550018, Challenging Exploratory Research, No.23655007, and Basic Science Research Projects from The Sumitomo Foundation, No.130550.

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