Electronic and Optical Properties of TiO 2 Solid ... - ACS Publications

Article pubs.acs.org/JPCC

Electronic and Optical Properties of TiO2 Solid-Solution Nanosheets for Bandgap Engineering: A Hybrid Functional Study Yanyu Liu,†,‡ Wei Zhou,*,†,‡ and Naoto Umezawa‡ †

Department of Applied Physics, Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparing Technology, Faculty of Science, Tianjin University, Tianjin 300072, P.R. China ‡ International Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan S Supporting Information *

ABSTRACT: Herein, the electronic and optical properties of TiO2(010) nanosheet solid solutions with transition metal oxycarbides, nitrides, and oxynitrides, (TiO2)2/3(M2O3C)1/3 (M = Nb or Ta), (TiO2)2/3(MN2)1/3 (M = W or Mo), and (TiO2)2/3(MOE)1/3 (M = W, Mo, E = C, and M = Nb, Ta, E = N) are systematically investigated. Forming a solid solution is a viable way to realize visible-light absorption and a direct band gap. The electron affinity of a solid-solution nanosheet closely depends on the energy level of the transition metal (M) d states; i.e., the hybridization of the M d states and Ti−O antibonding states introduces new bonding states, leading to a downward shift of the conduction band minimum. Meanwhile, the ionization potentials of these solid solutions are relatively low because of the introduction of high-lying occupied C/N 2p states, which lift the valence band maximum upward above that of the pristine TiO2. The modulation of band edges effectively narrows the band gaps of the solid solutions, except for transition metal oxynitrides. Among the examined solid solutions, (TiO2)2/3(WOC)1/3 was the most promising nanosheet for water splitting owing to its suitable band edges and responsive to visible and ultraviolet light. nanosheets (with Ti4+, Nb5+, Ta5+, W6+) are semiconducting or insulating materials.16 Their electronic diversities afford oxide nanosheet potential applications ranging from catalysis to electronics. In addition, since the nanosheets primarily consist of surface atoms arranged two-dimensionally, various reactions at the surface and interface could be investigated in depth. Undoubtedly, the fabrication of such novel nanosheets would be a breakthrough in nanotechnology and a common exercise in materials development, enabling the full exploitation of their fascinating properties in many fields. Research on TiO2 nanosheets can be traced back to the 1990s.18−20 Sasaki and co-workers exfoliated layered titanates and found Ti0.91O2 nanosheets with a thickness of 0.93 nm that exhibited semiconducting behavior similar to that of bulk anatase TiO2. A sharp optical absorption peak was observed at 265 nm (4.77 eV) for the Ti0.91O2 nanosheets, which indicated that their band gap is larger than that of bulk TiO2.16,21 Other research groups have made numerous attempts to exploit the optoelectronic properties of TiO2 nanosheets.22−25 For example, Wu et al. successfully prepared anatase TiO 2 nanosheets with exposed high-surface-energy (001) and (010) facets, whose band gaps are larger than 3.8 eV.23 In

1. INTRODUCTION Layered ultrathin two-dimensional (2D) nanomaterials have been a burgeoning research area since graphene was first exfoliated from graphite by Novoselov et al.1 2D nanosheets exhibit many extraordinary physical, chemical, and optical properties associated with quantum confinement effects and their ultrahigh specific surface area.2−5 Considerable efforts have focused on synthesizing layered ultrathin 2D nanomaterials with these unique properties to facilitate practical applications in electronic devices, catalysis, energy storage, and many other fields.6−11 Apart from exfoliation from a layered material, establishing alternative synthesis methods for novel 2D nanosheets from nonlayered materials has emerged as an important task to meet both the practical and scientific demand for these materials. Such a technique would open up a new field of designing the functionality of conventional materials by controlling the dimensionality. Moreover, several groups have reported the synthesis of functional oxide nanosheets from typically nonlayered materials, such as TiO2, WO3, In2O3, and MnO2, by delaminating precursor crystals of a layered oxide or generalized bottom-up synthetic methods.12−17 The exceptionally abundant structural diversity and electronic properties of oxide nanosheets give them several advantages over the layered materials. For example, MnO2 and RuO2.1 nanosheets exhibit metallic or semimetallic characters, while d0 transition metal oxide © 2017 American Chemical Society

Received: June 12, 2017 Revised: August 2, 2017 Published: August 4, 2017 18683

DOI: 10.1021/acs.jpcc.7b05734 J. Phys. Chem. C 2017, 121, 18683−18691

Article

The Journal of Physical Chemistry C

properties. The obtained band gap of bulk TiO2 (3.20 eV) agrees well with the experimental result (3.20 eV).39 Our computational band gap is somewhat smaller than the previously reported values given by HSE06 (3.58 eV40 or 3.73 eV41) due to the different functional used for the lattice relaxation. The anatase TiO2(010) p(1 × 2) nanosheets were built from the relaxed unit cell of bulk TiO2. The slab model includes three atomic layers with a 15 Å thick vacuum layer. We confirmed that the vacuum layer was sufficiently thick to avoid interactions between slabs in neighboring cells along the z direction. To identify different bonds, deq and dap are used to denote equatorial and apical Ti−O bonds, as shown in the inset of Figure 2(d). The imaginary part of the dielectric function was first calculated by the following formula

addition, as anodes of the coin-type Li ion cells, TiO2 nanosheets exhibit higher specific capacities than TiO 2 nanotubes and TiO2 nanoparticles, such as a reversible capacity of 82.2 mA h g−1 at a current density of 2000 mA g−1.24 Although these excellent properties have generated significant interest, the large intrinsic band gap severely limits their photoreaction efficiency. In order to improve the photocatalytic efficiency, TiO2 nanosheets should be modified to extend their absorption edge toward the visible-light region, while their band edges remain in the proper positions. Recently, a heterogeneous photocatalyst mixed from two kinds of materials with similar crystal structures has attracted increasing attention due to its high photocatalytic activity.26−30 The (GaN)1−x(ZnO)x solid solution represents the first successful example of tailoring the band gap to be smaller than 3.0 eV.28 As for the TiO2, an ∼0.4 eV type II band alignment exists in the two main phases of the anatase and rutile crystals with anatase possessing the higher electron affinity,31 whereas the anatase TiO2 usually exhibits a better photocatalytic performance than other TiO2 phases.32,33 Additionally, the free-standing of the anatase TiO2(010) nanosheet with atomic layer thickness has been experimentally synthesized recently.12 Therefore, in the present work, the solid-solution approach was applied to tune the band gap of anatase TiO2(010) nanosheets. The results demonstrate that most calculated TiO2 solid solutions are good visible-light absorbers in particular, and the (TiO2)2/3(WOC)1/3 nanosheets exhibit electronic structures that are remarkably well suited to be a visible-light-responsive photocatalyst.

⎛ 4π 2e 2 ⎞ ε2(ω) = ⎜ 2 2 ⎟∑ ⎝ m ω ⎠ i,j d3k

ε1(ω) = 1 +

a/Å deq/Å dap/Å

theory (LDA+U)43

3.80 1.94 1.98

3.78 1.93 1.97

3.84 1.96 2.00

2 P π

∫0

∞

ω′ε2(ω′)dω′ (ω′ 2 − ω 2)

(2)

Finally, the expressions for the absorption coefficient α(ω) now follow immediately45 α(ω) =

2 ω[ ε12(ω) + ε22(ω) − ε1(ω)]1/2

(3)

3. RESULTS AND DISCUSSION 3.1. Band Alignment of TiO2 Nanosheets with Different Numbers of Atomic Layers. The ultrathin TiO2 nanosheets with the high-energy (010) plane have been successfully synthesized with a large specific surface area of 298 m2 g−1,12,22 which would guarantee the nanosheet’s high chemical reaction activity. In order to verify the dependence of the conduction band minimum (CBM) on the number of atomic layers, the band alignments for different slab models were constructed with reference to the vacuum level.46 The results indicate that the CBM shifts upward with the decreasing number of the atomic layers (see Figure 1). This is consistent with the experimental results showing that the CBM of TiO2 nanosheets is higher than that of the bulk phase.22 In addition,

Table 1. Lattice Constants for Bulk Anatase TiO2 Calculated Using the PBE Functional Compared with the Theoretical and Experimental Values experiment42

(1)

Then, the real part ε1(ω) of the dielectric function could be obtained by the Kramer−Kronig transformation44

2. COMPUTATIONAL DETAILS All calculations were performed using the projector augmented wave (PAW) pseudopotentials, as implemented in the Vienna Ab initio Simulation Package (VASP).34−36 The electron wave functions were expanded in plane waves up to a cutoff energy of 450 eV. Monkhorst−Pack 5 × 5 × 2 k-point meshes were used for the 12-atom conventional cell of anatase TiO2, and 2 × 3 × 1 k-point meshes were set for the nanosheet models. The atomic positions were relaxed with Perdew−Burke−Ernzerhof (PBE) exchange-correlation functional until the residual forces were below 0.01 eV/Å. The obtained lattice constants of bulk anatase TiO2 were in good agreement with the reported theoretical and experimental values listed in Table 1.

this work

∫ ⟨i|MJ|⟩2 fi (1 − f j )δ(Ef − Ei − ω)

Standard density functional theory (DFT) functional is wellknown to often fail at accurately estimating the band gap of oxides due to residual self-interactions. This band gap problem can be solved by a hybrid functional37,38 suggested by Heyd, Scuseria, and Ernzerhof (HSE) that provides effectively improved descriptions of the electronic structure. In this work, the mixing parameter for the Hartree−Fock exchange was set to 25% (α = 0.25), and the screening parameter μ was set to 0.2; i.e., the original settings suggested by refs 37 and 38 (HSE06) were employed to calculate the electronic and optical

Figure 1. Band edge alignments of the bulk and nanosheet TiO2 from HSE06. 18684


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Figure 2. Total and projected DOS from HSE06 for (a) the bulk TiO2, (b) TiO2 nanosheets with three atomic layers, and (c) TiO2 nanosheets with two atomic layers. The right panel with (d), (e), and (f) shows the photoabsorption cross section of each system.

the band structures of the bulk TiO2 and TiO2 nanosheets demonstrate that the lower conduction band of TiO 2 nanosheets (Γ−F) is less dispersive than that of bulk TiO2 (Γ−X) (see Figure S1), which results in raising the CBM of TiO2 nanosheets. Here, the direction of Γ−F in the TiO2 nanosheets is equivalent to that of Γ−X in the bulk phase. Meanwhile, the valence band maximum (VBM) of TiO2 nanosheets and its bulk phase occur at different k-points due to the broken symmetry. As a consequence, the band gap of TiO2 nanosheets is wider than that of its bulk phase. Stevanovic et al. investigated the band alignments of a set of 17 materials, and the CBMs of the anatase TiO2(101) surface and rutile TiO2(110) surface are slightly lower than the H+/H2 reduction potential.47 Obviously, the anatase TiO2(010) nanosheet in this work possesses better edge positions than the above-reported TiO2 materials, which is beneficial for the H2 reduction. Figure 2 shows the calculated projected density of states (DOS) for the bulk and TiO2 nanosheets. The band character of the TiO2 nanosheets does not significantly depend on the number of atomic layers. Specifically, the valence and conduction bands still mainly consist of the filled O p states and the empty Ti d states for the pristine TiO2 nanosheets, which is consistent with our previous report.48 These findings imply that adjusting the number of atomic layers is a promising method to engineer the band edge and thus to improve the redox abilities of anatase TiO2. Although the TiO2 nanosheet with two atomic layers consists entirely of surface atoms, its band gap (about 3.96 eV) is too large to be modified for visiblelight absorption. However, in the TiO2 nanosheet with three atomic layers, the surface atoms still dominate the system, and its band gap is only slightly larger than that of the bulk phase. Thus, the three-layer TiO2 nanosheet is a good candidate material for designing a visible-light-responsive photoabsorber by modifying the electronic structure. Figure 2(d)−(f) shows the optical absorption coefficients for bulk TiO2 and TiO2 nanosheets, which are calculated using eq 3. The different incident directions were attributed to crystal anisotropy. The optical spectra show that the pristine bulk and nanosheet TiO2

only respond to ultraviolet (UV) light due to their large optical band gaps. 3.2. Formation Energies of TiO2 Solid-Solution Nanosheets. Numerous efforts have been devoted to chemically narrowing the band gap of TiO2 to improve its solar conversion rate but have achieved only marginal success. The traditional method is incorporating foreign elements into TiO2. In addition to doping, forming a solid solution with two different chemical compounds in one system has emerged as a successful approach. In the present work, therefore, the electronic structures of the anatase TiO2(010) nanosheets are modulated by forming solid solutions with other transition metal compounds. Here, C (N) and transition metals (Ta, Nb, W, Mo) are chosen to substitute for the O and Ti atoms, respectively. The introduction of foreign elements, which provide different atomic p and d orbital energies from those of the host elements, should affect the band edge positions.49 Taking into account the charge compensation, three different solid-solution models are presented in Figure 3. The models of

Figure 3. Optimized crystal structure of TiO2 solid solutions (a) (TiO 2 ) 2 / 3 (M 2 O 3 C) 1 / 3 , (b) (TiO 2 ) 2 / 3 (MN 2 ) 1 / 3 , and (c) (TiO2)2/3(MOE)1/3. Red, pink, blue, and green balls represent oxygen, nitrogen/carbon, titanium, and the transition metal, respectively. 18685


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Table 2. Calculated Formation Energies of the TiO2 Solid Solutions under O-Rich and O-Poor Conditions in Units of eV per Atom Ef (O-rich) Ef (O-poor)

W−C

Ta−C

Mo−N

Nb−N

Mo−C

Nb−C

W−N

Ta−N

−0.01 0.54

−0.26 0.11

0.30 0.82

−0.06 0.66

0.54 0.92

0.13 0.35

−0.28 0.42

−0.47 0.31

The upper bounds of μC, μN, and μTM are obtained from the formation enthalpy of the limiting phase52 (see Figure S2). The calculated formation energies of the solid-solution models are summarized in Table 2. The results indicate that these solid solutions are preferentially formed under O-rich condition rather than O-poor condition due to their lower formation energies. 3.3. Band Alignment of the TiO2 Solid-Solution Nanosheets. For visible-light water splitting, several criteria must be simultaneously satisfied, such as the appropriate band gap and suitable band-edge positions. In other words, the unoccupied states must be above the reduction potential and the occupied states below the oxidation potential. To search for optimal candidates to catalyze the overall water splitting reaction, the band-edge positions of the TiO2 solid solutions were evaluated with respect to the redox potential of water, as illustrated in Figure 4.46 Overall, the VBM and CBM shift

the (TiO2)2/3(M2O3C)1/3 solid solutions (M = Nb or Ta, hereafter Ta−C and Nb−C, respectively) are shown in Figure 3(a). Those of (TiO2)2/3(MN2)1/3 (M = W or Mo, hereafter W−N and Mo−N, respectively) are shown in Figure 3(b), and those of (TiO2)2/3(MOE)1/3 (M = W, Mo, E = C, hereafter W−C and Mo−C, respectively, and M = Nb, Ta, E = N, hereafter Nb−N and Ta−N, respectively) are shown in Figure 3(c). The ratio of TiO2 to the transition metal oxycarbides, nitrides, and oxynitrides was set to 2:1, which maintains the symmetry for both surface sides and results in a more stable structure than the other ratios. After calculating the formation energy for all possible solid-solution configurations with different doping sites in anatase TiO2(010) p(1 × 2) supercell slab models, only the most energetically stable model for each case was chosen to further investigate their properties. The stability of solid-solution nanosheets could be evaluated by calculating their formation energies with HSE06 Ef = Es − Ep −

∑ ni(μi + μi _0 )

(4)

where Ep and Es are the total energies of the pristine TiO2(010) nanosheets and their solid solutions with the same supercell size, respectively; ni is the number of the atoms being removed (ni < 0) or added (ni > 0) from the perfect TiO2 nanosheets; and μ1 is the chemical potential of a species in reference to its elemental phase (μ1_0). For the TiO2 crystal to form without other phases, the following conditions are required

HTiO ≥ μTi + μo

(5)

HTiO2 = μTi + 2μo

(6)

HTi2O3 ≥ 2μTi + 3μo

(7)

Figure 4. Band alignment of TiO2 nanosheets and their solid solutions with respect to the water reduction and oxidation potentials from HSE06 (upper and lower dotted lines, respectively), and the Ta−C and Nb−C solid solutions lead to additional gaps.

where HTiO, HTiO2, and HTiO3 are the formation enthalpies of TiO with the NaCl structure, anatase TiO2, and corundum Ti2O3, respectively.50 In this work, HTiO, HTiO2, and HTiO3 are equal to −5.31, −9.18, and −15.08 eV, respectively, which agree well with the previous experimental and theoretical results.48,51 To suppress the formation of other alternative phases, a stricter upper limit of μTi should be considered with the above conditions. In Figure S2, μO and μTi are visualized based on eqs 5−7, referencing the chemical potentials of molecular oxygen and bulk Ti, respectively. Based on eqs 5−7, the upper limit of μTi is −2.62 eV. With a higher value of μTi, the growth of other non-TiO2 phases will become dominated. The above analysis indicates that under O-rich conditions μO and μTi are equal to 0 eV and −9.18 eV, respectively, while they become −3.28 eV and −2.62 eV for O-poor conditions, respectively. In contrast, the chemical potentials of μC, μN, and μTM can be calculated from the formulas below: μC = H(TiC) − μTi

(8)

μ N = H(TiN) − μTi

(9)

μTM = [H(TMxOy ) − yμO]/x

upward and downward, respectively, relative to that of pristine TiO2, leading to the lower ionization potentials and higher electron affinities of the solid solutions, except for the cases of (TiO2)2/3(TaON)1/3 and (TiO2)2/3(NbON)1/3. However, only (TiO2)2/3(WOC)1/3 was found to be a desirable photocatalyst for water splitting under visible light. Although the band-edge positions of the pure TiO2 nanosheet, the (TiO2)2/3(TaON)1/3, and (TiO2)2/3(NbON)1/3 also straddle the water redox potentials, their large band gaps still hamper visible-light absorption. Fortunately, the smaller band gaps of the C-related solid solutions and (TiO2)2/3(MN2)1/3 enable them to fully absorb visible light, and the lower valence band edge ensures that they can produce O2. The origin of the band edge modulation in the solid solutions is discussed in the following section. 3.4. Electronic Structures of the TiO2 Solid-Solution Nanosheets. To explain the changes in the band edges, the electronic structure of solid-solution nanosheets is analyzed in this section. The DOSs of the oxycarbide solid solutions (TiO2)2/3(WOC)1/3 and (TiO2)2/3(Ta2O3C)1/3 are shown in

(10) 18686


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Figure 5. Total and projected DOS for (a)−(c) (TiO2)2/3(WOC)1/3 and (d)−(f) (TiO2)2/3(Ta2O3C)1/3 solid solutions from HSE06.

Figure 6. Total and projected DOS for (a)−(c) (TiO2)2/3(MoN2)1/3 and (d)−(f) (TiO2)2/3(NbON)1/3 solid solutions from HSE06.

band. The appearance of the intermediate states should be attributed to the much higher p orbital energy of C than that of O.49 In addition, we also found that the contribution of W d states at the CBM of (TiO2)2/3(WOC)1/3 is more pronounced than that of Ta d states in (TiO2)2/3(Ta2O3C)1/3. This can be attributed to the lower energy of W 5d states than that of the Ta 5d states.49 The electronic structures of the other oxycarbides (TiO2)2/3(MoOC)1/3 and (TiO2)2/3(Nb2O3C)1/3 are similar to those of (TiO 2 ) 2 / 3 (WOC) 1 / 3 and (TiO2)2/3(Ta2O3C)1/3, respectively (Figure S3). Because the

Figure 5. When the transition metal oxycarbides are incorporated into TiO2 nanosheets, the significant perturbation mainly occurs at the valence band. In (TiO2)2/3(WOC)1/3, the strong hybridization among the O p, C p, Ti d, and W d orbitals introduces intermediate states within the intrinsic band gap. Since the newly formed states are closely connected to the top of the host valence band, they extend the upper valence band in (TiO2)2/3(WOC)1/3, raising the band edge. In contrast, the intermediate states are somewhat more localized in (TiO2)2/3(Ta2O3C)1/3 and disconnected from the host valence 18687


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order to explore the possible reasons for this phenomenon, we compared the electronic structures of (TiO2)2/3(MoN2)1/3 and (TiO2)2/3(NbON)1/3. Since the N content is higher in (TiO2)2/3(MoN2)1/3, not all N atoms can form strong bonds with cations, and some of the N p states are therefore left as nonbonding states at the top of the valence band. By contrast, in (TiO2)2/3(NbON)1/3, all of the N nonbonding states are terminated by cointroduced Nb through the formation of Nb d−N p π bonds, thus eliminating the N-related band from the top of the valence band and leading to the low-lying VBM (high ionization potential), as observed in Figure 4. This mechanism is summarized in Figure 8. The strong interaction between the TiO2 nanosheet and the transition metal oxycarbides, nitrides, and oxynitrides not only remarkably narrows the band gap but also converts the band transition from indirect to direct at the Γ point. In Figure 9, we present the band structures of representative cases of this phenomenon. Clearly, the pure TiO2 nanosheet exhibits an indirect band transition from the VBM, which is between the Γ and F points to the Γ point of the CBM. In contrast, for the solid-solution nanosheets, both the VBM and CBM locate at the Γ point, resulting in a direct band gap. This indicates that the solid solutions are more advantageous for light absorption, which motivated us to investigate the photoabsorption properties of these systems, as discussed in the following section. The partial charge densities shown in Figure 9 indicate that the modulation of the band edge k points is attributed to the newly formed hybrid states from the transition metal oxycarbides, nitrides, and oxynitrides in the solid solutions, while the Ti d orbitals still make key contributions to the CBM, even in the solid solutions. The band gaps for various TiO2 solid-solution nanosheets are summarized in Table 3. According to the Shockley−Queisser limit,53,54 the optimum band gap for a thin film solar cell is 1.4 eV. Thus, the (TiO2)2/3(MoN2)1/3 solid solution is a good candidate for the photoabsorber material in photovoltaic solar energy applications. 3.5. Optical Absorption Coefficients of C- and NRelated TiO2 Solid-Solution Nanosheets. In this section, the optical absorption spectra of the TiO2 solid-solution nanosheets are calculated using eq 3. The calculation results show that anisotropy exists in the optical absorption. Therefore, to obtain the maximum solar conversion, the incident light’s direction should be taken into account. In addition to the enhanced UV light absorption, the absorption onset extends into the visible region for all the TiO2 solid-solution nanosheets except for the case of (TiO2)2/3(NbON)1/3 solid solution. The redshift of the absorption edge can be attributed to the electron transition from the C/N p orbitals in the upper valence band to the Ti/M d orbitals in the lower conduction band. Notably, a small peak appears near the absorption edge in Figure 10(c) and Figure S5(c). The electron transition between the bands formed by N p in the upper valence band and the Mo/W d in the lower conduction band results in the appearance of this absorption peak, which enhances the visible-light utilization. The above analysis demonstrates that the solid solution approach not only successfully narrows the band gap of the TiO2 nanosheets to effectively utilize the visible light but also improves the absorption of the UV light.

energy levels of Mo 4d and W 5d are comparable, so are those of Nb 4d and Ta 5d orbitals. The total and projected DOS for the nitride and oxynitride solid solutions (TiO2)2/3(MoN2)1/3 and (TiO2)2/3(NbON)1/3 are presented in Figure 6. There are strong interactions between the transition metal nitrides and TiO2 nanosheet in the upper valence band and lower conduction band for (TiO2)2/3(MoN2)1/3, while the hybridization primarily occurs in the upper valence band in (TiO2)2/3(NbON)1/3. In the lower conduction band of (TiO2)2/3(MoN2)1/3, the Mo d states overlap with Ti d states, thus making a primary contribution to the conduction band edge (Figure 6(c)), similar to the case of (TiO2)2/3(MoOC)1/3 (see Figure S3). The Nb d character is limited at the conduction band edges of (TiO2)2/3(NbON)1/3 and (TiO2)2/3(Nb2O3C)1/3 because Nb 4d states are higher than Ti 3d states and do not appear at the bottom of the conduction band. The electronic structures of the other nitride and oxynitride solid solutions can be understood analogously to the aforementioned nitride and oxynitride simply by replacing Mo by W or Nb by Ta (Figure S4). Furthermore, the band edge positions strongly depend on the energy level of the transition metal d orbitals. For example, the CBM is higher in (TiO 2 ) 2/3 (WOC) 1/3 than in (TiO2)2/3(MoOC)1/3, while the CBM in (TiO2)2/3(Ta2O3C)1/3 is higher than in (TiO2)2/3(Nb2O3C)1/3. This is because the 5d orbital energies of Ta and W are higher than those of the 4d orbitals of Nb and Mo, respectively.49 For the ionized cations, the 3d orbital energy of the Ti atom is lower than those of Ta, Nb, and W,49 which suggests that the CBM of solid solutions would be shifted up. In contrast, the CBM of these TiO2 solid solutions is lower than that of a pristine TiO2 nanosheet according to our results shown in Figure 4. By analyzing the band edge electronic structures, we found that the conduction band of a pure TiO2 nanosheet consists of nonbonding Ti d states at the bottom, followed by antibonding states of Ti d−O p π bonds. The introduction of another transition metal would promote the hybridization of M d with Ti−O antibonding states, forming weak π bonds, which effectively shifts the bottom of the conduction band downward, as illustrated in Figure 7. This mechanism reasonably explains

Figure 7. Schematic molecular orbitals at the conduction band edge for (a) TiO2 nanosheets and (b) TiO2 solid-solution nanosheets.

the lower CBM (higher electron affinity) of the solid solutions than that of the pristine TiO2 nanosheet, as observed in Figure 4. Moreover, the VBM of C-related systems is higher than that of the pristine TiO2 because of the introduction of high-lying occupied C p states. These modulations in the band edges all effectively narrow the band gaps. Surprisingly, the estimated ionization potentials of (TiO2)2/3(TaON)1/3 and (TiO2)2/3(NbON)1/3 are rather higher than that of the pristine TiO2 nanosheet, as shown in Figure 4, despite the incorporation of high-lying N p states. In 18688


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Figure 8. Schematic molecular orbitals and partial charge densities from HSE06 at the VBM of (a) (TiO2)2/3(MoN2) and (b) (TiO2)2/3(NbON)1/3 solid solutions. The magnitude of the partial charge density isosurface is 0.0006 electron/Å3 for (a) and 0.002/Å3 for (b) and (c).

Figure 9. Band structures from HSE06 of (a) TiO2 nanosheet, (b) (TiO2)2/3(WOC)1/3, (c) (TiO2)2/3(MoN2)1/3, and (d) (TiO2)2/3(TaON)1/3 solid solutions. The panels in (e), (f), (g), and (h) show the partial charge at the VBM (upper) and CBM (lower) of each system. The magnitude of the partial charge density isosurface is 0.002 electron/Å3.

Table 3. Calculated Band Gaps of the TiO2 Solid-Solution Nanosheets and Pure TiO2 Nanosheets with Three Atomic Layers Eg (eV)

pure

W−C

Ta−C

Mo−N

Nb−N

Mo−C

Nb−C

W−N

Ta−N

3.41

2.15

2.15

1.47

3.43

1.87

1.93

1.95

3.55

4. CONCLUSIONS In conclusion, solid-solution nanosheets of (TiO2):(M2O3C) (M = Nb or Ta), (TiO2):(MN2) (M = W or Mo), and (TiO2): (MOE) (M = W, Mo, E = C and M = Nb, Ta, E = N) were investigated with the HSE06 hybrid functional. The interaction between the TiO2 nanosheet and transition metal oxycarbides, nitrides, and oxynitrides not only converts the indirect band gap into a direct band gap but also successfully narrows the band gap, thus remarkably improving the solar conversion

efficiency. The introduction of high-lying occupied C/N 2p states raises the VBM above that of the pristine TiO2, which effectively narrows the band gaps of the solid solutions, except for the (TiO2)2/3(NbON)1/3 and (TiO2)2/3(TaON)1/3 nanosheets. In (TiO2)2/3(NbON)1/3 and (TiO2)2/3(TaON)1/3, the N nonbonding states are eliminated by the formation of Nb/Ta d−N p bonds, leading to the low-lying VBM. On the other hand, the CBM strongly depends on the energy of the d orbitals for the TiO2 solid-solution nanosheets. Their suitable 18689


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Figure 10. Optical properties of (a) (TiO2)2/3(WOC)1/3, (b) (TiO2)2/3(Ta2O3C)1/3, (c) (TiO2)2/3(MoN2)1/3, and (d) (TiO2)2/3(NbON)1/3 nanosheets from HSE06. (2) Chhowalla, M.; Shin, H. S.; Eda, G.; Li, L. J.; Loh, K. P.; Zhang, H. The Chemistry of Two-dimensional Layered Transition Metal Dichalcogenide Nanosheets. Nat. Chem. 2013, 5, 263−275. (3) Stojchevska, L.; Vaskivskyi, I.; Mertelj, T.; Kusar, P.; Svetin, D.; Brazovskii, S.; Mihailovic, D. Ultrafast Switching to a Stable Hidden Quantum State in an Electronic Crystal. Science 2014, 344, 177−180. (4) Wang, Q. H.; Kalantar-Zadeh, K.; Kis, A.; Coleman, J. N.; Strano, M. S. Electronics and Optoelectronics of Two-dimensional Transition Metal Dichalcogenides. Nat. Nanotechnol. 2012, 7, 699−712. (5) Stoller, M. D.; Zhu, S. P.; An, J.; Ruoff, R. S. Graphene-Based Ultracapacitors. Nano Lett. 2008, 8, 3498−3502. (6) Radisavljevic, B.; Radenovic, A.; Brivio, J.; Giacometti, V.; Kis, A. Single-layer MoS2 Transistors. Nat. Nanotechnol. 2011, 6, 147−150. (7) Yin, Z.; Li, H.; Li, H.; Jiang, L.; Shi, Y.; Sun, Y.; Lu, G.; Zhang, Q.; Chen, X.; Zhang, H. Single-layer MoS2 Phototransistors. ACS Nano 2012, 6, 74−80. (8) Morales-Guio, C. G.; Stern, L. A.; Hu, X. Nanostructured Hydrotreating Catalysts for Electrochemical Hydrogen Evolution. Chem. Soc. Rev. 2014, 43, 6555−6569. (9) Sun, Y.; Gao, S.; Lei, F.; Xie, Y. Atomically-thin Two-dimensional Sheets for Understanding Active Sites in Catalysis. Chem. Soc. Rev. 2015, 44, 623−636. (10) Du, G.; Guo, Z.; Wang, S.; Zeng, R.; Chen, Z.; Liu, H. Superior Stability and High Capacity of Restacked Molybdenum Disulfide as Anode Material for Lithium Ion Batteries. Chem. Commun. 2010, 46, 1106−1108. (11) Tsai, M. L.; Su, S. H.; Chang, J. K.; Tsai, D. S.; Chen, C. H.; Wu, C. I.; Li, L. J.; Chen, L. J.; He, J. H. Monolayer MoS2 Heterojunction Solar Cells. ACS Nano 2014, 8, 8317−22. (12) Sun, Z.; Liao, T.; Dou, Y.; Hwang, S. M.; Park, M. S.; Jiang, L.; Kim, J. H.; Dou, S. X. Generalized Self-assembly of Scalable Twodimensional Transition Metal Oxide Nanosheets. Nat. Commun. 2014, 5, 3813. (13) Sun, Y.; Sun, Z.; Gao, S.; Cheng, H.; Liu, Q.; Piao, J.; Yao, T.; Wu, C.; Hu, S.; Wei, S.; Xie, Y. Fabrication of Flexible and Freestanding Zinc Chalcogenide Single Layers. Nat. Commun. 2012, 3, 1057. (14) Lei, F.; Sun, Y.; Liu, K.; Gao, S.; Liang, L.; Pan, B.; Xie, Y. Oxygen Vacancies Confined in Ultrathin Indium Oxide Porous Sheets for Promoted Visible-light Water Splitting. J. Am. Chem. Soc. 2014, 136, 6826−9.

band edge and intensive absorption of both visible and UV light suggest that the (TiO2):(WOC) nanosheets are highly desirable for water-splitting applications.

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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.7b05734. Figures S1−S5. Additional data on band structures of TiO2 nanosheets with two atomic layers and three atomic layers, the chemical potential of the relevant elements under different conditions, the electronic structures and optical properties of (TiO2)2/3(MoOC)1/3, (TiO 2 ) 2/3 (Nb 2 O 3 C) 1/3 , (TiO 2 ) 2/3 (WN 2 ) 1/3 , and (TiO2)2/3(TaON)1/3 solid solutions (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +86 (0)22 27408599. Fax: +86 (0)22 27406852. ORCID

Wei Zhou: 0000-0002-8004-3996 Naoto Umezawa: 0000-0001-9572-9790 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank J. Ye and P. Wu for useful discussions. This work is partly supported by the Japan Science and Technology Agency (JST) Precursory Research for Embryonic Science and Technology (PRESTO) program and by the World Premier International Research Center Initiative on Materials Nanoarchitectonics (MANA), MEXT.

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REFERENCES

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Electronic and Optical Properties of TiO 2 Solid ... - ACS Publications

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