A Surface Science Approach to Unveiling the TiO2 Photocatalytic Mechanism: Correlation between Photocatalytic Activity and Carrier Lifetime

a Department of Chemistry, Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japan b Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan c Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan d SOKENDAI (The Graduate University for Advanced Studies), Tsukuba, Ibaraki 305-0801, Japan e Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan † Corresponding author: ozawa.k.ab@m.titech.ac.jp


I. INTRODUCTION
The outstanding photocatalytic activity of titanium dioxide (TiO2) has attracted considerable attraction since the discovery of electrochemical photolysis of water at a TiO2 electrode by Honda and Fujishima in the late 1960s [1,2]. TiO2 photocatalysis is not limited to the photolysis of water [1−3]; novel phenomena such as the oxidation of cyanide ions in aqueous solutions [4], decomposition of carbohydrate into H2 and CO2 [5], removal of dilute nitrogen oxides (NOx) in air [6], inactivation of E. coli [7], etc. were also reported in the 70s, 80s, and 90s. These properties pave the way for the use of TiO2 in environmental cleanup applications (air and water purification). Furthermore, the discovery of superhydrophilicity on the TiO2 surface by ultraviolet (UV) illumination in 1997 [8] has led to applications such as self-cleaning tiles and anti-fogging mirrors, whose surfaces are coated by TiO2 thin films. The global market for photocatalysis applications has grown steadily over the past decades [9] and is expected to keep expanding in the coming decades.

II. BRIEF OVERVIEW OF PHOTO-CATALYTIC ACTIVITY A. Role of photogenerated carriers
In TiO2 photocatalysis, a key factor is, evidently, photogenerated electrons and holes (Figure 1). Although a fraction of these carriers is lost by electron-hole recombination before they reach the catalyst surface, surviving electrons and holes initiate reduction and oxidation reactions, respectively, at the surface. In the case of photocatalytic water dissociation, two electrons and two holes are involved in the dissociation of a H2O molecule [2]: The photocatalytic decomposition of organic compounds is more complex. Firstly, electrons and holes are considered to generate reactive oxygen species (ROSs) in the following manner [10,11]: Because of the essential role of photogenerated carriers, it is indispensable to focus on the dynamics of these carriers. Laser-assisted time-resolved measurement techniques are very powerful for the elucidation of the carrier dynamics in the femtosecond to microsecond time domains. Figure 2 summarizes the carrier dynamics in each time domain [11,12]. Photogenerated electrons and holes are loosely bound by Coulomb forces, forming excitons. A large portion of the excitons undergoes immediate recombination after photogeneration, within femtoseconds. A remaining portion dissociates into free electrons and holes. In the TiO2 crystals, there are many carrier traps: "shallow traps" and "deep traps". The former is related to O defects, and the latter to unsaturated Ti atoms [13]. A part of migrated carriers is captured by these traps within femtoseconds to picoseconds after photogeneration, and the trap-mediated recombination process follows in picoseconds to nanoseconds. It is noted that electron-hole recombination via band-to-band transition occurs when the trap density is sufficiently low. Surviving free carriers reach the catalyst surface within nanoseconds to microseconds after photogeneration, and the transfer to adsorbates (adsorbed O2, for example) occurs in tens to hundreds of microseconds. It is estimated that photoexcited carriers that are utilized in photocatalytic reactions represent only 10% of all photoexcited carriers; the rest is quenched by electron-hole recombination [11,12,14].

B. Carrier lifetime measurements
It is well known that the photocatalytic activity is higher for anatase TiO2 than rutile TiO2 [15−20]. One of the earliest studies that reported this phenomenon was by Tanaka et al. in 1991 [15]. They compared the initial degradation rates of organic compounds (C2HCl2, CH2ClCOOH, and phenol) in aqueous solutions using commercially available TiO2 samples under illumination of a filtered mercury light and found that the TiO2 samples with a higher anatase content exhibited higher degradation rates. The authors proposed that the higher activity resulted from a lower concentration of surface OH species, i.e., the consumption of ROS via O 2 •− + OH was suppressed on the anatase surface [15]. On the other hand, a more preferred explanation for the structural dependence of the photocatalytic activity nowadays is the difference in photogenerated carrier lifetime. Photoexcited carriers in a bulk material is believed to have a longer lifetime in anatase TiO2 than rutile TiO2, reflecting a difference in the band-gap type of bulk crystals, i.e., a direct band gap for rutile TiO2 and an indirect band gap for anatase TiO2 [21]. Xu et al. experimentally demonstrated that the reaction rates of CO oxidation on anatase TiO2(101) and rutile TiO2(110) were correlated with the bulk carrier lifetimes [19]. Moreover, Luttrell et al. proposed that the carrier transport from the bulk to the surface should also be taken into account when studying the photocatalytic activity [20]. Therefore, it is logical to expect that the carrier lifetime as well as its dynamics determine the photocatalytic activity of TiO2.
However, the situation is not as simple as one may expect. Table 1 shows carrier lifetimes of TiO2 measured by various time-resolved techniques, reported in several studies [22− 28]. The values range from picoseconds to microseconds, irrespective of the crystal structure. It is obvious that factors other than the crystal structure affect the carrier lifetime. The morphology of the TiO2 catalyst (nanoparticles or single crystals) and the environment surrounding the catalysts (solution, air, or vacuum) are possible influential factors. Nevertheless, it is difficult to comprehensively interpret experimental data and to predict the trend of the carrier lifetime based on these data.

C. Surface potential barrier
TiO2 is an n-type wide band-gap semiconductor with a band-gap energy of approximately 3 eV (2.9−3.0 eV for rutile and 3.1−3.2 eV for anatase [29]). When the charge balance between the crystal surface and the bulk is disrupted, band bending is induced [ Figure 3(a−c)]. For both anatase and rutile TiO2 surfaces, when oxygen vacancies (VO) are formed, downward band bending is induced and a charge accumulation layer is formed because VO acts as an electron donor [ Figure 3(c)]. Such surfaces are easily obtained, as demonstrated in Figure 3(d), which shows a series of X-ray photoelectron spectroscopy (XPS) profiles in the valence-band region of rutile TiO2(110) surface. The sample was prepared by Ar + sputtering and annealing at 650 K in an ultrahigh vacuum (UHV). The photon energy (hν) dependence of the valence-band maximum (VBM) position, which moves from 3.14 eV (hν = 1465 eV) to 3.37 eV (hν = 100 eV), is suggestive of downward band bending, because the detection depth increases with increasing excitation energy, according to the inelastic-mean-free path of the emitted photoelectrons [30] and the definition of information depth [31].
However, downward band bending is partially or completely suppressed when the TiO2 surfaces are exposed to Figure 2: Time scale of the photoexcited carriers: from exciton formation to electron transfer to adsorbed O2 [11,12]. gases such as CO and O2 [ Figure 3(e)]. These molecules are adsorbed on the VO sites and withdraw donated electrons from the accumulation layer. O2 is more effective than CO because of its stronger electron-withdrawing ability. H2O, which is adsorbed dissociatively on the TiO2 surfaces, on the other hand, shifts the VBM to higher binding energies [32].
Since TiO2 photocatalysts usually function in air or in aqueous solutions, O2 and H2O cover the TiO2 surface. Thus, the type of the space charge region (SCR), i.e., a depletion type or an accumulation type, on the working photocatalysts depends on the adsorbed molecules and their coverages.
Considering the role of the photoexcited carriers (electrons and holes), the importance of the surface band structure must be recognized because the carrier dynamics is strongly affected by the SCR. The SCR acts as a potential a Crystal structure of the TiO2 nanoparticles is not mentioned [22] but is speculated from the particle size and thermodynamic stability. b Electron and hole lifetimes were separately evaluated [28]. barrier that carriers have to overcome on the crystal surface ( Figure 4). Although this issue was thoroughly addressed by Zhang and Yates [33], very few studies have focused on surface band bending. This phenomenon can be disregarded only when the TiO2 photocatalysts are in a powdered form, with a size of less than a few tens of nanometers [33]. This is because in this case, the width of the SCR is comparable to the particle size. Hence, the barrier height V s , which is defined by the difference between the energy level at the surface and that in the bulk (Figure 4), is comparable to or smaller than k B T, where k B and T are the Boltzmann constant and temperature, respectively. However, as the particle size for bulk single crystals is larger than a few tens of nanometers, the effect of the SCR on the carrier dynamics should be taken into account. Laser-based time-resolved measurement techniques such as transient absorption spectroscopy, photoluminescence spectroscopy, photoconductance measurements, etc., are not suitable for assessing the surface electronic structure and, thus, the band-bending structure of a TiO2 photocatalyst. On the other hand, photoelectron spectroscopy is ideal for measuring the electronic structure. Thus, if this technique is used to determine the carrier dynamics, the relation between the carrier lifetime and the surface potential barrier can be discussed. Time-resolved two-photon photoelectron spectroscopy (TR-2PPE) and time-resolved X-ray photoelectron spectroscopy (TRXPS) are two current time-resolved photoelectron spectroscopy techniques. In the present contribution, we mainly focus on recent achievements in TiO2 photocatalysis research using TRXPS.

III. TRXPS AND SPV A. Time-resolved XPS
Photoelectron spectroscopy is one of the most successful experimental techniques for characterizing material properties through non-destructive, element-specific, and quantitative measurements. It can probe not only electronic structures and elemental compositions of solid surfaces [34−36] but also material conversion processes such as catalytic reactions [37]. For XPS measurements, characteristic X-rays, typically Al Kα and Mg Kα lines, are used as laboratory light sources, while synchrotron radiation (SR) is also available and frequently used [38]. The biggest advantage of SR over laboratory light sources is the tunable photon energy. As a result, it is possible to obtain depth-resolved measurements of the electronic structure, as demonstrated in Figure 3(d), and an elemental distribution [39]. Moreover, bulk band structures of crystals can be determined by angle-resolved photoelectron spectroscopy (ARPES) combined with photon-energy dependent measurements [40]. Resonant photoemission measurements [41,42] and corehole clock measurements [43,44] are other photoelectron spectroscopy techniques where the photon energy tunability is used.
SR is an inherently pulsed radiation because it originates from individual electron bunches when they are radially accelerated by a magnet (a bending magnet) or by periodically arranged short-dipole magnets (an undulator) in a storage ring. In the A-mode operation of SPring-8, an SR facility in Japan, for example, the number of electron bunches in the storage ring is 203, with a revolution time of 4.789 μs [45,46]. Thus, the SR pulses are provided every 23.6 ns (= 4.789 μs/203). The pulse width is determined by the electron bunch length and is typically several tens of picoseconds [45,46].
The pulse characteristics of SR light offer a good opportunity to conduct time-resolved measurements using a pump-probe method. Here, a pump pulse generates an excited state, and its time evolution is monitored by a probe pulse ( Figure 5). This method is unique in that the relaxation process of the excited state can be tracked in real time by Figure 4: Schematic carrier diffusion in space charge regions (depletion and accumulation layers). In an upward band-bending material (a), the SCR acts as a barrier for electrons excited in the conduction band. In a downward band-bending material (b), holes in the valence band overcome the potential barrier when they reach the surface. The depletion and accumulation layers do not act as potential barriers for the holes and the electrons, respectively. The TR-2PPE technique with the pump-probe method usually uses femtosecond laser pulses in the visible and UV regions as the pump and probe lights [47]. An advantage of 2PPE is that electrons excited in the conduction bands are directly probed with a femtosecond time resolution. Hence, the dynamics of excited electrons have been successfully explored; for example, an ultrafast relaxation process in the conduction band, as demonstrated in Figure 6 [48], a single-to-triplet conversion at an organic p/n heterojunction [49], and a spin-injection process through the ferromagnet/organic semiconductor interface [50]. In TRXPS experiments, on the other hand, the femtosecond laser and the SR light in the X-ray region are combined, and photoexcited states are monitored via XPS [51,52]. TRXPS enables us, in principle, to have a local view of the excitation state, since the core electrons are localized at the atoms that they belong to and their binding energies are sensitive to the chemical environment surrounding the atoms. This is different from 2PPE, which probes the valence and conduction states, whose wave functions are spatially extended. Thus, TRXPS is more suitable for investigating a system that has multiple components. Figure 7 demonstrates the time evolution of the excited states of C60 and copper phthalocyanine (CuPc) in a CuPc/C60/TiO2(110) system, which are individually determined by analyzing the C 1s spectra [53].
The time resolution of TRXPS that uses SR light as a probe light is limited to several tens of picoseconds, even when a femtosecond laser is employed as a pump light. However, the use of an X-ray free-electron laser (XFEL) [54,55] or high-harmonic generation (HHG) [56] as a probe light enables results in a femtosecond time resolution because they provide ultrashort pulses of a femtosecond order. A laser-pump-XFEL-probe TRXPS study successfully captured an ultrafast charge transfer (< 1 ps), from a ruthenium-based dye N3 molecule to a ZnO substrate, by monitoring the transient chemical shift of the Ru 3d core-level peak [55].

B. Surface photovoltage (SPV)
The generation of a surface photovoltage (SPV) is a fundamental optical response of semiconductors when their surfaces are irradiated by light with energy higher than the band-gap energy [57]. A necessary condition for SPV generation is an SCR at the semiconductor surface. This is because the potential gradient in the SCR facilitates the dissociation of photogenerated excitons into electrons and holes, i.e., these charged particles are forced to drift in opposite directions. Separated electrons and holes in an accumulation Figure 7: C 1s spectra acquired by laser-pump-SR-probe TRXPS measurements of the CuPc/C60/TiO2(110) system (model structure is displayed in the upper-right corner). The experiment was performed at BL07LSU of SPring-8. The bottom spectrum is without the pump laser irradiation, whereas the upper spectrum was measured at a delay time of 0.1 ns. Enlarged spectra around the peak maximum in the inset show a pump-laser-induced peak shift to higher binding energies. After deconvolution of the C 1s spectrum into C60 (red line) and CuPc (blue line) components, pump-laserinduced spectral shifts can be individually traced, as shown in the upper-left panel (for the C60 component) and the lower-right panel (for the CuPc component). , and vice versa in a depletion layer. Such charge separation leads to a partial or complete cancelation of the built-in electric field that induces band bending, depending on the number of separated carriers. As a result, the magnitude of band bending, namely the surface potential, is diminished by VSPV. This is defined as the SPV and is determined experimentally from a light-induced energy-level shift on the semiconductor surface [ Figure 8(b)]. It is worth noting that, except for some special cases [58], the SPV effect always results in a reduction of band bending. In other words, one can predict the type of the layers (depletion layer or accumulation layer) based on the shift direction of the energy levels.
The generation process of the SPV by an ultrashort pulse is very fast and is usually completed in less than 50 ps, irrespective of the semiconductors, because the generation process is not detected by TRXPS (which has a time resolution of ~50 ps) [59−62].
The photoexcited carriers in the flat-band region beneath the SCR contribute less to the SPV than those in the SCR. This is because electron-hole charge separation occurs only when there is thermal fluctuation; hence, a large fraction of the separated charge is lost by electron-hole recombination during thermal diffusion.
The SPV diminishes gradually with time because the carriers at the bottom of the SCR diffuse back to the surface, overcome the surface potential barrier, and recombine with the counter carriers at the surface [ Figure 8(c)]. Compared with the SPV generation process, the decay process is generally slower, with time constants ranging from nanoseconds to microseconds. Figure 9 shows the SPV decay process evaluated with TRXPS measurements. When the 3.1-eV femtosecond laser pulse irradiates the graphene/SiC(0001) surface, both the C 1s and Si 2p core-level peaks move towards higher binding energies, i.e., the peaks are shifted by 0.22−0.24 eV at a delay time of 0.1 ns [62]. The shift gradually decreases, with a decay time constant of 3−4 ns, which is much slower than the generation of the SPV (< 0.1 ns).

C. Recombination time analyzed via SPV relaxation
Considering the decay process of the SPV in Figure 8(c), it is natural to speculate that the surface barrier height strongly influences the SPV relaxation time.
We assume that the band bending exists on the surface in dark conditions (Vs) ( Figure 4) and that there is SPV generation with a magnitude of VSPV upon electron-hole separation [ Figure 8(b)]. VSPV can be approximately expressed as [63]: where nph and n0 are densities of photoexcited and intrinsic carriers (electrons or holes), respectively. kB and T are the Boltzmann constant and temperature, respectively. The above equation is valid only if Vs − VSPV ≫ kBT. Moreover, Eq. (1) tells us that VSPV is proportional to ln(nph/n0) when Vs and VSPV are much larger than kBT. The value of VSPV is given by the following equation [63].
Here, η and γ are constants. After generation of the SPV, the number of photoexcited carriers nph gradually decreases due to electron-hole recombination. Thus, VSPV depends on the time t according to the following differential equation, derived from Eq. (2): nph is also a function of t and its differential equation is written as: τ is the carrier lifetime. The electron-hole recombination proceeds via a thermionic emission process, which is characterized by the carriers overpassing the surface potential barrier, as depicted in Figure 8(c). In this case, τ is determined by the barrier height. The carrier lifetime in the absence of the SPV is ∞ and τ is expressed as follows [64].
η in Eqs. (2) and (5) is called an ideality factor [65], which is an indicator of the electron-hole recombination rate before the carriers overpass the surface potential barrier. It generally has a value between 1 and 2. By inserting Eqs. (2) and (5) into Eq. (4), we obtain the following differential equation: Then, the insertion of Eqs. (2) and (6) into Eq. (3) leads to the following differential equation: Eq. (7) can be analytically solved, which leads to an equation that describes the time-dependent SPV: Here, V0 is the SPV at t = 0, i.e., VSPV(0) = V0. The SPV relaxation rate is described by ∞ , which is related to the carrier lifetime, as defined by Eq. (5). ∞ is a parameter of the carrier lifetime that can be determined experimentally.

IV. PHOTOCATALYTIC ACTIVITY
A. Surface science approach There are many factors that influence the photocatalytic activity of TiO2 (and other photocatalysts): crystal structures, crystal morphology (particle size and shape), surface orien-tation of the crystal, carrier doping, surrounding environments, wavelengths and powers of irradiated lights, etc. It is difficult to identify the main factor and to understand the mechanism of photocatalysis. Using practical catalysts under working conditions is essential to understand the photocatalytic activity. On the other hand, the surface science approach is more appropriate to clarify the underlying fundamental physics of photocatalysis.
The use of bulk single crystals or single crystalline films with well-defined surfaces is an example of the surface science approach. Pioneering works in this domain were conducted by the DuPont Company and Carnegie Mellon University in 1998 [66,67]. They compared the photoreduction of Ag + to Ag metal from an AgNO3 aqueous solution on different rutile TiO2 crystal facets under illumination of filtered mercury lump and found that the order of photocatalytic activity was (101) > (111) ≈ (001) > (100) ≈ (110). More recently, Ahmed et al. examined the photocatalytic oxidation and hydroxylation of organic molecules on single crystal anatase and rutile TiO2 surfaces in aqueous environments and found that the anatase (101) surface exhibited higher activity than the rutile surfaces with (001), (100), and (110) orientations [18]. Luttrell et al. also reported that the anatase (001) surface had higher photodecomposition activity (of methyl orange in an aqueous solution) than the rutile (101) surface [20]. These results are in good agreement with the already recognized trend; namely, the photocatalytic activity of anatase TiO2 is superior to that of rutile TiO2 [15−17].
Another surface science approach for evaluating the crystal orientation dependence is the microanalysis of TiO2 microcrystals. Ohno et al. used a scanning electron microscope and observed a number of Pt and PbO2 deposits, which were formed by liquid-phase photocatalytic redox reactions, on each micro-size crystal in the TiO2 powder [68]. They found that the rutile (011) and anatase (001) facets hosted oxidation sites, while reduction sites were mainly on rutile (110) and anatase (011) facets. Tachikawa et al. employed a single-molecule fluorescence imaging technique to compare the photocatalytic reduction of a dye molecule on the (001) and (101) facets of a micrometer-sized anatase TiO2 crystal [69]. An interesting finding is that the (101) facet exhibited activity even when the microfocused UV light was irradiated only on the (001) facet, i.e., the (101) facet remained dark.
The work by Pan et al. somewhat combines the catalytic and surface science approaches [70]. They prepared anatase TiO2 crystal powders with predominant (001), (101), or (010) facets by controlling the synthesis parameters (concentration of reactants and reaction temperature) and compared the photocatalytic H2 evolution from a methanol solution. Although the facets terminated by fluorine atoms exhibit relatively low photoreactivity without an apparent facet dependence, a higher activity was observed on fluorine-free surfaces, with an activity order of (010) > (101) > (001) [70]. The authors have proposed that a determining factor should be a reduction potential of the excited electrons owing to a higher CBM position which depends on the crystal facets.
The clean TiO2 surfaces had low-energy electron diffraction (LEED) patterns, as shown in Figure 10. The (1×1) patterns were observed on the (110), (100), and (001) surfaces of rutile TiO2 as well as on the anatase TiO2(101) surface. The other two surfaces are known to undergo characteristic reconstructions; the rutile TiO2(011) surface [also referred to as the (101) surface in literature] develops a (2×1) reconstructed structure, whose atomic arrangement has been extensively debated [74,75], whereas a well-known 4×1/1×4 double domain structure is developed on anatase TiO2(001) [76]. The LEED patterns on these surfaces shown in Figure  10 support these surface reconstruction concepts.

Acetic acid adsorption
The photocatalytic activity of single-crystal TiO2 surfaces was assessed by UV-induced decomposition of adsorbed molecules. We chose acetic acid as a probe molecule, whose decomposition by the UV light was qualitatively monitored by XPS. The XPS measurements was carried out at beam line (BL) 13B of The Photon Factory [77] using a SES200 photoelectron energy analyzer (Gamma Data/Scienta) ( Figure 11).
The adsorption of acetic acid was conducted in a loadlock chamber with a base pressure lower than 1 × 10 −6 Pa. The TiO2 samples were placed in the presence of acetic acid vapor. The samples were kept at room temperature during ad-sorption process. The exposure amounts were between 10 L and 20 L (Langmuir; 1 L = 1.3 × 10 −4 Pa s), which are sufficient for adsorption saturation [78−80].
Acetic acid is known to adsorb on TiO2 surfaces in the form of acetate (CH3COO − ). On rutile TiO2(110), the two O atoms of acetate are bonded to the five-coordinated surface Ti atoms (Ti5c) [ Figure 12(a)] with a saturation coverage of 0.5 ML (monolayer; 1 ML is defined as the density of the five-coordinated Ti atoms, i.e., 5.2 × 10 14 cm −2 ) [79]. Figure  12(b) shows the XPS profiles in the C 1s and valence band regions of the acetate-adsorbed rutile TiO2(110) surface. The C 1s spectra show two peaks, at 285.8 eV and 289.2 eV, which are associated with methyl carbon and carboxylate  : Schematic illustration of XPS measurement system at BL-13B of the Photon Factory. The system was composed of analysis, preparation, and loadlock chambers. Sample cleaning was carried out in the preparation chamber and acetic acid adsorption was conducted in the loadlock chamber. An UV laser module was attached to the rear of the analyzer view port. carbon, respectively. The adsorption process induces a shift of the TiO2 valence band towards higher binding energies [lower panel in Figure 12(b)], which results in a more intense band-gap state just below the Fermi level. This suggests an increase in the density of reduced Ti, i.e., Ti 3+ , in the surface region, since the band-gap state originates from the Ti 3d state of Ti 3+ species, which are inevitably formed by the loss of bridging O atoms [81] when the clean surface is prepared under UHV conditions. O2 adsorption effectively compensates the defects in the bridging O rows so that the band-gap state is suppressed, as shown in Figure 3(e). However, O defects are not compensated by acetate. On the contrary, our observation implies a partial charge transfer from acetate to the surface Ti atoms through acetate−Ti5c bonds. This result is in contrast with an earlier report on the same system [79], where acetic acid adsorption suppresses the band-gap state. A possible explanation is that acetate can occupy the O defects when the defect density is high; this is based on the fact that the band-gap state intensity is higher on the surface studied in Ref. 79 than on our prepared sur-face. We also observed this adsorption-induced suppression of the band-gap state in another study [73], which examined the adsorption on a rutile TiO2(110) defective surface.
The amount of adsorbed acetic acid depends on the surface orientation of the TiO2 crystals ( Figure 13). Among the rutile surfaces, the (100) surface can accommodate the largest amount of acetic acid (0.63 ML), followed by the (110) surface (0.50 ML), the (001) surface (0.45 ML), and the (011) surface (0.41 ML). The saturation coverages are similar on the two anatase TiO2 surfaces, with 0.56 ML and 0.54 ML on the (101) and (001) surfaces, respectively. The order of the saturation coverage reflects the order of chemical reactivity toward acetic acid adsorption. Thus, the rutile TiO2(100) surface has the highest chemical activity among the six TiO2 surfaces.
We also examined the adsorption activity of a defective surface. The defective surface was prepared by Ar + sputtering (1.25 kV in 6 × 10 −6 Pa for 10 min) of a clean rutile TiO2(110) surface. The defect density, estimated from the analysis of the Ti 2p XPS profile, was 2 × 10 14 cm −2 [73]. This corresponds to 38% of the density of the bridging O atoms. The defective surface exhibits an even higher adsorption activity, with a saturation coverage of 0.66 ML, compared to rutile TiO2(100). The high density of the defects apparently facilitates acetic acid adsorption.

Effect of UV irradiation
The photocatalytic activity of the TiO2 catalysts is usually evaluated by the reaction rates of molecules and ions in gas phases [6,69] or in solutions [1−5, 7, 15−18, 20, 66−68, 70]. On the other hand, direct measurements of molecules adsorbed on the catalyst surfaces have also been used to assess the photocatalytic activity [19,78]. In our study, the photocatalytic activity of rutile and anatase TiO2 surfaces under UHV was evaluated through the UV-induced decrease of the amount of adsorbed acetic acid, i.e., by monitoring the C 1s XPS peak intensity [73].
A continuous-wave UV laser with a wavelength of 375  nm (3.31 eV) was used to irradiate acetate-saturated TiO2 surfaces. The laser was delivered with a power of 2.4 W cm −2 by a diode module (Obis 357LX, Coherent Inc.). The module was mounted on an x-y stage, which was attached to a MgF2 viewport on the back side of the SES200 analyzer ( Figure 11). The UV laser, thus, irradiated the sample surface through an analyzer slit and analyzer lens. The C 1s XPS profiles of the sample surfaces were obtained using SR with an energy of 753 eV as an excitation source. The spot size of the laser had a diameter of 1.6 mm on the sample surface [73], while the irradiation area of the SR light, whose incidence angle was 65° from the sample normal direction, was 310 μm × 40 μm [77]. The spatial overlap between the laser and the SR light was confirmed by the large Si 2p XPS peak shift of a Si(111) wafer (70 meV toward a higher binding energies) as a result of UV-induced SPV [73]. UV-laser irradiation leads to a gradual intensity decrease of the acetate C 1s peaks. Figure 14 shows two examples. The spectra in Figure 14(a, d) show the time-dependent changes of the C 1s peaks of acetic-acid-saturated rutile TiO2(001) and anatase TiO2(101) surfaces under irradiation by the UV laser. The peak intensities are diminished to ~80% of their original intensities after approximately 1 h of irradiation on both surfaces. However, the UV-induced photocatalytic decomposition/desorption of acetate is not the only cause of the peak intensity decrease. As shown in Figure 14(b, e), the intensity decrease is also observed even when the UV laser is not active. Thus, the SR light causes damage to acetate molecules on TiO2; this should be distinguished from photocatalytic decomposition.
The decrease in the peak intensity induced by simultaneous irradiation of UV laser and SR light is apparently higher than that induced by irradiation of SR light alone [ Figure  14(c, f)]. The same behavior was also observed on other   (001) surface [73]. The UV laser induces the decomposition/desorption of acetate; this is attributed to the photocatalytic phenomenon. It is worth noting that the photocatalytic reaction can proceed even in the absence of O2 and H2O, both of which are essential to form ROSs for photocatalytic reactions in ambient conditions, as mentioned in Section II.A. Although this is not conclusive, we speculate the following reactions for photocatalytic acetate decomposition/desorption without ROSs [78]:

Photocatalytic activity
To quantitatively evaluate the contribution of photocatalysis, we study the difference between the UV-on and UV-off data of the C 1s peak intensities [ Figure 14(c, f)]. In Figure  15, the net changes of the C 1s intensity on six TiO2 surfaces are shown. The C 1s peak intensity is diminished on four surfaces, while no change is observed on rutile TiO2(100) and (011) surfaces. The two latter surfaces are inactive with regard to the photocatalytic decomposition of acetate. A more interesting finding is that, among the four photocatalytically active surfaces, the activity depends on the surface orientation. The solid lines in Figure 15 are the best-fitted results using an exponential function: where I, t, and τph are the normalized C 1s peak intensity, reaction time (UV-laser irradiation time), and a decay constant, respectively. Since the intensity decrease is accurately reproduced by the exponential function, the photocatalytic decomposition/desorption of acetate is regarded as a pseudo-first-order reaction with a reaction rate constant of kph = 1/τph. Experimentally determined values of τph and kph are summarized in Table 2. The largest kph value is obtained on rutile TiO2(110), followed by anatase TiO2(101), rutile TiO2(001), and anatase TiO2(001). This order should reflect the photocatalytic activity. Rutile TiO2(110) and (011) are photocatalytically inactive, with kph = 0 min −1 .
We also verified the photocatalytic activity on a defective surface. The defective surface was prepared by lightly sputtering a rutile TiO2(110) surface that had surface O vacancies (with a density of roughly 2 × 10 14 cm −2 ) [73]. Since such vacancy sites are generally active during molecular adsorption, a higher saturation coverage is achieved on the defective surface than on the pristine surface, as shown in Figure 13. However, the defective rutile TiO2(110) surface has a lower photocatalytic activity than the pristine surface. τph is determined to be 2100 min and, thus, kph = 0.5 × 10 −3 min −1 , which is less than 1/5 of the value for pristine rutile TiO2(110). This result implies that the surface chemical activity is not the most important factor that influences the photocatalytic activity of TiO2.
A fundamental question is why the photocatalytic activity differs depending on the crystal surfaces rather than the bulk crystal structures. Moreover, it is apparent that the order of the photocatalytic activity (Table 2) is not correlated with the surface chemical activity ( Figure 13). To answer this question, we evaluated the photoexcited carrier lifetime on each TiO2 surface and verified the relation between the carrier lifetime and photocatalytic activity.

V. CARRIER LIFETIME A. Lifetime determined by TRXPS
As mentioned in Section III.C, the lifetimes of photoexcited carriers are determinable from transient changes of the SPV. The SPV on the TiO2 surfaces after UV-laser pulse irradiation was evaluated by a transient shift of the Ti 2p3/2 XPS peak [71,72]. We examined the carrier lifetime on four TiO2 surfaces; anatase TiO2(001), rutile TiO2(110), rutile TiO2(011), and defective rutile TiO2(110). An example of TRXPS measurement results is shown in Figure 16(a). Here, the change in the Ti 2p3/2 spectrum of anatase TiO2(001) as a function of delay time is demonstrated.
The TRXPS measurements utilizing the pump-probe method were carried out at BL07LSU of SPring-8 [82]. A second harmonic of an amplified Ti:sapphire laser (405 nm = 3.06 eV) was used as a pump light. The pulse duration of the laser was 35 fs and the repetition rate was 1 kHz. The power densities of the pump laser were typically between 12 and 48 mJ cm −2 pulse −1 . For the probe light, a 600-eV SR light was used. The operation modes of the storage ring were an F mode (a 1/14-filling bunch train and 12 bunches) and an H mode (11/29-filling bunch train and a single bunch), and SR pulses from isolated bunches were used for the probe light. The SR pulse duration was approximately 50 ps, which is the time resolution of the TRXPS measurements. Photoelectron energies were analyzed by a time-of-flight electron spectrometer (VG Scienta ARTOF 10k). Details of the measurement system are described elsewhere [52,83].
The Ti 2p3/2 peak of anatase TiO2(001) moves toward  Figure  16(a)]. The transient peak shift is attributed to the SPV. The direction of the shift (toward lower binding energies) indicates that an accumulation layer is formed on the anatase TiO2(001) surface. This UV-induced peak shift toward lower binding energies is also observed on rutile TiO2(110) and (011) surfaces. Thus, accumulation-type SCRs are formed on these TiO2 surfaces. This is reasonable because electron-donating O vacancies are unavoidable on TiO2 surfaces that are subjected to surface cleaning in UHV conditions. Figure 16(b) shows the delay times of the SPV shifts on anatase TiO2(001) and rutile TiO2(110) and (011). The delay time on the Ar + -sputtered rutile TiO2(110) surface is also shown. On all four surfaces, the SPV decreases as the delay time is prolonged, reflecting the decrease in the number of photoexcited electrons and holes with time due to electron-hole recombination ( Figure 8). However, the decreasing rate differs depending on the surface; the SPV on rutile TiO2(011) is swiftly diminished to zero within several ns, whereas much slower decreases are observed on other surfaces. These SPV behaviors should reflect the electron-hole recombination rate and, thus, the carrier lifetime. Namely, photoexcited carriers have a short lifetime on rutile TiO2(011), while the carriers survive for much longer on the other three surfaces.
For a quantitative evaluation of the carrier lifetime, the delay-time dependent SPV curves were fitted by Eq. (8). In the fitting procedure, the ideality factor η was fixed at 1.4 [72] and V0 (the SPV at t = 0 ns) and ∞ (the relaxation time in the absence of the SPV) were treated as variables. The sample temperature was T = 300 K. The best-fitted curves obtained from least-square fitting are shown as thick solid lines in Figure 16 Table 3.
As discussed in Ref. 72, several factors influence the carrier lifetime, i.e., ∞ . These are surface potential barrier height Vs (Figure 4), carrier-capture cross-section, thermal velocities of the carriers, and densities of the carrier trap states. Among these factors, the surface potential barrier height has the most significant influence on the carrier lifetime. In the next section, we discuss the relation between the lifetime and the barrier height.

B. Lifetime on modified surfaces
The carrier lifetime ∞ depends on the surface potential barrier height Vs as follows [72]: Here, WSCR and Sp are the width of the SCR and the surface recombination velocity, respectively. Since ∞ depends on Vs exponentially, a small change in Vs leads to a large change in ∞ , whereas changes in WSCR and Sp have a lower effect on ∞ . Thus, if the surface condition is modified and the magnitude of surface band bending is altered, i.e., the Vs value is changed, ∞ differs from those listed in Table 3. This fact complicates the situation when the photocatalytic activity is discussed on the basis of the photoexcited carrier behavior.
In our study, we verified the photocatalytic activity of TiO2 on acetate-covered surfaces, whereas the carrier lifetime was measured on adsorbate-free surfaces. Thus, we should estimate the carrier lifetimes on acetate-covered surfaces. This can be done if the adsorption-induced band bending is experimentally determined. Figure 17 compares the valence-band spectra of clean (dashed lines) and acetate-covered (solid lines) TiO2 surfaces. Acetic acid adsorption modifies the spectral line shape and seems to push the TiO2 band down to the higher binding energy side, as judged from the position of the VBM. The accumulation layers are already formed on the clean TiO2 surfaces, as mentioned in Section V.A. Thus, the adsorption enhances downward band bending and, hence, the surface potential barrier height. The adsorption-induced changes of the barrier height ΔVs are 0.05 eV, 0.06 eV, and 0.04 eV for anatase TiO2(001), rutile TiO2(011), and rutile TiO2(110), respectively. On the sputtered surface, on the other hand, the VBM position is hardly affected by adsorption. Now, we can estimate the carrier lifetime on the acetate-saturated surface ( ∞,Ac ) using the following equation [73]: This equation is obtained from Eq. (10) under the assumption that changes in η, WSCL, and Sp are negligibly small before and after acetic acid adsorption. The calculated ∞,Ac are 360 ns, 7 ns, and 450 ns on acetic-acid saturated surfaces of anatase TiO2(001), rutile TiO2(011), and rutile TiO2(110), respectively.
Regarding the defective rutile TiO2(110) surface, the situation is not straightforward, because the O defect densities were not the same for the surface used for photocatalytic activity measurements (2 × 10 14 cm −2 ) and that used for carrier lifetime measurements (3 × 10 14 cm −2 ) [73]. The larger density results in a deeper VBM position because of a larger magnitude of band bending. The VBM was 3.55 eV on the surface used for carrier lifetime measurements, whereas it was 3.50 eV on the surface used for photocatalytic activity measurements [73]. If the VBM is unaffected when the defective surfaces are covered with acetate, as shown in Figure  17, the ΔVs value should be −0.05 eV. Therefore, the carrier lifetime on the acetate-covered defective surface is calculated to be ∞,Ac = 60 ns. The ΔVs and ∞,Ac values are also listed in Table 3.

VI. ACTIVITY-LIFETIME CORRELA-TION
Photocatalytic reactions are generally complex and many elemental steps contribute to the overall reaction path. However, all photocatalytic reactions are initiated by the chemical species adsorbed on the TiO2 surface capturing photoexcited electrons and holes. If this initial step is a rate-determining step, the reaction rate of the photocatalysis can be approximated as:  Figure 18 shows the relationship among these param-  eters. It is apparent that there is a linear and positive correlation between kph and ∞,Ac , whereas no correlation is observed between kph and [A]. Since a longer lifetime leads to higher carrier concentration on the surface, it is natural to correlate ∞,Ac with [c]. Therefore, regarding the photocatalytic decomposition/desorption of acetate, the carrier lifetime and resultant accumulation of carriers on the surface are major factors that influence the photocatalytic activity.
It should be noted that intensities of the UV lasers used in our study are much higher than the UV light intensity in the sunlight. For example, a time-averaged photon flux of the 405-nm pulsed laser with a power density of 12 mJ cm −2 pulse −1 , which was used to determine the SPVs on anatase TiO2(001) and rutile TiO2(110) (Figure 16), is in the order of 10 17 photons mm −2 s −1 , which is larger by four to five orders of magnitude than the photon flux of the 400-nm light in the sunlight. Namely, TiO2 photocatalysts under the sunlight work in a very weak excitation condition. It is known that the dynamics of the photoexcited carriers differs depending on the carrier concentration, i.e., the excitation condition [84]. Nevertheless, the essence of the carrier dynamics is kept intact as depicted in Figure 2. Thus, the correlation between the carrier lifetime and the photocatalytic activity could be also be found under the weak excitation condition.
Another important implication noticed from Figure 18 is that anatase TiO2 is not always more active than rutile TiO2. The surface potential barrier height Vs is the most influential parameter for the carrier lifetime, as inferred from Eq. (10). Thus, a TiO2 surface having a large Vs in the working condition should have a chance to exhibit a high photocatalytic activity regardless of the bulk structure. In other words, the photocatalytic activity is controllable through surface modification and the resulting change in Vs.
It is worth mentioning that the importance of Vs is lessened when the size of the photocatalysts is reduced to the nanometer. Zhang and Yates pointed out in their review paper [33] that band bending is negligible in nanoparticles with a diameter of less than 10 nm. In this case, the carrier trap process by defect states is more important for the carrier lifetime. Morgan and Watson theoretically verified the defect formation in anatase and rutile TiO2 crystals and found that the O defect formation is more favorable in anatase TiO2 than in rutile TiO2 [85]. Thus, we can speculate that anatase has a longer carrier lifetime than rutile in the form of nanocrystals.
One of our conclusions deduced from preceding previous study [71] is that the carrier lifetime is expected to be longer on anatase TiO2(001) than on rutile TiO2(110) in the absence of a surface potential barrier. This trend can be explained by the different type of bulk band gap (direct and indirect band gaps); however, the different defect concentration in the bulk of the crystals should also be taken into account. A more detailed discussion on the determining factors of carrier lifetime beyond the surface barrier potential can be found in Ref. 72.

VII. CONCLUDING REMARKS
An increasing demand for clean and renewable energy, in order to develop a sustainable society, has accelerated the research and development of photocatalysts. TiO2 has been the most extensively studied photocatalyst for nearly half a century [1, 2, 9−12], and considerable progress has been achieved in understanding various photocatalytic phenomena. One of the most interesting properties of TiO2 photocatalysis is the crystal-structure dependence of the photocatalytic activity, namely, a higher activity of the anatase form compared to that of the rutile form [15−20]. Another striking feature is the fact that crystal surfaces with different orientations exhibit different photocatalytic activities [18, 20, 66−70]. Both catalytic and surface-science techniques have been employed to establish a precise view of these photocatalytic properties.
The surface-orientation dependence is purely a surface phenomenon, since the bulk structure is identical. An often employed explanation is that each surface has a different chemical reactivity and hence, the photocatalytic activity depends on the surface orientation. On the other hand, pho- toexcited carriers also contribute to the surface-dependent activity. The carrier behavior is complex, especially in the near-surface region where a charge accumulation layer or a depletion layer is developed, because these space charge layers act as a surface potential barrier for electrons or holes when they diffuse from the bulk to the crystal surface [33]. Thus, if the relationship among the chemical reactivity, the carrier behavior, and the photocatalytic activity is clarified on each crystal surface, it will provide a significant insight on the mechanism of the surface-dependent photocatalytic activity and, thus, on the general photocatalysis mechanism of TiO2.
We employed a surface science approach to study this problem [71−73]. Using well-defined surfaces of anatase and rutile TiO2 single crystals, the chemical activity of acetic acid adsorption, lifetime of photoexcited carriers, and photocatalytic decomposition/desorption of adsorbed acetic acid were examined by XPS and TRXPS under UHV conditions. The chemical activity was assessed by the saturation amount of adsorbed acetic acid. The carrier lifetime was determined by temporal evolution of the UV-induced SPV. The photocatalytic activity was estimated via the time-dependent intensity decrease of the acetate C 1s XPS peak, a result of the UV-induced decomposition/desorption of acetate. Although there is no correlation between the photocatalytic activity and chemical reactivity, the photocatalytic activity is linearly and positively correlated with the carrier lifetime. This result indicates that the carrier lifetime is a more influential factor than the chemical activity of the photocatalyst surface with regard to the photocatalytic activity of acetic acid.
Another interesting finding is that the crystal structure of TiO2, i.e., anatase or rutile polymorph, is not a decisive factor [72] despite the prediction that the bulk carrier lifetime is longer in the anatase crystal than in the rutile crystal (owing to the bulk band structure [19] and/or the difference in the defect concentration in the bulk [85]). Instead, the potential barriers in the SCR of the crystal surfaces significantly affect the carries that are directly involved in the surface reactions [71,72]. Therefore, the surface electronic structure of the TiO2 crystals should be considered when discussing the photocatalytic activity in terms of carrier dynamics.
For future studies, the linear lifetime-activity correlation of molecules other than acetic acid should be examined. It is also important to confirm whether the same linear relation applies to photocatalytic reactions in working conditions, i.e., in the presence of O2 and H2O that are converted to ROSs [10,11]. Such measurements are challenging because it is difficult to evaluate the surface electronic structure by electron spectroscopy techniques like XPS due to the required UHV conditions. However, recent progress in the measurement of electron spectra in ambient and near-ambient conditions [86−89] enabled us to obtain results under these challenging conditions. Therefore, we can continue to explore the chemical and physical origin of the high photocatalytic activity of TiO2.