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Evidence for First-Order Charge Recombination in Dye-Sensitized Solar Cells Timothy J. Barr, and Gerald J. Meyer ACS Energy Lett., Just Accepted Manuscript • DOI: 10.1021/acsenergylett.7b00569 • Publication Date (Web): 07 Sep 2017 Downloaded from http://pubs.acs.org on September 11, 2017
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ACS Energy Letters
Evidence for First-Order Charge Recombination in Dye-Sensitized Solar Cells Timothy J. Barr and Gerald J. Meyer Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, United States
Abstract: Charge recombination between electrons injected into TiO2 (TiO2(e-)) and acceptors at the dye-sensitized electrolyte interface have been quantified by measurement of the open circuit photovoltage, VOC, as a function of the incident photon flux. Literature reports indicate that the order of the reaction with respect to TiO2(e-)s is less than unity, typically 0.5 -0.85. Herein an alternative model is proposed and tested that incorporates a characteristic temperature T0, to model the density of acceptor states, and photon flux dependent TiO2(e-) lifetimes, to account for shorter lifetimes at higher concentrations. Tests of this model with standard dyesensitized solar cells based on the di-tetrabutylammonium salt of cis-Ru(dcb)2(NCS)2 (N719, where dcb is 4,4’-(CO2H)2-2,2’-bipyridine) sensitizers in iodide/iodine acetonitrile electrolytes under 0.1 to 5 suns illumination revealed a reaction that is first-order in TiO2(e-)s with T0 = 1150 K. The first order reactivity is consistent with an underlying TiIV/III redox reaction and the kinetic data under 1 sun illumination suggests recombination to molecular iodine, I2. Other implications for solar energy conversion and quantitative analysis of dye-sensitized solar cells are discussed. For Table of Contents Only (this photo is institutional and does not require permission):
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Interfacial electron transfer reactions between wide bandgap semiconductors and solutionphase acceptors have received widespread attention for photovoltaic1 and photocatalytic2,3 applications. One reaction of particular importance is the so called ‘charge recombination’ reaction in dye-sensitized solar cells (DSSCs), where an electron injected into TiO2, abbreviated TiO2(e-)s, reacts with acceptors at the dye-sensitized electrolyte interface. These acceptors are often assumed to be triiodide and/or molecular iodine. Charge recombination is the primary loss pathway in DSSCs and is one limiting factor in the open-circuit voltage, VOC. Measurements of VOC as a function of light intensity have been universally reported to be greater than the idealized value of 59 mV/decade.4–8 A common explanation for this behavior has been termed ‘nonlinear’ charge recombination, wherein the reaction order with respect to TiO2(e-)s is less than unity.7–10 Herein an alternative model is proposed and tested that incorporates a characteristic temperature T0 and photon flux dependent TiO2(e-) lifetimes that provides strong evidence that the reaction order is in fact unity. The rate law for charge recombination between an injected electron, TiO2(e-), and a solution phase acceptor, A, is often written as a quasi-second-order reaction with rate constant , according to Equation 1, 10–12 = [] =
1
(1)
where [A] is the molar concentration of electron acceptors, n is the number of TiO2(e-)s, and is the reaction order with respect to TiO2(e-)s. Rate constants, whose magnitude depend only on temperature, have not been quantified so a characteristic ‘lifetime’ τ is utilized. Under typical operating DSSC conditions, the acceptor concentration is assumed to be present in large excess and the rate law is hence written as a pseudo-first order reaction in n, where τ = 1/k[A]. This assumption and definition of τ is used herein. Non-integer values of have been reported,13,14 where typical values range from 0.5-0.85.4–8 It has been difficult to assign physical or chemical meaning to such values. The TiO2(e-) lifetime, τ, is known to be correlated with the number of TiO2(e-)s n: the larger the number of injected electrons, the shorter the lifetime. Two models have been proposed to account for this correlation. The first uses Marcus-Gerischer theory with rate constants (or lifetimes) proportional to the energetic overlap between the TiO2(e-)s and the electron acceptors.15,9,10,16 The energetic overlap is proposed to increase as the quasi-Fermi level of the TiO2 is raised towards the vacuum level due to an increased number of TiO2(e-)s, n. The second model is based on a trap-limited diffusion/recombination that has been widely applied to explain electron transport and recombination in DSSCs.11,15 In the simplest form of this model, electrons only recombine from mobile or ‘conduction band’ states, whose occupancy is determined n.17,18 In DSSCs, the VOC condition is characterized by equal rates of charge injection and charge recombination. The charge injection rate can be approximated by the incident photon flux, , times the quantum yield for electron injection, , according to Equation 2. = 2 ACS Paragon Plus Environment
(2)
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ACS Energy Letters
Therefore, if the voltage dependence of n is known, VOC can be calculated by setting Equation 1 equal to Equation 2. In nanocrystalline TiO2 thin films used in DSSCs, the voltage-dependence of n is well modeled by an exponential distribution of acceptor states described by Equation 3, = [( )/# $% ]
(3)
where is the total number of acceptor states, # is Boltzmann’s constant, and $% is the characteristic temperature that describes the steepness of the exponential acceptor state distribution. Typical values for $% range from 800-1200 K,7,19 indicating that the electrons concentration is less sensitive to potential than an ideal semiconductor based on Fermi-Dirac statistics. By substituting equation 3 into equation 1, an expression for VOC is given in Equation 4.
&' =
# $% () ( ) * []
(4)
Equation 4 is a form of the “diode equation” similar to previous reports,20 but with two key additions. The first is in the use of the characteristic temperature, $% , as opposed to room temperature, that accounts for the non-ideal Fermi-Dirac (often approximated as a Boltzmann) distribution of acceptor states. The second is the explicit inclusion of the TiO2(e-) lifetime as a function of the number of injected electrons and hence the incident photon flux, as highlighted by (). The absolute value of VOC is dependent on many experimental variables, such as surface pretreatments21–24 and electrolyte additives,25–30 however the derivative with respect to the incident photon flux provides direct information on the reaction order according to Equation 5. + &' # $% 1 1 + = ) + ()* + () +
(5)
To test the validity of equation 5, DSSCs comprised of an N719 (the di-carboxyate salt of cisRu(dcb)2(NCS)2, where dcb is 4,4’-(CO2H)2-2,2’-bipyridine) sensitized mesoporous TiO2 thin film with a 100 mM LiClO4, 250 mM TBAI, where TBA+ is tetrabutylammonium, and 50 mM I2 CH3CN electrolyte were constructed. The DSSCs were light soaked under one-sun illumination until the i-V characteristics of the cell were time-insensitive, typically 15-30 minutes. This procedure was found to be sufficient for stable measurements over the course of several hours to days. The DSSCs were then analyzed on a home-built apparatus which is similar to previous reports,11,31 termed STRiVE and shown in Scheme 1.32 The STRiVE enables photon fluxes from 0.1 to 5 suns with capabilities for charge extraction and transient photovoltage measurements. Background illumination was provided by an array of white LEDs. For transient experiments, light pulses from a separate array of colored LEDs were superimposed on the background illumination while the voltage was monitored. The STRiVE independently quantified $% through charge extraction, () by transient photovoltage decay, and VOC vs light intensity to calculate 3 ACS Paragon Plus Environment
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the reaction order, , through equation 5 with as the only adjustable parameter. The details of this are described below.
Scheme 1. Basic layout of the Sequential Time-Resolved i-V Experiments (STRiVE). DSSCs are illuminated by an array of LEDs (white for background illumination and colored for short pulses) through a fluorine doped tin oxide (FTO) substrate that supports the dye-sensitized mesoporous thin film. The voltage is directly measured while the current is recorded as a voltage drop across a 1 Ohm resistor (amplified) in series with the circuit. The DSSC was maintained at open/short circuit by a fast solid state switch that was controlled by a National Instruments DAQ board that also recorded the voltage and current.
Figure 1 shows a semi-logarithmic plot of the electron concentration, measured by charge extraction,11,33,34 as a function of VOC. The charge extraction technique, first reported by Peter and coworkers, involves steady state illumination of the DSSC at a fixed photon flux until a constant VOC is measured, followed by rapid extraction of the charge within the film at the short circuit condition in the dark. The extracted charge is divided by the volume of the mesoporous thin film to provide n. The volume of this films with known geometric surface area were determined from the height, measured by profilometry, and the assumption of 50% porosity. The data in Figure 1 displayed an exponential increase in n with illumination that was well described by equation 3, resulting in a value for $% of 1150 K, in good agreement with previous studies.7,19
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Figure 1. The number of TiO2(e-)s, n, divided by the volume of the mesoporous thin film as a function of VOC for an N719 sensitized DSSC with iodide redox mediators in CH3CN electrolyte. The magnitude of VOC was controlled through the photon flux. The dotted line represents a best fit from which a $% = 1150 K was extracted from equation 3.
The TiO2(e-) lifetime, τ, was measured by transient photovoltage decay (TVD). In this small perturbation experiment, steady state white light of a fixed photon flux illuminated the DSSC through the counter electrode and pulsed blue LEDs generated a small increase in the VOC, termed ∆Photovoltage. Figure 2A shows the typical TVD data as a function of the white light photon flux. The blue LED pulse duration was adjusted to keep the maximum response at ~4 mV. Overlaid on the data is a fit to a bi-exponential model with pre-exponential factors of opposite sign: one represents the ∆Photovoltage rise as TiO2(e-)s diffuse toward the FTO that supports the mesoporous thin film; and the second represents the ∆Photovoltage decay back to the initial steady state VOC from which τ was extracted. Shown in Figure 2B is a plot of τ versus the log of the photon flux in suns, where 1 sun is 100 mW/cm2. The lifetimes became shorter as the photon flux (and hence n) increased. Overlaid on the data in Figure 2B is a best fit line that -
represents () and was used to calculate -. () in equation 5. A
B
Light Intensity
Figure 2. Transient phototovoltage decays of an N719 sensitized DSSC with iodide redox mediators in CH3CN electrolyte. Panel A shows the change in photovoltage induced by a pulsed blue LED as a function of the steady state white light photon flux. Overlaid on the data are fits to a bi-exponential kinetic model from which the TiO2(e-)
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lifetimes, τ, were extracted. Panel B shows the lifetimes as a function of the photon flux in suns, where 1 sun is 100 mW/cm2.
The line represents a best fit from which
-
-.
() in equation 5 was calculated.
The measured VOC values as a function of photon flux are provided on linear (A) and semilogarithmic (B) scales in Figure 3. The slope of 93.7 mV/decade indicates a diode ideality factor, = 1.58 that in conventional analysis methods where $% = 298 4 corresponds to a = 0.61 value which is within the range that is commonly reported.4–8 A
B
Figure 3. The open-circuit voltage, VOC, of an N719 sensitized DSSC with iodide redox mediators in CH3CN electrolyte as a function of the incident photon flux on linear (A) and logarithmic (B) scales. The best fit line in (B) provides the slope of 93.7 mV/decade of photon flux that corresponds to a diode ideality factor of 1.58.
The data in Figures 1-3 provide all the necessary information to test equation 5. The data in Figure 3A provides
-789 -.
, Figure 1 provides the characteristic temperature of the exponential
distribution of acceptor states, $% = 1150 K, and the photon flux dependency of the TiO2(e-) lifetime, (), was measured by TVD such that the derivative was readily calculated. With these quantities in hand, the reaction order in TiO2(e-)s, , was the only parameter in equation 5 that was not independently measured.
Figure 4. Derivative of VOC with respect to photon flux plotted against the photon flux in suns. The derivative was calculated from the fit in Figure 3A and computed at the measured VOC’s. Overlaid in red is a fit to equation 5.
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ACS Energy Letters
Figure 4 shows the calculated slope
-789 -.
versus the photon flux with an overlaid best fit line
to equation 5. The single parameter optimization results in an excellent fit with a value of 1.02. Corresponding data with an alternative sensitizer, [Ru(dcb)(dtb)2]2+, where dtb is 4,4’(tert-butyl)2-2,2’-bipyridine, provided = 0.91. These results indicates that charge recombination in TiO2 based DSSCs is in fact first-order in TiO2(e-)s. The reason equation 5 returned a value of value near unity while previous analysis results in ≪ 1 is two-fold. First, the experimentally measured exponential distribution of acceptor states was used in place of an ideal distribution that would follow Fermi-Dirac statistics (that are typically approximated as Boltzmann statistics). If this were the only difference, then VOC would be expected to increase by 59 T0/T mV/decade. However, as VOC increases the electron lifetime decreases. This has the effect of reducing the magnitude of the slope and, if the acceptor state distribution does follow Boltzmann statistics this would result in a slope of less than 59 mV/decade. Hence in a working DSSC, both the exponential distribution of acceptor states and the decreased TiO2(e-) electron lifetimes with acceptor state occupancy contribute to the observed VOC response to photon flux. The distribution of acceptor states had a stronger influence on VOC than did the lifetime and increased the slope above the ideal 59 mV/decade, however the slope was lower than 59 T0/T mV/decade because of the dependence of τ on n. While the data does not provide insights into the meaning of T0, it is important to note that this analysis does not require the involvement of conduction band electrons and instead can be accounted for by an experimentally determined exponential density of acceptor states. As was recently emphasized by Hamann35, in Marcus-Gerischer theory for interfacial electron transfer the rate constant ket is related to the energetic overlap between the donor (g(E)) and acceptor (W(E)) states according to equation 6: ;< =
=> ћ
H
@IH A(B)C(B)|EF# |= G(B)+B
(6)
where HAB is the electronic coupling matrix element.16 A very wide ~ 0.6 eV g(E) distribution of TiO2 donor states of ~ 0.46 eV was inferred from the charge extraction measurements under 1 sun illumination; integration over this entire energy range would be required if all underwent interfacial recombination. Unfortunately, the spatial heterogeneity of the injected electrons is unknown and the present study does not reveal what not fraction of the TiO2 states transfer electrons across the interface. Instead, the data indicates that the reaction is first order in TiO2(e-)s for those state(s) that do transfer electrons directly to the iodide redox mediators. An advantage of the transient photovoltage measurement is that it can be applied to operational DSSCs. A disadvantage is that the chemical nature of the acceptor(s) states and their distribution in energy W(E) are not uniquely identified. Nevertheless, the data reported herein provides some new insights into the identity of the relevant redox active species that undergo interfacial electron transfer. The reaction order of unity suggests that the donor is a localized TiIII state rather than a delocalized conduction band. The redox mediators consist of equilibrium mixtures of iodide and iodine and both I3- and I2 have been invoked as possible acceptors, Equations 7-10.36 The importance of identifying the reaction order in TiO2(e-)s as unity is that it 7 ACS Paragon Plus Environment
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rules out the possibility that TiO2 can access the 2e- reduction of I3- that is known to occur at the Pt counter electrode and at metals in general. Such 2e- redox chemistry may indeed occur at a TiO2 electrode under strong forward bias where the materials are known to have metal like behavior,37 but not at the TiO2(e-) concentrations in a DSSC even with 5 suns of solar photon flux. Hence the phenomenal success of the iodide redox mediators in DSSCs likely emanates from the one-electron transfer iodide chemistry that occurs at TiO2, likely to be localized TiIV/III redox chemistry, with 2e- chemistry occurring at the Pt metal electrode, Equation 10. I-+ I2
I3-
Keq = 106 M-1
(7)
TiIII + I2 TiIV + I2.-
Eo(I2.-/I2) = 0.0 V
(8)
TiIII + I3- TiIV + I- + I2.-
Eo(I3-/I2.-,I-) = -0.35 V
(9)
Pt(2e-) + I3- Pt + 3 I-
Eo(I3-/3I-) = +0.35 V
(10)
Data available in the literature indicates that dye regeneration by iodide is incomplete in DSSCs at the power point condition as well as at Voc, such that some of the TiO2(e-)s recombine with the oxidized dye.38–40 The fraction of electrons that recombine to the oxidized dyes is small,
