© EDP Sciences, 2017

1 Introduction

In resistive random access memory (ReRAM), the mechanism of valence change memory effect in Pt/TiO₂/Pt cell has attracted great interests in recent years [1]. Generally, TiO₂ layer with metal-electrodes (Pt, Al, Ti, Nb, etc.) always shows resistive switching phenomena [2–7]. The conductive paths in TiO₂ layer due to the interaction of the interface between the layer and those electrode-metals are hardly detected because of the deeply buried metal/metal-oxides/metal structure. To date, many related studies have been carried out on this topic above. Kwon et al. [2] made use of the transmission electron microscopy with high-resolution to probe the conductive filaments mainly composed of the oxygen vacancies in Pt/TiO₂/Pt. Huang et al. [8] illustrated the resistive-switching properties at room temperature in Ti/TiO₂/Pt cells. Guan et al. [9] clarified the unique reproducible nonpolar resistive switching behavior in Cu/ZrO₂:Cu/Pt cells. Do et al. [10] fabricated Al/TiO₂/Pt and Pt/TiO₂/Al cells where clockwise and counterclockwise bipolar switching behaviors were involved. Ismail et al. [11] reported the formation of the non-stoichiometric ZrO_y interfacial layer at the Zr/CeO_x interface. In these extensive works, these electrode-metals abound in the metal/metal-oxides interface, and react with the metal-oxides to modulate the conductive path there. This aroused us to investigate the interface effect on the formation of conductive path in metal/metal-oxides, e.g., metal/TiO₂ interface [12,13].

The interaction originating from the bonds between the metal-atoms and the Ti-ions or O-ions exist in the metal/TiO₂ interface, as the double-arrows shown in Figure 1(a). The lattice mismatch coefficients between Zr/Pt/Ti/Cu and TiO₂ are depicted in Table 1. To consider the larger lattice-mismatch coefficients of more than 10%, we feel it is hard to simultaneously investigate all the bonds effect of the interface on the formation of the conductive path. Therefore, we should simplify the model of the metal/TiO₂ interface and build the M-adsorption model (M = Zr/Pt/Cu/Ti). Those metal-atoms are supposed to adsorb at the position of “A–D” on the surface of TiO₂ layer, as indicated in Figure 1(b) and (c). Additionally, due to the symmetry feature between “A” and “D”, “B” and “C”, we could only discuss the adsorption location of “A” and “B”, as the red-circles shown in Figure 1(c). As the oxygen-ions aggregated at the metal/TiO₂ interface due to the external electric fields, their interaction with Ti-ions in TiO₂ layer below would be also considered in our M-adsorption model (M = Zr/Pt/Cu/Ti/O) [14–18].

Fig. 1 Schemes of the metal/TiO2 interface and its simplified models.

2 Method

The initial structure of 2 × 2 × 4 supercells (lattice parameters: a = b = 9.188 Å, c = 11.836 Å) was constructed via the primitive cell of the rutile TiO₂ (a = b = 4.594 Å, c = 2.959 Å). Then this structure was cleaved at (0 0 1) plane to build a surface. To avoid the interaction between the periodic images, a vacuum layer of 15 Å perpendicular to the cleaved surface was needed. The eight sets of oxygen vacancies (V_OS) as the blue-balls shown in Figure 2 substituted for the corresponding eight sets of oxygen-ions around centre-Ti-column. Due to the repulsive or attractive forces among the oxygen vacancies with the adjacent Ti-ions or O-ions, the geometry optimization was necessarily used to relax the initial surface and acquire a steady “substrate” considered as a defective rutile TiO₂(0 0 1) surface. Next, an atom (Zr/Pt/Cu/Ti/O), as the green-ball shown in Figure 2, was added above one 6-fold-coordinated Ti-ion (Ti_6c) in (1 1 0) plane where these oxygen vacancies (V_OS) locate or in another plane perpendicular to the (1 1 0) plane (we use “at 〈1 1 0〉 direction” instead), which corresponded to position “A” or “B” in Figure 1, respectively. For simplicity, these structures with such adsorption atoms were subsequently termed as “M₍₁₁₀₎” and “M_〈110〉” (M = Zr/Pt/Cu/Ti/O), respectively. We need to optimize all these surfaces and then discuss their properties. In Figure 2, the balls in gray and red were indicated as the Ti-ions and O-ions, respectively; the left and right insets in each figure of Figure 2 show the top-view and side-view, respectively.

The geometry optimization and properties calculations (electron density, density of states, electrostatics, etc.) were carried out by the spin-polarized DFT methods realized in DMol³ package [19]. The double numerical plus polarization at the value of 3.5 and DFT semi-core pseudopotentials were used for the geometry optimizations [20–22]. The exchange-correlation energy was mainly described by the commonly used Perdew–Burke–Ernzerhof (PBE) functional of generalized gradient approximation (GGA), which always got the underestimated bandgap for the transition-metal oxides [23]. The Monkhorst–Pack schemes with 6 × 6 × 8 grids for the sampling points in the Brillouin zone were adopted with the smearing of 0.14 eV, which could save the larger computational costs [24]. We set the convergence tolerances of 1 × 10⁻⁵ Ha for the energy, 2 × 10⁻³ Ha/Å for the force, and 5 × 10⁻³ Å for displacement during the geometric optimization, respectively. It needs to note that we mainly consider the formation or not of the conductive path in the TiO₂(0 0 1) surface below after the atoms are adsorbed. Therefore, the defect formation energies are addressed. The referenced energies to get the defect formation energies equal to the sum energies of “substrate” and each single absorbed atoms (Zr/Pt/Cu/Ti/O).

We further use Virtual NanoLab program to calculate the transmission coefficient with the DFT-PBE functional at 300 K [25,26]. The cutoff of the grid mesh is set to 40 Ha. The basis sets of double zetas and polarization orbitals are used to perform the transport simulations.

Fig. 2 M-adsorption models of (a) “M(110)” and (b) “M〈110〉” (M = Zr/Pt/Cu/Ti/O).

3 Results and discussions

We firstly discuss the fine structures of M₍₁₁₀₎ and M_〈110〉 with Zr/Pt/Cu adsorption, and then consider the structures with Ti/O adsorption. Figure 3 presents the optimized structures of Zr₍₁₁₀₎ (a), Pt₍₁₁₀₎ (b), Cu₍₁₁₀₎ (c), Zr_〈110〉 (d), Pt_〈110〉 (e), and Cu_〈110〉 (f). As shown in Figure 3, the balls in light-green, cyan, and pink are indicated as Zr, Pt, and Cu atoms, respectively. These adsorption atoms push the centre-Ti-columns towards the adjacent Ti-columns at upper-left sides in M₍₁₁₀₎ or at lower-right sides in M_〈110〉, respectively, as the left-inset of each figure shown in Figure 3. The following deformation electron densities are discussed to show the electrons profile in the structures above. Figure 4 shows the deformation electron densities of Zr₍₁₁₀₎ (a), Pt₍₁₁₀₎ (b), Cu₍₁₁₀₎ (c), Zr_〈110〉 (d), Pt_〈110〉 (e), and Cu_〈110〉 (f) at the slice cleaved along “I” dash-line, as shown in Figure 3(a). The deformation electron densities equal to the total densities subtracts the densities of the isolated atoms. Therefore, the blue and red in “blue–green–red” spectrums from −0.05 electrons/ų to 0.05 electrons/ų indicate the deficiencies and enrichments of electrons, respectively. Accordingly, the O-ions and Ti-ions correspond to the red and blue spots, respectively. “Ti₁–Ti₅” shows those Ti-ions at the centre-Ti-column. Looking the figures at top-row shown in Figure 4, the successive irregular red areas with electrons enrichment are filled among these Ti₁–Ti₅ ions. This seems the irregular conductive path occurs in the form of these delocalized electrons. In contrast, the conductive paths are failure to be seen due to the larger blue-gaps filled between the Ti₂-ion and Ti₃-ion in those figures at bottom-row. The detailed larger distances between Ti₂-ion and Ti₃-ion are listed in Table 2.

The partial density of states of Zr₍₁₁₀₎ (a), Pt₍₁₁₀₎ (b), Cu₍₁₁₀₎ (c), Zr_〈110〉 (d), Pt_〈110〉 (e), and Cu_〈110〉 (f) are depicted in Figure 5. The black, red and blue curves indicate the p-states, d-states and sum-states, respectively. The relative Fermi level locates at 0 eV. In Figure 5, more defect energy levels are found below the conductive band in the figures at left-column than those at right-column. Compared the p-states in black-lines to d-states in red-lines, the defect energy levels mainly originate from the contributions of the Ti-3d states. Accordingly, there have the bandgaps of almost 0.5 eV in left-column figures, while ones of 0.7 eV in right-column figures. The former smaller bandgaps correspond to metallic characteristics; the larger ones in latter case shows non-metallic features still exist in these structures with fewer delocalized electrons, although Fermi levels rightly locate at these defect energy levels. Additionally, the larger states at Fermi level in Figure 5(a) and (b) also shows larger concentration of delocalized electrons; smaller states at Fermi level but with narrower bandgap in Figure 5(c) still indicate more free electrons would be activated to the conduction band. These features illustrate that the conductive path exist in Zr₍₁₁₀₎, Pt₍₁₁₀₎, and Cu₍₁₁₀₎ rather than in Zr_〈110〉, Pt_〈110〉, and Cu_〈110〉.

The density of states in these Ti-ions including the center-Ti-ions (Ti₁–Ti₅) and their adjacent Ti-ions (Ti₆–Ti₉) are described in Figure 6. The defect energy levels from these Ti-ions in Zr₍₁₁₀₎, Pt₍₁₁₀₎, and Cu₍₁₁₀₎ more apparently reduce the bandgap than they do in Zr_〈110〉, Pt_〈110〉, and Cu_〈110〉. This means that the interaction among the Ti₁–Ti₉ in M₍₁₁₀₎ is larger than that in M_〈110〉 (M = Zr/Pt/Cu). That is to say, the metal adsorption at the (1 1 0) plane gives rise to the aggregation of Ti₁–Ti₉ ions and their interaction determines the formation of conductive path at some extents.

Figure 7 compares the electrostatic potential profile along 〈1 0 0〉 direction. In general, the peaks correspond to the potential of O-ions along 〈1 0 0〉 direction which acquires the valence electrons from Ti-ions. However, there have much higher peaks (A and B) in Figure 7, which indicate the aggregated Ti-ions, increasing the potential there. Moreover, the potential value of peak-A is larger than that of peak-B, especially in Figure 7(a), which means that much more delocalized electrons locate around the aggregated Ti-ions. Such results consistent with the reported phenomena are shown in Figure 4.

Viewing the results above, we discussed the dependent characteristics of the conductive path in defective TiO₂ on its Zr/Pt/Cu adsorption. Then, the adsorption of Ti or O atom would be investigated in the following.

The fine structures with the Ti/O adsorption are listed in Figure 8. The left and right insets in each figure show top and side views, respectively. The adsorbed Ti/O atoms are marked by the black-arrows. The center-Ti-ions incompletely move towards the adjacent Ti-ions, which differs from those in the structures with Zr/Pt/Cu atoms. The deformation electron densities of the slice cleaved along “II” dash-line in Figure 8 are described in Figure 9 to show the detailed electrons profile around each Ti-ion in the center-Ti-column. In Figure 9(a), the continuous irregular enrichment of electrons is located along Ti₁–Ti₅ ions, that is the conductive path. The much more aggregations of the delocalized electrons are filled in Ti₁–Ti₂ bond, Ti₃–Ti₄ bond, and Ti₄–Ti₅ bond of Figure 9(c), which are completely different with those in Figure 4. In Figure 9(b) and (d), no successive electrons-enrichments occur in the structure with O adsorption, indicating the inexistence of the conductive path.

Then, we would consider the partial density of states of Ti₍₁₁₀₎ (a), O₍₁₁₀₎ (b), Ti_〈110〉 (c), O_〈110〉 (d), as shown in Figure 10. In Figure 10(a), the larger state at Fermi level and smaller bandgap means more delocalized electrons. In Figure 10(c), although the states at Fermi level shows lower, its small bandgaps (〈0.5 eV) could result in more free electrons. However, the bandgaps of more than 0.5 eV and the lower states at Fermi level are found in Figure 10(b) and (d), which corresponds to no-evidence of the conductive path as said before.

These defect energy levels filling the whole bandgap induced by the Ti-adsorptions would offer a great possibility to provide more delocalized electrons under the external stress, e.g. electric field or high temperature, while less extent would be happened in those structures with Zr/Pt/Cu or O adsorption due to the fewer filled defect energy levels.

Similar to Figure 6, the sums of the partial density of states in Ti₁–Ti₉ are described in Figure 11. In Figure 11(a), the interactions between Ti₁–Ti₅ in the center-Ti-column and Ti₆–Ti₉ in the adjacent Ti-column are larger that they in Figure 11(b), which corresponds to the narrower bandgap in Ti₍₁₁₀₎ than that in Ti_〈110〉. Furthermore, due to the larger profile of the delocalized electrons in Ti–Ti bonds of Ti_〈110〉, more defect energy levels at −1 eV ∼ 0 eV are observed. The interaction between Ti₁–Ti₅ and Ti₆–Ti₉ in O₍₁₁₀₎ and O_〈110〉 plays little roles in narrowing the bandgap, which indicates the inexistence of conductive path again. It is interesting that there have two different shapes of conductive paths in Ti₍₁₁₀₎ and Ti_〈110〉: the former locates around the aggregated Ti-ions and the latter sits among the ordered Ti-ions, the difference of which we would discuss by density of states as shown in Figure 12. The co-contributions from aggregated Ti₁–Ti₉ ions narrow the bandgap, while ordered Ti₁–Ti₅ ions dominate to shorten the bandgap rather than the adjacent Ti₆–Ti₉ ions do. However, compared to the aggregated Ti₁–Ti₅ ions, these ordered Ti₁–Ti₅ ions result in more defect energy levels at −1 eV ∼ 1 eV, specially at 0.5 eV below Fermi level, which further indicates that the ordered Ti-ions would provide more delocalized electrons.

The electrostatic potential profiles along 〈1 0 0〉 direction in the structures with Ti/O adsorption are also discussed in Figure 13. As a comparison to Figure 7, only peak-C are found as the aggregation of Ti-ions in Ti₍₁₁₀₎ and O₍₁₁₀₎. This means that the center-Ti-ions in Ti_〈110〉 and O_〈110〉 keep in the central positions as shown in Figure 9(c) and (d).

The fine structures including the location of the adsorption atom and its bonding with the adjacent Ti-ions or O-ions are discussed in Figure 14. As shown in Figure 14, the figures in the top-row indicate the structures in the slice cleaved along 〈1 0 0〉 direction in M_〈110〉 as the dot-line shown in Figure 2(b). The distances between the adsorption atom and the adjacent Ti-ions or O-ions in M_〈110〉 of Figure 14(a)–(e) are listed in Table 3. The data in gray of Tables 3 and 4 indicate the un-bonding feature due to the larger distance between these ions. Moreover, the shorter distances mean the bonding of Zr_〈110〉–O₁, Zr_〈110〉–O₂, Pt_〈110〉–Ti₁₁, Cu_〈110〉–O₁, Cu_〈110〉–O₂, Cu_〈110〉–Ti₁₁, Ti_〈110〉–O₁, Ti_〈110〉–O₂, and O_〈110〉–Ti₁₁ appears, as shown in the top-row of Figure 14. The Mulliken charges of the M-ions in these bondings are 0.897e of Zr, 0.063e of Pt, 0.445e of Cu, 0.906e of Ti, and −0.504e of O, respectively, which corresponds to the more electrons transferred except those for Pt atom due to its inactive metal feature [27]. These phenomena are also found in M₍₁₁₀₎ at the below two rows of Figure 14. The second and third rows describe the partial structures on (110) plane and from top-view, respectively. Table 4 shows the distances between the adsorption atom and the adjacent Ti-ions or O-ions in M₍₁₁₀₎ of Figure 14(f)–(o). The shorter bonding lengths indicate the formation of the bonding in Zr₍₁₁₀₎–O₃, Zr₍₁₁₀₎–O₄, Zr₍₁₁₀₎–Ti₆, Pt₍₁₁₀₎–Ti₁₀, Pt₍₁₁₀₎–Ti₆, Cu₍₁₁₀₎–Ti₁₀, Cu₍₁₁₀₎–Ti₆, Ti₍₁₁₀₎–Ti₆, and Ti₍₁₁₀₎–O_3–6, as observed in Figure 14(f)–(o). The Mulliken charges of the M-ions in these bondings above are 0.779e of Zr, 0.238e of Cu, 0.85e of Ti, and −0.48e of O, respectively, which corresponds to the fewer electrons transferred than those in M_〈110〉. An exception of 0.105e in Pt_〈110〉 is also found because of its more bonding with lattice Ti-ions.

The work function on the surface in M₍₁₁₀₎ and M_〈110〉 are discussed in Figure 15. The lowest and largest work functions exist on the surface of Zr_〈110〉 and O_〈110〉, respectively. Further more, the difference of the work function between M₍₁₁₀₎ and M_〈110〉 are listed in the table of Figure 15. The largest difference is found on the surface with Zr-adsorption, while the lowest one occurs in that with Cu-adsorption. To our surprise, the similar differences of 0.08 eV are produced on the surface with Ti and Pt adsorption, which means that the adsorption location of Ti and Pt atoms presents the independent feature on the properties of the TiO₂(001) surface.

As discussions outlined in the structures of M₍₁₁₀₎ and M_〈110〉, the adsorption of Zr/Pt/Cu/Ti above one 6-fold-coordinated Ti-ion in (1 1 0) plane produce the conductive path, while Zr/Pt/Cu/O adsorbed above another 6-fold-coordinated Ti-ion at 〈1 1 0〉 direction perpendicular to the (1 1 0) plane fail to result in the conductive path. Although a gap among Ti-ions is found in the structure with Ti adsorption at 〈1 1 0〉 direction, the larger profiles of delocalized electrons locate on the Ti–Ti bonds, which maybe more easily produce the conductive path. So far, it is necessary to calculate the Bader charges of Ti₂–Ti₃ ions in the center-Ti-column to investigate their metallic characteristics.

Figure 16 shows the Bader charges of Ti₂–Ti₃ ions in the structures with Zr/Pt/Cu/Ti/O adsorption. Accordingly, the Bader charges of Ti₂–Ti₃ ions are larger in Zr₍₁₁₀₎, Pt₍₁₁₀₎, Cu₍₁₁₀₎, Ti ₍₁₁₀₎, and Ti_〈110〉 than in Zr_〈110〉, Pt_〈110〉, Cu_〈110〉, and O_〈110〉, which indicate more metallic characteristics of Ti₂–Ti₃ ions existing in the former structures than those in latter structures. However, regarding the defect formation energy in Figure 17, the lower defect formation energy reveals more easily formed structure of Ti ₍₁₁₀₎, Ti_〈110〉 and Zr_〈110〉, specially in Ti_〈110〉 where the conductive path compose of ordered Ti-ions. This implies that the real conductive filaments maybe mainly compose of the ordered metallic Ti-ions which bring less distorted structure. Larger differences of the defect formation energies between Zr₍₁₁₀₎ and Zr_〈110〉 illustrate that Zr-adsorption would lower down the stability of the conductive path due to its anisotropic properties. Lower defect formation energies exist in structures with Ti/Zr/Cu/Pt/O-adsorptions at 〈1 1 0〉 direction than those on (1 1 0) plane, as the light-green and light-yellow shown in Figure 17. Although Zr/Cu/Pt/O adsorptions at 〈1 1 0〉 direction could not result in the formation of conductive path, their lower defect formation energies shows that other defects introduced at 〈1 1 0〉 direction, e.g., Zr/Cu/Pt/O substitutions or interstitials, may benefit the occurrence of conductive path.

Moreover, due to the unformed conductive path in Zr_〈110〉 and the evitable differences of work functions between Zr₍₁₁₀₎ and Zr_〈110〉, we consider Ti-atoms are the favorable species adsorbed on TiO₂(0 0 1) surface effectively resulting in the formation of conductive path. The transport coefficients about these structures of M₍₁₁₀₎ and M_〈110〉 are also calculated as shown in Figure 18. The solid-lines and dash-lines indicate the transport coefficients of the structures of M₍₁₁₀₎ and M_〈110〉, respectively. The transport coefficients at Fermi level (E_f = 0 eV) are extracted as shown in Figure 19. The larger transport coefficients in Figure 19 appear in Ti₍₁₁₀₎ and Ti_〈110〉, corresponding to the larger conductivities in Ti₍₁₁₀₎ and Ti_〈110〉.

Fig. 3 Optimized fine structures of Zr(110) (a), Pt(110) (b), Cu(110) (c), Zr〈110〉 (d), Pt〈110〉 (e), and Cu〈110〉 (f).

Fig. 4 Deformation electron densities for the structures of Zr(110) (a), Pt(110) (b), Cu(110) (c), Zr〈110〉 (d), Pt〈110〉 (e), and Cu〈110〉 (f) at the slice cleaved along “I” dash-line in Figure 3.

Fig. 5 Partial density of states for the structures of Zr(110) (a), Pt(110) (b), Cu(110) (c), Zr〈110〉 (d), Pt〈110〉 (e), and Cu〈110〉 (f).

Fig. 6 Sum of the partial density of states for the center-Ti-ions (Ti1–Ti5) and the adjacent Ti-ions (Ti6–Ti9) for the structures of Zr-adsorption (a), Pt-adsorption (b), and Cu-adsorption (c).

Fig. 7 Potential profile along 〈1 0 0〉 direction for the structures with Zr-adsorption (a), Pt-adsorption (b), and Cu-adsorption (c).

Fig. 8 Optimized fine structures of Ti(110) (a), O(110) (b), Ti〈110〉 (c), and O〈110〉 (d).

Fig. 9 Deformation electron densities for the structures of Ti(110) (a), O(110) (b), Ti〈110〉 (c), and O〈110〉 (d) at the slice cleaved along “II” dash-line in Figure 8.

Fig. 10 Partial density of states for the structures of Ti(110) (a), O(110) (b), Ti〈110〉 (c), O〈110〉 (d).

Fig. 11 Sum of the partial density of states in Ti1–Ti9 in the structures with Ti-adsorption (a) and O-adsorption (b).

Fig. 12 Comparison of the sum in the partial density of states between Ti1–Ti5 ions and Ti6–Ti9 ions in the structures of Ti(110) (a) and Ti〈110〉 (b).

Fig. 13 Potential profiles along 〈100〉 direction in the structure with Ti-adsorption (a) and O-adsorption (b).

Fig. 14 Detailed fine structures including the location of atom adsorption and its bonding with the adjacent Ti-ions or O-ions. The top row: the structures of the slice cleaved along 〈100〉 direction in M〈110〉 as the dot line shown in Figure 2(b); the second and third rows: the structures of M(110) on (110) plane and from the top view.

Fig. 15 Work function on the surface in the structures of M(110) and M〈110〉.

Fig. 16 Bader charges of Ti2–Ti3 ions in the structure with Zr/Pt/Cu/Ti/O adsorption.

Fig. 17 Defect formation energy in the structures of M(110) and M〈110〉.

Fig. 18 Transport coefficients for the structures of M(110) and M〈110〉.

Fig. 19 Comparison of the transport coefficients at Ef for the structures of M(110) and M〈110〉.

4 Conclusions

We have performed ab initio calculations to study the feature of the defective TiO₂(0 0 1) surface with the Ti/Zr/Cu/Pt/O adsorptions. The impact of these adsorptions at two sites on the production of the conductive path has been discussed. The results demonstrated that Ti adsorptions above a lattice Ti-ion in (1 1 0) plane or at 〈1 1 0〉 direction both favorably produced the conductive path rather than the Zr/Cu/Pt-adsorptions did; the O-adsorption in both sites played little role in the formation of conductive path. These theoretical results are hopeful to further understand the mechanism of TiO₂-based resistive switching.

Acknowledgments

The authors acknowledge the support from National Natural Science Foundation of China under grant nos. 61774014, 61076102 and 61272105, Natural Science Foundation of Jiangsu Province of China under grant nos. BK2012614 and BK20141196. We are grateful to the useful discussions with Prof. Qi Liu and Dr. Hannes Mähne. We also would like to thank the editors and reviewers for their time spent on conducting our manuscript and their comments helping us improving the article.

References

All Tables

All Figures

	Fig. 1 Schemes of the metal/TiO2 interface and its simplified models.
In the text

	Fig. 2 M-adsorption models of (a) “M(110)” and (b) “M〈110〉” (M = Zr/Pt/Cu/Ti/O).
In the text

	Fig. 3 Optimized fine structures of Zr(110) (a), Pt(110) (b), Cu(110) (c), Zr〈110〉 (d), Pt〈110〉 (e), and Cu〈110〉 (f).
In the text

	Fig. 4 Deformation electron densities for the structures of Zr(110) (a), Pt(110) (b), Cu(110) (c), Zr〈110〉 (d), Pt〈110〉 (e), and Cu〈110〉 (f) at the slice cleaved along “I” dash-line in Figure 3.
In the text

	Fig. 5 Partial density of states for the structures of Zr(110) (a), Pt(110) (b), Cu(110) (c), Zr〈110〉 (d), Pt〈110〉 (e), and Cu〈110〉 (f).
In the text

	Fig. 6 Sum of the partial density of states for the center-Ti-ions (Ti1–Ti5) and the adjacent Ti-ions (Ti6–Ti9) for the structures of Zr-adsorption (a), Pt-adsorption (b), and Cu-adsorption (c).
In the text

	Fig. 7 Potential profile along 〈1 0 0〉 direction for the structures with Zr-adsorption (a), Pt-adsorption (b), and Cu-adsorption (c).
In the text

	Fig. 8 Optimized fine structures of Ti(110) (a), O(110) (b), Ti〈110〉 (c), and O〈110〉 (d).
In the text

	Fig. 9 Deformation electron densities for the structures of Ti(110) (a), O(110) (b), Ti〈110〉 (c), and O〈110〉 (d) at the slice cleaved along “II” dash-line in Figure 8.
In the text

	Fig. 10 Partial density of states for the structures of Ti(110) (a), O(110) (b), Ti〈110〉 (c), O〈110〉 (d).
In the text

	Fig. 11 Sum of the partial density of states in Ti1–Ti9 in the structures with Ti-adsorption (a) and O-adsorption (b).
In the text

	Fig. 12 Comparison of the sum in the partial density of states between Ti1–Ti5 ions and Ti6–Ti9 ions in the structures of Ti(110) (a) and Ti〈110〉 (b).
In the text

	Fig. 13 Potential profiles along 〈100〉 direction in the structure with Ti-adsorption (a) and O-adsorption (b).
In the text

	Fig. 14 Detailed fine structures including the location of atom adsorption and its bonding with the adjacent Ti-ions or O-ions. The top row: the structures of the slice cleaved along 〈100〉 direction in M〈110〉 as the dot line shown in Figure 2(b); the second and third rows: the structures of M(110) on (110) plane and from the top view.
In the text

	Fig. 15 Work function on the surface in the structures of M(110) and M〈110〉.
In the text

	Fig. 16 Bader charges of Ti2–Ti3 ions in the structure with Zr/Pt/Cu/Ti/O adsorption.
In the text

	Fig. 17 Defect formation energy in the structures of M(110) and M〈110〉.
In the text

	Fig. 18 Transport coefficients for the structures of M(110) and M〈110〉.
In the text

	Fig. 19 Comparison of the transport coefficients at Ef for the structures of M(110) and M〈110〉.
In the text