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MoS2-MX2 in-plane superlattices: Electronic properties and bandgap engineering via strain
Computational Materials Science 132 (2017) 30–35
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MoS2-MX2 in-plane superlattices: Electronic properties and bandgap engineering via strain Xiangying Su ⇑, Hongling Cui, Weiwei Ju, Yongliang Yong, Qingxiao Zhou, Xiaohong Li, Fengzhang Ren School of Physics & Engineering, Henan University of Science & Technology, 263, Kaiyuan Road, Luoyang 471023, China
a r t i c l e
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Article history: Received 21 October 2016 Received in revised form 13 February 2017 Accepted 15 February 2017
Keywords: Transition metal dichalcogenides in-plane superlattices Electronic properties Bandgap engineering Biaxial strain First principles calculation
a b s t r a c t Using density functional theory calculations, we performed a study of the electronic properties of transition metal dichalcogenides (TMDCs) in-plane superlattices MoS2-MX2 (MX2 = WS2, MoSe2, WSe2). Particular attention has been focused on the bandgap engineering by applying biaxial strain. All the three superlattices show semiconducting characteristics retaining the direct bandgap character of TMDCs monolayer. Moreover, the bandgap can be widely tuned by applying biaxial strain and a universal semiconductor-metal (S-M) transition occur at a critical strain. Especially, the direct bandgap can also be modulated in a range by moderate strain. The shift of metal atoms d orbitals toward the Fermi level is mainly responsible for the bandgap variation although a different physical mechanism was induced by tensile and compressive strain. As a result MoS2-WS2 heterostructure needs a bigger critical strain for SM transition due to the bigger bandgap. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction Layered transition metal dichalcogenides (TMDCs) materials have emerged as promising materials to complement graphene, not only because they possess similar layered structural characteristics but also monolayer TMDCs show a lot of mechanical, optical, chemical, thermal and electronic properties that are comparable to or better than those of graphene [1,2], for example, the monolayer MoS2 based transistor exhibits a high room-temperature current on/off ratios of 1 108 and mobility of 200 cm2 v1 s1, similar to the mobility of graphene nanoribbons [1]. Due to their distinct properties, TMDCs materials have potential applications in a wide range, such as in gas sensors [3], energy storage [4], optoelectronic devices [5] and field-effect transistors [6]. Furthermore, the properties of TMDCs materials can be modulated by many ways, e.g., strain engineering [7,8], external electrical field [9], alloying [10] or doping [11]. More recently, fabricating the van der Waals (vdW) heterostructures opens up a new avenue to tune the electronic properties [12–14]. The diverse characters of individual TMDCs monolayer offer promising candidates to further formation of various heterostructures for nanoscience and next generation nanophotonic and nanoelectronic devices [15,16]. Heterostructures assembled by vertical stacking of different TMDCs materials have been realized by the transfer of their as-grown or exfoliated ⇑ Corresponding author. E-mail address: [email protected] (X. Su). http://dx.doi.org/10.1016/j.commatsci.2017.02.020 0927-0256/Ó 2017 Elsevier B.V. All rights reserved.
flakes [17,18]. At the same time, many theoretical calculations have been performed and tunable electronic properties have been obtained [19–21]. In addition, superlattices builded by interfacing alternating monolayer MoS2 and other TMDCs monolayers have been studied and multiple quantum wells have been formed [22]. Though the electronic properties can be effectively tuned by stacking, there exists a defect, which is the direct bandgap characteristics lost. Among those vertical heterostructures reported only MoS2/WSe2 heterobilayers maintains the direct bandgap character and a very small biaxial strain (1%) can turn it into an indirect semiconductor [23]. MoS2/MX2 superlattices all show indirect bandgaps [22]. In the effort to retain the direct bandgap character of semi-conductive TMDCs monolayer, maybe the in-plane heterostructures could be constructed. Moreover, the in-plane heterostructures could also lead to interesting new properties and applications. Furthermore, some transition metal dichalcogenide monolayer alloys such as Mo1xWxS2 and Mo1xWxSe2 with different x values have been synthesized in experiment [24,25]. Based on these preparation technologies and the similarity of the structures, we think that the in-plane superlattice MoS2/MX2 should be experimentally realized, too. In the present work, we therefore provide a detailed description of the electronic properties of TMDCs in-plane superlattices by using first-principles calculations in the framework of density functional theory (DFT). Monolayer WS2, MoSe2 and WSe2 were chosen to form in-plane superlattices with the most studied MoS2 described as MoS2-MX2 (MX2 = WS2, MoSe2, WSe2).
X. Su et al. / Computational Materials Science 132 (2017) 30–35
In addition, due to strain has been regarded as one of the best strategies to modulate the bandgap of monolayer TMDCs. We think that the effect of strain on the electronic properties of in-plane superlattices will also be interesting. Here, the influence of biaxial strain including tensile and compressive strain on the bandgaps of MoS2-MX2 in-plane superlattices will be studied, too. 2. Model and calculation methods MoS2-MX2 in-plane superlattice supercell was composed of 2 MoS2 units and 2 MX2 units as shown in Fig. 1. In order to obtain the optimum values of the lattice constant, the total energy of heterostructures as functions of the lattice constant a is shown in Fig. 1(b). The optimum values of the lattice constants of the three systems are 6.37 Å, 6.50 Å and 6.50 Å, respectively, just the average of the optimized lattice constants of 2 2 supercells of the two components (6.36 Å, 6.38 Å, 6.64 Å, and 6.64 Å for MoS2, WS2, MoSe2, and WSe2, respectively). All of the calculations, including the geometry optimization and electronic properties calculations were performed with the Vienna ab initio simulation package (VASP) [26–27], based on density functional theory (DFT) and projector-augmented-wave (PAW) potentials [28]. The Perdew-Burke-Ernzerhof (PBE) [29] version of generalized gradient approximation (GGA) was used to describe the electron exchange-correlation interactions. The geometric structures are relaxed until the forces have converged to 0.01 eV/Å and the convergence criteria for energy is 106 eV. The plane wave cutoff was set at 400 eV. A k-point sampling of 7 7 1 was used for the geometry optimization and a 15 15 1 Monkhorst-Pack mesh was set for static electronic structure calculations. A sufficient vacuum of 20 Å was employed to avoid interaction between periodic images of slabs in the zdirection. On the base of the optimized structures, a hybrid functional in the Heyd-Scuseria-Ernaerhof (HSE06) method was adopted to give more accurate bandgaps [30]. In order to assess the spin-orbital coupling (SOC) effects on electronic structures, PBE + SOC was also performed 3. Results and discussion 3.1. Stability of the supperlattices The stability of the supperlattices can be judged by the formation energy that can be calculated by:
Ef ¼ ESL 2EMoS2 2EMX 2
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where ESL , EMoS2 and EMX 2 are energies of the supperlattices, freestanding MoS2 and MX2 per formula unit, respectively. The calculated results are listed in Table 1 and the negative values indicate that the three systems are all stable. Also, in order to further verify the structural stability, molecular dynamics (MD) simulations were performed at room temperature. The changes of bond lengths with the MD steps are shown in Fig. 2. Considering the symmetry structure, only the results of half bonds in the supperlattice are shown. During the entire MD simulation process of 2 ps with the time step of 1 fs, no bond breaking is observed for all the supperlattices, suggesting high stability of these supperlattices. 3.2. Electronic structures of MoS2-MX2 in-plane superlattices The PBE band structures in Fig. 3 (left) revealed that all MoS2MX2 in-plane superlattices show semiconducting characteristics with a direct bandgaps and the conduction band minimum (CBM) and the valence band maximum (VBM) are both located at K point, similar to the semi-conductive TMDCs monolayer. No significant differences among the band structures of the three systems were observed but different bandgaps (see Table 1). The bandgap value is different from the constituent monolayer (1.67 eV, 1.80 eV, 1.45 eV and 1.52 eV for monolayer MoS2, WS2, MoSe2 and WSe2, respectively), indicating significant potential for bandgap engineering by seamlessly stitching TMDCs monolayers. Previous works proved that SOC has important influences on electronic properties of TMDCs [31–33]. Here the band structures obtained by PBE + SOC are also shown in Fig. 3 (middle). We see that the bandgaps become smaller and SOC results in significant valence band splitting: 272 meV, 164 meV and 311 meV for MoS2-WS2, MoS2-MoSe2 and MoS2-WSe2 systems, respectively. However, compared to SOC unconsidered, the trend of the bandgap under strain is almost the same (see Fig. S1 (Supporting Information)). So, when study the effect of strain on the bandgap, SOC is insignificant. In addition, as we all know, the PBE functional generally underestimates the bandgap value. In order to improve the accuracy, the HSE06 functional was used and the relevant results are also expressed in Fig. 3 (right). It can be seen that all systems have the expected bigger bandgap. However, except for the bigger bandgap the band structures with the CBM and VBM are similar to those based on PBE computation. So, considering the high computational cost associated with HSE06 computation and in order to compare with previous results based on PBE calculation, the following calculations including the charge density and the band structure tuned by strain engineering were all based on PBE func-
Fig. 1. (a) Top and (b) side views of TMDCs in-plane superlattices. (c) The total energy as a function of a lattice constant.
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Table 1 Formation energies (E) and bandgaps (Eg) calculated using PBE, PBE + SOC and HSE06 fuctionals.
E (eV) PBE Eg (eV) PBE + SOC Eg (eV) HSE06 Eg (eV)
MoS2-WS2
MoS2-MoSe2
MoS2-WSe2
0.24 1.72 1.57 2.21
0.46 1.50 1.40 1.95
0.02 1.45 1.30 1.92
question, we calculated the charge density of the CBM and VBM states and summarized it in Fig. 4. It can be found that electrons and holes are both confined in MoS2 and MX2, indicating no type-Ⅱband alignment, a fundamentally different scenario than that for vertical TMDCs heterostructures and superlattices. Fig. 4 also suggests that CBM and VBM are mainly composed of both Mo and W atoms, consistent with the partial density of states (PDOS) results given in the below. 3.3. Application of biaxial strain
Fig. 2. The changes of bond lengths with the MD steps (1 fs/step) at room temperature.
tional, unless otherwise mentioned. Moreover, when focusing on the trend of the bandgap with respect to biaxial strain, the underestimation of the bandgap is less important and will not affect the main results. Previous reports have revealed that vertical TMDCs heterostructues and superlattices all show type-Ⅱ band alignment [21]. What is about the in-plane superlattices? In order to answer this
The biaxial strain on MoS2-MX2 in-plane superlattices was applied by changing the supercell parameters (a and b, equally), at the same time relaxing the structure along the c-axis, and the biaxial strain is defined as e = Da/a0, where a0 and Da + a0 are unstrained and strained supercell lattice constants, respectively. The effect of biaxial strain on the band structure was submitted in Fig. 5. It can be seen that with either tensile or compressive strain a first general variation is the reduction of the bandgap, and eventually the semiconductor-metal (S-M) transition occur, agreeing with previous studies on the variations of the bandgap as functions of strained TMDCs monolayer and vertical heterostructures (obtained by PBE) [21,34]. Another prominent phenomenon observed is the direct-indirect bandgap transition. The direct bandgap of the three systems studied here are all only maintained in a certain range, 6% to 0.4%, 4% to 0.5%, 2% to 0.5% for MoS2-WS2, MoS2-MoSe2 and MoS2-WSe2, respectively (where positive and negative strain represent tensile and compressive strain, respectively), much larger than the one of MoS2 monolayer, 1.3% to 0.3% [34], which is advantageous for the application of optoelectronic devices. Previous calculations [21] also proved that compressive strain could tune the two vertical heterostructures MoS2-MoSe2 and MoS2-WSe2 to have the direct bandgap, which is in the range of 3% to 1%, 3.5% to 0%, respectively, the nearly similar range of corresponding in-plane superlattices, but any strain could not tune vertical heterostructure MoS2-WS2 into direct bandgap. We also found that the variation of the bandgaps are similar for the three in-plane superlattices, but for
Fig. 3. Band structures of TMDCs in-plane superlattices obtained by use of PBE (left), PBE + SOC (middle), and HSE06 (right) fuctionals.
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Fig. 4. Charge densities of CBM (a) and VBM (b) states for TMDCs in-plane superlattices. The isosurface values are taken as1.5 103 e/Å3 for CBM and 7.5 105 e/Å3 for VBM, respectively.
Fig. 5. Bandgaps (Eg) with respect to tensile and compressive biaxial strains. The zones distinguished by different colors and denoted by ‘‘D”, ‘‘I”, and ‘‘M” indicate ‘‘direct”, ‘‘indirect”, and ‘‘metal” characters, respectively.
MoS2-MoSe2 and MoS2-WSe2, the critical strain for S-M transition is nearly the same while MoS2-WS2 need a little bigger critical strain both under tensile and compressive strain. Here, it should be pointed out that when the strain is very large (14% or 18%) the superlattice structures should be still stable and undestroyed, because of the high elasticity of MoS2 monolayer (could even be strained to 25%) [35] and the similarity of the structures of the superlattices and monolayer. To reveal the changes of the electronic properties of MoS2-MX2 in-plane superlattices with respect to the biaxial strain, the variations of the band structures and PDOS were studied in detail. The effect of the tensile strain was firstly studied and taking MoS2-WS2 system as an example, the band structures and PDOS under several selected strain were presented in Fig. 6. For equilibrium state, MoS2-MX2 lateral heterostructues bandgaps are mainly decided by metal atoms (Mo and W) 4d orbitals, similar to monolayer TMDCs semiconductor [36]. When tensile strain was applied, the prominent changes of the band structure occur at the energy states near K and C points: the conduction and valence band at K point drop gradually, and the top of the valence band at C point moves up a little, resulting in the bandgap decreasing. Analysis of the PDOS indicates that the CBM at K point and VBM at C point are especially described by dz2 orbitals of Mo and W. The applied tensile strain results in the change of the distance between the atoms,
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and then a different superposition of the atoms orbitals, causing dz2 orbitals to move toward the Fermi level. With a 10% biaxial tensile strain, the CBM at K point and VBM at C point cross the Fermi level and lead to a transition from semiconductor to metal. Due to the bandgap changes are dominated by metal atoms, so the bandgap changes of the three systems are very similar and MoS2-WS2 has a little bigger critical strain for S-M transition because of the bigger bandgap. We also found that for all the three in-plane superlattices a very small tensile strain (not larger than 0.5%) could lead the bandgaps to transfer from direct to indirect character. This is because that for unstrained MoS2-MX2 system the energy difference between the valence band at C and K points is so small that a slight shift of the two states under tensile strain is sufficient to let the VBM located at C from K, breaking the direct bandgap. Beside tensile strain, compressive strain is also responsible for the bandgap modification, although here a different trend of the bandgap shift is observed. For a relatively small strain (not bigger than 2%), compressive and tensile strains have opposite effects on the band structure: the bandgap is slightly increased under compressive strain, while it is decreased when tensile strain is applied. When the compressive strain increasing (over 4%), the bandgap change is very similar to the case of applied tensile strain: the band gap decreasing and the S-M transition occurring and a little bigger critical strain for MoS2-WS2 system. The variation of the band structure and PDOS were studied and the selected cases of MoS2-WS2 heterostructure were provided in Fig. 7. The prominent changes of the band structure also occur at the energy states near K and C points: the conduction and valence band at K point move down gradually, and the valence band at C point drop at first and then rise. Actually, when compressive strain is smaller than 2%, the CBM at K point shifts upward a little and results in the bandgap slightly increasing. Then with increasing compressive strain, the conduction band at K point drop faster than the valence band, making the bandgap decreasing. However, for bigger compressive strain (over 10%), the decreasing bandgap could attribute to the dropping conduction band at K and the rising valence band at C point. Analysis of the PDOS proves that the bottom of the conduction band at K is mainly composed of dxy dx2 y2 and dz2 orbitals of Mo and W atoms. With compressive strain increasing, the contribution of the in-plane xy atomic orbitals becomes more significant, due to the bigger changes of distances between the atoms. As the result under a 6% compressive strain, the CBM is no longer located at K point and the direct bandgap character is lost. With a 16% compressive strain applied to MoS2-WS2 heterostructure, the increasing overlapping of px and py orbitals as well as dxy dx2 y2 and dz2 orbitals is so great that the VBM at C and the bottom of conduction near K cross the Fermi level, the S-M transition thus also happens, but involves a slightly different physical mechanism compared to that of tensile strain.
4. Conclusions In summary, the structural and electronic properties of TMDCs in-plane superlattices have been investigated. The three systems studied here all show direct bandgaps. Particular attention of this work has been focused on the bandgap engineering by application of biaxial strain. The intriguing result is that the direct bandgap can retain in a moderate strain range, 6% to 0.4%, 4% to 0.5%, 2% to 0.5% for MoS2-WS2, MoS2-MoSe2 and MoS2-WSe2 heterostructures, respectively. Moreover, the influence of tensile and compressive strain on the bandgap is roughly the same: the bandgap value decreasing with the increasing strain and ultimately a universal S-M transition realizing. Because the metal atoms are primarily responsible for the bandgap change, MoS2-WS2 system needs a
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Fig. 6. Band structures and the projected densities of states (PDOS) of Mo, W and S atoms for MoS2-WS2 in-plane superlattice at (a) 0, (b) 4%, and (c) 10% tensile biaxial strain e.
Fig. 7. Band structures and the projected densities of states (PDOS) of Mo, W and S atoms for MoS2-WS2 in-plane superlattice at (a) 0, (b) 6%, (c) 12%, and (d) 10% compressive biaxial strain e.
bigger critical strain for S-M transition due to the bigger bandgap. However, the physical mechanism of S-M transition under tensile and compressive strain is slightly different: dz2 orbital moving toward the Fermi level under tensile strain is responsible for the bandgap closing, while the overlapping of the in-plane xy atomic
orbitals as well as dz2 orbitals is the main reason in the case of compressive strain. Our study offers new insights into designing new heterostructures to modify electronic properties of 2D TMDCs materials and opens up the possibility for their usage in a wider range of application.
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Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 11547153, 11404096), the Youth Foundation of Henan University of Science and Technology (No. 13350038), the Innovation Team of Henan University of Science and Technology (No. 2015XTD001) and the International Science and Technology Cooperation Projects of Henan Province (152102410035). Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.commatsci.2017. 02.020. References [1] B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti, A. Kis, Single-layer MoS2 transistors, Nat. Nanotechnol. 6 (2011) 147–150. [2] Y. Yoon, K. Ganapathi, S. Salahuddin, How good can monolayer MoS2 transistors be?, Nano Lett 11 (2011) 3768–3773. [3] D.J. Late, Y.-K. Huang, B. Liu, J. Acharya, S.N. Shirodkar, J. Luo, A. Yan, D. Charles, U.V. Waghmare, V.P. Dravid, C.N.R. Rao, Sensing behavior of atomically thinlayered MoS2 transistors, ACS Nano 7 (2013) 4879–4891. [4] Y. Zhao, Y. Zhang, Z. Zhang, Y. Yan, K. Sun, Synthesis of MoS2 and MoO2 for their applications in H2 generation and lithium ion batteries: a review, Sci. Technol. Adv. Mater. 14 (2013) 43501–43512. [5] K. Xu, Z. Wang, X. Du, M. Safdar, C. Jiang, J. He, Atomic-layer triangular WSe2 sheets: synthesis and layer-dependent photoluminescence property, Nanotechnology 24 (2013), 465705-465705. [6] M. Chhowalla, H.S. Shin, G. Eda, L.-J. Li, K.P. Loh, H. Zhang, The chemistry of two-dimensional layered transition metal dichalcogenide nanosheets, Nat. Chem. 5 (2013) 263–275. [7] S. Bhattacharyya, A.K. Singh, Semiconductor-metal transition in semiconducting bilayer sheets of transition-metal dichalcogenides, Phys. Rev. B 86 (2012) 075454. [8] H.J. Conley, B. Wang, J.I. Ziegler, R.F. Haglund Jr., S.T. Pantelides, K.I. Bolotin, Bandgap engineering of strained monolayer and bilayer MoS2, Nano Lett. 13 (2013) 3626–3630. [9] A. Ramasubramaniam, D. Naveh, E. Towe, Tunable band gaps in bilayer transition-metal dichalcogenides, Phys. Rev. B 84 (2011) 205325. [10] H.P. Komsa, A.V. Krasheninnikov, Two-dimensional transition metal dichalcogenides alloys: stability and electronic properties, J. Phys. Chem. Lett. 3 (2012) 3652–3656. [11] H.P. Komsa, J. Kotakoski, S. Kurasch, O. Lehtinen, U. Kaiser, A.V. Krasheninnikov, Two-dimensional transition metal dichalcogenides under electron irradiation: defect production and doping, Phys. Rev. Lett. 109 (2012) 035503. [12] A.K. Geim, I.V. Grigorieva, Van der Waals heterostructures, Nature 499 (2013) 419–425. [13] Q.S. Zeng, H. Wang, W. Fu, Y.J. Gong, W. Zhou, P.M. Ajayan, J. Lou, Z. Liu, Band engineering for novel two-dimensional atomic layers, Small 11 (2014) 1868– 1884. [14] B. Amin, N. Singh, U. Schwingenschlögl, Heterostructures of transition metal dichalcogenides, Phys. Rev. B 92 (2015) 075439. [15] Y.J. Zhang, T. Oka, R. Suzuki, J.T. Ye, Y. Iwasa, Electrically switchable chiral light-emitting transistor, Science 344 (2014) 725–728.
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
MoS2-MX2 in-plane superlattices: Electronic properties and bandgap engineering via strain Xiangying Su ⇑, Hongling Cui, Weiwei Ju, Yongliang Yong, Qingxiao Zhou, Xiaohong Li, Fengzhang Ren School of Physics & Engineering, Henan University of Science & Technology, 263, Kaiyuan Road, Luoyang 471023, China
a r t i c l e
i n f o
Article history: Received 21 October 2016 Received in revised form 13 February 2017 Accepted 15 February 2017
Keywords: Transition metal dichalcogenides in-plane superlattices Electronic properties Bandgap engineering Biaxial strain First principles calculation
a b s t r a c t Using density functional theory calculations, we performed a study of the electronic properties of transition metal dichalcogenides (TMDCs) in-plane superlattices MoS2-MX2 (MX2 = WS2, MoSe2, WSe2). Particular attention has been focused on the bandgap engineering by applying biaxial strain. All the three superlattices show semiconducting characteristics retaining the direct bandgap character of TMDCs monolayer. Moreover, the bandgap can be widely tuned by applying biaxial strain and a universal semiconductor-metal (S-M) transition occur at a critical strain. Especially, the direct bandgap can also be modulated in a range by moderate strain. The shift of metal atoms d orbitals toward the Fermi level is mainly responsible for the bandgap variation although a different physical mechanism was induced by tensile and compressive strain. As a result MoS2-WS2 heterostructure needs a bigger critical strain for SM transition due to the bigger bandgap. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction Layered transition metal dichalcogenides (TMDCs) materials have emerged as promising materials to complement graphene, not only because they possess similar layered structural characteristics but also monolayer TMDCs show a lot of mechanical, optical, chemical, thermal and electronic properties that are comparable to or better than those of graphene [1,2], for example, the monolayer MoS2 based transistor exhibits a high room-temperature current on/off ratios of 1 108 and mobility of 200 cm2 v1 s1, similar to the mobility of graphene nanoribbons [1]. Due to their distinct properties, TMDCs materials have potential applications in a wide range, such as in gas sensors [3], energy storage [4], optoelectronic devices [5] and field-effect transistors [6]. Furthermore, the properties of TMDCs materials can be modulated by many ways, e.g., strain engineering [7,8], external electrical field [9], alloying [10] or doping [11]. More recently, fabricating the van der Waals (vdW) heterostructures opens up a new avenue to tune the electronic properties [12–14]. The diverse characters of individual TMDCs monolayer offer promising candidates to further formation of various heterostructures for nanoscience and next generation nanophotonic and nanoelectronic devices [15,16]. Heterostructures assembled by vertical stacking of different TMDCs materials have been realized by the transfer of their as-grown or exfoliated ⇑ Corresponding author. E-mail address: [email protected] (X. Su). http://dx.doi.org/10.1016/j.commatsci.2017.02.020 0927-0256/Ó 2017 Elsevier B.V. All rights reserved.
flakes [17,18]. At the same time, many theoretical calculations have been performed and tunable electronic properties have been obtained [19–21]. In addition, superlattices builded by interfacing alternating monolayer MoS2 and other TMDCs monolayers have been studied and multiple quantum wells have been formed [22]. Though the electronic properties can be effectively tuned by stacking, there exists a defect, which is the direct bandgap characteristics lost. Among those vertical heterostructures reported only MoS2/WSe2 heterobilayers maintains the direct bandgap character and a very small biaxial strain (1%) can turn it into an indirect semiconductor [23]. MoS2/MX2 superlattices all show indirect bandgaps [22]. In the effort to retain the direct bandgap character of semi-conductive TMDCs monolayer, maybe the in-plane heterostructures could be constructed. Moreover, the in-plane heterostructures could also lead to interesting new properties and applications. Furthermore, some transition metal dichalcogenide monolayer alloys such as Mo1xWxS2 and Mo1xWxSe2 with different x values have been synthesized in experiment [24,25]. Based on these preparation technologies and the similarity of the structures, we think that the in-plane superlattice MoS2/MX2 should be experimentally realized, too. In the present work, we therefore provide a detailed description of the electronic properties of TMDCs in-plane superlattices by using first-principles calculations in the framework of density functional theory (DFT). Monolayer WS2, MoSe2 and WSe2 were chosen to form in-plane superlattices with the most studied MoS2 described as MoS2-MX2 (MX2 = WS2, MoSe2, WSe2).
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In addition, due to strain has been regarded as one of the best strategies to modulate the bandgap of monolayer TMDCs. We think that the effect of strain on the electronic properties of in-plane superlattices will also be interesting. Here, the influence of biaxial strain including tensile and compressive strain on the bandgaps of MoS2-MX2 in-plane superlattices will be studied, too. 2. Model and calculation methods MoS2-MX2 in-plane superlattice supercell was composed of 2 MoS2 units and 2 MX2 units as shown in Fig. 1. In order to obtain the optimum values of the lattice constant, the total energy of heterostructures as functions of the lattice constant a is shown in Fig. 1(b). The optimum values of the lattice constants of the three systems are 6.37 Å, 6.50 Å and 6.50 Å, respectively, just the average of the optimized lattice constants of 2 2 supercells of the two components (6.36 Å, 6.38 Å, 6.64 Å, and 6.64 Å for MoS2, WS2, MoSe2, and WSe2, respectively). All of the calculations, including the geometry optimization and electronic properties calculations were performed with the Vienna ab initio simulation package (VASP) [26–27], based on density functional theory (DFT) and projector-augmented-wave (PAW) potentials [28]. The Perdew-Burke-Ernzerhof (PBE) [29] version of generalized gradient approximation (GGA) was used to describe the electron exchange-correlation interactions. The geometric structures are relaxed until the forces have converged to 0.01 eV/Å and the convergence criteria for energy is 106 eV. The plane wave cutoff was set at 400 eV. A k-point sampling of 7 7 1 was used for the geometry optimization and a 15 15 1 Monkhorst-Pack mesh was set for static electronic structure calculations. A sufficient vacuum of 20 Å was employed to avoid interaction between periodic images of slabs in the zdirection. On the base of the optimized structures, a hybrid functional in the Heyd-Scuseria-Ernaerhof (HSE06) method was adopted to give more accurate bandgaps [30]. In order to assess the spin-orbital coupling (SOC) effects on electronic structures, PBE + SOC was also performed 3. Results and discussion 3.1. Stability of the supperlattices The stability of the supperlattices can be judged by the formation energy that can be calculated by:
Ef ¼ ESL 2EMoS2 2EMX 2
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where ESL , EMoS2 and EMX 2 are energies of the supperlattices, freestanding MoS2 and MX2 per formula unit, respectively. The calculated results are listed in Table 1 and the negative values indicate that the three systems are all stable. Also, in order to further verify the structural stability, molecular dynamics (MD) simulations were performed at room temperature. The changes of bond lengths with the MD steps are shown in Fig. 2. Considering the symmetry structure, only the results of half bonds in the supperlattice are shown. During the entire MD simulation process of 2 ps with the time step of 1 fs, no bond breaking is observed for all the supperlattices, suggesting high stability of these supperlattices. 3.2. Electronic structures of MoS2-MX2 in-plane superlattices The PBE band structures in Fig. 3 (left) revealed that all MoS2MX2 in-plane superlattices show semiconducting characteristics with a direct bandgaps and the conduction band minimum (CBM) and the valence band maximum (VBM) are both located at K point, similar to the semi-conductive TMDCs monolayer. No significant differences among the band structures of the three systems were observed but different bandgaps (see Table 1). The bandgap value is different from the constituent monolayer (1.67 eV, 1.80 eV, 1.45 eV and 1.52 eV for monolayer MoS2, WS2, MoSe2 and WSe2, respectively), indicating significant potential for bandgap engineering by seamlessly stitching TMDCs monolayers. Previous works proved that SOC has important influences on electronic properties of TMDCs [31–33]. Here the band structures obtained by PBE + SOC are also shown in Fig. 3 (middle). We see that the bandgaps become smaller and SOC results in significant valence band splitting: 272 meV, 164 meV and 311 meV for MoS2-WS2, MoS2-MoSe2 and MoS2-WSe2 systems, respectively. However, compared to SOC unconsidered, the trend of the bandgap under strain is almost the same (see Fig. S1 (Supporting Information)). So, when study the effect of strain on the bandgap, SOC is insignificant. In addition, as we all know, the PBE functional generally underestimates the bandgap value. In order to improve the accuracy, the HSE06 functional was used and the relevant results are also expressed in Fig. 3 (right). It can be seen that all systems have the expected bigger bandgap. However, except for the bigger bandgap the band structures with the CBM and VBM are similar to those based on PBE computation. So, considering the high computational cost associated with HSE06 computation and in order to compare with previous results based on PBE calculation, the following calculations including the charge density and the band structure tuned by strain engineering were all based on PBE func-
Fig. 1. (a) Top and (b) side views of TMDCs in-plane superlattices. (c) The total energy as a function of a lattice constant.
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Table 1 Formation energies (E) and bandgaps (Eg) calculated using PBE, PBE + SOC and HSE06 fuctionals.
E (eV) PBE Eg (eV) PBE + SOC Eg (eV) HSE06 Eg (eV)
MoS2-WS2
MoS2-MoSe2
MoS2-WSe2
0.24 1.72 1.57 2.21
0.46 1.50 1.40 1.95
0.02 1.45 1.30 1.92
question, we calculated the charge density of the CBM and VBM states and summarized it in Fig. 4. It can be found that electrons and holes are both confined in MoS2 and MX2, indicating no type-Ⅱband alignment, a fundamentally different scenario than that for vertical TMDCs heterostructures and superlattices. Fig. 4 also suggests that CBM and VBM are mainly composed of both Mo and W atoms, consistent with the partial density of states (PDOS) results given in the below. 3.3. Application of biaxial strain
Fig. 2. The changes of bond lengths with the MD steps (1 fs/step) at room temperature.
tional, unless otherwise mentioned. Moreover, when focusing on the trend of the bandgap with respect to biaxial strain, the underestimation of the bandgap is less important and will not affect the main results. Previous reports have revealed that vertical TMDCs heterostructues and superlattices all show type-Ⅱ band alignment [21]. What is about the in-plane superlattices? In order to answer this
The biaxial strain on MoS2-MX2 in-plane superlattices was applied by changing the supercell parameters (a and b, equally), at the same time relaxing the structure along the c-axis, and the biaxial strain is defined as e = Da/a0, where a0 and Da + a0 are unstrained and strained supercell lattice constants, respectively. The effect of biaxial strain on the band structure was submitted in Fig. 5. It can be seen that with either tensile or compressive strain a first general variation is the reduction of the bandgap, and eventually the semiconductor-metal (S-M) transition occur, agreeing with previous studies on the variations of the bandgap as functions of strained TMDCs monolayer and vertical heterostructures (obtained by PBE) [21,34]. Another prominent phenomenon observed is the direct-indirect bandgap transition. The direct bandgap of the three systems studied here are all only maintained in a certain range, 6% to 0.4%, 4% to 0.5%, 2% to 0.5% for MoS2-WS2, MoS2-MoSe2 and MoS2-WSe2, respectively (where positive and negative strain represent tensile and compressive strain, respectively), much larger than the one of MoS2 monolayer, 1.3% to 0.3% [34], which is advantageous for the application of optoelectronic devices. Previous calculations [21] also proved that compressive strain could tune the two vertical heterostructures MoS2-MoSe2 and MoS2-WSe2 to have the direct bandgap, which is in the range of 3% to 1%, 3.5% to 0%, respectively, the nearly similar range of corresponding in-plane superlattices, but any strain could not tune vertical heterostructure MoS2-WS2 into direct bandgap. We also found that the variation of the bandgaps are similar for the three in-plane superlattices, but for
Fig. 3. Band structures of TMDCs in-plane superlattices obtained by use of PBE (left), PBE + SOC (middle), and HSE06 (right) fuctionals.
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Fig. 4. Charge densities of CBM (a) and VBM (b) states for TMDCs in-plane superlattices. The isosurface values are taken as1.5 103 e/Å3 for CBM and 7.5 105 e/Å3 for VBM, respectively.
Fig. 5. Bandgaps (Eg) with respect to tensile and compressive biaxial strains. The zones distinguished by different colors and denoted by ‘‘D”, ‘‘I”, and ‘‘M” indicate ‘‘direct”, ‘‘indirect”, and ‘‘metal” characters, respectively.
MoS2-MoSe2 and MoS2-WSe2, the critical strain for S-M transition is nearly the same while MoS2-WS2 need a little bigger critical strain both under tensile and compressive strain. Here, it should be pointed out that when the strain is very large (14% or 18%) the superlattice structures should be still stable and undestroyed, because of the high elasticity of MoS2 monolayer (could even be strained to 25%) [35] and the similarity of the structures of the superlattices and monolayer. To reveal the changes of the electronic properties of MoS2-MX2 in-plane superlattices with respect to the biaxial strain, the variations of the band structures and PDOS were studied in detail. The effect of the tensile strain was firstly studied and taking MoS2-WS2 system as an example, the band structures and PDOS under several selected strain were presented in Fig. 6. For equilibrium state, MoS2-MX2 lateral heterostructues bandgaps are mainly decided by metal atoms (Mo and W) 4d orbitals, similar to monolayer TMDCs semiconductor [36]. When tensile strain was applied, the prominent changes of the band structure occur at the energy states near K and C points: the conduction and valence band at K point drop gradually, and the top of the valence band at C point moves up a little, resulting in the bandgap decreasing. Analysis of the PDOS indicates that the CBM at K point and VBM at C point are especially described by dz2 orbitals of Mo and W. The applied tensile strain results in the change of the distance between the atoms,
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and then a different superposition of the atoms orbitals, causing dz2 orbitals to move toward the Fermi level. With a 10% biaxial tensile strain, the CBM at K point and VBM at C point cross the Fermi level and lead to a transition from semiconductor to metal. Due to the bandgap changes are dominated by metal atoms, so the bandgap changes of the three systems are very similar and MoS2-WS2 has a little bigger critical strain for S-M transition because of the bigger bandgap. We also found that for all the three in-plane superlattices a very small tensile strain (not larger than 0.5%) could lead the bandgaps to transfer from direct to indirect character. This is because that for unstrained MoS2-MX2 system the energy difference between the valence band at C and K points is so small that a slight shift of the two states under tensile strain is sufficient to let the VBM located at C from K, breaking the direct bandgap. Beside tensile strain, compressive strain is also responsible for the bandgap modification, although here a different trend of the bandgap shift is observed. For a relatively small strain (not bigger than 2%), compressive and tensile strains have opposite effects on the band structure: the bandgap is slightly increased under compressive strain, while it is decreased when tensile strain is applied. When the compressive strain increasing (over 4%), the bandgap change is very similar to the case of applied tensile strain: the band gap decreasing and the S-M transition occurring and a little bigger critical strain for MoS2-WS2 system. The variation of the band structure and PDOS were studied and the selected cases of MoS2-WS2 heterostructure were provided in Fig. 7. The prominent changes of the band structure also occur at the energy states near K and C points: the conduction and valence band at K point move down gradually, and the valence band at C point drop at first and then rise. Actually, when compressive strain is smaller than 2%, the CBM at K point shifts upward a little and results in the bandgap slightly increasing. Then with increasing compressive strain, the conduction band at K point drop faster than the valence band, making the bandgap decreasing. However, for bigger compressive strain (over 10%), the decreasing bandgap could attribute to the dropping conduction band at K and the rising valence band at C point. Analysis of the PDOS proves that the bottom of the conduction band at K is mainly composed of dxy dx2 y2 and dz2 orbitals of Mo and W atoms. With compressive strain increasing, the contribution of the in-plane xy atomic orbitals becomes more significant, due to the bigger changes of distances between the atoms. As the result under a 6% compressive strain, the CBM is no longer located at K point and the direct bandgap character is lost. With a 16% compressive strain applied to MoS2-WS2 heterostructure, the increasing overlapping of px and py orbitals as well as dxy dx2 y2 and dz2 orbitals is so great that the VBM at C and the bottom of conduction near K cross the Fermi level, the S-M transition thus also happens, but involves a slightly different physical mechanism compared to that of tensile strain.
4. Conclusions In summary, the structural and electronic properties of TMDCs in-plane superlattices have been investigated. The three systems studied here all show direct bandgaps. Particular attention of this work has been focused on the bandgap engineering by application of biaxial strain. The intriguing result is that the direct bandgap can retain in a moderate strain range, 6% to 0.4%, 4% to 0.5%, 2% to 0.5% for MoS2-WS2, MoS2-MoSe2 and MoS2-WSe2 heterostructures, respectively. Moreover, the influence of tensile and compressive strain on the bandgap is roughly the same: the bandgap value decreasing with the increasing strain and ultimately a universal S-M transition realizing. Because the metal atoms are primarily responsible for the bandgap change, MoS2-WS2 system needs a
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Fig. 6. Band structures and the projected densities of states (PDOS) of Mo, W and S atoms for MoS2-WS2 in-plane superlattice at (a) 0, (b) 4%, and (c) 10% tensile biaxial strain e.
Fig. 7. Band structures and the projected densities of states (PDOS) of Mo, W and S atoms for MoS2-WS2 in-plane superlattice at (a) 0, (b) 6%, (c) 12%, and (d) 10% compressive biaxial strain e.
bigger critical strain for S-M transition due to the bigger bandgap. However, the physical mechanism of S-M transition under tensile and compressive strain is slightly different: dz2 orbital moving toward the Fermi level under tensile strain is responsible for the bandgap closing, while the overlapping of the in-plane xy atomic
orbitals as well as dz2 orbitals is the main reason in the case of compressive strain. Our study offers new insights into designing new heterostructures to modify electronic properties of 2D TMDCs materials and opens up the possibility for their usage in a wider range of application.
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Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 11547153, 11404096), the Youth Foundation of Henan University of Science and Technology (No. 13350038), the Innovation Team of Henan University of Science and Technology (No. 2015XTD001) and the International Science and Technology Cooperation Projects of Henan Province (152102410035). Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.commatsci.2017. 02.020. References [1] B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti, A. Kis, Single-layer MoS2 transistors, Nat. Nanotechnol. 6 (2011) 147–150. [2] Y. Yoon, K. Ganapathi, S. Salahuddin, How good can monolayer MoS2 transistors be?, Nano Lett 11 (2011) 3768–3773. [3] D.J. Late, Y.-K. Huang, B. Liu, J. Acharya, S.N. Shirodkar, J. Luo, A. Yan, D. Charles, U.V. Waghmare, V.P. Dravid, C.N.R. Rao, Sensing behavior of atomically thinlayered MoS2 transistors, ACS Nano 7 (2013) 4879–4891. [4] Y. Zhao, Y. Zhang, Z. Zhang, Y. Yan, K. Sun, Synthesis of MoS2 and MoO2 for their applications in H2 generation and lithium ion batteries: a review, Sci. Technol. Adv. Mater. 14 (2013) 43501–43512. [5] K. Xu, Z. Wang, X. Du, M. Safdar, C. Jiang, J. He, Atomic-layer triangular WSe2 sheets: synthesis and layer-dependent photoluminescence property, Nanotechnology 24 (2013), 465705-465705. [6] M. Chhowalla, H.S. Shin, G. Eda, L.-J. Li, K.P. Loh, H. Zhang, The chemistry of two-dimensional layered transition metal dichalcogenide nanosheets, Nat. Chem. 5 (2013) 263–275. [7] S. Bhattacharyya, A.K. Singh, Semiconductor-metal transition in semiconducting bilayer sheets of transition-metal dichalcogenides, Phys. Rev. B 86 (2012) 075454. [8] H.J. Conley, B. Wang, J.I. Ziegler, R.F. Haglund Jr., S.T. Pantelides, K.I. Bolotin, Bandgap engineering of strained monolayer and bilayer MoS2, Nano Lett. 13 (2013) 3626–3630. [9] A. Ramasubramaniam, D. Naveh, E. Towe, Tunable band gaps in bilayer transition-metal dichalcogenides, Phys. Rev. B 84 (2011) 205325. [10] H.P. Komsa, A.V. Krasheninnikov, Two-dimensional transition metal dichalcogenides alloys: stability and electronic properties, J. Phys. Chem. Lett. 3 (2012) 3652–3656. [11] H.P. Komsa, J. Kotakoski, S. Kurasch, O. Lehtinen, U. Kaiser, A.V. Krasheninnikov, Two-dimensional transition metal dichalcogenides under electron irradiation: defect production and doping, Phys. Rev. Lett. 109 (2012) 035503. [12] A.K. Geim, I.V. Grigorieva, Van der Waals heterostructures, Nature 499 (2013) 419–425. [13] Q.S. Zeng, H. Wang, W. Fu, Y.J. Gong, W. Zhou, P.M. Ajayan, J. Lou, Z. Liu, Band engineering for novel two-dimensional atomic layers, Small 11 (2014) 1868– 1884. [14] B. Amin, N. Singh, U. Schwingenschlögl, Heterostructures of transition metal dichalcogenides, Phys. Rev. B 92 (2015) 075439. [15] Y.J. Zhang, T. Oka, R. Suzuki, J.T. Ye, Y. Iwasa, Electrically switchable chiral light-emitting transistor, Science 344 (2014) 725–728.
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