MoS2(WS2) van der Waals heterostructures for visible-light photocatalysis and energy conversion

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Two-dimensional H-TiO2/MoS2(WS2) van der Waals heterostructures for visible-light photocatalysis and energy conversion ⁎

Wen-Zhi Xiaoa, ,1, Liang Xub, Ling-Ling Wangc

⁎,1

, Qing-Yan Ronga, Xiong-Ying Daia, Chuan-Pin Chenga,

a

School of Science, Hunan Institute of Engineering, Xiangtan 411104, China Energy Materials Computing Center, Jiangxi University of Science and Technology, Nanchang 330013, China c School of Physics and Electronics, Hunan University, Changsha 410082, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: TiO2 sheet Two-dimensional Heterostructure Visible-light photocatalysis Water splitting Solar energy

Titanium dioxide (TiO2) has promising applications in photocatalysis and energy-conversion devices due to its low cost, outstanding conductivity, and excellent electrochemical activity. However, its large band gap and insufficient-sized surface hinder its applications under visible-light radiation, so designing a highly efficient TiO2-based electrode structure is challenging. Herein, we constructed novel van der Waals (vdW) heterostructures using two-dimensional hexagonal TiO2 (H-TiO2) and 2D MoS2 (WS2) components. By density functional theory, we found that the 2D H-TiO2 has robust stability in energy and mechanics, as well as higher ductility than graphene and MoS2. The estimated indirect band gap ranged within 4.30–4.62 eV, resulting in hardly any visible-light absorbance. The vdW heterostructures of MoS2/TiO2 and WS2/TiO2 had the following characteristics: direct band gap, type-II band alignment, built-in electronic field, mobility as high as that of MoS2 (WS2), and remarkably improved visible-light absorption. These features enabled the heterostructures to have highly improved photocatalytic performance and solar-to-electric power conversion efficiency. Thus, these materials have high potential application in photocatalytic water splitting and solar energy-conversion devices.

1. Introduction Light-driven water splitting was observed on titanium dioxide (TiO2) electrode by Fujishima and Honda in 1972 [1]. Since then, TiO2based materials have been widely investigated experimentally and theoretically in energy-related issues [2–7], such as in the fields of photocatalysts for water splitting [8] and solar cells [9]. Thus far, TiO2based materials have attracted increasing interest due to their advantages, such as low cost, nontoxicity, high mobility, recyclability, and stability [7]. Recently, three kinds of ultrathin 2D TiO2 nanosheets have been successfully fabricated and investigated [6,10–14]. These 2D TiO2 nanomaterials exhibit unique properties different from its corresponding bulk forms, such as large and highly chemically reactive surfaces and significant quantum confinement effect. Lepidocrocite-type TiO2 nanosheet (LNS) is first fabricated by soft chemical procedure [10]. H-TiO2 is proposed using state-of-the-art theoretical calculations [14]. Formation energy estimations reveal that the H-TiO2 has the lowest energy among the three kinds of sheets [14]. Interestingly, detailed analyses of gap and band alignment unveiled

that all 2D TiO2 satisfy the criteria of water splitting, which requires that the conduction band minimum (CBM) should be more negative than the redox potential of H+/H2 (0.0 eV vs normal hydrogen electrode) and the valence band maximum (VBM) should be more positive than the redox potential of O2/H2O (1.23 eV) [15]. Compared with bulk materials, although a larger chemically reactive surface is an advantage for 2D TiO2 nanosheet, the widened band gap due to quantum size effect results in weak photocatalytic activity. For instance, the theoretical values of LNS and H-TiO2 are 4.55 [10] and 5.05 eV [14], which are higher than that of the traditional rutile/anatase phase TiO2 (> 3.33 eV) at the HSE06 functional level. Such large band gap renders TiO2 unsuitable for visible-light photocatalysts and hinders solar energy harvesting because solar energy is primarily concentrated in the visiblelight region [16]. At the same time, the high recombination rate of carriers considerably reduces the photocatalytic efficiency [17] due to the lack of built-in electric fields that are responsible for greater photogenerated carrier separation. Therefore, designing high-performance photocatalysts based on 2D TiO2 materials is challenging. The construction of heterostructures [7,15,18–20] is believed to be

⁎

Corresponding authors. E-mail addresses: [email protected] (W.-Z. Xiao), [email protected] (L. Xu). 1 Contributed equally to this work. https://doi.org/10.1016/j.apsusc.2019.144425 Received 10 August 2019; Received in revised form 22 September 2019; Accepted 16 October 2019 Available online 31 October 2019 0169-4332/ © 2019 Elsevier B.V. All rights reserved.

Please cite this article as: Wen-Zhi Xiao, et al., Applied Surface Science, https://doi.org/10.1016/j.apsusc.2019.144425

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stable structure is found for the SnO2 monolayer [36], ordering in space group P6/mmm (#191). The optimized lattice constants are a = b = 6.05 Å with a thickness of h = 4.73 Å. The Ti–O bond lengths at the plane of [-Ti6-O6-]n are 1.826 Å, while those joining the rings of [-Ti6-O6-]n are 1.823 Å. To confirm the stability of H-TiO2, we first calculated the total energy with respect to other well-known stable TiO2 allotropes. For comparison, Table 1 shows the relative energy (Er) of different TiO2 allotropes. The Er of rutile phase is lower than those of HTiO2 and LNS by 25 and 19 meV per atom, respectively, which are close to the previously reported values of 20 and 13 meV, respectively [14]. The experimentally successful synthesis of LNS [37] indicates that preparation of H-TiO2 on some suitable substrates is also feasible because it has more stable energy. The phonon dispersion plotted in Fig. S1(a) shows no negative frequency, indicating its dynamic stability. AIMD simulations presented in Fig. S1(b) verify its thermal stability at a temperature of up to 500 K.

a very effective strategy to improve photo-induced charge separation and expand the absorption of solar light from UV to visible light. For instance, coupling of MoS2 and TiO2 to form a heterojunction remarkably expands the absorption spectrum into the visible-light region and decreases the recombination rate of the photogenerated electron/ hole pairs [7,21,22]. Similarly, the MoS2/GaN [18,23] and α-AsP/GaN [19] van der Waals (vdW) heterostructures show type-II band alignments, which ensure fast carrier transport and separation, as well as exhibit substantially improved photocatalytic properties under visiblelight irradiation. Besides, layered MoS2 and WS2-based 2D materials have been successfully synthesized experimentally and show excellent photocatalytic performance. The high performances in photocatalytic hydrogen evolution were experimentally observed in MoS2 nanosheetcoated TiO2 nanobelt heterostructures [24] and composite material consisting of TiO2 nanocrystals grown in the presence of a layered MoS2/graphene hybrid [25]. The Ag nanoparticles bridged g-C3N4 and WS2 heterojunction was prepared successfully, which significantly improved the H2 production up to 68.62 μmol h−1 [26]. Therefore, construction of vdW heterostructures indeed plays an important role in modulating the electronic and optical properties of 2D layered materials. Although theoretical studies have been carried out to understand the structure, stability, electronic property, and band alignment of HTiO2, some important properties, such as reliable band gap, carrier effective mass, mechanical and optical properties, and potential applications in solar energy harvesting and visible-light photocatalysis of heterostructures remain poorly understood. In the present work, we design new vdW heterostructures using H-TiO2 and MoS2(WS2) monolayers and systemically study their mechanical, electronic and optical properties, and carrier effective mass. We demonstrate that the heterostructures integrate the merits of both ingredients and have potential as efficient visible-light photocatalysts for water splitting and solar energy harvesting.

3.2. Mechanical property A freestanding monolayer should have enough strength of stiffness against external strains to maintain is structural stability when subjected to in-plane strains. We then further investigate the mechanical stability of the H-TiO2 monolayer in terms of ideal strengths and elastic constants. Within the linear elastic limit, the linear elastic constants can be obtained according to the energy–strain relation:

U =

V 2

6

6

∑ ∑ Ci,j ei ej, i=1 j=1

where V is the volume of the undistorted lattice cell, U is the elastic potential energy, Ci,j is the matrix of the elastic constants, and ei is the matrix element of the strain vector e= (e1, e2, e3, e4, e5, e6). This method is described in detail elsewhere [36,38,39]. For 2D materials belonging to the hexagonal crystal system, only two independent elastic constants are used: C11 = C22 and C12 = C21. Correspondingly, the Young’s modulus (in-plane stiffness C), Shear modulus, and Poisson ratio can be 2 2 - C12 )/C11, obtained from the following expressions: Y = (C11 G = C66 = (C11 - C12 )/2 , and ν = C12/C11, respectively. Our calculated elastic constants and Young’s modulus are listed in Table 2. The predicted values of MoS2 monolayer in this work are in excellent agreement with the previous theoretical values (127 N/m) [40], which proves the reliability of the above computational method. The fitted energy–strain curves for H-TiO2 are shown in Fig. S2. The calculated elastic constants are C11 = 100.50 N/m, C12 = 30.76 N/m, and C66 = 34.87 N/m for H-TiO2 monolayer. The corresponding Y, G, and ν values are 99.88 N/m, 34.88 N/m, and 0.306, respectively. For the 2D hexagonal crystal system, the mechanical stability criteria should satisfy the relation C11 > C12 and C66 > 0 [41] according to the Born–Huang criteria [42]. Thus, the H-TiO2 is mechanically stable. Young’s modulus is comparable with that of MoS2 (123–130 N/m) [43] and higher than that of phosphorene (26 and 88 N/m in the zigzag and armchair directions, respectively) [44], but considerably lower than that of grapheme (~334 N/m) [39,45]. For the 2D hexagonal crystal, the Poisson’s ratio ν and Young’s modulus are independent of the directions, demonstrating isotropy in the mechanical response [46]. Following the approach proposed by Li et al. [43], we further examine the mechanical response by calculating the stress–strain and energy–strain relations along the x (zigzag direction) and y (armchair direction) axes, as shown in Fig. 3(a). The energy response (or stress response) is near degenerate along the x and y directions under uniaxial strain, implying that the H-TiO2 is a virtually elastic isotropic 2D material at last within the linear elastic limit. The energy–strain curves evidently demonstrates a quadratic form when the tensile strain is not more than 10%, but when the strain increases up to approximately 16%, the curves exhibit linear characteristics. To calculate the ideal strength of H-TiO2, we assume that its effective thickness (h = 4.73 Å)

2. Computational methodology All structural optimizations and electronic structure calculations were carried out using density functional theory as implemented in Vienna Ab Initio Simulation Package [27]. Generalized gradient approximation [28] in the form of Perdew–Burke–Ernzernhof (PBE) functional level [29] was used for the exchange-correlation potential. Projector augmented-wave method was used for the electron–ion interactions with a plane wave cutoff energy of 500 eV for all the calculations [30]. All the structures were fully optimized using conjugate gradient method. The criteria for the total energy and the maximum Hellmann–Feynman force acting on each atom were less than 10−6 eV and 0.01 eV/Å, respectively. The vacuum space between layers from the nearest supercell was set to be larger than 12 Å. The 13 × 13 × 1 Гcentered Monkhorst–Pack [31] k-point meshes were adopted for the HTiO2 unit cell and its vdW structures, as shown in Fig. 1. To correctly describe dispersive interactions, DFT-D3 vdW method was implemented [32]. Phonon spectra were obtained using the phonopy package [33]. The thermodynamic stability was analyzed through ab initio molecular dynamics (AIMD) simulations by Nosé–Hoover method [34] at 500 K. To obtain more reliable band gap values and optical properties, the Heyd–Scuseria–Ernzerhof (HSE) hybrid functional level [35] with different Hartree–Fock exchange energies (α) were also adopted. 3. Results and discussion 3.1. Structure and stability As shown in Fig. 1(a), the H-TiO2 exhibits a clear double-layered graphene-like morphology that can be viewed as double [-Ti6-O6-]n hexagonal rings parallel-packed together via joint O atoms. A similar 2

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Fig. 1. (a) Top and side views of H-TiO2 monolayer. Schematic views of the TiO2/MoS2(WS2) heterostructures with various stackings: all O atoms on the top of (b) Mo(W) atoms, (c) S atoms, (d) hexagonal hollows, and (e) the middle of the Mo(W)-S bonds. ΔEMo and ΔEW are the energy difference relative to most stable configuration for MoS2-based and WS2-based heterostructures, respectively.

is the distance between the two outmost O atom planes of the monolayer. As seen in Fig. 3(a), the critical tensile strengths of H-TiO2 nearly simultaneously emerge at the strain of around 25% under the uniaxial or biaxial strains along the high-symmetry direction, and the corresponding ultimate strength values are approximately 41.4 and 36.1 GPa. The biaxial ultimate strength is considerably lower than that of graphene (99 GPa) but is higher than those of MoS2 (26 GPa), GaS (12 Ga), and GaSe (10 GPa) [47]. The ultimate strain (25%) is not less than those of grapheme (20%) [47] and MoS2 (25%) [43], indicating that H-TiO2 is more ductile than graphene and MoS2. Although this material can withstand a tensile strain of up to ~25%, the increased tensile strains severely degrade the stability of the material. Whether the dynamical stability can be retained before the strain approaches the critical point at the stress–strain curve should be investigated. We further calculated the phonon spectra of H-TiO2 under various strains. The calculated phonon spectra, as displayed in Fig. S3 of the Supplemental Material, verify that H-TiO2 can remain dynamically stable when the biaxial tensile strain reaches up to 10%. Overall, the MoS2 monolayer and H-TiO2 demonstrate similar mechanical properties, which facilitate the construction of heterostructure by coupling H-TiO2 and MoS2 monolayers.

based on PBE and HSE06 functional levels, respectively, with the VBM and CBM at Г and K points [14], respectively, as shown in Fig. S4. The predicted band gap of H-TiO2 is larger than that of bulk TiO2 in the rutile phase (Fig. S5) due to quantum confinement effect, which is consistent with the previous value of 5.05 eV [14]. The HSE06 scheme produced values of 3.33 and 4.55 eV for 3D bulk rutile TiO2 and LNS, whereas the experimental values are 3.0 [48] and 3.85 eV [11], respectively. We therefore rationally conjecture that the HSE06 approach overestimates the band gaps for 2D TiO2. To obtain a relatively accurate band gap of H-TiO2, we conduct a series of calculations using HSE functional level with different short-range Hartree–Fock exchange energy α for TiO2 in rutile phase, LNS, and H-TiO2. The corresponding results are summarized in Table 1 and visualized in Figs. S4–S5. We reproduce the experimental band gap for rutile TiO2 and LNS when the parameters α = 0.20 and 0.15 are selected, respectively. We consequently have reason to believe that the reliable parameter α should range from 15% to 20%; thus, the corresponding band-gap values range within 4.295–4.618 eV for H-TiO2. The true band gap is yet to be proven by further experiments. It should be noted that the band gaps increase and decrease upon biaxial compressive and tensile strain, respectively, in the range of −4% to 10%. [14]

3.3. Electronic structure and band gap

3.4. Effective mass and carrier mobility From the viewpoint of applications, a material with high carrier

The H-TiO2 features an indirect band gap of 3.373 and 4.995 eV

Fig. 2. The calculated stress–strain and energy–strain relations for H-TiO2 along the x (zigzag) or/and y (armchair) axis. The σx, σy, and σxy are the stresses along the x, y, and double axes, respectively. (b) The energy level band edge with respect to vacuum level with biaxial strain for H-TiO2. The inset in left panel shows the crystal structure of H-TiO2 in orthogonal setting. The peak stresses are 108.8, 114.7, and 95.0 GPa for σx, σy, and σxy under the strain at 25%, 26% and 24%, respectively. Inset shows the charge density at VBM and CBM of H-TiO2.

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Table 1 Calculated lattice constant (a, b and c in Å), symmetry, relative energy (ΔEr in meV per atom) of TiO2 with respect to rutile phase, band-gap (Eg in eV) at PBE level and HSE level with different Fock exchange parameter α. Structure

Lattice constant

Rutile LNS H-TiO2 H-MoS2 H-WS2 TiO2/MoS2 TiO2/WS2

ΔEr

Symmetry

a

b

c

4.649 3.0254 6.050 3.174 3.181 6.213 6.219

4.649 3.751

2.968

P42/mnm Pmmn P6/mmm P-6 m2 P-6 m2 P3m1 P3m1

0 25 (20) [14] 19 (13) [14]

C11

C12

Y

E1e

E1h

me*/mh*

μe/μh

H-TiO2 MoS2 MoS2 [40] MoS2 [69] WS2 TiO2/MoS2 TiO2/WS2

100.5 134.3

30.8 33.0

6.10 11.14 11.12

8.55 5.61 5.53

148.1 244.7 253.8

32.1 83.0 80.8

99.9 126.5 127.8 123 141 216.4 228.2

13.69 7.51 6.75

4.87 6.42 5.94

1.27/1.80 0.481/0.60 0.475/0.585 0.47/0.60 0.330/0.442 1.11/0.669 1.20/0.464

23.63/5.98 62.5/158.4 66.24/176.19 79/194 97.98/431.6 44.2/166.1 49.3/426.0

mobility and sufficiently large electronic band gap is highly desired. The carrier mobility of 2D materials can be estimated by the expression [49–51]:

μ=

1.790 2.980 3.373 1.666 1.821

Eg with different α 0.10

0.15

0.25

2.333

2.627 3.872 4.295 1.958 2.114

3.328 4.550 4.995 2.141 2.308

3.9714 1.865 2.016 1.995 1.794

1.974

and E1 as the deformation potential (DP) proposed by Bardeen and Shockley (DP denotes the shift of the band edges induced by a small strain) [52]. Assuming that the electronic structure exhibits a parabolic form, one can deduce the carrier effective mass m* from the expression: m ∗ = ħ2/(∂2E (k )/ ∂k 2) , where E(k) is the energy, and k is the momentum. By quadratic fitting of the energy band curvature around the VBM and CBM, the effective mass of hole (mh∗) and electron (me∗) can be obtained, respectively. The positions of VBM and CBM with respect to vacuum level are given in Fig. 2(b) for H-TiO2. Clearly, the energy level of band edge behaves as a linear function of strain ɛ within the range of ± 1.5% with a step of 0.5%. By linear fitting of the CBM (VBM)–strain relation, the slope of the valence edge or CB edge, which is equivalent to the DP for electron (E1e) or hole (E1h) states, can be obtained. The calculated DP, effective masses of electron and hole at the CBM (me∗), and VBM (mh∗) are tabulated in Table 2 for HTiO2, MoS2, WS2, and their heterojunctions. As shown in Table 2, the effective masses and carrier mobility for MoS2 are 1.27/1.80 me and 23.63/ 5.98 cm2·V−1·S–1 for electron/hole, respectively; such values are well consistent with previous reports [40]. For H-TiO2, the obtained mh∗ and me∗ are as high as 1.27me and 1.80me, respectively, which are roughly three and four times larger than those of MoS2 and WS2, respectively. The mobilities of the electron and hole are only 23.63 and 5.98 cm2·V−1·S–1, respectively, which are considerably lower than those of the MoS2 and WS2 monolayers.

Table 2 Calculated elastic constants (C11, C12 and Y in N/m), deformation potential constants for CBM and VBM (E1e and E1h in eV), effective mass (mh* and me* in me), carrier mobility (μe and μh in cm2 V−1 s−1) at 300 K. Subscripts “e” and “h” denote “electron” and “hole”, respectively. Structure

EgPBE

2eħ3C , 3kB T |m∗|2 E12

where e is the electron charge, ħ is the reduced Planck constant, C is the in-plane elastic modulus, KB is the Boltzmann constant, and T is the temperature. The temperature T is set to 300 K in this work. Given that Young’s modulus is nearly independent of the directions for hexagonal crystal H-TiO2 and MoS2 [40,43], we take the calculated Young’s modulus as C for arbitrary direction, m* as the carrier effective mass,

Fig. 3. Calculated (a) band edge positions with reference to the vacuum level, and (b) absorption spectra as a function of photon energy for H-TiO2, MoS2, WS2, MoS2/TiO2, and WS2/TiO2. The vertical dashed lines indicate the visible light range. The horizontal dashed lines indicate the water reduction (H+/H2) and oxidation (H2O/O2) potentials at pH = 0.

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that the CBM and VBM of MoS2 (WS2) shift upward by 0.28 and 2.09 eV (0.07 and 1.74 eV), respectively, relative to those of the H-TiO2. Thus, the MoS2/TiO2 and WS2/TiO2 interfaces are conventional type II heterojunctions. To further verify the type II band alignment, the band decomposed charge densities are visualized in the insets of Fig. 4. The highest occupied levels of the heterostructures primarily comprise S-3p orbitals, whereas the lowest unoccupied band arises mostly from Ti-3d orbitals. Fig. 3(a) illustrates the band edge alignments of H-TiO2, MoS2, WS2, and their heterostructures with absolute vacuum scale as reference. As reported in previous works, the H-TiO2 [14], MoS2 [18,23,61], and [62] WS2 monolayers are potential catalysts for water splitting given their negative VBM position and positive CBM position with respect to the water oxidation potential and the hydrogen reduction potential, respectively. Compared with pristine MoS2, the conduction band (CB) potential of MoS2/TiO2 shifts upward by 0.135 eV, and the valence band (VB) potential shows a negligible downward shift. For WS2/TiO2, the CB and VB potentials shift upward by 0.278 and 0.188 eV, respectively, which is relative to those of the pristine WS2 monolayer. This occurrence will facilitate the electron transfer process and hence enhance charge separation. The calculated carrier mobility and all the relevant results are presented in Table 2. The hole’s mobility at 300 K for MoS2/TiO2 (WS2/TiO2) is approximately 166 (426) cm2·V–1 s−1, which is close to that of MoS2 (WS2). The electron’s mobility is more than twice as high as that of H-TiO2 but slightly lower than that of the pristine MoS2 (WS2). Therefore, enhancement in the carrier mobility is achieved by building vdW heterostructures. In addition to the favorable band gap positions for photocatalytic water splitting, excellent response to visible light is highly desirable for efficient solar energy harvesting. Fig. 3(b) shows the optical absorption curves of H-TiO2 and its heterostructures. For H-TiO2, the absorption edge is larger than the corresponding value of the fundamental band gap due to its indirect band gap, and the absorption spectrum predominantly falls in the ultra-violet (UV) range without any in the visible-light region. We further consider the effect of electron hole interaction on optical absorption spectra. Fig. S10 shows the imaginary part of the dielectric function of monolayer H-TiO2 obtained from HSE06 + TDHF. The light absorbance descends dramatically about 0.6 eV, indicating the exciton effect is apparent. Upon forming heterostructures with MoS2 or WS2, the absorption edges shift downward at around 2.0 eV, and the first absorption peak occurs near the UV region. Compared with WS2/TiO2, the MoS2/TiO2 vdW heterostructure exhibits more excellent absorption performance in the visible-light range. Nevertheless, a substantially enhanced absorption is observed in the visible-light range, suggesting that the photocatalysts of the vdW heterostructures can be activated under visible light. Taking the WS2/TiO2 vdW heterostructure as an example, Fig. 5 illustrates the mechanism of the photocatalytic reactions driven by solar energy. The calculated work functional Φ for the WS2 and DiHTiO2 monolayer is 5.997 and 8.308 eV, respectively, indicating that the electron will flow from the WS2 side to the TiO2 side when the heterostructure is built. Redistribution of charges occurs at the interface of the heterostructure, as shown in Fig. 6. Consequently, a built-in electric field forms with direction pointing from the WS2 layer to the TiO2 layer, which is beneficial for the migration of carriers. Under solar light, the electrons are excited from the VB of WS2 to its CB, and then the photoexcited electrons migrate to the CB of TiO2 with the help of the interface electric field, whereas the photogenerated holes in the VB of TiO2 transfer to the VB of WS2. As a result, the photogenerated electrons and holes are accumulated in the CB of TiO2 and in the VB of WS2, respectively, thereby realizing the spatial separation of the photogenerated charge carriers. Finally, the photogenerated electrons and holes participate in the oxidation and reduction reactions at the TiO2 and WS2 sides, respectively, producing hydrogen and oxygen, respectively. In addition to photocatalytic applications, 2D type II vdW

3.5. Heterostructure for visible-light photocatalysis Sizable band gap, favorable positions of band edges, and carrier mobility are the three primary requirements among many factors for an ideal semiconductor photocatalyst. The band gap is first required to exceed the free energy of water splitting (1.23 eV). Moreover, to ensure efficient visible-light absorption, the band gap should be larger than 2.0 eV [53,54]. For spontaneous water splitting, the energy levels of the CBM and VBM must be higher and lower than the hydrogen-reduction (H+/H2) and water-oxidation (O2/H2O) potential levels, respectively. The reduction and oxidation potential levels are dependent on the pH value [55], and they can be calculated according to the equations: EHred = −4. 44 + pH × 0.059 eV and EOox2 /H2O = −5. 67 + pH × 0.059 + /H2 eV, respectively. Therefore, the standard reduction and oxidation potentials with respect to the vacuum level are −4.44 and −5.67 eV for H+/H2 and O2/H2O, respectively, at pH = 0. Fig. 3(a) illustrates the alignment of VBM and CBM at pH = 0 relative to vacuum level for HTiO2, MoS2 and WS2. Although the H-TiO2 band gap meets the requirements, its band edges are situated in energetically favorable positions for water splitting [14], as shown in Fig. 3(a). Such large indirect band gap impedes the harvesting of solar energy. Considering the lattice match and symmetry, numerous mesopores, suitable band gap, stability, and high carrier mobility of MoS2 and WS2 monolayers, the physical properties of MoS2/TiO2 and WS2/TiO2 heterostructures are interesting; these heterostructures can be adopted as photocatalysts for water splitting and solar cell. To minimize the interlayer lattice mismatches, we build the MoS2/TiO2 and WS2/TiO2 heterostructures using a unit cell from HTiO2 and a 2 × 2 × 1 supercell from MoS2 (or WS2). The relaxed lattice constant of MoS2 and WS2 are 3.174 and 3.181 Å, respectively. We build four most possible stacking configurations as illustrated in Fig. 1. The configuration [Fig. 1(e)] finally converts into the most stable configuration [Fig. 1(b)] after geometrical optimization. Fig. 1 shows the differences in the total energy (ΔE) of other stacking configurations compared with the most stable configuration. For the most stable MoS2/TiO2 and WS2/TiO2, the relaxed lattice constants are 6.215 and 6.213 Å, respectively, and the corresponding interlayer distances are 2.839 and 2.891 Å, respectively. Although the obtained lattice mismatch is ~2.5% for both heterostructures, the calculated phonon spectra in Figs. S6 and S7 confirm their thermodynamic stability. Moreover, the elastic constants C11 and C12 in Table 1 indicate that the heterostructures are mechanically stable. Interestingly, the calculated Young’s modulus of the heterostructure approximately equals the sum of that of TiO2 and MoS2 (WS2). To obtain reliable band gap, band alignment, and optical property, we carefully selected short-range Hartree–Fock exchange energy α when the HSE functional level is adopted to calculate the properties. For MoS2 monolayer, a large intrinsic band gap of 1.8 eV is observed [56–58], whereas the theoretically predicted values are 1.67 and 2.14 eV at standard PBE and HSE06 hybrid functional levels, respectively. As shown in Fig. S8, the HSE with α = 10% produces a band gap of 1.86 eV, approaching the experimental band gap of 1.8 eV. Similarly, when setting α = 15%, the calculated band gap of WS2 is 2.11 eV (Fig. S9), which agrees reasonably well with the experimental value of ~ 2.05 eV [59,60]. Considering the possible band gap of H-TiO2 discussed above, the HSE hybrid functional levels with α = 10% and α = 15% hereafter are used for MoS2/TiO2 and WS2/TiO2 heterojunctions, respectively, if not explicitly mentioned. As shown in Fig. 4, the electronic structures of both vdW heterostructures exhibit direct-band-gap materials with the VBM and CBM at the Г point. The estimated band gap value of 1.995 and 1.974 eV for MoS2/TiO2 and WS2/TiO2 are considerably smaller than that of H-TiO2; such moderately direct band gaps cause their absorption to fall perfectly in the visible region, indicating that the vdW heterostructures are highly appealing to use for visible-light photocatalysts for water splitting and solar cell devices. The projected band structures in Fig. 4 show 5

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Fig. 4. Projected band structures of (a) MoS2/TiO2 and (b) WS2/TiO2 heterostructures calculated using HSE method with α = 10% and 15% respectively. The valence band maximum is set to zero.

Fig. 6. Planar-averaged electron density difference of (a) WS2/TiO2 and (b) WS2/TiO2 composite models. The cyan and yellow regions represent electron accumulation and depletion, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) ∞

η=

0.65(Eg − ΔEc − 0.3) ∫E P (ħϖ )d(ħϖ ) g

∞ ∫0 P (ħϖ )d(ħϖ )

where 0.65 is the band-fill factor, P(ħϖ) is the AM 1.5 solar energy flux at the photon energy (ħϖ), and Eg is the band gap of the donor (MoS2 or WS2). ΔEc is the CB offset between donor (MoS2 or WS2) and acceptor (TiO2). The (Eg-ΔEc-0.3) term is an estimation of the maximum open circuit voltage. The maximum efficiency depends critically on the donor band gap and the CB offset. Fig. 5(b) shows the power conversion efficiency contour as a function of the donor band gap and CB offset. More calculation details are given in the Supporting Information. The CB offset is 0.28 and 0.07 eV for WS2/TiO2 and MoS2/TiO2, respectively, and the band gaps of the donors are 2.23 and 2.06 eV, respectively. Thus, the estimated maximum efficiencies for WS2/TiO2 and MoS2/TiO2 are around 11.5% and 13.5%, respectively, which are higher than that of the single-bulk-heterojunction solar cell (10%) [66]. These values are comparable with those of nanocarbon-based photovoltaics (9%–13%) [67], but are lower than those of the currently

Fig. 5. (a) Schematic illustration of type-II donor–acceptor band alignments and charge carrier transformation in WS2/TiO2 heterojunction. (b) Contour plots showing the energy-conversion efficiency versus the donor bandgap and the conduction band offset. All the energy levels are referenced to the reduction (H+/H2) potential.

heterostructures have potential applications in solar cells due to their high solar-to-electric power conversion efficiency [19,63,64]. As discussed above, these heterostructures exhibit excellent photo response under visible light, remarkably improving the separation efficiency of the photogenerated charge carriers, which make them useful in highefficiency solar cells [65]. The power conversion efficiency of heterojunction solar cells can be estimated according to the equation below [66]: 6

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W.-Z. Xiao, et al.

proposed heterojunctions, such as AsP/GaN (22%) [19], edge-modified phosphorene nanoflake (20%) [68], and nanorribon (20%) [63] heterojunctions.

S. Goedecker, M. Amsler, Chem. Mater. 29 (2017) 8594–8603. [15] A. Kudo, Y. Miseki, Chem. Soc. Rev. 38 (2009) 253–278. [16] M.D. Hernandez-Alonso, F. Fresno, S. Suarez, J.M. Coronado, Energy Environ. Sci. 2 (2009) 1231. [17] J. Schneider, M. Matsuoka, M. Takeuchi, J. Zhang, Y. Horiuchi, M. Anpo, D.W. Bahnemann, Chem. Rev. 114 (2014) 9919–9986. [18] J. Liao, B. Sa, J. Zhou, R. Ahuja, Z. Sun, J. Phys. Chem. C 118 (2014) 17594–17599. [19] M. Xie, S. Zhang, B. Cai, Y. Huang, Y. Zou, B. Guo, G. Yu, H. Zeng, Nano Energy 28 (2016) 433–439. [20] Y. Qi, Q. Liang, R. Lv, W. Shen, F. Kang, Z.H. Huang, Roy. Soc. Open Sci. 5 (2018) 180187. [21] M. Sabarinathan, S. Harish, J. Archana, M. Navaneethan, H. Ikedab, Y. Hayakawa, RSC Adv. 7 (2017) 24754–24763. [22] C. Li, S. Zhang, Y. Zhou, J. Li, J. Mater Sci: Mater Electron 28 (2017) 9003–9010. [23] Z. Zhang, Q. Qian, B. Li, K.J. Chen, ACS Appl. Mater. Inter. 10 (2018) 17419–17426. [24] K. Chang, Z. Mei, T. Wang, Q. Kang, S. Ouyang, J. Ye, ACS Nano 8 (7) (2014) 7078–7087. [25] W. Zhou, Z. Yin, Y. Du, X. Huang, Z. Zeng, Z. Fan, H. Liu, J. Wang, H. Zhang, Small 9 (1) (2013) 140–147. [26] Y. Ma, J. Li, E. Liu, J. Wan, X. Hu, J. Fan, Appl. Catal. B-Environ. 219 (2017) 467–478. [27] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169. [28] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [29] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. [30] P.E. Blöchl, Phys. Rev. B 50 (1994) 17953. [31] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [32] S. Grimme, S. Ehrlich, L. Goerigk, J. Comp. Chem. 32 (2011) 1456–1465. [33] A. Togo, I. Tanaka, Scr. Mater. 108 (2015) 1–5. [34] S. Nosé, A unified formulation of the constant temperature molecular dynamics methods, J. Chem. Phys. 81 (1984) 511–519. [35] A.V. Krukau, O.A. Vydrov, A.F. Izmaylov, G.E. Scuseria, J. Chem. Phys. 125 (2006) 224106. [36] W.Z. Xiao, G. Xiao, L.L. Wang, J. Chem. Phys. 145 (2016) 174702–174710. [37] T. Orzali, M. Casarin, G. Granozzi, M. Sambi, A. Vittadini, Phys. Rev. Lett. 97 (2006) 156101. [38] S.Q. Wang, H.Q. Ye, J. Phys.: Condens. Matt. 15 (2003) 5307. [39] E. Cadelano, P.L. Palla, S. Giordano, L. Colombo, Phys. Rev. B 82 (2010) 235414. [40] Y. Cai, G. Zhang, Y.W. Zhang, J. Am. Chem. Soc. 136 (2014) 6269–6275. [41] Z.J. Wu, E.J. Zhao, H.P. Xiang, X.F. Hao, X.J. Liu, J. Meng, Phys. Rev. B 76 (2007) 054115. [42] M. Born, K. Huang, Dynamical Theory of Crystal Lattices Oxford Classic Texts in the Physical Sciences, Clarendon, Oxford, 1988. [43] J. Li, N.V. Medhekar, V.B. Shenoy, J. Phys. Chem. C 117 (2013) 15842–15848. [44] M. Elahi, K. Khaliji, S.M. Tabatabaei, M. Pourfath, R. Asgari, Phys. Rev. B 91 (2015) 115412. [45] F. Liu, P. Ming, J. Li, Phys. Rev. B 76 (2007) 064120. [46] L. Wang, A. Kutana, X. Zou, B.I. Yakobson, Nanoscale 7 (2015) 9746–9751. [47] M. Yagmurcukardes, R.T. Senger, F.M. Peeters, H. Sahin, Phys. Rev. B 94 (2016) 245407. [48] J.K. Burdett, T. Hughbanks, G.J. Miller, J.W. Richardson, J.V. Smith, J. Am. Chem. Soc. 109 (1987) 3639–3646. [49] S. Bruzzone, G. Fiori, Appl. Phys. Lett. 99 (2011) 2108. [50] S.-I. Takagi, A. Toriumi, M. Iwase, H. Tango, IEEE Trans Electr. Dev. 41 (1994) 2357–2362. [51] J. Xi, M. Long, L. Tang, D. Wang, Z. Shuai, Nanoscale 4 (2012) 4348–4369. [52] J. Bardeen, W. Shockley, Phys. Rev. 80 (1950) 72. [53] B.D. Alexander, P.J. Kulesza, L. Rutkowska, R. Solarska, J. Augustynski, J. Mater. Chem. 18 (2008) 2298–2303. [54] T. Bak, J. Nowotny, M. Rekas, C.C. Sorrell, Int. J. Hydrogen Energy 27 (2002) 991–1022. [55] V. Chakrapani, J.C. Angus, A.B. Anderson, S.D. Wolter, B.R. Stoner, G.U. Sumanasekera, Science 318 (2007) 1424. [56] A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C.-Y. Chim, G. Galli, F. Wang, Nano Lett. 10 (2010) 1271. [57] K.F. Ma, C. Lee, J. Hone, J. Shan, T.F. Heinz, Phys. Rev. Lett. 105 (2011) 136805. [58] B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti, A. Kis, Nat. Nanotechnol. 6 (2011) 147. [59] G.L. Frey, R. Tenne, M.J. Matthews, M.S. Dresselhaus, G. Dresselhaus, J. Mater. Res. 13 (1998) 2412. [60] M. Hong, X. Zhou, J. Shi, Y. Qi, Z. Zhang, Q. Fang, Y. Guo, Y. Sun, Z. Liu, Y. Li, Q. Wang, Y. Zhang, Nano. Res. 10 (2017) 3875–3884. [61] S.S. Ding, W.Q. Huang, Y.C. Yang, B.X. Zhou, W.Y. Hu, M.Q. Long, P. Peng, G.F. Huang, J. Appl. Phys. 119 (2016) 205704. [62] Q. Peng, Z. Wang, B. Sa, B. Wu, Z. Sun, Sci. Rep. 6 (2016) 31994. [63] W. Hu, L. Lin, R. Zhang, C. Yang, J. Yang, J. Am. Chem. Soc. 139 (2017) 15429–15436. [64] A. Bandyopadhyay, D. Ghosh, S.K. Pati, J. Phys. Chem. Lett. 9 (2018) 1605–1612. [65] I. Ramiro, J. Villa, C. Tablero, E. Antolín, A. Luque, A. Martí, J. Hwang, J. Phillips, A.J. Martin, J. Millunchick, Phy. Rev. B 96 (2017) 125422. [66] M.C. Scharber, D. Mühlbacher, M. Koppe, P. Denk, C. Waldauf, A.J. Heeger, C.J. Brabec, Adv. Mater. 18 (2006) 789–794. [67] M. Bernardi, J. Lohrman, P.V. Kumar, A. Kirkeminde, N. Ferralis, J.C. Grossman, S. Ren, ACS Nano 6 (2012) 8896–8903. [68] W. Hu, L. Lin, C. Yang, J. Dai, J. Yang, Nano Lett. 16 (2016) 1675–1682. [69] S. Yu, H.D. Xiong, K. Eshun, H. Yuan, Q. Li, Appl. Surf. Sci. 325 (2015) 27–32.

4. Summary We further studied the stability, band gap, electronic mobility, mechanical, and optical properties of H-TiO2 by first-principle calculations. The 2D H-TiO2 exhibits robust thermodynamic, energy, and mechanical stability. Especially, H-TiO2 demonstrates higher ductility than graphene and MoS2 and can withstand a tensile strain of up to ~25%. H-TiO2 can remain dynamically stable when the biaxial tensile strain reaches up to 10%. The estimated indirect band gap ranges within 4.30–4.62 eV by HSE-based calculations, which result in hardly any visible-light absorbance. Although the mobilities of the electron and hole are only 23.63 and 5.98 cm2·V−1·S–1, respectively, we find that the construction of vdW heterostructures MoS2/TiO2 and WS2/TiO2 remarkably improves the mobility. Interestingly, we find that the heterostructures integrate the merits of both components. As a result, these heterostructures exhibit the features of direct band gap, mobility as high as MoS2 (or WS2), type-II band alignment, built-in electronic field, and visible-light absorption, which make them suitable for visible-light photocatalysts for water splitting and solar energy-conversion devices. The theoretically estimated maximum conversion efficiencies for WS2/ TiO2 and MoS2/TiO2 are around 11.5% and 13.5%, respectively. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 11764018 and No. 51701071), Hunan Provincial Natural Science Foundation under Grant No. 2017JJ3049 and No. 2018JJ2080, and the Scientific Research Fund of Hunan Provincial Education Department (Nos. 18A347 and 16C0391). We acknowledge the computational support provided by the computing platform of the Network Information Center of Hunan Institute of Engineering. Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.apsusc.2019.144425. References [1] A. Fujishima, K. Honda, Nature 238 (1972) 37. [2] H. Xu, S. Ouyang, L. Liu, P. Reunchan, N. Umezawa, J. Ye, Mater. Chem. A 2 (2014) 12642–12661. [3] X. Chen, A. Selloni, Chem. Rev. 114 (2014) 9281–9282. [4] M.C. Beard, J.M. Luther, A.J. Nozik, Nat. Nanotechnol. 9 (2014) 951–954. [5] R. Yu, Q.F. Lin, S.F. Leung, Z.Y. Fan, Nano Energy 1 (2012) 57–72. [6] T. Liao, Z. Sun, S.X. Dou, ACS Appl. Mater. Inter. 9 (2017) 8255–8262. [7] E.C. Cho, C.W. Chang-Jian, J.H. Zheng, J.H. Huang, K.C. Lee, B.C. Ho, Y.S. Hsiao, J. Taiwan Inst. Chem. 91 (2018) 489–498. [8] S. Ida, N. Kim, E. Ertekin, S. Takenaka, T. Ishihara, J. Am. Chem. Soc. 137 (2015) 1239–1244. [9] N. Singh, Z. Salam, A. Subasri, N. Sivasankar, A. Subramania, Sol. Energ. Mat. Sol. C 179 (2018) 417–426. [10] T. Sasaki, M. Watanabe, J. Phys. Chem. B 101 (1997) 10159–10161. [11] N. Sakai, Y. Ebina, K. Takada, T. Sasaki, J. Am. Chem. Soc. 126 (2004) 5851–5858. [12] Z. Sun, T. Liao, Y. Dou, S.M. Hwang, M.S. Park, L. Jiang, J.H. Kim, S.X. Dou, Nat. Commun. 5 (2014) 3813. [13] W. Zhou, N. Umezawa, R. Ma, N. Sakai, Y. Ebina, K. Sano, M. Liu, Y. Ishida, T. Aida, T. Sasaki, Chem. Mater. 30 (2018) 6449–6457. [14] H.A. Eivari, S.A. Ghasemi, H. Tahmasbi, S. Rostami, S. Faraji, R. Rasoulkhani,

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