Unusual properties and potential applications of strain BN-MS2 (M = Mo, W) heterostructures

Heterostructures receive intensive attentions due to their excellent intrinsic properties and wide applications. Here, we investigate the natural physical properties and performances of strain BN-MS2 (M = Mo, W) heterostructure by density functional theory. Different to compressive monolayer MS2, corresponding BN-MS2 heterostructures keep direct band-gap characters because effects of charge transfer on anti-bonding dz2 orbitals are stronger than those of Poisson effect. Mexican-hat-like bands without magnetic moments are observed at strain BN-MS2 heterostructures when the compression is enough. Consequently, electron mobilities of strain BN-MS2 heterostructures are slightly reduced at first and then enlarged with increasing compressive strain. Note that, strain BN-MS2 heterostructures reduce the band edges of MS2 layers and extend their application in photocatalytic water splitting. But just the n-type and p-type Schottky barriers of devices with strain BN-MS2 heterostructures are reduced and even vanished with the increasing tensile and compressive, respectively. Besides, electron mobilities of strain BN-MoS2 and BN-WS2 heterostructures can be enhanced to 1290 and 1926 cm2  V −1 s−1, respectively, with increasing tensile strain. Interestingly, the exciton binding energies of strain BN-MS2 heterostructures exhibit oscillation variations, different to those of strain monolayer MS2.

Two-dimensional transition metal dichalcogenides (TMDs) are an emerging class of materials with atomic thickness, pristine surface, unique and tunable electronic properties which make them highly attractive for applications ranging from nanoelectronics to optoelectronics with high performances 1,2 . However, many studies have revealed that the performances of nanodevices based on TMDs in experiment are lower than the theoretical expectations [1][2][3][4] . For examples, most measured carrier mobilities of monolayer MoS 2 nanodevices under room temperature are far lower than the theoretical predication of 410 cm 2 V −1 s −1 5-7 . That can be ascribed to three main reasons: first, the fabricated TMDs flakes in experiment containing several defects, like vacancies, which enhance the scattering effects and deteriorate the intrinsic properties of TMDs 8,9 . Second, oxide substrates with surface roughness induce strong interfacial charged impurities at substrates-TMDs interfaces [10][11][12][13][14] . Third, metal-TMDs interfaces usually have large contact resistances and Schottky barrier heights (SBHs) which limit the carrier injection efficiency [15][16][17][18][19] . To overcome these issues, van der Waals heterostructures engineering, especially BN-TMDs heterostructures, have been employed. Moreover, such approaches have evidently improved the performances of nanodevices based on TMDs. For examples, Wang, et al. have fabricated MoS 2 , MoSe 2 and WS 2 layers on hexagonal boron nitride (BN) substrates to form BN-TMDs heterostructures, which enhanced the photoluminescence and room-temperature mobilities of TMDs due to the reduced substrate traps and improved fake quality [20][21][22][23][24] . Liao et al. have found that forming BN-TMDs heterostructures in metal-TMDs interface regions not only modulated the work function and fermi level pinning effect, but also reduced the SBHs and contacts resistances of metal-TMDs interfaces by an order of magnitude 25,26 . Moreover, BN-TMDs heterostructures between gate and channel layer could change the main noise source in channel from charged impurities to trapping-detrapping process 27 . Thus, BN-TMDs heterostructures have been widely used in the high performance nanodevices, including integration 28 , photoresponse 29 , self-biased diode 30 , etc.
It should be noted that MS 2 (M = Mo, W) as typical members of TMDs are not only suitable for above mentioned nanodevices, but also have great potentials in applications of flexible nanodevices, such as flexible battery 31  humidity sensing 32 , flexible supercapacitor 33 , and so on. However, the performances of flexible nanodevices based on MS 2 , like carrier mobilities, in experiment are far lower than expectation [34][35][36] . Moreover, direct-to-indirect transitions occur in band gaps of monolayer MS 2 in the flexible nanodevices [37][38][39][40][41] . Such characters are not conductive to realize high performance flexible nanodevices. Inspired by the excellent performance of BN-TMDs heterostructure in optoelectronics as above mentioned, forming strain BN-MS 2 heterostructure with great potential to improve the performance flexible nanodevices. However, few studies have focused on the strain BN-MS 2 heterostructures, although the carrier mobilities of monolayer MoS 2 flexible transistors had been enlarged from 30 to 45 cm 2 V −1 s −1 when monolayer MoS 2 was substituted by strain BN-MoS 2 heterostructure 34,42 . Moreover, so far few theoretical studies have focused on the natural physical properties of strain BN-MS 2 heterostructures. Hence, in this work, the electronic, magnetic, transport, optical properties, and additional potential application of strain BN-MS 2 (M = Mo, W) heterostructures were comprehensively investigated by first principles calculations.

Results and Discussion
Geometric structure. Before exploring the strain BN-MS 2 (M = Mo, W) heterostructures (Fig. 1a,b), the geometric structures of isolated monolayer BN, MoS 2 , WS 2 were investigated and listed in Table 1. The lattice constants of isolated monolayer BN and MS 2 are in good agreement with previous studies [43][44][45][46][47][48] . BN-MS 2 heterostructures are constructed by stacking the BN and MS 2 monolayers on top of each other. To study the natural physical properties of strain BN-MS 2 heterostructures accurately, 5 × 5 BN supercells are constructed and strained to match with the 4 × 4 MS 2 supercells, as shown in Fig. 1    www.nature.com/scientificreports www.nature.com/scientificreports/  Table 1. Note that, although these band gaps are lower than the experimental values 50 , they are closer to the transport band gaps in nanodevices compared to the band gap calculated by GW and HSE functional 19,51 . That is because the strong Coulombic screening by metal electrodes can minimize the exciton binding energies and many body effects of 2D materials 16,27 . Moreover, the electronic structures of MS 2 calculated by PBE functional are similar to those calculated by HSE functional (as demonstrated in Fig. S2). It suggests that PBE functional is sufficient to study the electronic properties of MS 2 layers and BN-MS 2 heterostructures.
When monolayer MS 2 undergoes tensile strain, the band gap reduces gradually and accompanies with a direct-to-indirect band gap transition. That is because the thickness of MS 2 (as listed in Table 1) is reduced by tensile strains due to the Poisson effect. Such thickness reduction strengthens the coupling between the p z orbitals of S atoms and d z 2 orbitals of M atoms, and such biaxial tensile strain weakens the coupling between the p p x y + orbitals of S atoms and + − d d xy x y 2 2 orbitals of M atoms. As a result, the energies of anti-bonding band A and bonding band B reduce, and the energies of anti-bonding band C and bonding band D enlarge. Thus, the VBM shifts up and moves from K to Γ point, and the CBM at the K point shifts down, leading to the reduction of band gaps with increasing tensile strain, as shown in Fig. 2b. On the contrary, application of compressive strain enlarges the thickness of monolayer MS 2 (as listed in Table 1), and then weakens the coupling between the p z orbitals of S atoms and d z 2 orbitals of M atoms and enhances coupling between the + p p x y orbitals of S atoms and + − d d xy x y 2 2 orbitals of M atoms. Consequently, the anti-bonding bands A and C shift up and down, respectively. The position of CBM transforms from anti-bonding band A to anti-bonding band C, leading to a direct-to-indirect band gap transition, as displayed in Fig. 2c,d. Nevertheless, it should be noted that the energy of anti-bonding band C is higher than that of anti-bonding band A of monolayer MS 2 without strain, and it decreases slightly with the increasing compressive strain. As a result, the energy of band C of monolayer MS 2 with small compressive strain is still higher than that of band A of monolayer MS 2 without strain. Thus, the band gaps of monolayer MS 2 slightly enlarge at first and then decrease with the increasing enlarge compressive strain, as displayed in Fig. 3a, which is consistent with previous reports 41 . In addition, the enhanced coupling between the p p x y + orbitals of S atoms and + − d d xy x y 2 2 orbitals of M atoms induced by compressive strain also rises the energy of bonding band E, as shown in Fig. 2c. When the compressive strain is larger than 8%, such raised bonding band E can surpass that of raised bonding band B. Consequently, the position of VBM shifts from the bonding band B at the K point to bonding band E at the M point, leading to a direct-to-indirect transition, as shown in Fig. 2d.  Fig. 2e. Moreover, the components and positions of CBM and VBM of BN-MS 2 heterostructures are similar to those of monolayer MS 2 . It suggests that the intrinsic electronic properties can be remained when monolayer MS 2 transforms to type-I BN-MS 2 heterostructure. However, the band gaps reduce slightly to be 1.72 and 1.88 eV for BN-MoS 2 and BN-WS 2 heterostructures, respectively. That is because the weak charge transfer between BN and MS 2 layers (as shown in Fig. S3) slightly reduce the anti-bonding band A. When BN-MS 2 heterostructures undergo tensile strain, they keep type-I heterostructure characters, and their CBM and VBM are still dominated by MS 2 layer. Moreover, variations of band gaps and band edges of tensile BN-MS 2 heterostructures (see Fig. 2f) are similar to those of tensile monolayer MS 2 since the biaxial tensile also induces the reduction of MS 2 layer thickness in BN-MS 2 heterostructures (as listed in Table 1). However, the reduction indirect band gaps of tensile BN-MS 2 heterostructures are slightly lower than those of corresponding tensile monolayer MS 2 , as exhibited in Fig. 3a. That is because additional charges are accumulated at the MS 2 layer of BN-MS 2 heterostructures (as displayed in Fig. S3), which can further reduce the energy of anti-bonding d z 2 (viz. band A). In the case of BN-MS 2 heterostructures with compressive strain, they keep type-I heterostructure characters. The MS 2 layer of compressive BN-MS 2 heterostructures are still direct band semiconductor with CBM and VBM located at K point, as displayed in Fig. 2g. This is different to those of corresponding monolayer MS 2 although compressive strain also induces the enlarged thickness of MS 2 layer. That is because although the Poisson effect rises the anti-bonding orbitals d z 2 and reduces the anti-bonding orbitals d d xy x y . Hence, the energy of anti-bonding band C is still higher than that of anti-bonding band A at the K point which dominates the CBM of BN-MS 2 heterostructure. It should be noted that, except for the Poisson effect induced by compressive strain, the wrinkle phenomenon is also introduced to the MS 2 layer of BN-MS 2 heterostructure as the compressive strain continue to increases, which induce a heterogeneous charge transfer between BN and MS 2 layers of BN-MS 2 heterostructures (as displayed in Fig. S4). As a result, the energy of anti-bonding orbitals d d xy x y 2 2 + − is close to that of anti-bonding orbitals d z 2, and a Mexican-hat-like band around K point is formed, as shown in Fig. 2g,h. In general, the Mexican-hat-bands suggesting an obviously magnetic moments 52 . Nevertheless, nonmagnetic states are observed for BN-TMDs with larger compressive strain, as displayed in Fig. S5. When the compressive strain continues enlarging, such a Mexican-hat-like band becomes more evident, and a direct-to-indirect band gap transition is www.nature.com/scientificreports www.nature.com/scientificreports/ observed, as displayed in Fig. 2h. That is because the weak interaction is insufficient to hamper the increasing energy of the bonding band E at the M point. Figure 3b displays the band edges of BN-MS 2 heterostructures and monolayer MS 2 on an absolute energy scale with respect to the vacuum level. For monolayer MS 2 , their band edges of VBM and CBM states of monolayer MoS 2 and WS 2 are −5.97, −4.18 eV and, −5.56, −3.63 eV, respectively, which are consistent with previous reports 49 . The VBMs are enhanced with both the increasing compressive and tensile strains since compressive and tensile strain can enhance the bonding band B and bonding band D, respectively. The CBMs reduce monotonously with the increasing tensile strain, while they enlarge at first and then reduce with the increasing compressive strain due to the transfer of CBM due to the transformation of CBM, as above analysis. For strain BN-MS 2 heterostructures, similar characters are observed. Nevertheless, the band edges of BN-MS 2 heterostructures are lower than those of corresponding MS 2 due to the charge transfer between BN and MS 2 layer, as above analysis.

Band levels and applications.
It is well known that the band levels are related to the applications in photocatalytic and electronic fields. Figure 3c demonstrates the schematic of photocatalytic water splitting. A good photocatalytic material for water-splitting requires that the CBM and VBM are lower and higher than the reduction and oxidation potentials of water, respectively 49 . Thus, monolayer WS 2 is not a good photocatalytic material, as displayed in Fig. 3b. However, the CBM and VBM of BN-WS 2 heterostructures are higher and lower than reduction and oxidation potentials of water, respectively. Moreover, such characteristics remain when the compressive and tensile strains of BN-WS 2 heterostructures are lower than 2%. In other words, forming BN-WS 2 heterostructures can extend the application of monolayer WS 2 in the photocatalytic water splitting. For the monolayer MoS 2 , its band edges are outside of the reduction and oxidation potentials of water when compressive strain is lower than 4%. It means that monolayer MoS 2 may be suitable for the application of photocatalytic water splitting, but the compressive strain is limited to be 4%. Upon forming BN-MoS 2 heterostructure, similar characters can be observed when the compressive strain is up to 6%. It suggests that forming BN-MoS 2 heterostructures can extend the application of strain monolayer MoS 2 in photocatalytic water splitting. Figure 3d displays the schematic diagrams of metal/semiconductor contacts in FETs which is usually used to calculate ideal SBH values according to Schottky-Mott rule without Fermi level pinning. For metal/MS 2 contacts with strong Fermi level pinning effects, their large SBHs are difficult to be obtained by such methods, and they are difficult to be reduced and vanished by strained monolayer MS 2 . Different to metal/MS 2 contacts, metal/MoS 2 contacts with BN-MoS 2 heterostructures show negligible Fermi level pinning effect 16,18 . The SBHs at metal/MoS 2 contacts with strain BN-MS 2 heterostructures can be obtained directly from the difference between band levels heterostructures and work functions (WFs) of metal electrodes.  16,18 . When BN-MoS 2 heterostructures undergo tensile strain, these n-type SBHs continue reducing and even vanishing, as exhibited in Fig. 3f. For examples, the lowest n-type SBHs of Ti/MoS 2 , and Ag/MoS 2 contacts with tensile BN-MoS 2 heterostructures are low to −1.04 and −0.83 eV, respectively. In addition, the p-type SBH of Pt/MoS 2 contact with BN-MoS 2 heterostructure is about 0.19 eV which is far lower than that of pure Pt/MoS 2 contact 16,18 . Moreover, such p-type SBH can be further vanished when the compressive strain is larger than 2%, as shown in Fig. 3f. As to metal/WS 2 contacts with strain BN-WS 2 heterostructures, similar characteristics are also found, as displayed in Fig. 3f. Such results indicate that substituting strain monolayer MS 2 in flexible devices by strain BN-MS 2 heterostructures can realize high performance MS 2 devices with low contact properties. transport properties. Figure 4 gives the carrier effective masses and room-temperature mobilities of strained monolayer MS 2 and BN-MS 2 heterostructures. For monolayer MS 2 , the electron and hole mobilities at room-temperature of monolayer MoS 2 and WS 2 are 77.17, 155.79 cm 2 V −1 s −1 , and 163.22, 651.56 cm 2 V −1 s −1 , respectively, and the effective electron and hole masses of monolayer MoS 2 and WS 2 are 0.48, 0.64 m 0 , and 0.30, 0.38 m 0 , respectively, which are in good agreement with previous reports 48,53 . These effective electron masses reduce because either compressive or tensile strains are added to monolayer MS 2 . These effective hole masses enhance at first and then reduce with the increasing tensile strain since the position of VBM occurs a K-to-Γ transition; while they enlarge monotonically with the increasing compressive strain. Note that, when the compressive strain is larger than 8%, partial effective hole masses are reduced significantly, indicating an evidently anisotropic transport properties for monolayer MS 2 with large compressive strain. That is because a K-to-M transition occurs at the position of VBM when the compressive strain is larger than 8%. In general, the small effective mass indicates the large carrier mobility. As a result, the variations of electron and hole mobilities of strain monolayer MS 2 are opposite to these of corresponding effective masses, as exhibited in Fig. 4. In other words, both compressive and tensile strains can enlarge the electron mobilities of monolayer MS 2 . It should be noted that, nevertheless, the experimental electron mobilities of strain monolayer MS 2 in flexible nanodevices are lower than those of monolayer MS 2 due to the interfacial charged impurities induced by Si/SiO 2 substrates with large surface roughness 4,34 .
For optical properties. Except for the transport properties, the variations of effective masses can also modulate the exciton binding energies. The calculated exciton binding energies of monolayer MoS 2 and WS 2 are about 0.98 and 0.61 eV, respectively, which are close to previous studies [53][54][55][56][57][58] . Moreover, these exciton binding energies enlarge at first and then reduce as the strain changes from compressive to tensile. Upon forming the BN-MoS 2 and BN-WS 2 heterostructures, the exciton binding energies are enhanced 1.05 and 0.65 eV, respectively, because MS 2 layers accept charges from BN layers 55 , as shown in Fig. S3. Interestingly, the exciton binding energies of strain BN-MS 2 heterostructures exhibit oscillation variation, just like a "M", as demonstrated in Fig. 5a. In addition, the absorption coefficients of strain BN-MS 2 heterostructures are enlarged compared to those monolayer MS 2 , no matter what strains are added to monolayer and BN-MS 2 heterostructures, as the examples illustrated in Fig. 5b.

Conclusion
In summary, electronic and optical properties of strain monolayer MS 2 and BN-MS 2 heterostructures and their potential performance are comprehensively investigated by density functional theory. All strain BN-MS 2 heterostructures are type-I heterostructures, irrespective of compressive and tensile strain. However, different to the indirect band gap characters of compressive monolayer MS 2 , corresponding compressive BN-MS 2 heterostructures keep direct band gap characters because effects of charge transfer on anti-bonding d z2 orbitals are stronger than those of Poisson effect. Moreover, Mexican-hat-like bands without magnetic moments are observed for www.nature.com/scientificreports www.nature.com/scientificreports/ compressive BN-MS 2 heterostructures due to the non-uniform charge transfer induced by wrinkle. Consequently, electron mobilities of flexible devices with BN-MS 2 heterostructures are reduced at first and then enlarged with the increasing compressive strain, different to those of compressive monolayer MS 2 . In addition, although strain can induce similar variations of band edges between BN-MS 2 heterostructures and monolayer MS 2 , and extend their application in photocatalytic water splitting, strain just can reduce the Schottky barriers of devices with BN-MS 2 heterostructures. Moreover, the n-type and p-type Schottky barriers are reduced and even vanished with the increasing tensile and compressive strain, respectively. For tensile BN-MS 2 heterostructures, variations of their transport properties are similar to those of monolayer MS 2 , except for higher electron and hole mobilities and lower effective electron and hole masses. The room-temperature electron mobilities of MoS 2 and WS 2 layers in tensile BN-MS 2 heterostructures can be up to 1290 and 1926 cm 2 V −1 s −1 , respectively. In addition, the exciton binding energies of strain BN-MS 2 heterostructures exhibit oscillation variations, different to those of strain monolayer MS 2 .

Computational Methodology
All calculations were performed within first-principles density functional theory (DFT) using projector augmented-wave (PAW) pseudopotentials, as implemented in the Vienna Ab Initio Simulation Package (VASP) 59,60 . The Generalized Gradient Approximaton (GGA) parameterized by Perdew-Burke-Ernzerhof (PBE) 61 was employed to adopt for the exchange-correction functional. The van der Waals (vdW) interactions were considered using the method of Grimme (D2). The cut-off energy was set to be 450 eV. The convergence criterions were 1 × 10 −6 eV for the self-consistent field energy and 0.01 eV/Å for the residual forces on each atom, respectively. The Monkhorst-Pack k-point mesh was sampled with a separation of about 0.015 Å −1 in the Brillouin zone during the relaxation and electronic calculation periods. To minimize the interlayer interactions under the periodic boundary condition, vacuums of 15 Å were added perpendicular to the layer planes of heterostructure.
The carrier mobilities were calculated by the following expression 62 , where ħ is the Planck constant, k B is Boltzmann constant, T is the temperature (set to be 300 K). m* is the effective mass which is calculated by . E is the deformation potential constant which denotes the shift of the band edges induced by strain. C is the elastic modulus of a uniformly deformed crystal for simulating the lattice distortion activated by the strain, defined by C = [∂ 2 E/∂δ 2 ]/S 0 , where E is the total energy of the supercell, δ is the applied uniaxial strain, and S 0 is the area of the optimized supercell.
All the exciton binding energies of monolayer MS 2 and BN-MS 2 heterostructures were calculated by adopting the simplified hydrogen-like Wannier-Mott exciton modes 56,57 where E b is the excition binding energy, μ ex is the reduced exciton mass (μ ex = m e × m h /(m e + m h )), m e and m h are the effective electron and hole masses, respectively, R y is the atomic Rydberg energy, and ε r is the relative dielectric constant.