Subsurface Polaron Concentration As a Factor in the Chemistry of

Department of Physics and Astronomy, Uppsala University, Box 516, 75120 Uppsala, Sweden. J. Phys. Chem. C , 2017, 121 (21), pp 11325–11334. DOI: 10...
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Subsurface Polaron Concentration As a Factor in the Chemistry of Reduced TiO2 (110) Surfaces Taizo Shibuya,*,† Kenji Yasuoka,† Susanne Mirbt,‡ and Biplab Sanyal‡ †

Department of Mechanical Engineering, Keio University, Yokohama 223-8522, Japan Department of Physics and Astronomy, Uppsala University, Box 516, 75120 Uppsala, Sweden

‡

S Supporting Information *

ABSTRACT: Surface reactivity of rutile TiO2 (110) surfaces has long been ascribed to bridging oxygen vacancies (VO), but recently, excess electrons introduced by donor defects are being considered as the main players. However, the spatial distribution of them is not yet clear due to difficulties in interpreting filled state images of scanning tunneling microscopy (STM). In this study, several different images available in the literature are consistently interpreted using density functional theory (DFT). The key factors are polarons in the second layer below Ti5c row (Ti5c‑2nd polarons) and a temperature dependence of their concentration. Bright blobs in the experimental images are interpreted as Ti5c‑2nd polarons. At 78 K, their concentration reaches 33.3% ML, where 1 ML is defined as the density of (1 × 1) unit cells, regardless of VO coverage. In contrast, at 5 K, it is twice the VO coverage. This discrepancy is understood by the ionization of donor defects other than VO, most probably subsurface Ti interstitials, and subsequent diffusion of polarons to Ti5c‑2nd sites at high temperature. This mechanism explains seemingly contradicting reports on oxygen chemisorption on this surface, which suggests that the so-called oxygen-vacancy model needs to be modified at temperature above at least 78 K.

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INTRODUCTION TiO2 has a variety of functions ranging from water splitting by solar energy to elimination of pathogens, in which surface reactions play essential roles. Its surface also serves as a model surface of functional metal oxides, being of great interest among scientists.1,2 One of the major achievements in the research is the so-called oxygen-vacancy model established for the most well-studied surface, rutile (110), in the 1970s.3 The surface consists of alternating Ti5c and bridging oxygen (Obr) rows, and according to the model, the surface reactivity is ascribed to Obrvacancies (VO), each of which introduces two Ti3+ ions nearby. Recently, the understanding of the reactivity is being revisited reflecting advancements in theory and experiments.4,5 The main players in this trend are “excess electrons” introduced not only by VO but also donor defects such as Ti interstitials (Tiint) or bridging hydroxyls (OHb), placing Ti3+ ions as one form of them. The corresponding electronic states exist above the valence band of this wide band gap material and play important roles in surface reactions. For example, new adsorption sites for O2 and CO molecules are found in addition to VO.6,7 They are associated with the excess electrons originating from non-VO defects or being in delocalized form. Gold nanoparticles, the key components of low-temperature CO oxidation, are reported to be stabilized by excess electrons introduced by various donor defects.8,9 On the other hand, it is known that hole-mediated photolysis of trimethyl acetate (TMA) is hindered by the excess electrons formed in the photolysis itself.10 Recently, this effect was confirmed to be caused also by excess electrons associated with OHb.11 On top of that, more © 2017 American Chemical Society

generally, the difference between anatase and rutile in photocatalytic activity is explained by the different localization tendency of excess electrons in each crystal phase.12,13 It also explains the enhancement in the photocatalytic activity in their mixed form. Although these experimental and computational attempts to comprehend the surface reactivity are in the early phase at this moment, during this process we could potentially establish a more handy way to perceive the surface reactivity of metal oxides, leading to the massive expansion in the application of them. To pursue the goal, a spatial distribution of excess electrons should be clearly understood. However, the way to access the information is not completely established even for reduced surface (TiO2−x) of rutile (110), the most basic setup in which excess electrons are introduced only by intrinsic defects. One purpose of the present paper is to demonstrate a deeper potential of electronic structure calculations in this context, and the other is to reveal the spatial distribution of excess electrons in the reduced surface itself. The latter is strongly related to recent debates about the origin of the surface states and the consequent confusion in O2 adsorption.14−18 The reduced surface usually has the Fermi energy at the conduction band edge (CB-edge), showing n-type conductivity.19 It also has the band gap states about 1 eV below the CBReceived: January 29, 2017 Revised: April 17, 2017 Published: April 25, 2017 11325

DOI: 10.1021/acs.jpcc.7b00935 J. Phys. Chem. C 2017, 121, 11325−11334

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first revisit the properties of polarons at the surface, focusing on the spatial extent of Ti5c‑2nd polarons. Then, it is shown that there is a maximum concentration of Ti5c‑2nd polarons, 33.3% ML, under electron-rich condition regardless of VO coverage up to 16.7% ML, where 1 ML is defined as the density of (1 × 1) unit cells, 5.2 × 1014 cm−2. Only after this maximum concentration is reached, the excess electrons start to form shallow donor states. They are likely to be found below the second layer, thus, are not probed by filled state STM. The features in reported images are ascribed to Ti5c‑2nd polarons. Differences among images are explained by temperature, which suggests that the surface excess electrons are provided only by VO at a low temperature, whereas other donor defects become important at a higher temperature. Finally, the complicated absorption behavior of O2 is discussed within this view.

edge.3,14,20,21 They are interpreted as polaronic Ti3+ states, each of which is formed by an excess electron localized at an empty Ti-3d orbital with a locally distorted lattice structure. These facts suggest that the excess electrons exist in two forms in the surface, one with delocalized character at the CB-edge and the other with a localized character in the band gap. Importantly, their spatial distribution remains an open question. In principle, one can access this information by scanning tunneling microscopy (STM) in the filled state image applying a negative bias voltage. Although there are several high resolution images taken at various temperatures below 78 K in the literature,12,22−24 there has been no agreement in the interpretations so far. While Minato et al. reported that VO-induced Ti 3d states are delocalized on the first layer,22 Papageorgiou et al. concluded that they are delocalized at first to third layer and only −2 charged VO can reproduce the STM images.23 Recently, Setvin et al. and Yim et al. correlated them with Ti 3d states localized at the second layer.12,24 These discrepancies stem from the condition of electronic structure calculations, especially the ones based on the density functional theory (DFT), which are necessary for STM interpretation. It had not been well-recognized that the exchange correlation functional, surface size and initial structure of relaxation crucially affect the calculation result in this system. Recently, it is recognized that the localized electrons in d0 transition metal oxides can be properly described by hybrid DFT or DFT+U, which corrects the self-interaction error in standard DFT.25−29 Furthermore, particularly in this system, it is becoming clear that by carefully controlling the initial structure in geometry optimization, the excess electrons can form polaronic Ti3+ state at almost any Ti site, the most stable polaron being at the second layer.30−33 In order to reflect these findings to the interpretation of the filled state STM, there is one hurdle. The previous DFT studies focused on describing the localized states of the excess electrons, leaving the nature of the delocalized states behind. Recently, Janotti et al. reported a mechanism of the coexistence of the former and the latter, or polaronic Ti3+ state and shallow donor states, using hybrid DFT in bulk.34 However, there is no study for the surface at which the excess electrons behave differently from bulk due to the symmetry breaking. Each Ti site is no longer equivalent at the surface and can be categorized as presented in Figure 1. In this work, therefore, we studied the behavior of excess electrons at the surface including its dependence on electron chemical potential. Particularly, electron-rich condition where the localized and delocalized electrons coexist is of interest. We

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RESULTS AND DISCUSSION Nature of Polarons in a p(4 × 2) Surface. First, we will discuss the possible polaron configurations, their stability, spatial extent, and dependence on each other. Figure 2a−d presents four different configurations of a four-layer p(4 × 2) surface with a neutral VO with varying positions of two polarons. The spatial extent of polarons is shown in the top panel, and the position of polarons in the bottom panel. They cover four possible sites for a polaron formation, Ti5c‑1st, Ti5c‑2nd, Ti6c‑1st, and Ti6c‑2nd. A configuration in Figure 2a has two Ti5c‑2nd polarons, which is known to be the most stable one,30−33 while others have at least one polaron at non-Ti5c‑2nd sites. On top of Figure 2a−d, relative total energy of each configuration is shown. Energies are measured relative to the most stable structure in Figure 2a. One can clearly observe the connection between the trend in total energies and the position of the gap states for various cases. For example, the energy difference between Figure 2a and b is explained in the following way. While the structure in Figure 2a has two Ti5c‑2nd polarons, one of them becomes Ti6c‑2nd polaron in Figure 2b. In the densities of states (DOS) shown in Figure 2e, a Ti6c‑2nd polaron appears about 0.25 eV higher compared to a Ti5c‑2nd polaron, which corresponds to the energy difference between the two structures. This exact correspondence suggests that each polaron is energetically independent, in accordance with the previous study.30 As can be seen in the top panel of Figure 2a−d, a polaron extends to surrounding Ti sites. According to the Bader charge analysis, about 0.7 electrons are found at the center of the polaron. In the case of a polaron at Ti5c‑1st, Ti5c‑2nd, and Ti6c‑2nd site, 0.05 electrons are found at two adjacent Ti sites. For the most stable configuration, a slice of the second layer is presented in Figure 3. It is clearly seen that one polaron occupies three Ti5c‑2nd sites. As we had previously reported, an overlap of Ti5c‑2nd polarons results in an energy increase of about 0.3 eV.32 This spatial extent of the polaronic states demands a large lateral supercell to minimize the overlap between periodic images. It is further discussed in the next section. There are four different Ti5c‑2nd sites marked as 1−4 in Figure 3. In order to check whether the polaron prefer certain Ti5c‑2nd, the total energies of four different configurations, in which the position of one polaron was varied from 1 to 4 while keeping the other polaron at a fixed position, were computed. It is found that the variation in total energies is of the order of few meV only indicating that all the possible Ti5c‑2nd sites are almost equally probable to host a polaron.

Figure 1. Illustration of a defect-free surface: dark circle (red), O; light circle (blue), Ti. Distinct Ti sites are labeled according to their row and layer. 11326

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Figure 2. Electronic structure of polarons in a four-layer p(4 × 2) surface with a neutral VO. Charge density (top) and localization position (bottom) of polarons at (a) two Ti5c‑2nd, (b) Ti6c‑2nd and Ti5c‑2nd, (c) Ti5c‑1st and Ti5c‑2nd, and (d) Ti6c‑1st and Ti6c‑2nd. Isosurface level = 0.0014 e/Å3. Relative stabilities of each structure is shown on top of the image. (e) Corresponding density of states.

Figure 3. Charge density of two Ti5c‑2nd polarons in a four-layer p(4 × 2) surface with a neutral VO: whole view (bottom) and top-view (top) of the second-layer. Numbers denote the position of the Ti5c‑2nd polaron. Charge density is drawn only for the second-layer. Isosurface level = 0.0014 e/Å3.

Ti5c‑2nd Sites under Electron-Rich Conditions. Given that the excess electrons form stable Ti5c‑2nd polarons, it is highly likely that filled state STM images are affected by them. Then the meaningful question is, how many Ti5c‑2nd polarons exist under n-type condition at a given VO coverage? In this section, a typical case with the VO coverage of about 10% ML is first discussed, followed by the extreme one where there is no VO. The stability of polarons is studied through the formation energy analysis of VO and ideal surface in various charge states, the latter corresponding to no VO case. They are plotted in Figures 4 and 5 as a function of electron chemical potential, or the Fermi energy. The charge state of the surface can be translated into the “Ti5c‑2nd polaron concentration” which is more closely related to our interest. It is defined as the number of Ti5c‑2nd polarons divided by the number of available sites. For example in Figure 3, there are two Ti5c‑2nd polarons in p(4 × 2) surface, which has 8 Ti5c‑2nd sites. It corresponds to the Ti5c‑2nd polaron concentration of 25% ML. One can expect this value to become higher as electron chemical potential increases. At this point, however, it should be mentioned that the maximum Ti5c‑2nd polaron concentration is strongly constrained by a surface cell size due to polaron’s repulsive nature and the

Figure 4. Stable polaron configurations of a charged VO in a four-layer p(4 × 2) and p(6 × 2) surface under a given electron chemical potential. (a) Formation energy as a function of Fermi energy under Ti-rich condition. The kinks in the curves indicate transitions between charge states. (b−g) Charge density of the gap states for the stable configuration; only the second layer is shown.

periodicity of the surface itself. As discussed previously, the polaron occupies three Ti5c‑2nd sites and the system becomes unstable when it overlaps with another one. This property restricts the maximum polaron concentration to unnecessarily low value in a certain size of the cell. This is clearly seen in Figure 4, where the VO formation energies in two different surface cells, p(4 × 2) and p(6 × 2), are compared. Under ntype condition, or Fermi energy at the CB-edge, there are two polarons in p(4 × 2) surface, whereas four polarons exist in p(6 × 2). They correspond to the polaron concentration of 25% ML and 33.3% ML, respectively. The important fact is that at 11327

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33.3% ML. In this section, we investigate how this n-type condition is met. n-Type condition means an existence of delocalized shallow donor states formed by adding excess electrons to the system. In bulk, the condition is readily met due to an energy barrier between the shallow donor states and the localized polaronic states.34 Excess electrons provided in delocalized form, though it is a metastable state, remain in that form due to the energy barrier. However, whether the above statement holds for surfaces is an open question. To shed light on this matter, we calculated energy barrier between localized and delocalized states of one excess electron in an ideal surface slab. As discussed earlier, to avoid the artificial frustration for the polaron formation, a five-layer p(3 × 2) surface was adopted. In order to reveal the condition under which excess electrons start to form delocalized states, two systems are compared: (i) ideal surface plus one excess electron and (ii) ideal surface with Ti5c‑2nd sites effectively fully occupied plus one excess electron. The results are shown in Figures 6 and 7, Figure 5. Stable polaron configurations of a charged five-layer p(3 × 2) surface under a given electron chemical potential. (a) Formation energy as a function of Fermi energy. (b−d) Charge density of the gap states for the stable configuration; only the second layer is shown.

the p(4 × 2) surface, there are still two “empty” Ti5c‑2nd sites, which cannot host polarons because of the periodic boundary condition. In contrast, there are no such empty Ti5c‑2nd site in p(6 × 2), because six is an integral multiple of three, which is a unit for a Ti5c‑2nd polaron. The p(3m × n) surface, where m and n are integer numbers, is a better choice to avoid such an artificial frustration. Based on this insight, we adopt the p(6 × 2) surface where one VO amounts to the VO coverage of 8.3% ML. Under the typical V O coverage, n-type surface has the polaron concentration of 33.3% ML, the configuration to which we refer as Ti5c‑2nd sites “effectively fully occupied” by polarons. For the same reason, p(3 × 2) surface is adopted to investigate an extreme case where the surface has no VO, the result shown in Figure 5. It is clearly seen that −2 charged surface is the most stable under the Fermi energy close to the CB-edge. It means that the polaron concentration reaches 33.3% ML under n-type condition. To summarize, it has been shown that when the VO coverage is 0 and 8.3% ML, polaron concentration reaches 33.3% ML under n-type condition. Since VO just attract polarons,35 it is concluded that Ti5c‑2nd sites are effectively fully occupied by polarons under n-type condition regardless of VO coverage from 0 to 8.3% ML. Regarding the VO coverage above 8.3% ML, probably there is an upper limit in VO coverage due to the Ti5c‑2nd polaron concentration. When the VO coverage reaches 16.7% ML, oxygen vacancies provide sufficient amount of polarons to effectively fully occupy Ti5c‑2nd sites. Above this coverage, excess electrons introduced by VO should be accommodated in different ways, which is expected to cost much energy.32 In fact, such a high VO coverage is not observed experimentally, suggesting that the energy cost to form either non-Ti5c‑2nd polarons or Ti5c‑2nd polarons exceeding the concentration of 33.3% ML is rather high. Thus, it is inferred that Ti5c‑2nd sites are effectively fully occupied by polarons under n-type condition, regardless of VO coverage from 0 to 16.7% ML. Formation of Shallow Donor States. It has been shown that under n-type condition, the polaron concentration reaches

Figure 6. One extra electron added to a defect-free five-layer p(3 × 2) surface. (a) Charge density of the extra electron localized at Ti5c‑2nd and (b) in delocalized form. (c) Self-consistent total energies of various configurations that are interpolated between localized (left) and delocalized (right) configuration. Isosurface level = 0.005 e/Å3.

respectively. In the first case, we could easily localize an electron at Ti5c‑2nd as shown in Figure 6a. At the same time, we could also stabilize a delocalized state, which is less stable by about 300 meV, as shown in Figure 6b. The procedure is found in the Computational Details. We estimated an energy barrier between the two structures by calculating the self-consistent total energies of various lattice configurations which are obtained by linearly interpolating the two structures. The result is shown in Figure 6c. There is no barrier between them, suggesting that delocalized electrons cannot be in that form in this condition. In the second case, two excess electrons are set to effectively fully occupy Ti5c‑2nd sites in advance so that the added electron cannot form a polaron there. We could stabilize both localized 11328

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Similar results are confirmed in p(4 × 2) surface, the detail being found in Supporting Information. This conclusion suggests the existence of other donor defects. The reduced surface is usually n-type at typical VO coverage of 10% ML, and one VO provide only two excess electrons. It leads to the polaron concentration of 20% ML, which is not enough to achieve n-type condition. Excess electrons should be provided from other sources to the surface. The source is probably Ti interstitials at the subsurface region. The mechanism can be the following. Above about 4 K, Ti interstitials ionize to provide excess electrons.36 The polarons easily hop in (110) and (100) direction at finite temperature.37 They are attracted by VO,35 occupying Ti5c‑2nd sites. Conversely, it is expected that there is little such effect at very low temperature; polarons are frozen near their original defects, leading to Ti5c‑2nd sites occupied almost only by nonhopping VO-oriented polarons. 78 K Image. We are now ready to interpret experimental images. In this section, 78 K images reported by Minato et al. and Setvin et al.are interpreted. They are presented in Figure 8a,b. Note that in Figure 8b our main interest is at the top panel with the bias voltage of −1.4 V, which probes the band gap states. Though the value is not explicitly stated in the text, their images apparently differ in VO coverage, which is estimated to be about 6% ML and 15% ML, respectively. Nevertheless, the images are similar to each other characterized by bright oval blobs, each of which covers two Ti5c‑1st sites, spread all around. The images were taken under the bias voltages of −1.1 and −1.4 V which probe states below the Fermi energy with an energy window of 1.1 and 1.4 eV in DOS, respectively. The Fermi energy should be somewhere between the polaronic band gap states and the CB-edge. It means that the images are potentially affected by delocalized states at the CB-edge, nonTi5c‑2nd polarons and Ti5c‑2nd polarons. However, we can exclude the first two from a cause of the bright blobs because as discussed earlier they exist most likely below the second layer, having much smaller effect on the filled state image than the Ti5c‑2nd polarons. In fact, we confirmed that the filled state STM image of the structures in Figure 7a,b are dominated by Ti5c‑2nd polarons. On top of that, it was found that the non-Ti5c‑2nd polarons cause bright spots in Ti6c row, which is not observed in the experiments, supporting our argument. Further discussion regarding the last two points are found in Supporting Information. Thus, we can conclude that this image is dominated by 33.3% ML of Ti5c‑2nd polarons. The calculated STM image of p(6 × 2) with one VO and 33.3% ML of Ti5c‑2nd polarons is presented in Figure 8d. It well reproduces the features of the typical image around VO presented in Figure 8c. The DOS of the system and the charge density of the band gap states are displayed in Figure 9a and b, respectively. The charge density of these states are shown in Figure 9b. The side-view of one Ti5c row and the top-view of the first layer are shown in Figure 9c and d, respectively. From these figures it is evident that two tails of each polaron contribute to one blob in the STM image. It is worth noting that in Figure 8b the bright blobs are not always separated by a clear depression. Instead, some parts look rather like bright lines. In this area, excess electrons are probably not sufficiently provided for some reasons and polarons can hop easily. It might be related to the hopping polaron model proposed recently by Yim et al.24 Depending on the configuration of oxygen vacancies, the surface may have a

Figure 7. Three extra electrons added to a defect-free five-layer p(3 × 2) surface. (a) Charge density of the extra electrons localized at Ti5c‑2nd and Ti5c‑4th sites. (b) Charge density of the extra electrons, two of them being localized at Ti5c‑2nd sites and one in delocalized form. (c) Selfconsistent total energies of various configurations which are interpolated between localized (left) and delocalized (right) configuration. (d) Density of states of the localized (top) and delocalized (bottom) configuration. Isosurface level = 0.005 e/Å3.

and delocalized state, as shown in Figure 7a and b, respectively. In this case, the energy difference is 50 meV being much smaller than the first case. Importantly, there is an energy barrier between them, as presented in Figure 7c, which enables the coexistence of the two forms. As can be seen in Figure 7d, the delocalized state is located right below the CB-edge, corresponding to the shallow donor states. From these results, we conclude that the system starts to be n-type after Ti5c‑2nd sites are effectively fully occupied, regardless of VO coverage. When electrons are doped to the system, they first form Ti5c‑2nd polarons until the polaron concentration reaches 33.3% ML. After that, delocalized states are formed most probably below the second layer in a more bulk-like region, for example, at the fifth layer, as shown in Figure 7b. 11329

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Figure 8. Reported and calculated filled state STM images. (a) Image taken at 78 K by Minato et al.22 (3.4 × 2.8 nm; Vs = −1.1 V) and (b) Setvin et al.12 (7 × 7 nm; Vs = −1.4 (top); Vs = −0.6 V (bottom)). Circles indicate oxygen vacancies. (c) The expanded image of (a) around VO (yellow rectangle). Arrows indicate a position of Ti5c species. (d) Calculated image. In the calculation, band gap states appeared at about 1 eV below the CBedge in the density of states (Figure 9a) are imaged with a tip−sample distance of about 3 Å; red sphere, Ti; blue sphere, O. Visualizations were made using VESTA.38 (a) and (c) Reproduced with permission from ref 22. AIP Copyright 2009. (b) Copyright (2014) by The American Physical Society.

per VO depends on temperature. These Ti5c‑2nd polarons should be the electrons which play a major role in the surface reactivity. In this section, based on this view, we comment on a recent debate about oxygen chemisorption on the surface at low temperature. This debate is related to the validity of the oxygen-vacancy model, which explains the reactivity of reduced surfaces only by VO. While Kimmel and Petrik concluded that the saturation coverage of O2 depends almost linearly on VO coverage,15 Lira et al. reported that it highly depends on the sample preparation history;16 the former supports the oxygen-vacancy model, the latter proposing the dominance of Ti interstitials in the surface reactivity.5 Also, there is a wide variation in the value itself. Under the typical VO coverage of 8% ML, Henderson et al. suggested that three O2 molecules adsorb per one VO,14 Kimmel and Petrik concluded about two,15 and Lira et al. reported five in one sample.16 A key to understand these discrepancies lies in an adsorption temperature (Tad) of O2 molecules. While Kimmel and Petrik conducted O2 exposure at 25 K, Henderson et al. and Lira et al. did it at 120−130 K. We have shown that, at very low temperature, the number of Ti5c‑2nd polarons around VO is kept constant at two up to the VO coverage of 16.7% ML. This explains the linear behavior of the O2 saturation coverage reported by Kimmel and Petrik under Tad = 25 K. In contrast, we have shown that at a temperature as high as 78 K the concentration of Ti5c‑2nd polaron is 33.3% ML independent of VO coverage. It is probably because subsurface Ti interstitials are fully ionized and provide excess electrons to Ti5c‑2nd sites. It implies that there can be other excess electrons below the second layer such as Ti5c‑4th polarons as shown in Figure 7b, depending on the concentration of Ti interstitials. Those subsurface electrons are expected to occupy the Ti5c‑2nd sites when Ti5c‑2nd polarons are consumed in reactions. As long as Ti5c‑2nd sites are devoid of polarons, these sites can accept them. This mechanism explains the preparation history dependence of the O2 saturation coverage reported by Lira et al., and consequently accounts for the big difference between Lira et al. and Henderson et al. It is worth noting that Kimmel and Petrik reported a subtle nonlinear behavior in which the saturation coverage of O2

potential structure in which all the Ti5c‑1st near VO are energetically equivalent, leading to the line-like feature. In addition, it should be noted that the bright features of Setvin et al.’s −0.6 V image shown in Figure 8b can be interpreted as delocalized electrons below the second layer for the following reason. With this bias voltage it is impossible to probe Ti5c‑2nd polarons. Also, they cannot be non-Ti5c‑2nd polarons, which result in bright features in Ti6c row. 5 K Image. The 5 K image reported by Papageorgiou et al. is reprinted in Figure 10a. The VO coverage is estimated to be about 10% ML from the figure. Although it shares the particular characteristic with 78 K images in which almost only Ti5c rows are bright, it is obviously different from 78 K images in having very bright spots as well as faint and broad lines. Based on the earlier discussion, it is assumed that n-type condition is not met at this temperature and VO coverage. It means that there are only Ti5c‑2nd polarons introduced by VO at the surface, and the experimental image is reproduced by the polarons. It is because the Fermi energy is at least above the polaronic band gap states, which assures that the bias voltage of −2 V captures only polarons in the band gap. Since one VO introduces two excess electrons, 10% ML of VO coverage corresponds to 20% ML of Ti5c‑2nd polaron concentration. This is close to a p(6 × 2) surface with a neutral VO, which corresponds to 8.3% ML of VO coverage and 16.7% ML of the polaron concentration. The corresponding filled state image is shown in Figure 10b. It well reproduces the main features of the experimental figure. The charge density of the band gap states and the DOS of the system are presented in Figure 10c−e. The very bright spot is interpreted as the Ti5c‑2nd polaron itself, and the faint line is a tail of it. One can check our assumption by counting the number of bright blobs and comparing it with the number of VO. The VOpolaron ratio is about 1:2, which is consistent with the assumption. Note that their image includes a small number of surface bridging OH defects. Two surface OH defects were counted as one VO, since an OH defect is known to introduce one excess electron.27,39 Temperature Dependence of VO Reactivity. It has been shown that the surface excess electrons observed via STM in filled state images are Ti5c‑2nd polarons, and the number of them 11330

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surface region provide excess electrons to Ti5c‑2nd even at low temperature.40 In short, the oxygen-vacancy model seems to be valid at a very low temperature. However, it can be surmised that the model needs to be modified at temperature above at least 78 K. Above that temperature, VO reactivity could depend on the density of Ti interstitials in the subsurface region, which is determined by the sample preparation history. Very recently Yim et al. reported the temperature dependence of the filled state images, ascribing all the bright blobs to only VO.24 As discussed earlier, their model seems reasonable at least in a region where the excess electrons are not sufficiently provided. However, it should be noted that their model cannot explain the puzzle of the oxygen adsorption since the number of available electrons does not vary in the model. In order to elucidate this point, further studies at various temperatures and preparation histories are needed.

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CONCLUSION

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COMPUTATIONAL DETAILS

Hybrid DFT calculations were carried out in order to establish a coherent interpretation of filled state STM images of reduced TiO2 (110) surfaces. It was shown that polaronic Ti3+ states are the most stable at Ti5c‑2nd sites. The polaron has a finite extension, which limits the maximum polaron concentration in the second layer to 33.3% ML. From the formation energy analysis of the charged system, it was predicted that the polaron concentration reaches the maximum value under n-type conditions independent of VO coverage. This view also explains why the VO coverage does not exceed about 15% ML in experiments. From calculated energy barriers, it was suggested that having the maximum polaron concentration in the second layer is a prerequisite for the formation of shallow donor states. Based on these understandings, STM images were interpreted. It was concluded that only polarons at Ti5c‑2nd sites are seen in filled state images and one polaron is imaged as a bright blob in Ti5c row. The fact that two 78 K images with different VO coverages look similar confirmed our prediction that, at that temperature, n-type conditions are met and the polaron concentration of the second layer is 33.3% ML, regardless of the VO coverage. This can be explained by a supply of excess electrons to Ti5c‑2nd sites from donor defects other than VO such as Ti interstitials in the subsurface region. On the contrary, for 5 K image it was concluded that the polaron concentration is about twice the VO coverage. This is consistent with our view that, at this temperature, the ionization of Ti interstitials does not occur and, consequently, VO is always neutral. This mechanism can explain seemingly contradicting reports on O2 saturation coverage at a low temperature. Based on the above arguments, it was proposed that the oxygen-vacancy model needs to be modified at temperature above 78 K. Above that temperature, excess electrons belonging to subsurface Ti interstitials are expected to take part in the surface reactions via Ti5c‑2nd sites. These understandings are important not only for this particular surface but also potentially have an impact on other metal oxide surfaces especially for a d0 system such as MoO3 or CeO2.

Figure 9. Electronic structure of −2 charged VO in a four-layer p(6 × 2) surface. (a) Density of states and (b) whole-view of the charge density of the band gap states. (c) Side-view of one Ti5c row and (d) top-view of the first layer of the charge density; view points and areas are indicated by arrows and planes, respectively, in the whole-view. Only the gap states about 1 eV below the CB-edge are imaged. Fermi level is aligned at the CB-edge; red sphere, Ti; blue sphere, O. Isosurface level = 0.001 e/Å3.

decreases from 2.35 to 2.1 as VO coverage grows from 8% ML to 14.5% ML. By assuming that one polaron is consumed for one O2 adsorption, it can be understood as following. At 25 K, probably Ti interstitials are partially ionized and the 8 VO% surface has more than two Ti5c‑2nd polarons per VO, which explains the value of 2.35. On the other hand, since the 14.5% ML surface is close to the maximum VO coverage, the number of Ti5c‑2nd polarons per VO reaches to the minimum value of 2. In fact, our recent study suggests that Ti interstitials in the near

The calculations were performed using a DFT code, VASP41,42 that employs a plane wave basis set. The exchange-correlation potential was approximated within the generalized gradient approximation (GGA) by the Perdew−Burke−Ernzerhof 11331

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Figure 10. Reported and calculated filled state images at low temperature. (a) Image taken at 5 K by Papageorgiou et al.23 (4.4 × 4.4 nm; Vs = −2 V.) The squares indicate the position of VO (green), OHb (purple) features associated with VO, and other impurity (white). (b) Calculated image with a tip−sample distance of about 3 Å. (c) Top-view of the first layer and (d) whole-view of the corresponding charge density of band gap states about 1 eV below the CB-edge with an isosurface level = 0.0001 e/Å3; viewpoint and area are indicated by an arrow and planes, respectively, in the whole-view. (e) Density of states of the system, a four-layer p(6 × 2) surface with a neutral VO.

(PBE).43 In order to overcome GGA’s semilocal description, we employed screened hybrid functional (HSE06),44,45 where correlation is described in GGA (PBE) and the exchange is a mixture of 25% exact (HF) exchange and 75% PBE exchange. The HSE screening parameter was set to 0.2 Å−1. The surface was modeled by a p(6 × 2) geometry with a slab thickness of 4 layers separated by 10 Å vacuum. This amounts to 192 O and 96 Ti ions. When needed, four-layer p(4 × 2) or five-layer p(3 × 2) surface was also used. The bottom layer was fixed at bulk positions and terminated by pseudohydrogen46atoms. Positions of polarons were controlled by initial structure of the relaxation as described in a previous work.35 The charge state of VO was controlled by varying number of total valence electrons in the system. The extra charge was compensated by a neutralizing uniform background charge. The plane wave cutoff energy was 450 eV and the core−valence interaction was described by the projector augmented wave (PAW) approach. The Brillouin zone was sampled by Γ point. Lattice parameters of a = 4.60 Å, and c = 2.95 Åwere used. During relaxation, Hellmann− Feynman forces were reduced below 0.02 eV/Å. STM images were calculated based on the Tersoff-Hamann approach.47,48 The formation energy of charged VO is defined as follows: VO,q VO,q Eform = Etot +

1 ideal μ + q(εv + E F) − Etot 2 O2

deficient surface was corrected. The shift amounted to 34 and 19 meV for the p(4 × 2) and p(6 × 2) surface, respectively. Similarly, the formation energy of charged defect-free surface, which can be read as the polaron formation energy, is defined as follows: ideal,q ideal,q ideal Eform = Etot + q(εv + E F) − Etot

(2)

where Eideal,q is the total energy of the +q charged system. tot For the energy barrier study of one extra electron in an ideal surface, the structure with a delocalized electron shown in Figure 6b was obtained by adding an electron to a defect-free relaxed surface while keeping the lattice structure fixed. In order to obtain the energy barrier plotted in Figure 6c, the position of ions in Figure 6a,b were dealt as two end points. Seven ionic configurations were generated by interpolating the end points, and the self-consistent calculations were conducted while keeping the ionic positions of each configuration. In the case of three extra electrons shown in Figure 7b, it was determined through the following procedure. First, two electrons are added to a defect-free surface and stabilized at Ti5c‑2nd sites. Then, another electron was added while keeping the lattice structure fixed. Finally, the system was relaxed. The energy barrier was obtained by the same way as the one extra electron case. The reason why the Ti5c‑4th site was selected as the third localization site is the following. In our previous work, it was shown that the lowest unoccupied state of the defect-free surface has a main contribution from Ti5c‑2nd sites and this was the reason for Ti5c‑2nd being the most stable position for the localization.32 The lowest unoccupied state had the second biggest contribution from Ti5c‑4th sites in the study which suggests that the site is the second stable one.

(1)

EVtotO,q is the calculated total energy of the TiO2 (110) surface containing a VO in charge state q. Eideal tot is the calculated total energy of the neutral defect-free surface. μO2 is the chemical potential of the oxygen reservoir. We fixed the value of μO2 to the total energy of bulk TiO2 minus the total energy of bulk hcp Ti. This choice corresponds to the Ti-rich limit. εv is the valence band maximum of the neutral defect-free surface at the Γ point. EF is the Fermi level, that is, the electron chemical potential regulating if electrons are available to charge the defect. The energy scale has been adjusted such that EF is zero at εv, and it varies between zero and the conduction band minimum. The shift of the electrostatic potential49 of an O

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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.7b00935. Additional supporting figures (PDF). 11332

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Taizo Shibuya: 0000-0002-8212-866X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The computation in this work has been partially done using the facilities of the Supercomputer Center, the Institute for Solid State Physics, the University of Tokyo.

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