What Determines the Lifetime of Photoexcited Carriers on TiO2

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What Determines the Lifetime of Photoexcited Carriers on TiO Surfaces? Kenichi Ozawa, Susumu Yamamoto, Ryu Yukawa, Roya Liu, Masato Emori, Koki Inoue, Taku Higuchi, Hiroshi Sakama, Kazuhiko Mase, and Iwao Matsuda J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b10136 • Publication Date (Web): 08 Dec 2016 Downloaded from http://pubs.acs.org on December 9, 2016

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The Journal of Physical Chemistry

What Determines the Lifetime of Photoexcited Carriers on TiO2 Surfaces? Kenichi Ozawa,∗,† Susumu Yamamoto,‡ Ryu Yukawa,‡,⊥ Roya Liu,‡ Masato Emori,¶ Koki Inoue,¶ Taku Higuchi,¶ Hiroshi Sakama,¶ Kazuhiko Mase,§,∥ and Iwao Matsuda‡ Department of Chemistry, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551, Japan, Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan, Department of Physics, Sophia University, Chiyoda-ku, Tokyo 102-8554, Japan, Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan, and SOKENDAI (The Graduate University for Advanced Studies), Tsukuba, Ibaraki 305-0801, Japan E-mail: [email protected] Phone: +81 3 5734 3532. Fax: +81 3 5734 2655

∗

To whom correspondence should be addressed Tokyo Institute of Technology ‡ The University of Tokyo ¶ Sophia University § KEK ∥ SOKENDAI ⊥ Current address: Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan †

1 ACS Paragon Plus Environment


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Abstract Pump-probe time-resolved X-ray photoelectron spectroscopy measurements have been carried out to comparatively assess the relaxation process of the photoexcited states on pristine and Ar+ -sputtered TiO2 (110) surfaces and a TiO2 (011)-2×1 surface, on which the accumulation-type space charge layers are developed. Ultraviolet laser irradiation induces a surface photovoltage (SPV) of around 0.1 eV. The SPV relaxation time on pristine TiO2 (110) is determined to be approximately 100 ns and is doubled on the sputtered surface. In contrast, a much shorter time of 1 ns is observed on TiO2 (011)-2 × 1. The difference in the relaxation time on the two TiO2 (110) surfaces is explained by differences in the O vacancy density on the surface as well as the barrier height of the surface potential for the photoexcited holes. A large hole capture cross section of a state characteristic of TiO2 (011)-2 × 1 is, on the other hand, responsible for the fast SPV relaxation on this surface.

INTRODUCTION A novel property of titanium dioxide (TiO2 ) as a photocatalyst has attracted attention from both scientific and industrial communities since the discovery of the Honda-Fujishima effect. 1 Photocatalytic activity is emerged by absorption of the ultraviolet light and creation of excited electrons and holes, which diffuse to the surface and interact with adsorbed species. Therefore, extensive effort has been devoted to elucidate dynamics of excited carriers by timeresolved techniques such as reflectance spectroscopy, 2–4 absorption spectroscopy, 5–7 photoluminescence measurements, 6,8 photoconductance measurements, 6,9,10 photoelectron spectroscopy, 11,12 etc. There is a positive correlation between the photoexcited carrier lifetime and the photocatalytic activity; namely, the longer the carrier lifetime is, the higher the photocatalytic activity is. 3,6,9,11 Although a recent study has suggested that a relation between the activity and the carrier lifetimes is more complex in real TiO2 catalysts, 7 a simple activity-lifetime 2 ACS Paragon Plus Environment

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relevance is naturally understood because a chain reaction of a photocatalytic reaction is initiated by the interaction of a photoexcited carrier with an adsorbate so that there is an increasing chance for the carriers to interact with the chemical species as the carriers survive longer. The carriers behave under a strong influence of the electronic structure of the photocatalyst surface. Band bending near the surface plays an essential role because the carriers must overcome a potential barrier by this band bending to be transported from the bulk to the surface. 13 Although many studies have been conducted to assess the carrier dynamics, only a few have paid attention to the effect of band bending on the carrier lifetime. One of such studies is our time-resolved X-ray photoelectron spectroscopy (TRXPS) study, 11 which has indicated a relevance between the magnitude of band bending and the carrier lifetime on rutile and anatase TiO2 surfaces. It is revealed that the photoexcited carriers survive longer on the anatase TiO2 surface than on the rutile TiO2 surface if the surface barrier heights are comparable. This result explains well the higher photocatalytic activity of anatase TiO2 than rutile TiO2 . Moreover, the results imply the possible control of the activity by the manipulation of band bending. While the importance of band bending has been recognized, 11,13 a contribution of a thermal velocity of the carriers, a carrier capture cross section as well as a density of the capture states, all of which can be determining factors of the lifetime besides band bending, 14 should also be taken into account. Otherwise, we cannot answer the question why the carrier lifetimes are longer on some semiconductor surfaces than the others even when the magnitudes of band bending are equivalent. In the present study, TRXPS has been employed to comparatively determine the relaxation time of laser-induced surface photovoltage (SPV) on three rutile TiO2 surfaces, i.e., pristine and Ar+ -sputtered TiO2 (110) surfaces and a TiO2 (011)-2 × 1 surface. The SPV relaxation time, and henceforth the lifetime of the photoexcited carriers, is found to be longer on the sputtered TiO2 (110) surface than on the pristine surface, and the SPV relaxes much faster on TiO2 (011) than on TiO2 (110). The origin of the surface dependence of the



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relaxation times is discussed within the framework of the thermionic emission model.

EXPERIMENTAL METHODS Single crystals of rutile TiO2 with (110) orientation (Shinkosha Co.) and (011) orientation (MTI Co.) were used as substrates. The substrate surfaces were cleaned by cycles of Ar+ sputtering (1 kV in 1 × 10−4 Pa Ar for 10 min) and annealing at 900 K in O2 atmosphere (1 × 10−4 Pa) for 30 min until no carbon-related peak was detected in the photoelectron spectra and sharp low energy electron diffraction (LEED) patterns were obtained. The LEED measurements revealed that, while the TiO2 (110) surface was unreconstructed, a well-known 2 × 1 superstructure was formed on TiO2 (011). 15 Structural models of these surfaces are shown in Figure 1a. The clean TiO2 (110) surface was further subjected to Ar+ sputtering (1.25 kV in 6×10−6 Pa Ar for 10 min) in order to change the density of surface O vacancies. The sputtered surface did not give any LEED pattern, but the LEED spots were again observable after short annealing at 900 K in O2 atmosphere. To assess the electronic structure of the clean TiO2 (110) and (011) surfaces, high resolution photoelectron spectroscopy measurements were carried out using a synchrotron radiation (SR) light at the beamline (BL) 13 B of the Photon Factory, High Energy Accelerator Research Organization (KEK). 16 The spectra were acquired by an hemispherical electron energy analyzer (Gamma Data/Scienta SES200) with overall energy resolutions of 90 meV at the photon energy (hν) of 100 eV and 130 meV at hν = 600 eV, which were evaluated from the Fermi cut-off of a Ta foil. Binding energies (BEs) of the spectra were referenced to this cut-off position. The TRXPS study was done at BL07LSU of SPring-8. 17 A pump-probe method was employed for the time-resolved measurements. The second harmonic of an amplified Ti:sapphire laser pulse with a duration of 35 fs and a repetition rate of 1 kHz was used for the pump


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light. The photon energy of the pump laser (3.06 eV) exceeded the band gap energy of rutile TiO2 (Eg = 3.0 eV 18 ). The SR light (hν = 600 eV) was used for the probe light. The width of the SR pulse was about 50 ps, and a time interval between the pulses was 4.79 µs (an H-mode operation). A time-of-flight electron energy analyzer (VG Scienta ARTOF 10 k) was used to acquire TRXPS spectra. Details of the measurement system are found elsewhere. 19,20 The BE of the spectra was referenced to the Au 4f7/2 peak of a gold foil, which was in electrical contact with the TiO2 samples. All the measurements were carried out at room temperature.

RESULTS Figure 1b shows valence-band spectra of the clean TiO2 (110) and TiO2 (011)-2 × 1 surfaces. The O 2p dominant band is observed between 3 and 10 eV on both surfaces with valence-band maximum (VBM) positions, determined by extrapolating the leading edge to the baseline, at 3.40 eV and 3.48 eV on the (110) and (011) surfaces, respectively. Deeper positioning of the states on TiO2 (011) than on TiO2 (110) is also observed in Ti 2p core levels. The Ti 2p3/2 peak positions are determined at 459.1 eV and 459.2 eV on TiO2 (110) and TiO2 (011), respectively (Figure 1c). The energy difference (0.1 eV) is almost the same as the difference of the VBM position (0.08 eV). These results imply that the BE differences should reflect the difference in the magnitude of band bending on the two surfaces. The TiO2 crystals used in this study were nearly transparent. However, they turned to be bluish after annealing during sample cleaning as a result of the formation of bulk O vacancies and the electron donation, 21 This leads to an increase in the chemical potential in the bulk. Since the cleaning procedure was the same for both TiO2 (110) and (011), the Fermi-level positions within the band gap in the bulk should be nearly the same. Assuming that the Fermi level lies just below the conduction band minimum (CBM) in the bulk, 22,23 the BE of the bulk VBM is around 3.0 eV because of Eg = 3.0 eV. On the other hand, the



(a) Surface structures (side view)

TiO2(110)

hn = 100 eV

TiO2(011)-2㽢1

TiO2(110)

TiO2(110)

x 30

sputtered TiO2(110)

x 30

0

(d) In−gap states on TiO2(011) Intensity (arb. units)

TiO2(011)

x 30

10 5 Binding Energy (eV)

(c) Ti 2p core level hn = 600 eV

TiO2(011)


hn = 100 eV

hn = 74 eV Intensity

O

(b) Valence band Intensity (arb. units)

Ti

Intensity (arb. units)

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clean 3

3

H dosed

2 1 0 Binding Energy (eV)


0

Figure 1: (a) Schematic structural models of the TiO2 (110)-1 × 1 and TiO2 (011)-2 × 1 surfaces. (b) Valence-band spectra of TiO2 (110) (both pristine and sputtered surfaces) and TiO2 (011)-2 × 1. (c) Ti 2p core-level spectra of pristine TiO2 (110) and TiO2 (011)-2 × 1. Triangles in Figure 1b indicate the in-gap states. Vertical bars in Figures 1b and 1c show the positions of the VBM and the Ti 2p3/2 peak, respectively. (d) The spectral lineshape in the band gap region of TiO2 (011) (shown by dots) is reproduced by two Gaussian peaks (red solid lines) with a background curve (a black solid line), also drawn by a Gaussian function. An inset shows the influence of H exposure on the in-gap states. The H atoms, which were formed by cracking H2 by a hot tungsten filament, were dosed onto TiO2 (011)-2 × 1 at room temperature.


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determined surface VBMs are larger than 3.0 eV on both surfaces. Thus, the TiO2 bands should bend downwardly at the surfaces to form accumulation-type space charge layers. A larger downward bending is induced on TiO2 (011) than TiO2 (110) because of the deeper positioning of the VBM on the former surface than the latter. A close examination of the spectrum of TiO2 (110) shows an electronic state in the band gap region (Figure 1b). This peak, whose maximum is at 0.8 eV, is assigned to the Ti 3d state of reduced Ti3+ formed upon the formation of surface O vacancies. 24 In contrast, two states are found at 0.7 eV and 2.2 eV on TiO2 (011). The shallower state is also associated with the reduced Ti3+ species, since the intensity of this state is enlarged upon H adsorption, as demonstrated in the inset of Figure 1d. This intensity enhancement is due to the fact that adsorbed H acts as an electron donor and donated electrons reside in the Ti 3d state. 25 Thus, the Ti 3d states of Ti3+ are formed at < 1 eV irrespective of surface orientation. The H-dosed experiment also suggests that the deeper state (2.2 eV) on TiO2 (011) is another surface-localized state, since the H adsorption reduces the emission intensity (Figure 1d). Although the exact origin of this state is not known at present, it could be related to a “new” two-dimensional TiO2 phase with the (2 × 1) structure, 26 which is different from that shown in Figure 1a. Unlike the TiO2 (011) surface prepared in the preceding study, 26 a fractional coverage of the new phase is minor in the present study because the intensity of the deep state is very low (Figure 1d). This may explain the reason why the direction of band bending is different between the present study (downward bending) and the preceding study (upward bending). 26 As the TiO2 surfaces are subjected to Ar+ sputtering, the O vacancies are preferentially formed and the density of reduced Ti3+ is increased. This leads to the growth of the Ti 3d state of Ti3+ at 0.8 eV, as demonstrated in the valence-band spectrum in Figure 1b. Furthermore, Ti 2p3/2 spectra in Figure 2a capture the feature of the increasing density of Ti3+ by Ar+ sputtering. The intensity of the Ti3+ -originated Ti 2p3/2 peak, which is shifted by 1.3 eV from the Ti4+ peak, is small on the pristine TiO2 (110) and (011) surfaces.



(a) Ti 2p3/2

(b) VB

hν = 600 eV

hν = 600 eV WSCL = 3 nm

TiO2(011)−2x1 CBM

0.0 0.5


Eg = 3.0 eV

TiO2(110)

VBM +

Ar −sputtered TiO2(110)

TiO2(011)

Ti

4+

3.0 3.5

Binding Energy (eV)

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sputtered TiO2(110)

Ti

3+

TiO2(011)−2x1 +


TiO2(110) VBM

gap

TiO2(110) VB

460 Binding Energy (eV)

455


0

Figure 2: (a) Ti 2p core-level spectra of three TiO2 surfaces. Curves drawn by dots are the raw spectra, and dashed lines are the Shirley-type background curves. The background subtracted peaks are fitted by Voigt functions, which reproduce both Ti4+ and Ti3+ components (indicated by hatched areas). (b) Photoelectron spectra in the valence-band onset region. Vertical bars indicate the VBM positions, which correspond to the intersections of the leading edge lines and the baselines. An inset shows band bending profiles of the three surfaces.


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However, there is a substantial Ti3+ contribution on the sputtered TiO2 (110) surface. The intensity ratio of the Ti3+ peak to the total Ti 2p3/2 peak (the sum of the Ti3+ and Ti4+ peaks) is 4.5% on pristine TiO2 (110), while it increases to 19.5% after sputtering. The Ti3+ intensity accounts for 3.5% on TiO2 (011)-2×1. From these intensity ratios, the Ti3+ densities are estimated to be 1.7 × 1014 cm−2 [TiO2 (110)], 6 × 1014 cm−2 [Ar+ -sputtered TiO2 (110)] and 8 × 1013 cm−2 [TiO2 (011)-2 × 1]. Details of the estimation procedure are given in the Supporting Information. The amount of Ti3+ seems to correlate with the VBM position on the surface. Figure 2b shows enlarged valence-band spectra in the VBM region measured with hν = 600 eV. The VBMs on TiO2 (110) and (011) are, respectively, 3.40 eV and 3.50 eV, which are nearly the same as those determined from the spectra in Figure 1b. The BE of the VBM on sputtered TiO2 (110) is the largest among the three surfaces to be 3.55 eV. Thus, the VBM tends to be deeper as the surface density of Ti3+ is larger. In the inset of Figure 2b, the profiles of band bending on the three TiO2 surfaces are depicted. Here, it is assumed that the bulk CBM lies just above the Fermi level and that the band gap energy is 3.0 eV irrespective of the depth from the surface. The magnitudes of band bending (Vs ) are, thus, 0.40 eV, 0.55 eV and 0.50 eV for pristine and sputtered TiO2 (110) and TiO2 (011)-2 × 1, respectively. The overall band bending profile is obtained by solving the Poisson’s equation (see the Supporting Information). The width of the space charge layer (WSCL ) is ∼3 nm. In Table 1, Vs and WSCL on each TiO2 surface are listed. Although there are several differences in the band bending profiles, i.e., Vs , WSCL and the band bending curvature, the overall structure is similar among the three surfaces. However, they exhibit a characteristic and interesting photoresponse depending on the surface. Figure 3a shows results of the pump-probe TRXPS measurements of the Ti 2p3/2 core level. Delaytime dependences of the spectra for the three surfaces are compared. The delay time (t) is defined as a time difference between the pump laser pulse and the probe synchrotron radiation pulse. The bottom curve in each panel is a spectrum without irradiation of the



(a) Ti 2p3/2 spectra delay time

TiO2(110)

0.2

2

10 ns

0.1

0.5 ns Laser off


+

Ar −sputtered TiO2(110) delay time 48 mJ/(cm2pulse) 10 ns

SPV (VSPV) (eV)

1 ns

0.0 +


0.2 0.1

Laser off

TiO2(011)

0.2 0.1 0.0

0.1 TiO2(011)

40 mJ/(cm2pulse)

delay time 1 ns

100 1 10 Delay Time ( t ) (ns)

(d) SPV process

0.5 ns 0.2 ns Laser off

4

2 0 −2 −4 Relative Binding Energy (eV)

40

trap states

band gap

bulk

1 ns delay

10 2 Laser off

0.2

2 0 −2 −4 Relative Binding Energy (eV) 1 ns delay

TiO2(110)

0.1 0.0

0 20 40 2 Laser Power ( I ) [mJ/(cm pulse)]

e

CBM

VBM

TiO2(110)

19

4

1 ns 0.4 ns

2

mJ/(cm pulse)

0.0

SPV (VSPV) (eV)

40 mJ/(cm pulse)

laser power


TiO2(110)

(c) Laser PW dependence

(b) SPV relaxation

laser

SPV relaxation surface

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h

[ground state]

SPV

shift

(generation) (separation) (diffusion & capture) (recombination)

Figure 3: (a) Delay-time dependences of the Ti 2p3/2 spectra with the Shirley-type backgrounds subtracted. The 3.06-eV laser and the 600-eV synchrotron radiation were used as pump and probe lights, respectively. The laser power densities used are displayed in each panel. Smooth lines through the spectra are results of least-square fitting by Voigt functions, whose maxima are indicated by triangles. The “laser-off” and “laser-on” spectra were measured with 208 kHz and 1 kHz repetition rates, respectively. We have confirmed that there is no energy shift even when the laser-off spectra are measured at 1 kHz. (b) Change in the SPV as a function of the delay time. Circles with error bars are the experimental data. The error bar represents the 95% confidence interval of the peak position determined by peak fitting. Some data points are average values for multiple measurements, and the error bar in this case covers these multiple data points. (c) Upper: A laser power dependence of the Ti 2p3/2 spectrum of pristine TiO2 (110). The spectra were measured at the delay time of 1 ns. Lower: Change in the SPV as a function of the laser power. The experimental data are shown by circles with error bars. A solid line is obtained by VSPV = ηkB T ln(1 + γI) with η = 1.4 and γ = 1 cm2 mJ−1 . (d) A schematic drawing of a temporal evolution of the laser-induced SPV.


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pump laser, and its peak position is used as a BE reference. As the surfaces are shot by the laser pulse, a shift towards the lower BE side is induced on all surfaces. The shift amount is large at short delay times and diminishes at longer times. Such a delay-time dependence is easily recognized in Figure 3b, where the peak shift is plotted against the delay time. On both pristine and sputtered TiO2 (110) surfaces, the laser-induced shift is around 0.1 eV at t < 1 ns and decreases to zero at > 100 ns. In contrast, the peak shift is already negligible at 1 ns on TiO2 (011), and the observable shift is limited at < 1 ns. The laser induced Ti 2p3/2 peak shift is interpreted to be caused by an SPV, because (1) the shift towards the lower BE side coincides with a partial reduction of downward band bending and (2) the magnitude of the shift is enlarged with the intensity of the pump laser. Figure 3c demonstrates the latter phenomenon. As the laser intensity is increased, the Ti 2p3/2 peak shift, which is equal to the induced SPV, is enlarged. The relation between the laser intensity (I) and the SPV (VSPV ) is given by VSPV = ηkB T ln(1 + γI). 27 kB and T are the Boltzmann constant and the sample temperature, respectively. η is an ideality factor in a Schottky diode model. 28 γ defines the efficiency of the optical response. A solid line in the lower panel of Figure 3c is a result of least squares fitting, in which η and γ are treated as variables. The best-fitted curve is obtained with η = 1.4 and γ = 1 cm2 mJ−1 . According to the study by Sah et al., η takes a value between 1 and 2, 28 and η = 1.4 falls in this predicted range. The value of 1.4 means that a fraction of the photoexcited electrons and holes should be recombined in a region other than the surface, although the dominant recombination still proceeds on the surface as we will discuss in Sec. IV. The γ value, on the other hand, is much smaller than those for Si-related systems such as SiO2 /Si(100) (2 × 104 cm2 mJ−1 ) 27 and In/Si(111) (1 × 104 cm2 mJ−1 ), 29 but it is within the range of the reported values for metal-oxide systems, 31,32 This suggests that the observation of the SPV is more difficult on the oxide surfaces than on the Si surfaces, although γ depends largely on both the energy of the pump laser and the band gap of the materials.



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Table 1: Surface potential barrier heights (Vs ), widths of the space charge layer (WSCL ), SPV relaxation times (τ∞ ), effective surface recombination velocities (Sp∗ ), and densities of hole capture states (Npt ).

a

Vs Npt WSCL τ∞ a Sp∗ −1 (eV) (nm) (ns) (cm s ) (cm−2 ) TiO2 (110) 0.40 2.8 110 (70–220) 2.5 1.7 × 1014 sputtered TiO2 (110) 0.55 2.9 230 (150–420) 1.3 6 × 1014 TiO2 (011)-2 × 1 0.50 3.4 1.3 (0.9–2) 2.6 × 102 1.6 × 1014b Values are obtained at η = 1.4, and those in parentheses are given when η varies between 2 and 1. b Npt = Npt,sh + Npt,dp with Npt,sh = Npt,dp .

DISCUSSION Figure 3d depicts a time sequence of the optical response that the TiO2 surfaces exhibit from the electron-hole pair generation upon laser pulse irradiation to the electron-hole recombination. The SPV is induced when the electrons and the holes are spatially separated and diminishes gradually during the diffusion-and-capture process. The important finding of the present study is that the SPV relaxation time depends strongly on orientation of the rutile TiO2 crystal, i.e. the (110) and (011) surfaces, rather than the degree of the surface reduction, i.e. the pristine and sputtered (110) surfaces (Figure 3b). A faster relaxation on TiO2 (011) than TiO2 (110) is in good agreement with the results of the microwave photoconductivity decay measurements, 10 although the decay time is longer in Ref. 10 (a sub-microsecond range) than in the present study probably because of the different excitation condition. To quantify the SPV relaxation, the relaxation time is evaluated by least-square fitting of the VSPV − t plots (Figure 3b) using the equation which expresses the temporal variation of the SPV [VSPV (t)]. In the framework of the thermionic emission model, 27,30 VSPV (t) is expressed as

{

[

(

V0 VSPV (t) = −ηkB T ln 1 − 1 − exp − ηkB T

}

)]

e

−t/τ∞

.

(1)

τ∞ defines how fast the SPV curve decays. From the definition, 27 τ∞ is a relaxation time


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in the absence of the SPV (VSPV = 0 eV). V0 is the SPV at t = 0 ns. Least-squared fitting was carried out while V0 and τ∞ were treated as variables, and the best-fitted results are shown by solid lines in Figure 3b. Assuming η = 1.4 for all three surfaces, τ∞ is 110 ns and 230 ns for the pristine and sputtered TiO2 (110) surfaces, respectively, whereas a much smaller value of 1.3 ns is obtained for TiO2 (011). The same data sets give τ∞ = 70–220 ns for TiO(110), 150–420 ns for sputtered TiO2 (110) and 0.9–2 ns for TiO2 (011) when η varies between 2 and 1. V0 is 0.12 eV irrespective of the η values for all three surfaces. Since the error bar at each data point is large (Figure 3b), evaluated τ∞ should have relatively large uncertainty. However, the relaxation time for pristine TiO2 (110) is in good agreement with that reported for the same surface in our previous study (τ∞ = 80–280 ns), 11 indicating the validity of the present quantitative analysis. In summary, when the O vacancies are introduced on TiO2 (110) by Ar+ sputtering, the relaxation becomes about twice slower than that on the pristine surface. In contrast, the relaxation on TiO2 (011) is around 100 times faster than on TiO2 (110). As the electrons and holes are generated in the space charge layer, they are swiftly drifted to the opposite direction along the potential gradient. As illustrated in Figure 3d, the electrons move to the surface and are trapped by a surface trap state (most probably an unoccupied Ti 3d state). A fraction of the excited electrons arriving at the surface may also be accommodated in the bottom of the potential well, while they are eventually trapped by the surface trap state. The holes are, on the other hand, drifted to the bulk end of the space charge layer. Subsequently, they thermally diffuse back to the surface and are trapped by occupied trap states. Therefore, the SPV relaxation time should be governed by the hole diffusion-and-capture process rather than the electron drift-and-capture process in the present systems where the space charge layer is an accumulation type. It is important to note that the “surface” mentioned here is a boundary between the region where the carrier trap states are negligible and the region which contains the trap states such as the O-vacancyderived Ti 3d states. The O vacancies should be formed not only on the very surfaces of the



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crystals but also in the second or third layers, especially on the sputtered TiO2 (110) surface. Thus, the electrons and holes arriving at the trap-state-containing region are trapped and recombine so that the boundary is treated as a virtual surface. In the hole diffusion-and-capture process, the accumulation layer acts as a potential barrier with a height of Vs . Thus, it is easy to speculate that the SPV relaxation becomes slower on the surface with larger Vs . Such a simple dependence of τ∞ on Vs is valid as far as we compare the same materials with different surface electronic structures. In the present study, all the systems we examine are rutile TiO2 single crystals with different surface conditions. Nevertheless, τ∞ apparently does not correlate with Vs (Table 1). This indicates that some factors other than Vs should have a large influence on the relaxation. In the hole-related process, τ∞ is given by the sum of a surface-recombination-velocity term and a diffusion term; 33

τ∞ =

WSCL 4 + ∗ Sp Dp

(

WSCL π

)2

.

(2)

Here, the space-charge-layer width WSCL is used instead of the thickness of the sample crystal because the photoexcited carriers distribute within the space charge layer and because dynamics of these carriers determines the SPV relaxation time. Sp∗ is an “effective” surface recombination velocity of the holes, which is defined by eq. 3 described below. Dp is a hole diffusion constant. Eq. 2 holds when the electron-hole recombination proceeds only on the surface side and is negligible at the bulk end of the accumulation layer. 33 This condition is rationalized by the anisotropic distribution of the electrons and holes in the space charge layer after the charge separation. Since WSCL and Dp are ∼3 nm (Table 1) and 1.34 × 10−2 cm2 s−1 , 34 respectively, the contribution of the diffusion term to the overall relaxation time τ∞ is quite small with < 2 ps. Thus, the relaxation time is approximated as τ∞ ≃ WSCL /Sp∗ in the present TiO2 systems. In Table 1, evaluated Sp∗ values on three surfaces are given.


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The effective surface recombination velocity is defined as a surface recombination velocity Sp on the surface with a surface potential Vs . It is given by 14,35 Sp∗ = Sp exp[−Vs /(ηkB T )],

(3)

Sp = σp vpth Npt ,

where σp , vpth and Npt are a hole capture cross section, a thermal velocity of the holes and a surface density of the hole capture states, respectively. As the holes diffuse to the surfaces, they are captured by the “surface”-localized occupied states which should lie above the VBM. The candidate of such a state on pristine and sputtered TiO2 (110) is the Ti 3d-derived in-gap state at < 1 eV. The density of this state equals the Ti3+ density and, thus, Npt are 1.7 × 1014 cm−2 and 6 × 1014 cm−2 for the two TiO2 (110) surfaces (Table 1). The hole thermal velocity in rutile TiO2 is 3 × 106 cm s−1 , which is estimated from vpth = (kB T /m∗p )1/2 with a hole effective mass m∗p ≃ 6me 36 (me being the rest mass of an electron). Thus, the hole capture cross sections are determined by eq. 3 to be σp = 3 × 10−16 cm2 and 3 × 10−15 cm2 on pristine and sputtered TiO2 (110), respectively. The difference may reflect the difference in nature of the in-gap states. Nevertheless, σp of the shallow in-gap state is of the order of 10−16 –10−15 cm2 . On TiO2 (011)-2 × 1, the deep in-gap state at 2.2 eV is also considered as a hole capture state along with the shallow Ti 3d states at 0.7 eV. When two levels are involved in the hole capture process, eq. 3 is rewritten as Sp∗ = (σp,sh Npt,sh + σp,dp Npt,dp )vpth exp[−Vs /(ηkB T )],

(4)

where sh and dp in the subscripts indicate the shallow and deep in-gap states, respectively. The density of the shallow state is Npt,sh = 8 × 1013 cm−2 , which is equivalent to the surface Ti3+ density. That of the deep state Npt,dp is, then, estimated from the intensity ratio between the deep and shallow states (Figure 1d). We have confirmed from the repeated 15 ACS Paragon Plus Environment


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experiments that the intensities of the two in-gap states on TiO2 (011)-2 × 1 are always nearly the same as far as the same sample cleaning procedure is taken. Thus, Npt,dp ≃ Npt,sh = 8 × 1013 cm−2 is a rough but reasonable approximation. If σp,sh on TiO2 (011) is the same as the corresponding σp on TiO2 (110) mentioned above, σp,sh should be of the order of 10−16 –10−15 cm2 . Taking σp,sh as an average of two σp for TiO2 (110) (3 × 10−16 cm2 and 3 × 10−15 cm2 ), i.e. σp,sh = 1.7 × 10−16 cm2 , and also using the parameters of TiO2 (011)-2 × 1 listed in Table 1, the hole capture cross section of the deep in-gap state is obtained from eq. 4 as σp,dp = 1 × 10−12 cm2 . The above analysis clarifies the origin of the surface dependence of τ∞ . On the TiO2 (110) surface, the surface reduction by Ar+ sputtering leads to the slower SPV relaxation. The prolonged relaxation is caused by an enhancement of the surface barrier height Vs . This overwhelms the effect of the increase in Npt , which should contribute to the faster relaxation. Since τ∞ is proportional to the exponential of Vs and to the reciprocal of Npt according to eqs. 2 and 3, a decrease in the τ∞ value by the change of Npt from 1.7 × 1014 cm−2 [pristine TiO2 (110)] to 6 × 1014 cm−2 [sputtered TiO2 (110)] can be compensated by only a small change of Vs by 0.04 eV. However, the actual Vs change is 0.15 eV (Table 1) so that the relaxation time is prolonged. On the other hand, the short relaxation time on TiO2 (011) is owing to the large hole capture cross section of the deep trap state. Since σp,dp is three to four orders of magnitude larger than σp,sh , the electron-hole recombination via the deep in-gap state is a dominant path on TiO2 (011). Tao et al. have studied the electronic and atomic structures of the TiO2 (011)-2×1 surface and assigned the state at 2.1 eV, which is similar to the deep in-gap state in the present study, to the state originated from the two dimensional TiO2 phase. 26 This surface structure should govern the photoexcited carrier dynamics on this surface, although the fractional coverage is very small as expected from the low emission intensity (Figure 1b). In other words, if we modify the TiO2 (011)-2 × 1 surface by, for example, H adsorption as demonstrated in Figure 1d, the carrier dynamics and, thus, the surface photoresponse can be controlled to a desired


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level. As far as we know, there is no literature which reports the hole capture cross section in the bulk or on the surface of TiO2 . On the other hand, the electron capture cross section of the surface state on TiO2 has been reported to be 10−17 –10−16 cm2 by Wilson. 37 Although Salvador posed a question that the value was considerably smaller than the value estimated from geometrical consideration of the surface state density on TiO2 , 38 our estimated values for the hole capture cross sections are orders of magnitude larger than the Wilson’s value. This means that the holes arriving at the surface are almost certainly captured by the capture states without being reflected back to the bulk. From the view point of photocatalysis, the large capture cross section and the resultant shortening of the carrier lifetime contribute negatively to photocatalytic activity. 3,6,9,11 Thus, it is expected that TiO2 (110) should be more active than TiO2 (011)-2 × 1. Actually, a recent study by Mao et al. 39 has indicated that the reaction rate of photocatalyzed oxidation of methanol is lower on TiO2 (011)-2 × 1 than TiO2 (110)-1 × 1, both of which were prepared in a similar manner as the present work. Therefore, a correlation between the carrier lifetime and the photocatalytic activity is also applicable to the rutile TiO2 surfaces.

CONCLUSION Pump-probe TRXPS measurements have been carried out to comparatively assess the relaxation process of the laser-induced SPV on the pristine and Ar+ -sputtered TiO2 (110) surfaces and the TiO2 (011)-2 × 1 surface. The SPV of the initial magnitude of 0.12 eV is induced upon laser irradiation as a result of charge separation and the resultant anisotropic distribution of the electrons and holes. Subsequently, the SPV relaxation proceeds during the hole diffusion-and-capture process. The relaxation time τ∞ is determined to be about 100 ns on TiO2 (110), but τ∞ on the sputtered surface is about twofold larger than that on the pristine surface. The increase in the surface potential barrier height is responsible for the prolonged



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relaxation. In contrast, the SPV relaxation is only 1 ns on TiO2 (011). There are two hole capture states within the band gap on TiO2 (011); one is a Ti 3d-derived state at 0.7 eV, and the other is a state located at 2.2 eV and is characteristic of TiO2 (011)-2 × 1. Hole capture cross sections are determined to be 10−16 –10−15 cm2 and 10−12 cm2 for the former and latter states, respectively. The large cross section of the deeper states is responsible for the fast SPV relaxation on TiO2 (011). The present study demonstrates that TRXPS is a powerful tool to provide insight into the factors that determine the lifetime of the photoexcited carriers on the surfaces of photoresponse materials.

Supporting Information Available Estimation of surface Ti3+ density and band bending profile (PDF). This material is available free of charge via the Internet at http://pubs.acs.org/. AUTHOR INFORMATION Corresponding Author ∗

E-mail: [email protected] (K.O.)

Notes The authors declare no competing financial interest.

Acknowledgement This work was supported in part by a Grant-in-Aid for Scientific Research (Grant No. 16H03867) from Ministry of Education, Culture, Sports, Science, and Technology of Japan. The measurements at BL07LSU of SPring-8 were carried out using facilities of the Synchrotron Radiation Research Organization, The University of Tokyo (Proposal Nos. 2014A7463 and 2015A7487). The measurements at BL-13B of the Photon Factory were performed under the approval of the Photon Factory Advisory Committee (Proposal No. 2012S2-006).


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SPV (eV)


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TiO 2(110)

−0.1 0.0

TiO 2(011) 0.1

1 10 100 Delay Time (ns)

e TiO 2(011)

TiO 2(110) 2 0 Binding Energy (eV)

h

TOC Graph


What Determines the Lifetime of Photoexcited Carriers on TiO2

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