Rational Interpretation of Correlated Kinetics of Mobile and Trapped

Aug 29, 2017 - Bismuth vanadate (BiVO4) offers a unique combination of advantages, including being a stable, earth abundant, and visible-light respons...
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Rational Interpretation of Correlated Kinetics of Mobile and Trapped Charge Carriers: Analysis of Ultrafast Carrier Dynamics in BiVO4 Yohichi Suzuki,† Dharmapura H. K. Murthy,† Hiroyuki Matsuzaki,† Akihiro Furube,†,‡ Qian Wang,§ Takashi Hisatomi,§ Kazunari Domen,§ and Kazuhiko Seki*,† †

National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba Central 5, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan ‡ Department of Optical Science, Tokushima University, 2-1, Minamijosanjima-cho, Tokushima 770-8506, Japan § Department of Chemical System Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan S Supporting Information *

ABSTRACT: Bismuth vanadate (BiVO4) offers a unique combination of advantages, including being a stable, earth abundant, and visible-light responsive photocatalyst capable of water oxidation. One strategy that is widely employed to enhance the photocatalytic performance of BiVO4 is to improve the carrier transport, which is governed by the interplay between trapping and recombination. To further elucidate the photophysical processes, we investigate the dynamics of often ignored mobile electrons (3435 nm probe) and holes (580 nm probe) using transient absorption spectroscopy. Mobile electrons decay virtually to completion by ∼300 ps, while holes decay in significantly longer periods that far exceed 3000 ps. Furthermore, we use a theoretical model to rationalize the effect of light intensity on the distinctive decay pathways for electrons and holes by trapping and recombination. By employing a simple yet effective formula, we transform the electron decay profile to obtain a hole decay profile that agrees with the experimentally observed transient. A detailed theoretical analysis enables us to determine relevant photophysical parameters such as rate constant values for recombination and trapping, energy levels of traps, and number densities of traps. Results indicate that the electron-trapping process is efficient in BiVO4, and thus direct recombination of electrons with holes is suppressed. Although trapping lowers the electron mobility, it prolongs the lifetimes of holes, which is beneficial for the water-oxidation reaction.

1. INTRODUCTION

themselves unsuitable for efficient water splitting under sunlight irradiation. Bismuth vanadate (BiVO4) is one of the promising photocatalysts that fulfill the above requirements, and it is capable of water oxidation.4 Several crystalline phases of BiVO4 are known, of which monoclinic scheelite BiVO4 shows high photocatalytic activities.4,5 The band gap of monoclinic scheelite BiVO4 is reported as 2.4 eV,6 and it is theoretically possible to generate a 7.5 mA/cm2 photocurrent and to attain a 9% solar-to-chemical conversion efficiency under AM 1.5 sunlight illumination.7,8 However, the reported efficiency has been modest and lower than the theoretical limit; therefore, there remains room for improved performance. To overcome these performance bottlenecks, various approaches have been attempted, such as surface modifications,8−13 doping,8,13−19 heterojunctions,20−25 and nanostructuring.26 The charge-carrier dynamics in BiVO4 is also investigated to understand the photophysics of photogenerated carriers using transient absorption spectroscopy (TAS). These studies revealed the kinetics of photogenerated carriers such as

In recent years, because of the depletion of fossil fuels and environmental pollution, the development of clean and renewable energies is essential to realizing a sustainable society. Hydrogen has attracted much attention as an alternative fuel source, and it is also an important chemical raw material. Water splitting driven by solar energy is an ideal way of obtaining hydrogen because of the abundance of water resources and sunlight.1,2 Since water splitting was first achieved using TiO2,3 many studies have been done to enhance the efficiency of water splitting. In order to achieve high-performance solar water splitting, there are minimum requirements for photocatalysts, including stability in aqueous solution and the efficient utilization of irradiated photons. With respect to the stability, of several classes of materials, metal oxides such as TiO2, WO3, Fe2O3, and BiVO4 are considered to be relatively stable in aqueous solution. The second requirement for determining the efficiency of solar water splitting is the band gap of the photocatalyst. Photocatalysts are semiconductors that absorb photon energy exceeding the band gap, and it is therefore important that photocatalysts utilize large parts of the solar spectrum, i.e., the visible light region. This criterion indicates that materials with a large band gap, such as TiO2, are by © 2017 American Chemical Society

Received: June 6, 2017 Revised: August 10, 2017 Published: August 29, 2017 19044

DOI: 10.1021/acs.jpcc.7b05574 J. Phys. Chem. C 2017, 121, 19044−19052

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The Journal of Physical Chemistry C

transient absorption intensity of the TRDR measurements is presented as a percentage absorption, where absorption (%) = 100(1 − R/R0), using R and R0 as the intensities of the diffusereflected light with and without excitation, respectively. For a more detailed description of the fs-TRDR setup, see refs 34 and 35. The nondoped powdered BiVO4 sample was synthesized via a solid−liquid reaction, and detailed preparation methods are given in refs 31 and 32.

electron−hole recombination and carrier trapping/detrapping in various time scales, and they provided insights into the carrier dynamics of BiVO4.19,23,25,27−30 However, the number of publications related to the carrier dynamics in BiVO4 is still limited and does not enable a comprehensive understanding of the relationship between the charge-carrier dynamics and photocatalytic performance of BiVO4. In particular, to the best of our knowledge, transient absorption attributed to mobile electrons has not been reported, and our understanding of the correlation between charge carriers, such as mobile electrons and holes, is limited. According to our analysis, the electrontrapping process is efficient in BiVO4, and thus a direct recombination of electron with holes is suppressed. In this paper, we analyze time-resolved diffuse reflectance (TRDR) measurements of a powdered nondoped BiVO4 sample synthesized by Wang et al.31 using a solid−liquid reaction.32 We show the dynamics of mobile electrons and holes, which are selectively probed. On the basis of the measured results, we introduced a kinetic model to explain electron and hole decay, and we discuss the correlated kinetics of electrons and holes. In terms of the correlation, we propose a method for transient decay analysis. Although the method requires some assumptions, it is general and enables us to extract the recombination rate constant of electrons and holes from the decay profiles of TAS. In addition, we also analyze the electron-decay mechanisms and extract material parameters such as the energy levels of the electron traps, trapping rate constants, and the number densities of the electron traps. We show that electron trapping is very efficient in BiVO4, which has two direct implications in carrier dynamics: (i) as electrons are trapped and become immobile, their mobility decreases,9,33 and (ii) electron trapping suppresses the direct recombination of electrons and holes, which prolongs the lifetimes of holes in BiVO4; it is thus beneficial for the water-oxidation reaction.

3. RESULTS AND DISCUSSION Here, we outline the following analysis for carrier dynamics in BiVO4. In section 3.1, we identified decay species probed at 580 and 3435 nm by comparing decays of the transient signals both in the absence and presence of an electron scavenger and a hole scavenger. On the basis of the assignment, it is shown that the decay of mobile electrons is faster than that of holes. Then, we introduce a theoretical model to explain the different decays of charge carriers in section 3.2, and we derive the general relation between electron and hole decays. Using this relation, the electron decay profile is transformed to a hole decay, and the electron−hole recombination rate constant is extracted. To confirm the validity of the introduced model, in section 3.3, we examine the transformation of transient profiles of electrons recorded at multiple pump fluences to holes. In section 3.4, we analyze the electron decay based on the introduced model with extracted parameters in section 3.2. We extracted material parameters such as the rate constant values of electron trapping, energy levels of traps, and number density of traps. In section 3.5, we discuss the effect of electron trapping on the survival probability of holes, and we show that the electron trapping suppresses electron−hole recombination. 3.1. Assignment of Decay Species in Transient Absorption Spectroscopy. To understand carrier dynamics in BiVO4, we analyzed time-resolved diffuse reflectance (TRDR) signals. The TRDR measurements are applicable to opaque samples, and they provide insights to help us understand carrier loss and transport mechanisms.34−36 Figure 1 shows normalized transient profiles of the TRDR measurements with 3435 nm (upper) and 580 nm (bottom) probe wavelengths. (See Figure S1 for the transient absorption spectra in the region between 850 and 1400 nm.) We used a pump wavelength of 400 nm with an intensity of 0.6 and 2 μJ/ pulse to probe at 3435 and 580 nm. In addition to the different probe wavelength measurements in the air, we also performed the TRDR measurements in aqueous silver nitrate (AgNO3) solution and in methanol (MeOH). It is known that AgNO3 acts as an electron scavenger and MeOH is a hole scavenger, and it is therefore possible to determine the nature of probed charge carriers by comparing the TRDR signals in the absence and presence of scavengers. In the case of the 3435 nm probe, we observed faster decay of the TRDR signal in the presence of AgNO3 as shown in Figure 1a. This fact indicates that electrons are monitored at 3435 nm. Furthermore, slower decay of the TRDR signal in the presence of MeOH confirmed this assignment (Figure S2). On the basis of the results of measurements in both the presence and absence of scavengers, we consider that the IR (3435 nm) probe wavelength monitors mobile electrons. Typically, the IR probe wavelength is considered to monitor free carriers in semiconductors in which the absorption exhibits monotonic and structureless spectrum with respect to the wavelength.37,38 Therefore, the

2. EXPERIMENTAL SECTION In femtosecond transient diffuse reflectance (fs-TRDR) measurements, a femtosecond Ti:sapphire laser with a regenerative amplifier (Spectra-Physics, Solstice, wavelength of 800 nm, pulse width of 150 fs, pulse energy of 3.5 mJ/pulse, and repetition rate of 1 kHz) was used as a light source. The output from the laser was split to allow the excitation of an optical parametric amplifier (OPA: Spectra-Physics, TOPAS Prime) and a time-plate-type harmonic generator (SpectraPhysics, TP-F) to generate 400 nm and for the generation of white light continuum by focusing the fundamental light (800 nm) into a sapphire plate. In the present study, the 400 nm pump light is generated from the harmonic generation. For the 580 nm probe, we used a white light continuum that ranges from 500 to 1600 nm. For the infrared (IR) probe, we used a 3435 nm light generated from the OPA with a differencefrequency generation crystal. The time resolution of the system was about 150 fs. The powder samples are taken in 1 mm quartz cuvettes. The diameter of the pump beam on the sample was about 0.5 mm, as observed with a charge-coupled device (CCD) camera. We used an amplified Si photodetector to probe at 580 nm, and liquid nitrogen cooled mercury− cadmium−telluride (MCT) photodetector was used for the IR probe (3435 nm) experiments. For measuring the TA spectra in the region between 850 and 1400 nm, an amplified InGaAs photodetector is employed. The diffuse-reflected light from the sample was passed through a grating monochromator (Princeton Instruments, Acton SP2150) for data acquisition. The 19045

DOI: 10.1021/acs.jpcc.7b05574 J. Phys. Chem. C 2017, 121, 19044−19052

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The Journal of Physical Chemistry C

Figure 2. Comparison between normalized electron (3435 nm) and hole (580 nm) decays at comparable pump powers. The transient profile attributed to mobile electrons is fitted to a double-exponential function (dashed line). The solid line is the theoretical curve for hole decay and is obtained by transforming the electron decay profile (see the details in the main text).

for the 3435 nm probe (circles in Figure 2) and 0.2 μJ/pulse for 580 nm probe (triangles in Figure 2). Clearly, long-lived holes are observed. Interestingly, the mobile electrons decay within 300 ps, which is significantly faster than holes. Here, we model the photogenerated carrier kinetics based on electron and hole decay profiles. If the decay for electrons/ holes occurs only via recombination within the bulk, we expect similarities in both electron and hole decay behavior; however, this was not observed. The results indicate that electron trapping makes mobile electron decay faster than hole decay. We assume that the only mobile electrons are measurable, and trapped electrons were not observed in the 3435 nm probe experiments (see Figure 3). In addition, in section 3.4, we

Figure 1. Normalized transient profiles at different probe wavelengths: 3435 nm (a) and 580 nm (b). These measurements are performed in both the absence and presence of an electron scavenger (AgNO3) and a hole scavenger (MeOH).

absorption probed at the IR wavelength is assigned to the intraband transition in the same band.38 In the case of the 580 nm probe, the MeOH atmosphere makes the signal decay faster, indicating that holes are probed. This assignment is in agreement with a previous report by Ma et al.28 By following the procedure reported by Grigioni et al.,23 the transient profile of the 580 nm probe in the absence of MeOH is fitted to a double-exponential function: A1e−k1t + A2e−k2t, while the transient profile measured in the presence of MeOH was fitted to a triexponential function: Ahse−khst + A1e−k1t + A2e−k2t. The fitted parameters are listed in Table S1 (Supporting Information), and we found that the slow decay components k1 and k2 are not significantly affected by the presence of MeOH. Therefore, it is reasonable to consider that the fast component of hole decay (khs) is assigned to kinetics of holes, which are scavenged by electrons donated by MeOH before being trapped, and the slow components (k1 and k2) correspond to the kinetics of trapped holes. This also indicates that both mobile and trapped holes are monitored by the 580 nm probe. It should be noted that Aiga et al. reported a relatively slow rise of the transient absorption signal probed between 550 and 671 nm that is attributed to hole trapping process. In addition, coupling of trapped holes with the phonon modes in the BiVO4 was also observed.27 However, such slow rise and oscillating features are not clearly observed in our 580 nm probe measurements. We believe that this difference may be caused by a difference in the adopted synthesis procedure, which is expected to significantly influence the dynamics. 3.2. Transient Profile Analysis by Correlating Electron and Hole Dynamics. Figure 2 shows normalized decay profiles of the mobile electron (3435 nm probe) and hole (580 nm probe) with comparable pump powers. The experiments are achieved using the lowest possible pump powers to reduce many-body interactions between charge carriers; 0.25 μJ/pulse

Figure 3. Schematic picture of carrier dynamics in our model. The model comprises the photogeneration of carriers (i), electron trapping/detrapping at multiple energy levels (ii), and direct electron−hole recombination (iii). The trapped electrons are assumed not to be probed at 3435 nm.

assume that multiple electron trap levels reproduce electron decay. As explained in the previous section, we do not distinguish between mobile and trapped holes as the 580 nm probe measurements monitor both mobile and trapped holes (hereafter, we refer to them as holes). Further, as reported by Ravensbergen et al., hole traps are populated in a very short time scale (∼5 ps).29 This indicates that the energy levels of the hole trap are expected to be very shallow (very close to the energy levels of mobile holes). In general, carrier trapping to shallow trap levels is a fast process because a large number of 19046

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We now consider the relation between the decay of mobile electrons and holes. Because photogenerated electrons and holes are monitored in the TRDR measurements, the number densities of excess electrons Δn(t) and holes Δp(t) with respect to the number densities of electrons and holes under dark condition are introduced, i.e., n(t) = neq + Δn(t) and p(t) = peq + Δp(t) . Considering that BiVO4 is an n-type semiconductor (neq ≫ peq), eq 3 can be approximated as ∂Δp/∂t = −kr(neq + Δn)Δp. Because the approximated expression can be rearranged as ∂ ln Δp/∂t = −kr(neq + Δn), the formal expression of Δp can be written as Δp(t) = Δp(0) exp[−kr∫ t0dt′{neq + Δn(t′)}]. If the observed signals in the TRDR measurements are proportional to Δn(t) and Δp(t), the reduced eq 3 can be further rewritten using observable quantities Se(t) = αeΔn(t) and Sh(t) = αhΔp(t):

unoccupied traps are present. Carrier detrapping from shallow traps is also a fast process as long as the activation energy is given by the energy difference between the traps and the valence band maximum. Accordingly, we assume a single representative energy level for the mobile and trapped holes. Our model comprises the photogeneration of carriers (Figure 3i), electron trapping/detrapping (Figure 3ii), and the recombination of mobile electrons and holes (Figure 3iii). The carrier dynamics is described by ∂n = −k r(np − ni 2) − ∂t

N

∑ k t(j)[n(Nt(j) − q(j)) − n1(j)q(j)] j=1

(1)

∂q(j) = k t(j)[n(Nt(j) − q(j)) − n1(j)q(j)] ∂t

∂p = −k r(np − ni 2) ∂t

⎡ S h (t ) k = exp⎢ −k rneq t − r S h(0) αe ⎣

(2)

(3)

∫0

t

⎤ dt ′ Se(t ′)⎥ ⎦

(4)

where Se(t) and Sh(t) are the experimentally observed transient profiles for mobile electrons and holes, respectively. αe and αh are factors of proportionality to excess electrons and holes, respectively. The expression in eq 4 indicates that it is possible to transform the transient profile of electrons Se(t) to hole decay Sh(t) using appropriate parameters krneq and kr/αe. It should be noted that eq 4 provides the relation between electron and hole decays based on eq 3, which does not describe the time evolution of electrons but holes. Therefore, eq 4 is always valid regardless of the detailed mechanisms of electron decay. To check the validity of our model, which considers electron−hole recombination and electron trapping, the transient profile of mobile electrons is transformed to obtain the decay of holes by following two procedures. First, the transient profile of electrons is fitted to an analytically integrable function. In this case, we found that the electron decay can be fitted to a double-exponential function: Se(t) = y0 + A1 exp(−t/τ1) + A2 exp(−t/τ2) with y0 = 7.05 × 10−3, A1 = 3.00 × 10−1, τ1 = 1.17 × 102 ps, A2 = 4.03 × 10−1, and τ2 = 7.07 ps. Although this procedure is not always necessary, the transformation will be easier because numerical integration can be avoided. Furthermore, the numerical integration of experimental data containing noise causes an accumulation of errors and could result in inaccurate transformation for longtime regimes. Second, the parameters krneq and kr/αe in eq 4 are optimized by fitting such that the right-hand side of eq 4 reproduces experimental results (hole decay). Accordingly, the electron decay profile Se(t) is transformed into the hole decay Sh(t) in this procedure using eq 4. The solid line in Figure 2 is the transformed result obtained with the aid of computer program Igor Pro, and the obtained parameters are krneq = 1.64 × 10−4 ps−1 and kr/αe = 6.62 × 10−3 ps−1. We also estimated the recombination rate constant by employing neq based on reported values.5,20,41 The effective density of states for mobile electrons Nc = 2.14 × 1019 cm−3 is evaluated in accordance with Nc = 2(m*e kBT/2πℏ2)3/2,42 where the value of the effective mass for mobile electrons m*e = 0.9m05 was adopted. The number density of electrons under the dark condition is obtained as neq = Nc exp[−(Ec − EF)/(kBT)] = 2.00 × 1014 cm−3 by employing the values of the energy level of mobile electrons as Ec = −4.46 eV20 and the Fermi level as EF = −4.76 eV.41 The recombination rate constant is determined to be kr = 8.20 × 10−7 cm3 s−1, and the factor of proportionality

(j)

where n, q , and p are the number density of mobile electrons, trapped electrons in the jth energy level, and holes, respectively. The first terms on the right-hand sides of eqs 1 and 3 represent the electron−hole recombination with a rate constant kr, and ni2 = neqpeq, where neq and peq are the number density of electrons and holes, respectively, under dark conditions.39 The second term of the right-hand side of eq 1 represents the exchange of electrons between the energy level of mobile electrons and multiple N trap levels (see the details below). The time evolution of the number density of the trapped electrons in the jth energy level E(j) t is described by eq 2 with a rate constant k(j) t . The multiple energy levels of traps are (j+1) numbered so that E(j) is satisfied. To obtain eq 2, we t < Et assumed that the trapping rate is proportional to the product of the number density of mobile electrons n and the number density of unoccupied electron traps N(j) − q(j), i.e., the t (j) (j) (j) (j) trapping rate = kt n(Nt − q ), where Nt is the total number density of traps in the jth energy level. The detrapping rate is also considered to be proportional to the product of the number density of trapped electrons q(j) and the number density of the unoccupied states for mobile electrons Nc − n, (j) i.e., detrapping rate = −k(j) d (Nc − n)q , where Nc is the effective density of states for mobile electrons and k(j) d is the detrapping rate constant. When n ≪ Nc is satisfied, as confirmed in following analysis, the detrapping rate is approximated by (j) (j) (j) −k(j) d Ncq . Owing to the detailed balance condition kt neq(Nt (j) (j) (j) − qeq ) = kd Ncqeq , the detrapping rate constants can be (j) (j) (j) (j) (j) expressed as k(j) d = kt neq(Nt − qeq )/(Ncqeq ), where qeq is the number density of trapped electrons under dark conditions. The statistics of trapped electrons under the dark condition are (j) followed by the Fermi distribution function, i.e., q(j) eq = Nt / {exp[(E(j) − E )/(k T)] + 1}, where E is the Fermi level and t F B F kB is the Boltzmann constant. When the difference in the energy level of mobile electrons Ec and Fermi level EF is greater than several kBT units, neq can be described by neq = Nc (j) exp[−(Ec − EF)/(kBT)]. Substituting k(j) d , qeq , and neq into the (j) (j) sum of the jth trapping and detrapping rates k(j) t n(Nt − q ) − (j) (j) (j) (j) kd Ncq yields eq 2, where n1 is written as n1 = Nc exp[−(Ec 40 − E(j) It should be noted that trap-mediated t )/(kBT)]. electron−hole recombination is not considered. As shown in section 3.4, the trap levels are close to the energy level of mobile electrons. Therefore, the traps are less likely to form recombination centers during the measurement period. 19047

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The Journal of Physical Chemistry C between Se(t) and Δn(t) is also calculated as αe = 1.24 × 10−16 cm3. We also deduced the number density of the photogenerated carriers at t = 0, i.e., Δn(t = 0) = Se(t = 0)/αe. We estimated the initial absorption by extrapolating the doubleexponential function Se(t = 0) = 0.71. The number density of the photogenerated carriers can be obtained as Δn(t = 0) = 5.73 × 1015 cm−3 and is greater than the number density of electrons under dark condition. In addition, the condition n = neq + Δn ≪ Nc can also be confirmed. 3.3. Pump Power Dependence on Dynamics of Electrons and Holes. In the previous section, we demonstrated that the decay of electrons is transformed to the decay of holes using a pair of electron and hole profiles at lower pump fluence, where many-body interaction is reduced. In the transformation, the decay pathway for holes is assumed to occur only via recombination with electrons. In addition, when mobile electrons are captured by traps, they are not observable. In order to confirm the validity of this assumption, we study the pump power dependence of electron and hole decay profiles using the transformation because, in general, the kinetics involving the second-order recombination reaction depends on the initial charge density, which can be controlled by pump power. If the transformation can be applied to transients recorded at both lower and higher pump fluences, the underlying mechanism can be considered to be more plausible. It should be noted that the parameters krneq and kr/αe appearing in eq 4 are considered to be independent of pump powers. This indicates that a unique set of parameters krneq and kr/αe is to be employed when studying other pairs of transient profiles. Accordingly, we further examine other pairs of electron and hole decays with similar/identical pump powers by performing a global transformation. The procedure of the transformation is almost the same as that for the lowest pump power; however, we regard the initial values of Sh(t = 0) at different pump powers as additional fitting parameters. We selected three pairs of transient profiles of electrons and holes at different pump powers: the lowest pump is rated at 0.25 μJ/pulse for a 3435 nm probe and 0.2 μJ/pulse for a 580 nm probe (Figure 4a); 1 μJ/pulse for 3435 and 580 nm probes (Figure 4b); and 2 μJ/pulse for 3435 and 580 nm probes (Figure 4c). In the same manner as before, the transient profiles of electrons are initially fitted to double-exponential functions in order to avoid numerical integration. The fitted values are listed in Table S2 (Supporting Information), and fitted curves are shown as dotted lines in Figure 4. In the cases of 1 and 2 μJ/pulse, we did not perform long-time (>300 ps) measurements because the decay was virtually completed by 300 ps, and the decay beyond 300 ps is not expected to differ upon changing the pump intensity. Hence, transformed transients are only shown up to 300 ps. Because parameters krneq and kr/α are independent of pump powers, five parameters (krneq, kr/αe, and three initial values of Sh(t = 0) at different pump powers) are needed to perform the transformation. The global fitting (>0.5 ps) is done with the aid of the computer program Igor Pro. The transformed profiles are shown as solid lines in Figure 4. The obtained parameters are krneq = 2.42 × 10−4 ps−1 and kr/αe = 2.55 × 10−3 ps−1, and these values are consistent with parameter values obtained in the preceding section. The values of Sh(t = 0) at 0.2, 1, and 2 μJ/pulse are also obtained as 6.24 × 10−1, 2.87, and 5.42, respectively. For the cases of 1 and 2 μJ/pulse, the experimental results probed by the 580 nm (red triangles) up to the ∼2 ps regime

Figure 4. Global transformation of transient profiles of electrons to holes: (a) at ∼0.2 μJ/pulse, (b) at 1 μJ/pulse, and (c) at 2 μJ/pulse. The decays of electrons (circles) are fitted to double-exponential functions (dashed lines). The transformations are done using eq 4 to fit the transient profiles of holes probed at 580 nm (triangles).

deviate from the transformed profiles (solid lines in Figure 4b,c). One possible reason would be the oversimplification of the kinetics of holes. In our analysis, we did not take into account the detailed mechanism of hole trapping because the process would be very fast (∼5 ps),29 and it is expected to be absent in a long-time regime. This can be confirmed by the agreement between experimental results and the transformed profiles in the >2 ps regime. The agreement between experimental results and transformed profiles for the longtime regime is expected to improve if the transformation in the short-time regime is excluded. 3.4. Analysis of Electron Decay Using Multiple Trapping Levels. Here, we study electron-trapping mechanisms. Initially, by considering that the transient profiles of electrons can be fitted to double-exponential functions, we tried to explain the electron decay using a model that considers a single trap level of electrons and electron−hole recombination. (1) (1) Specifically, the parameters k(1) t , Nt , and Et in eqs 1 and 2 are regarded as fitting parameters, and the electron decay given by eq 1 was fitted to experimental data (see details in the Supporting Information). As a result, the model with a single trap level was found to be inadequate to reproduce the 19048

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5.73 × 1015 cm−3. We solved the nonlinear partial differential equations numerically, and we performed fitting with the aid of Matlab43 command lsqnonlin which minimizes the sum of squared residuals between experimental and theoretical results. For simplicity, we introduced an effective trapping rate constant kt = k(1) = k(2) t t , and the total number densities of traps at different energy levels are assumed to be comparable, i.e., Nt = = N(2) (see the ratio of roughly estimated values of N(1) N(1) t t t (2) and Nt in the Supporting Information), and parameters kt, Nt, (2) E(1) t , and Et were optimized. Figure 5a shows the transient profile of electrons at 0.25 μJ/ pulse pump power, and the theoretical curve (solid line) with the optimized parameters kt = 6.87 × 10−7 cm3 s−1, Nt = 9.98 × = −4.797 eV, and E(2) = −4.600 eV. The 1016 cm−3, E(1) t t random distribution of residuals between experimental results and model predictions is confirmed in Figure S3b. Figure 5b shows the time dependence of excess electron densities in the jth trap, which is given by Δq(j) = q(j) − q(j) eq . Both the profiles of excess electron densities in the traps exhibit nonmonotonic behaviors, and the peak positions and their amplitudes depend on the trap energy levels. The nonmonotonic profile of excess electrons in the shallow trap (trap 2 in the inset of Figure 5b) is explained by the efficient thermalization of electrons by capture and release. By contrast, the capture of electrons to the deep trap level (trap1 in the inset of Figure 5b) and their release are relatively slow processes. The trap-level dependence on the electron capture and release can be confirmed by examining carrier dynamics of excess electron densities in traps in the absence of electron−hole recombination. The kinetics of excess electron densities in the jth trap can be approximated by (j) (j) ∂Δq(j)/∂t = vjΔn − wjΔq(j), where vj = k(j) t (Nt − qeq ) and wj = (j) (j) kt (neq + n1 ) are the first-order trapping and detrapping rates, respectively (see details in the Supporting Information). Because the shallow trap levels are less occupied, fast trapping is expected to the shallow trap levels. In addition, detrapping from shallow traps is also a fast process owing to the detailed balance condition. In fact, vj and wj increase as E(j) t increases, and the trap at deeper levels exhibits slower trapping and (j) detrapping of electrons if N(j) t and kt are comparable between the shallow and deep trap levels. It should be noted that electron capture to deep traps takes place even though the trap level is lower than the Fermi level. Because the trap level E(1) t is slightly lower than the Fermi level (see the inset of Figure 5), unoccupied traps exist and are able to capture electrons. It is important to note that in our model the kinetics of electron trapping is greatly simplified, considering that the actual trap levels and rate constants are likely to be energetically distributed. Our analysis indicates that the two trap levels would be considered as representative levels if the traps are energetically distributed. In addition, although it is difficult to identify the origin of electron traps, it was theoretically predicted that oxygen vacancies are shallow donor defects in the preceding works.44,45 3.5. Effect of Electron Trapping on the Survival Probability of Holes. BiVO4 is capable of water oxidation by holes. Although detailed kinetics was studied for electrons, it is more relevant to study a portion of photogenerated holes that survived from recombining with electrons for relating carrier dynamics with photoelectrochemical activities. Here, we discuss the survival probability (normalized profile of TRDR measurements) of holes in terms of electron trapping and detrapping kinetics shown in the preceding section. As shown

transients of mobile electrons because residuals between experimental results and model predictions (fitted results) which spanned the 10−100 ps regime tend to deviate positively, whereas residuals for the >1 ns regime tend to deviate negatively; i.e., residuals are not distributed randomly (see Figure S3a in the Supporting Information). Accordingly, we (2) introduced electron traps with two energy levels (E(1) t and Et , as shown in the inset of Figure 5b, to achieve a satisfactory fit with the experimental data).

Figure 5. (a) Transient profiles of mobile electrons and (b) excess electron densities for different trap levels. The solid line represents the theoretical curve with fitted parameters, and the circles represent the experimental results at 0.25 μJ/pulse. The excess electron densities in deep (trap 1) and shallow (trap 2) traps are plotted using dashed and dotted lines. The inset shows the energy levels of electron traps and the Fermi level.

Before fitting the experimental data based on eqs 1−3, we (j) (j) roughly estimate material parameters such as k(j) t , Nt , and Et because reasonable initial guesses of the material parameters are needed to perform nonlinear optimization. In the estimation, we employed a model with multiple trap levels in the absence of recombination because electron decay in the 500 ps regime is found to be the detrapping-limited recombination because the decay features of survival probability of holes (Figure 6) and the density of excess electrons at the deep trap level (Figure 5b) are almost the same in this time regime. It should be noted that the onset of trap-limited recombination is found to occur beyond several tens of nanoseconds, as reported by Ravensbergen et al.29 However, our observation time is too short to examine the power-law decay in the >10 ns regime. Although the electron traps contribute to the extension of hole lifetimes, the lowering of the electron mobility is also 19050

DOI: 10.1021/acs.jpcc.7b05574 J. Phys. Chem. C 2017, 121, 19044−19052

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b05574. Transient absorption spectra in the region between 850 and 1400 nm; transient absorption signals probed at 3435 nm in the absence and presence of MeOH; table of fitted parameters of transient profiles at 580 nm probe in the absence and presence of MeOH; table of fitted parameters of transient profiles of mobile electrons (probed by 3435 nm) at different pump powers; fitting procedure of electron decay in a model with a single trap level and electron−hole recombination; residuals between experimental transients of mobile electrons at 0.25 μJ/pulse and predictions of a model with a single trap level and multiple trap levels; analytical expressions for decay of electrons in a model with multiple trap levels in the absence of recombination (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (K.S.). ORCID

Takashi Hisatomi: 0000-0002-5009-2383 Kazunari Domen: 0000-0001-7995-4832 Kazuhiko Seki: 0000-0001-9858-2552 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the Research Project for Future Development: Artificial Photosynthetic Chemical Process (ARPChem) (METI/NEDO, Japan: 2012-2022).

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REFERENCES

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