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Effect of biaxial strain and external electric field on electronic properties of MoS2 monolayer: A first-principle study
Accepted Manuscript Effect of biaxial strain and external electric field on electronic properties of MoS2 monolayer: A first-principle study Chuong V. Nguyen, Nguyen N. Hieu PII: DOI: Reference:
S0301-0104(15)30202-0 http://dx.doi.org/10.1016/j.chemphys.2016.01.009 CHEMPH 9472
To appear in:
Chemical Physics
Received Date: Accepted Date:
21 December 2015 25 January 2016
Please cite this article as: C.V. Nguyen, N.N. Hieu, Effect of biaxial strain and external electric field on electronic properties of MoS2 monolayer: A first-principle study, Chemical Physics (2016), doi: http://dx.doi.org/10.1016/ j.chemphys.2016.01.009
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Effect of biaxial strain and external electric field on electronic properties of MoS2 monolayer: A first-principle study
Chuong V. Nguyen a,b,∗ , Nguyen N. Hieu a a Institute b School
of Research and Development, Duy Tan University, Da Nang, Vietnam
of Mechanical Engineering, Le Quy Don Technical University, Ha Noi, Vietnam
Abstract
In this work, making use of density functional theory (DFT) computations, we systematically investigate the effect of biaxial strain engineering and external electric field applied perpendicular to the layers on the band gaps and electronic properties of monolayer MoS2 . The direct-to-indirect band gaps and semiconductor-to-metal transition are observed in monolayer MoS2 when strain and electric field are applied in our calculation. We show that when the biaxial strain and external electric field are introduced, the electronic properties including band gaps of monolayer MoS2 can be reduced to zero. Our results provide many useful insights for the wide applications of monolayer MoS2 in electronics and optoelectronics. Key words: Molybdenum disulphide; Band structure; Dispersion-corrected density functional theory; Uniaxial strain; Electric field
∗ Corresponding author. Email address: [email protected] (Chuong V. Nguyen).
Preprint submitted to Elsevier
30 January 2016
1
Introduction Molybdenum disulphide (MoS2 ) is currently one of most promising candi-
dates for applications in nanoelectromechanical devices due to its novel mechanical and electronic properties [1–4]. MoS2 has a layered structure with weak interaction between layers. Physical properties of MoS2 have been both theoretically and experimentally studied in recent years [5–8]. Together with the large energy band gap, the high carrier mobility [9, 10] makes MoS2 well suited for applications in transitors [11], photo-detectors [12], lithium ion batteries [13] and memory devices [14]. It is well-known that bulk MoS2 is a semiconductor with indirect band gap of 1.23 eV [15] opening between the lowest energy of the conduction band located between the Γ and K points, and the highest energy of the valence band located at the Γ point. While bulk material has an indirect gap, monolayer MoS2 is a direct gap semiconductor with 1.80 eV [15] opening at the K point in reciprocal lattice space. Monolayer MoS2 has been successfully fabricated through chemical vapor deposition [16] and mechanical exfoliation [17–19]. The electronic properties of MoS2 are very sensitive to structural perfection [20] and they can be controlled and tuned by chemical treatment, nanopatterning, functionalization through adatom adsorption, applied external electric field or strain engineering [21–24]. In recent years, many works have been focused on the strain engineering of MoS2 from both the experimental [15, 25] and theoretical [26–28] studies to explore the effect of strain on the physical properties of MoS2 [1, 2]. Besides, the carrier mobility of MoS2 nanoribbons has also been studied by first principles calculations [29]. In this work, by using density functional theory (DFT) computations, we systematically investigate the effect of biaxial strain engineering and external electric field applied perpendicular to the layers on the band gaps and electronic properties of monolayer MoS2 . The direct-to-indirect band gaps and semiconductor-to-metal
2
transition are observed in monolayer MoS2 when strain and electric field are applied in our calculation. We show that the electronic properties including band gaps of monolayer MoS2 can be reduced to zero when subjected to a biaxial strain and external electric field. Our results provide many useful insights for the wide applications of monolayer MoS2 in electronics and optoelectronics.
2
Computational Method and Model Our calculations are performed within density functional theory using ac-
curate frozen-core full-potential projector augmented-wave (PAW) pseudopotentials [30,31]. All calculations are performed using the Quantum Espresso code [32]. We use the generalized gradient approximation (GGA) with the parametrization of Perdew-Burke-Ernzerhof (PBE). This combination is important for investigating the interaction between MoS2 layers. This approach has been successful in describing graphene-based structures [33]. The electronic wavefunctions are described by plane-wave basis sets with a kinetic energy cutoff of 30 Ry, and the energy cutoff for the charge density was set to 300 Ry. The Brillouin zone integration is carried out using an 18 × 18 × 1 k-mesh according to the Monkhorst-Pack scheme. For the different layers of the MoS2 , the supercells are constructed with a vacuum space ˚ along the z-direction. The strain is simulated by setting the lattice parameof 20 A ter to a fixed larger value and relaxing the atomic positions. The magnitude of the strain is defined as: ε = (a − a0 )/a0 , where a0 and a are the lattice parameters of the unstrained and strained systems, respectively. The interaction of electrons with the external electrostatic field along the yaxis is determined by the following expression:
Uext (r) = |e| × E × r, 3
(1)
Fig. 1. Relaxed atomic structure of monolayer MoS2 under an applied external electric field along z direction (a) and biaxial strain engineering along xy direction (b). Green and violet balls stand for Mo and S atoms, respectively.
where U is used to distinguish the potential energy in the electrostatic field from all other potential terms of the Kohn-Sham equation VKS (r) =
R
dr0
n(r0 ) |r−r0 |
+ Vion (r) +
Vxc (r). In order to consider Eext , the Kohn-Sham equations can be interpreted as:
−
h ¯2 2 ∇ + VKS + Uext Ψi (r) = εi Ψi (r). 2m
(2)
The applied electrostatic potential changes linearly along the entire unit cell; therefore, to observe periodic boundary conditions, the original value should be recovered at the cell boundary. Thus, a sawtooth potential shape with period equal to the unit cell period along the z-axis is most suitable [Fig. 1(a)]. The scheme of relative placement of the slab and external electrostatic potential is shown in Fig. 1(a). When the entire volume of MoS2 is in the electric field Eext and the simulated cell size along the z-axis is L, then the gauge field E ∗ is defined as: E ∗ = −Eext (z/L). The minus sign indicates that the E ∗ direction is always opposite to the Eext direction. 4
3 3.1
Results and discussion Effect of biaxial strain engineering To study the effect of biaxial strain and electric field on the band gap and elec-
tronic properties of graphene-like MoS2 monolayer, we first use the DFT method to optimize the geometry of monolayer MoS2 . Our calculations show that the op˚ and the bond distance timized value of the lattice constant a0 is equal to 3.18 A, ˚ This result is in good agreement with between Mo and S atoms dM o−S = 2.42 A. the previous theoretical [34–38] and experimental [39] studies. By using the DFT calculations, the direct gap of MoS2 monolayer is found to be 1.70 eV. This value is very close to the recent DFT based approach (1.72 eV) by Matte et al. [40]. Although our calculation for the direct gap of MoS2 monolayer is in good agreement with Matte’s calculations [40] and with those of other groups [26,41–43], this value is still smaller than the band gap which is measured using complementary techniques of optical absorption, photoluminescence and photoconductivity (1.80 eV) of monolayer thick MoS2 [15]. The band gap problem can be addressed more accurately by using a GW approximation [34, 44]. In the present work, we do not focus on this problem. This trend is not generalized, and more often depends on the material considered. For example, based on the many-body GW method the authors of Refs. [34, 44] showed a higher band gap of 2.78 eV. Therefore, we believe the dispersion-corrected density functional theory is a suitable method for calculation of the MoS2 structure and a new idea of the trends can be obtained from our study. The strained cell is modeled by stretching the hexagonal ring in the xy plane. A scheme of MoS2 monolayer with hexagonal symmetry under biaxial strain is shown in Fig. 1. The strain engineering is applied in a biaxial expansion along the xy-direction. The component of biaxial strain is noted as εb . The strains are
5
Fig. 2. Total energy (a) and band gaps (b) of monolayer MoS2 as function of biaxial strain engineering. Band structure of monolayer MoS2 under strain engineering of 0 % (c), 10 % (d) and 18 % (e)
evaluated as the lattice stretching percentage. A wide range of strain (up to 20%) along both directions has been employed in this study. Fig. 2(a) shows the total energy of monolayer MoS2 as function of biaxial strain εb . We can see that monolayer MoS2 becomes unstable under biaxial strain. Our calculations demonstrated that, as shown in Fig. 2, biaxial strain has a significant impact on the band gap and electronic properties of monolayer MoS2 . At the equilibrium state, MoS2 monolayer is a semiconductor with a direct gap of 1.70 eV at the K-point, which is in good agreement with previous calculations [26, 40–43]. From Fig. 2 we can see that the electronic properties of MoS2 are particularly sen6
sitive to mechanical strain. Under biaxial strain, monolayer MoS2 becomes an indirect gap semiconductor. While the lowest energy of the conduction band is still located at the K point, the highest energy of the valence band is located at the Γ point in reciprocal space. We can easily see the direct-to-indirect gap transition in Figs. 2(c,d,e). A shift of a energy levels leads to a change in the nature of the energy band gap for the monolayer MoS2 , from direct to indirect, even for an applied biaxial strain of less than 1 %. It means that, at a biaxial strain of εb = 1%, monolayer MoS2 is an indirect semiconductor. Fig. 2(b) shows the dependence of the band gap of MoS2 on the biaxial strain εb . When εb increases, the band gap of MoS2 decreases, which can be described as a part of parabola. Interestingly, the MoS2 band gap is equal to zero at εb = 18%. It means that the metal-semiconductor transition in MoS2 occurs at an elongation of 18 %. In this case, the lowest subband of the conduction band and the highest subband of the valence band cross the Fermi level at the K point and Γ point, respectively [see Fig. 2(e)] The projected density of state of Mo-d, S-p and S-s orbitals in bilayer MoS2 under strain and external electric field is shown in Fig. 3. As shown in Fig. 3(a), at the equilibrium state the bottom of the conduction band is mainly contributed to by Mo-d orbitals and the top of the valence band is contributed to by Mo-d and S-p orbitals. Mo-d and S-p orbitals are hybridized with each other at the top of the valence band. It means that the bonding between Mo and S atoms is strong. However, the mirror symmetrical bonding configuration in the trilayer S-Mo-S system results in a weak π bond-like interaction. This weak interaction is very sensitive to strain, resulting in the changed band structure under strain. Fig. 3(a) also shows clearly that the semiconductor-metal transition in monolayer MoS2 occurs at εb = 18%.
7
Fig. 3. Projected density of state of Mo-d, S-p and S-s orbitals in bilayer MoS2 under applied strain (a) and applied electric field (b).
3.2
Effect of external electric field We applied an external electric field perpendicular to the plane of the MoS2
monolayers, as shown in Fig. 1(a). In the present work, the applied electric field ˚ The dependence of the total energy on strength is in the range from 0 to 1.2 V/A. the electric field is shown in Fig. 4(a). We can see that the total energy decreases as a function of the electric field and the dependence of the total energy on the electric field can be described as a part of a parabola. The effect of the electric field on the electronic band structure of MoS2 monolayers is shown in Figs. 4(c,d,e). Our calculations show that MoS2 monolayers can become semiconductor with an indirect band gap under external electric field. However, in the limit of small elec˚ the band gap remains almost constant as shown in tric field (from 0 to 0.6 V/A), 8
Fig. 4. Total energy (a) and band gaps (b) of monolayer MoS2 as function of external electric field. Band structure of monolayer MoS2 upon the application of external electric ˚ (c), 8 V/A ˚ (d) and 10 V/A ˚ (e) field of 0 V/A
˚ to 1.0 V/A, ˚ the Fig. 4(b). Additionally, in small range of electric field from 0.6 V/A band gap decreases abruptly to zero and MoS2 monolayers becomes metallic when ˚ In this case, in the band structure of MoS2 monolayer, the valence Eb ≥ 1.0 V/A. and conduction bands cross at the Γ point as shown in Fig. 4(e). The decrease of the band gap is as a function of the electric field because of the increase of polarization leading to the change of the dipole moment. The band gap modulation studied here should be attributed to the well-known Stark effect, resulting in a shift of the bands and in a change of the band structure in the presence of an external electric field, especially in the conduction region. 9
Fig. 5. Isosurface plot of the charge density (n) of monolayer MoS2 (top view) correspond˚ (c), ing to the VBM at the equilibrium state (a), at εb = 10 % (b) and at Ev = 1.0 V/A respectively; and corresponding to the CBM at the equilibrium state (d), at εb = 10 % (e) ˚ (f), respectively. The isosurface value was taken as 0.005 eV/A ˚ . and at Ev = 0.8 V/A Green and violet balls stand for Mo and S atoms, respectively.
This effect has been observed in our previous studies on graphene nanoribbon heterostructures. The changes in the energies of the valence band maximum (VBM) and conduction band maximum (CBM) with the electric field are shown in Fig. ˚ , monolayer MoS2 is a 3b. It shows that under an electric field of less than 0.6 V/A semiconductor with direct band gap of 1.70 eV. The VBM and CBM in this case are ˚ up to 1.0 V/A ˚ monoat the K point. With the critical electric field from 0.6 V/A layer MoS2 is a semiconductor with indirect band gaps. The VBM is located at the K point, while the CBM is moved to the Γ point. In addition, with critical electric ˚ the band gap of MoS2 monolayer is 1.47 eV and decreases down to field of 0.7 V/A, ˚ , and semiconductor-metal transition 0.156 eV with the electric field up to 0.9 V/A 10
is observed at large electric field (Ev ≥ 1). Fig. 3b shows the partial density of states (PDOS) of Mo-d, S-p and S-s or˚ and 1.0 V/A, ˚ respecbitals at the equilibrium state with applied field of 0.8 V/A tively. As noted above, at the equilibrium state the bottom of the conduction band is mainly contributed to by Mo-d orbitals, while the top of the valence band is contributed to by Mo-d orbitals and S-p orbitals. Mo-d and S-p orbitals are hybridized with each other at the top of the valence band, indicating strong bonding between Mo and S atoms. Field-induced repulsion among the electronic levels leads to an upshift of the VBM and a downshift of the CBM at the Γ point, resulting in a decrease of the band gap. To validate our above analysis, we also show the isosurface of the charge densities corresponding to VBM and CBM of monolayer MoS2 at the equilibrium state, under biaxial strain and with the applied electric field, as seen in Fig. 5. It shows that, the VBM and CBM at Γ- and K-points are mainly d2z and pz orbitals for Mo and S atoms, respectively. Compared to the unstrained state, under biaxial strain, the isosurface of VBM and CBM changes more significantly than that with electric field.
4
Conclusion In this paper, we studied the electronic properties of monolayer MoS2 under
biaxial strain engineering and external electric field by using first-principles calculations based on density functional theory. We have seen that mechanical strain and electric field reduce the band gap of semiconducting monolayer MoS2 , causing an direct-to-indirect band gap and a semiconductor-to-metal transition. Our calcuations demonstrated that the semiconductor–metal transition occurs in monolayer MoS2 under a biaxial strain of εb = 18% and an external electric field of Eb = 1 11
˚ The appearance of a phase transition in monolayer MoS2 opens many ways V/A. for applications in nanoelectronmechanical devices based on monolayer MoS2 . References [1] M. Chhowalla, H. S. Shin, G. Eda, L.-J. Li, K. P. Loh, and H. Zhang. The chemistry of two-dimensional layered transition metal dichalcogenide nanosheets.
Nature
Chemistry, 5(4):263–275, April 2013. [2] A. M. van der Zande, P. Y. Huang, D. A. Chenet, T. C. Berkelbach, Y. You, GH. Lee, T. F. Heinz, D. R. Reichman, D. A. Muller, and J. C. Hone. Grains and grain boundaries in highly crystalline monolayer molybdenum disulphide. Nat Mater, 12(6):554–561, June 2013. [3] Yafei Li, Dihua Wu, Zhen Zhou, Carlos R. Cabrera, and Zhongfang Chen. Enhanced li adsorption and diffusion on mos2 zigzag nanoribbons by edge effects: A computational study. J. Phys. Chem. Lett., 3(16):2221–2227, August 2012. [4] Yu Jing, Edwin O. Ortiz-Quiles, Carlos R. Cabrera, Zhongfang Chen, and Zhen Zhou. Layer-by-layer hybrids of mos2 and reduced graphene oxide for lithium ion batteries. Electrochimica Acta, 147:392–400, November 2014. [5] E. Cappelluti, R. Roldan, J. A. Silva-Guillen, P. Ordejon, and F. Guinea. Tight-binding model and direct-gap/indirect-gap transition in single-layer and multilayer mos2 . Phys. Rev. B, 88(7):075409, August 2013. [6] K. Kaasbjerg, K. S. Thygesen, and K. W. Jacobsen. Phonon-limited mobility in n-type single-layer mos2 from first principles. Phys. Rev. B, 85(11):115317–, March 2012. [7] Qing Tang and Zhen Zhou. Graphene-analogous low-dimensional materials. Progress in Materials Science, 58(8):1244–1315, 2013. [8] Qing Tang, Zhen Zhou, and Zhongfang Chen. Innovation and discovery of graphenelike materials via density-functional theory computations. Wiley Interdisciplinary
12
Reviews: Computational Molecular Science, 5(5):360–379, 2015. [9] Britton W. H. Baugher, Hugh O. H. Churchill, Yafang Yang, and Pablo Jarillo-Herrero. Intrinsic electronic transport properties of high-quality monolayer and bilayer mos2. Nano Lett., 13(9):4212–4216, September 2013. [10] Branimir Radisavljevic and Andras Kis. Mobility engineering and a metal-insulator transition in monolayer mos2. Nat Mater, 12(9):815–820, September 2013. [11] Gwan-Hyoung Lee, Young-Jun Yu, Xu Cui, Nicholas Petrone, Chul-Ho Lee, Min Sup Choi, Dae-Yeong Lee, Changgu Lee, Won Jong Yoo, Kenji Watanabe, Takashi Taniguchi, Colin Nuckolls, Philip Kim, and James Hone. Flexible and transparent mos2 field-effect transistors on hexagonal boron nitride-graphene heterostructures. ACS Nano, 7(9):7931–7936, September 2013. [12] L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko, Y.-J. Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko, A. K. Geim, C. Casiraghi, A. H. Castro Neto, and K. S. Novoselov. Strong light-matter interactions in heterostructures of atomically thin films. Science, 340(6138):1311–1314, June 2013. [13] Yu Jing, Zhen Zhou, Carlos R. Cabrera, and Zhongfang Chen. Graphene, inorganic graphene analogs and their composites for lithium ion batteries. J. Mater. Chem. A, 2:12104–12122, 2014. [14] Min Sup Choi, Gwan-Hyoung Lee, Young-Jun Yu, Dae-Yeong Lee, Seung Hwan Lee, Philip Kim, James Hone, and Won Jong Yoo.
Controlled charge trapping by
molybdenum disulphide and graphene in ultrathin heterostructured memory devices. Nat Commun, 4:1624, March 2013. [15] Kin Fai Mak, Changgu Lee, James Hone, Jie Shan, and Tony F. Heinz. Atomically thin mos2 : A new direct-gap semiconductor. Phys. Rev. Lett., 105:136805, Sep 2010.
13
[16] Daeho Kim, Dezheng Sun, Wenhao Lu, Zhihai Cheng, Yeming Zhu, Duy Le, Talat S. Rahman, and Ludwig Bartels. Toward the growth of an aligned single-layer mos2 film. Langmuir, 27(18):11650–11653, 2011. PMID: 21812475. [17] Rudren Ganatra and Qing Zhang.
Few-layer mos2: A promising layered
semiconductor. ACS Nano, 8(5):4074–4099, 2014. PMID: 24660756. [18] K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim. Two-dimensional atomic crystals. Proceedings of the National Academy of Sciences of the United States of America, 102(30):10451–10453, 2005. [19] Jonathan N. Coleman, Mustafa Lotya, Arlene ONeill, Shane D. Bergin, Paul J. King, Umar Khan, Karen Young, Alexandre Gaucher, Sukanta De, Ronan J. Smith, Igor V. Shvets, Sunil K. Arora, George Stanton, Hye-Young Kim, Kangho Lee, Gyu Tae Kim, Georg S. Duesberg, Toby Hallam, John J. Boland, Jing Jing Wang, John F. Donegan, Jaime C. Grunlan, Gregory Moriarty, Aleksey Shmeliov, Rebecca J. Nicholls, James M. Perkins, Eleanor M. Grieveson, Koenraad Theuwissen, David W. McComb, Peter D. Nellist, and Valeria Nicolosi.
Two-dimensional nanosheets
produced by liquid exfoliation of layered materials. Science, 331(6017):568–571, 2011. [20] Jinhua Hong, Zhixin Hu, Matt Probert, Kun Li, Danhui Lv, Xinan Yang, Lin Gu, Nannan Mao, Qingliang Feng, Liming Xie, Jin Zhang, Dianzhong Wu, Zhiyong Zhang, Chuanhong Jin, Wei Ji, Xixiang Zhang, Jun Yuan, and Ze Zhang. Exploring atomic defects in molybdenum disulphide monolayers.
Nat Commun, 6:6293,
February 2015. [21] Wei-Bin Xu, Bao-Jun Huang, Ping Li, Feng Li, Chang-Wen Zhang, and Pei-Ji Wang. The electronic structure and optical properties of mn and b, c, n co-doped mos2 monolayers. Nanoscale Research Letters, 9(1):554, 2014. [22] Qu Yue, Zhengzheng Shao, Shengli Chang, and Jingbo Li.
14
Adsorption of gas
molecules on monolayer mos2 and effect of applied electric field. Nanoscale Research Letters, 8(1):425, 2013. [23] Xiaodan Li, Shunqing Wu, Sen Zhou, and Zizhong Zhu. Structural and electronic properties of germanene/mos2 monolayer and silicene/mos2 monolayer superlattices. Nanoscale Research Letters, 9(1):110, 2014. [24] Shang-Chun Lu and Jean-Pierre Leburton.
Electronic structures of defects and
magnetic impurities in mos2 monolayers. Nanoscale Research Letters, 9(1):676, 2014. [25] SW Han, Hyuksang Kwon, Seong Keun Kim, Sunmin Ryu, Won Seok Yun, DH Kim, JH Hwang, J-S Kang, J Baik, HJ Shin, et al. Band-gap transition induced by interlayer van der waals interaction in mos 2. Physical Review B, 84(4):045409, 2011. [26] S Lebegue and O Eriksson. Electronic structure of two-dimensional crystals from ab initio theory. Physical Review B, 79(11):115409, 2009. [27] Tianshu Li and Giulia Galli. Electronic properties of mos2 nanoparticles. The Journal of Physical Chemistry C, 111(44):16192–16196, 2007. [28] C. Ataca, M. Topsakal, E. Aktrk, and S. Ciraci. A comparative study of lattice dynamics of three- and two-dimensional mos2. The Journal of Physical Chemistry C, 115(33):16354–16361, 2011. [29] Yafei Li, Zhen Zhou, Shengbai Zhang, and Zhongfang Chen. Mos2 nanoribbons: High stability and unusual electronic and magnetic properties. J. Am. Chem. Soc., 130(49):16739–16744, December 2008. [30] Peter E Bl¨ochl. Projector augmented-wave method. Physical Review B, 50(24):17953, 1994. [31] G. Kresse and D Joubert. From ultrasoft pseudopotentials to the projector augmentedwave method. Physical Review B, 59(3):1758, 1999.
15
[32] Paolo Giannozzi, Stefano Baroni, Nicola Bonini, Matteo Calandra, Roberto Car, Carlo Cavazzoni, Davide Ceresoli, Guido L Chiarotti, Matteo Cococcioni, Ismaila Dabo, Andrea Dal Corso, Stefano de Gironcoli, Stefano Fabris, Guido Fratesi, Ralph Gebauer, Uwe Gerstmann, Christos Gougoussis, Anton Kokalj, Michele Lazzeri, Layla Martin-Samos, Nicola Marzari, Francesco Mauri, Riccardo Mazzarello, Stefano Paolini, Alfredo Pasquarello, Lorenzo Paulatto, Carlo Sbraccia, Sandro Scandolo, Gabriele Sclauzero, Ari P Seitsonen, Alexander Smogunov, Paolo Umari, and Renata M Wentzcovitch. Quantum espresso: a modular and open-source software project for quantum simulations of materials. Journal of Physics: Condensed Matter, 21(39):395502–, 2009. [33] Chuong V Nguyen, Victor V IIyasov, and Hieu N Nguyen. Tuning the electronic properties of armchair graphene nanoribbons by strain engineering. Physica Scripta, 90(1):015802–, 2015. [34] C. Ataca, H. ahin, E. Aktrk, and S. Ciraci. Mechanical and electronic properties of mos2 nanoribbons and their defects.
The Journal of Physical Chemistry C,
115(10):3934–3941, 2011. [35] Ashok Kumar and PK Ahluwalia. A first principle comparative study of electronic and optical properties of 1h–mos 2 and 2h–mos 2. Materials Chemistry and Physics, 135(2):755–761, 2012. [36] Yi Ding, Yanli Wang, Jun Ni, Lin Shi, Siqi Shi, and Weihua Tang. First principles study of structural, vibrational and electronic properties of graphene-like mx 2 (m= mo, nb, w, ta; x= s, se, te) monolayers. Physica B: Condensed Matter, 406(11):2254– 2260, 2011. [37] Priya Johari and Vivek B Shenoy. Tuning the electronic properties of semiconducting transition metal dichalcogenides by applying mechanical strains. 6(6):5449–5456, 2012.
16
ACS nano,
[38] Ya ping Miao, Fei Ma, Yu hong Huang, and Ke wei Xu. Strain effects on electronic states and lattice vibration of monolayer mos2. Physica E: Low-dimensional Systems and Nanostructures, 71:1 – 6, 2015. [39] JA Wilson and AD Yoffe.
The transition metal dichalcogenides discussion and
interpretation of the observed optical, electrical and structural properties. Advances in Physics, 18(73):193–335, 1969. [40] H.S.S. RamakrishnaMatte, A. Gomathi, ArunK. Manna, DattatrayJ. Late, Ranjan Datta, SwapanK. Pati, and C.N.R. Rao.
Mos2 and ws2 analogues of graphene.
Angewandte Chemie International Edition, 49(24):4059–4062, 2010. [41] A. Kuc, N. Zibouche, and T. Heine.
Influence of quantum confinement on the
electronic structure of the transition metal sulfide ts2 . Phys. Rev. B, 83:245213, Jun 2011. [42] Ali Hussain Reshak and S. Auluck. Calculated optical properties of 2h − mos2 intercalated with lithium. Phys. Rev. B, 68:125101, Sep 2003. [43] Ali Hussain Reshak and Sushil Auluck.
Band structure and optical response of
2h-MoX2 compounds (x = S, se, and te). Phys. Rev. B, 71:155114, Apr 2005. [44] C. Ataca and S. Ciraci. Functionalization of single-layer mos2 honeycomb structures. J. Phys. Chem. C, 115(27):13303–13311, July 2011.
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S0301-0104(15)30202-0 http://dx.doi.org/10.1016/j.chemphys.2016.01.009 CHEMPH 9472
To appear in:
Chemical Physics
Received Date: Accepted Date:
21 December 2015 25 January 2016
Please cite this article as: C.V. Nguyen, N.N. Hieu, Effect of biaxial strain and external electric field on electronic properties of MoS2 monolayer: A first-principle study, Chemical Physics (2016), doi: http://dx.doi.org/10.1016/ j.chemphys.2016.01.009
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Effect of biaxial strain and external electric field on electronic properties of MoS2 monolayer: A first-principle study
Chuong V. Nguyen a,b,∗ , Nguyen N. Hieu a a Institute b School
of Research and Development, Duy Tan University, Da Nang, Vietnam
of Mechanical Engineering, Le Quy Don Technical University, Ha Noi, Vietnam
Abstract
In this work, making use of density functional theory (DFT) computations, we systematically investigate the effect of biaxial strain engineering and external electric field applied perpendicular to the layers on the band gaps and electronic properties of monolayer MoS2 . The direct-to-indirect band gaps and semiconductor-to-metal transition are observed in monolayer MoS2 when strain and electric field are applied in our calculation. We show that when the biaxial strain and external electric field are introduced, the electronic properties including band gaps of monolayer MoS2 can be reduced to zero. Our results provide many useful insights for the wide applications of monolayer MoS2 in electronics and optoelectronics. Key words: Molybdenum disulphide; Band structure; Dispersion-corrected density functional theory; Uniaxial strain; Electric field
∗ Corresponding author. Email address: [email protected] (Chuong V. Nguyen).
Preprint submitted to Elsevier
30 January 2016
1
Introduction Molybdenum disulphide (MoS2 ) is currently one of most promising candi-
dates for applications in nanoelectromechanical devices due to its novel mechanical and electronic properties [1–4]. MoS2 has a layered structure with weak interaction between layers. Physical properties of MoS2 have been both theoretically and experimentally studied in recent years [5–8]. Together with the large energy band gap, the high carrier mobility [9, 10] makes MoS2 well suited for applications in transitors [11], photo-detectors [12], lithium ion batteries [13] and memory devices [14]. It is well-known that bulk MoS2 is a semiconductor with indirect band gap of 1.23 eV [15] opening between the lowest energy of the conduction band located between the Γ and K points, and the highest energy of the valence band located at the Γ point. While bulk material has an indirect gap, monolayer MoS2 is a direct gap semiconductor with 1.80 eV [15] opening at the K point in reciprocal lattice space. Monolayer MoS2 has been successfully fabricated through chemical vapor deposition [16] and mechanical exfoliation [17–19]. The electronic properties of MoS2 are very sensitive to structural perfection [20] and they can be controlled and tuned by chemical treatment, nanopatterning, functionalization through adatom adsorption, applied external electric field or strain engineering [21–24]. In recent years, many works have been focused on the strain engineering of MoS2 from both the experimental [15, 25] and theoretical [26–28] studies to explore the effect of strain on the physical properties of MoS2 [1, 2]. Besides, the carrier mobility of MoS2 nanoribbons has also been studied by first principles calculations [29]. In this work, by using density functional theory (DFT) computations, we systematically investigate the effect of biaxial strain engineering and external electric field applied perpendicular to the layers on the band gaps and electronic properties of monolayer MoS2 . The direct-to-indirect band gaps and semiconductor-to-metal
2
transition are observed in monolayer MoS2 when strain and electric field are applied in our calculation. We show that the electronic properties including band gaps of monolayer MoS2 can be reduced to zero when subjected to a biaxial strain and external electric field. Our results provide many useful insights for the wide applications of monolayer MoS2 in electronics and optoelectronics.
2
Computational Method and Model Our calculations are performed within density functional theory using ac-
curate frozen-core full-potential projector augmented-wave (PAW) pseudopotentials [30,31]. All calculations are performed using the Quantum Espresso code [32]. We use the generalized gradient approximation (GGA) with the parametrization of Perdew-Burke-Ernzerhof (PBE). This combination is important for investigating the interaction between MoS2 layers. This approach has been successful in describing graphene-based structures [33]. The electronic wavefunctions are described by plane-wave basis sets with a kinetic energy cutoff of 30 Ry, and the energy cutoff for the charge density was set to 300 Ry. The Brillouin zone integration is carried out using an 18 × 18 × 1 k-mesh according to the Monkhorst-Pack scheme. For the different layers of the MoS2 , the supercells are constructed with a vacuum space ˚ along the z-direction. The strain is simulated by setting the lattice parameof 20 A ter to a fixed larger value and relaxing the atomic positions. The magnitude of the strain is defined as: ε = (a − a0 )/a0 , where a0 and a are the lattice parameters of the unstrained and strained systems, respectively. The interaction of electrons with the external electrostatic field along the yaxis is determined by the following expression:
Uext (r) = |e| × E × r, 3
(1)
Fig. 1. Relaxed atomic structure of monolayer MoS2 under an applied external electric field along z direction (a) and biaxial strain engineering along xy direction (b). Green and violet balls stand for Mo and S atoms, respectively.
where U is used to distinguish the potential energy in the electrostatic field from all other potential terms of the Kohn-Sham equation VKS (r) =
R
dr0
n(r0 ) |r−r0 |
+ Vion (r) +
Vxc (r). In order to consider Eext , the Kohn-Sham equations can be interpreted as:
−
h ¯2 2 ∇ + VKS + Uext Ψi (r) = εi Ψi (r). 2m
(2)
The applied electrostatic potential changes linearly along the entire unit cell; therefore, to observe periodic boundary conditions, the original value should be recovered at the cell boundary. Thus, a sawtooth potential shape with period equal to the unit cell period along the z-axis is most suitable [Fig. 1(a)]. The scheme of relative placement of the slab and external electrostatic potential is shown in Fig. 1(a). When the entire volume of MoS2 is in the electric field Eext and the simulated cell size along the z-axis is L, then the gauge field E ∗ is defined as: E ∗ = −Eext (z/L). The minus sign indicates that the E ∗ direction is always opposite to the Eext direction. 4
3 3.1
Results and discussion Effect of biaxial strain engineering To study the effect of biaxial strain and electric field on the band gap and elec-
tronic properties of graphene-like MoS2 monolayer, we first use the DFT method to optimize the geometry of monolayer MoS2 . Our calculations show that the op˚ and the bond distance timized value of the lattice constant a0 is equal to 3.18 A, ˚ This result is in good agreement with between Mo and S atoms dM o−S = 2.42 A. the previous theoretical [34–38] and experimental [39] studies. By using the DFT calculations, the direct gap of MoS2 monolayer is found to be 1.70 eV. This value is very close to the recent DFT based approach (1.72 eV) by Matte et al. [40]. Although our calculation for the direct gap of MoS2 monolayer is in good agreement with Matte’s calculations [40] and with those of other groups [26,41–43], this value is still smaller than the band gap which is measured using complementary techniques of optical absorption, photoluminescence and photoconductivity (1.80 eV) of monolayer thick MoS2 [15]. The band gap problem can be addressed more accurately by using a GW approximation [34, 44]. In the present work, we do not focus on this problem. This trend is not generalized, and more often depends on the material considered. For example, based on the many-body GW method the authors of Refs. [34, 44] showed a higher band gap of 2.78 eV. Therefore, we believe the dispersion-corrected density functional theory is a suitable method for calculation of the MoS2 structure and a new idea of the trends can be obtained from our study. The strained cell is modeled by stretching the hexagonal ring in the xy plane. A scheme of MoS2 monolayer with hexagonal symmetry under biaxial strain is shown in Fig. 1. The strain engineering is applied in a biaxial expansion along the xy-direction. The component of biaxial strain is noted as εb . The strains are
5
Fig. 2. Total energy (a) and band gaps (b) of monolayer MoS2 as function of biaxial strain engineering. Band structure of monolayer MoS2 under strain engineering of 0 % (c), 10 % (d) and 18 % (e)
evaluated as the lattice stretching percentage. A wide range of strain (up to 20%) along both directions has been employed in this study. Fig. 2(a) shows the total energy of monolayer MoS2 as function of biaxial strain εb . We can see that monolayer MoS2 becomes unstable under biaxial strain. Our calculations demonstrated that, as shown in Fig. 2, biaxial strain has a significant impact on the band gap and electronic properties of monolayer MoS2 . At the equilibrium state, MoS2 monolayer is a semiconductor with a direct gap of 1.70 eV at the K-point, which is in good agreement with previous calculations [26, 40–43]. From Fig. 2 we can see that the electronic properties of MoS2 are particularly sen6
sitive to mechanical strain. Under biaxial strain, monolayer MoS2 becomes an indirect gap semiconductor. While the lowest energy of the conduction band is still located at the K point, the highest energy of the valence band is located at the Γ point in reciprocal space. We can easily see the direct-to-indirect gap transition in Figs. 2(c,d,e). A shift of a energy levels leads to a change in the nature of the energy band gap for the monolayer MoS2 , from direct to indirect, even for an applied biaxial strain of less than 1 %. It means that, at a biaxial strain of εb = 1%, monolayer MoS2 is an indirect semiconductor. Fig. 2(b) shows the dependence of the band gap of MoS2 on the biaxial strain εb . When εb increases, the band gap of MoS2 decreases, which can be described as a part of parabola. Interestingly, the MoS2 band gap is equal to zero at εb = 18%. It means that the metal-semiconductor transition in MoS2 occurs at an elongation of 18 %. In this case, the lowest subband of the conduction band and the highest subband of the valence band cross the Fermi level at the K point and Γ point, respectively [see Fig. 2(e)] The projected density of state of Mo-d, S-p and S-s orbitals in bilayer MoS2 under strain and external electric field is shown in Fig. 3. As shown in Fig. 3(a), at the equilibrium state the bottom of the conduction band is mainly contributed to by Mo-d orbitals and the top of the valence band is contributed to by Mo-d and S-p orbitals. Mo-d and S-p orbitals are hybridized with each other at the top of the valence band. It means that the bonding between Mo and S atoms is strong. However, the mirror symmetrical bonding configuration in the trilayer S-Mo-S system results in a weak π bond-like interaction. This weak interaction is very sensitive to strain, resulting in the changed band structure under strain. Fig. 3(a) also shows clearly that the semiconductor-metal transition in monolayer MoS2 occurs at εb = 18%.
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Fig. 3. Projected density of state of Mo-d, S-p and S-s orbitals in bilayer MoS2 under applied strain (a) and applied electric field (b).
3.2
Effect of external electric field We applied an external electric field perpendicular to the plane of the MoS2
monolayers, as shown in Fig. 1(a). In the present work, the applied electric field ˚ The dependence of the total energy on strength is in the range from 0 to 1.2 V/A. the electric field is shown in Fig. 4(a). We can see that the total energy decreases as a function of the electric field and the dependence of the total energy on the electric field can be described as a part of a parabola. The effect of the electric field on the electronic band structure of MoS2 monolayers is shown in Figs. 4(c,d,e). Our calculations show that MoS2 monolayers can become semiconductor with an indirect band gap under external electric field. However, in the limit of small elec˚ the band gap remains almost constant as shown in tric field (from 0 to 0.6 V/A), 8
Fig. 4. Total energy (a) and band gaps (b) of monolayer MoS2 as function of external electric field. Band structure of monolayer MoS2 upon the application of external electric ˚ (c), 8 V/A ˚ (d) and 10 V/A ˚ (e) field of 0 V/A
˚ to 1.0 V/A, ˚ the Fig. 4(b). Additionally, in small range of electric field from 0.6 V/A band gap decreases abruptly to zero and MoS2 monolayers becomes metallic when ˚ In this case, in the band structure of MoS2 monolayer, the valence Eb ≥ 1.0 V/A. and conduction bands cross at the Γ point as shown in Fig. 4(e). The decrease of the band gap is as a function of the electric field because of the increase of polarization leading to the change of the dipole moment. The band gap modulation studied here should be attributed to the well-known Stark effect, resulting in a shift of the bands and in a change of the band structure in the presence of an external electric field, especially in the conduction region. 9
Fig. 5. Isosurface plot of the charge density (n) of monolayer MoS2 (top view) correspond˚ (c), ing to the VBM at the equilibrium state (a), at εb = 10 % (b) and at Ev = 1.0 V/A respectively; and corresponding to the CBM at the equilibrium state (d), at εb = 10 % (e) ˚ (f), respectively. The isosurface value was taken as 0.005 eV/A ˚ . and at Ev = 0.8 V/A Green and violet balls stand for Mo and S atoms, respectively.
This effect has been observed in our previous studies on graphene nanoribbon heterostructures. The changes in the energies of the valence band maximum (VBM) and conduction band maximum (CBM) with the electric field are shown in Fig. ˚ , monolayer MoS2 is a 3b. It shows that under an electric field of less than 0.6 V/A semiconductor with direct band gap of 1.70 eV. The VBM and CBM in this case are ˚ up to 1.0 V/A ˚ monoat the K point. With the critical electric field from 0.6 V/A layer MoS2 is a semiconductor with indirect band gaps. The VBM is located at the K point, while the CBM is moved to the Γ point. In addition, with critical electric ˚ the band gap of MoS2 monolayer is 1.47 eV and decreases down to field of 0.7 V/A, ˚ , and semiconductor-metal transition 0.156 eV with the electric field up to 0.9 V/A 10
is observed at large electric field (Ev ≥ 1). Fig. 3b shows the partial density of states (PDOS) of Mo-d, S-p and S-s or˚ and 1.0 V/A, ˚ respecbitals at the equilibrium state with applied field of 0.8 V/A tively. As noted above, at the equilibrium state the bottom of the conduction band is mainly contributed to by Mo-d orbitals, while the top of the valence band is contributed to by Mo-d orbitals and S-p orbitals. Mo-d and S-p orbitals are hybridized with each other at the top of the valence band, indicating strong bonding between Mo and S atoms. Field-induced repulsion among the electronic levels leads to an upshift of the VBM and a downshift of the CBM at the Γ point, resulting in a decrease of the band gap. To validate our above analysis, we also show the isosurface of the charge densities corresponding to VBM and CBM of monolayer MoS2 at the equilibrium state, under biaxial strain and with the applied electric field, as seen in Fig. 5. It shows that, the VBM and CBM at Γ- and K-points are mainly d2z and pz orbitals for Mo and S atoms, respectively. Compared to the unstrained state, under biaxial strain, the isosurface of VBM and CBM changes more significantly than that with electric field.
4
Conclusion In this paper, we studied the electronic properties of monolayer MoS2 under
biaxial strain engineering and external electric field by using first-principles calculations based on density functional theory. We have seen that mechanical strain and electric field reduce the band gap of semiconducting monolayer MoS2 , causing an direct-to-indirect band gap and a semiconductor-to-metal transition. Our calcuations demonstrated that the semiconductor–metal transition occurs in monolayer MoS2 under a biaxial strain of εb = 18% and an external electric field of Eb = 1 11
˚ The appearance of a phase transition in monolayer MoS2 opens many ways V/A. for applications in nanoelectronmechanical devices based on monolayer MoS2 . References [1] M. Chhowalla, H. S. Shin, G. Eda, L.-J. Li, K. P. Loh, and H. Zhang. The chemistry of two-dimensional layered transition metal dichalcogenide nanosheets.
Nature
Chemistry, 5(4):263–275, April 2013. [2] A. M. van der Zande, P. Y. Huang, D. A. Chenet, T. C. Berkelbach, Y. You, GH. Lee, T. F. Heinz, D. R. Reichman, D. A. Muller, and J. C. Hone. Grains and grain boundaries in highly crystalline monolayer molybdenum disulphide. Nat Mater, 12(6):554–561, June 2013. [3] Yafei Li, Dihua Wu, Zhen Zhou, Carlos R. Cabrera, and Zhongfang Chen. Enhanced li adsorption and diffusion on mos2 zigzag nanoribbons by edge effects: A computational study. J. Phys. Chem. Lett., 3(16):2221–2227, August 2012. [4] Yu Jing, Edwin O. Ortiz-Quiles, Carlos R. Cabrera, Zhongfang Chen, and Zhen Zhou. Layer-by-layer hybrids of mos2 and reduced graphene oxide for lithium ion batteries. Electrochimica Acta, 147:392–400, November 2014. [5] E. Cappelluti, R. Roldan, J. A. Silva-Guillen, P. Ordejon, and F. Guinea. Tight-binding model and direct-gap/indirect-gap transition in single-layer and multilayer mos2 . Phys. Rev. B, 88(7):075409, August 2013. [6] K. Kaasbjerg, K. S. Thygesen, and K. W. Jacobsen. Phonon-limited mobility in n-type single-layer mos2 from first principles. Phys. Rev. B, 85(11):115317–, March 2012. [7] Qing Tang and Zhen Zhou. Graphene-analogous low-dimensional materials. Progress in Materials Science, 58(8):1244–1315, 2013. [8] Qing Tang, Zhen Zhou, and Zhongfang Chen. Innovation and discovery of graphenelike materials via density-functional theory computations. Wiley Interdisciplinary
12
Reviews: Computational Molecular Science, 5(5):360–379, 2015. [9] Britton W. H. Baugher, Hugh O. H. Churchill, Yafang Yang, and Pablo Jarillo-Herrero. Intrinsic electronic transport properties of high-quality monolayer and bilayer mos2. Nano Lett., 13(9):4212–4216, September 2013. [10] Branimir Radisavljevic and Andras Kis. Mobility engineering and a metal-insulator transition in monolayer mos2. Nat Mater, 12(9):815–820, September 2013. [11] Gwan-Hyoung Lee, Young-Jun Yu, Xu Cui, Nicholas Petrone, Chul-Ho Lee, Min Sup Choi, Dae-Yeong Lee, Changgu Lee, Won Jong Yoo, Kenji Watanabe, Takashi Taniguchi, Colin Nuckolls, Philip Kim, and James Hone. Flexible and transparent mos2 field-effect transistors on hexagonal boron nitride-graphene heterostructures. ACS Nano, 7(9):7931–7936, September 2013. [12] L. Britnell, R. M. Ribeiro, A. Eckmann, R. Jalil, B. D. Belle, A. Mishchenko, Y.-J. Kim, R. V. Gorbachev, T. Georgiou, S. V. Morozov, A. N. Grigorenko, A. K. Geim, C. Casiraghi, A. H. Castro Neto, and K. S. Novoselov. Strong light-matter interactions in heterostructures of atomically thin films. Science, 340(6138):1311–1314, June 2013. [13] Yu Jing, Zhen Zhou, Carlos R. Cabrera, and Zhongfang Chen. Graphene, inorganic graphene analogs and their composites for lithium ion batteries. J. Mater. Chem. A, 2:12104–12122, 2014. [14] Min Sup Choi, Gwan-Hyoung Lee, Young-Jun Yu, Dae-Yeong Lee, Seung Hwan Lee, Philip Kim, James Hone, and Won Jong Yoo.
Controlled charge trapping by
molybdenum disulphide and graphene in ultrathin heterostructured memory devices. Nat Commun, 4:1624, March 2013. [15] Kin Fai Mak, Changgu Lee, James Hone, Jie Shan, and Tony F. Heinz. Atomically thin mos2 : A new direct-gap semiconductor. Phys. Rev. Lett., 105:136805, Sep 2010.
13
[16] Daeho Kim, Dezheng Sun, Wenhao Lu, Zhihai Cheng, Yeming Zhu, Duy Le, Talat S. Rahman, and Ludwig Bartels. Toward the growth of an aligned single-layer mos2 film. Langmuir, 27(18):11650–11653, 2011. PMID: 21812475. [17] Rudren Ganatra and Qing Zhang.
Few-layer mos2: A promising layered
semiconductor. ACS Nano, 8(5):4074–4099, 2014. PMID: 24660756. [18] K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim. Two-dimensional atomic crystals. Proceedings of the National Academy of Sciences of the United States of America, 102(30):10451–10453, 2005. [19] Jonathan N. Coleman, Mustafa Lotya, Arlene ONeill, Shane D. Bergin, Paul J. King, Umar Khan, Karen Young, Alexandre Gaucher, Sukanta De, Ronan J. Smith, Igor V. Shvets, Sunil K. Arora, George Stanton, Hye-Young Kim, Kangho Lee, Gyu Tae Kim, Georg S. Duesberg, Toby Hallam, John J. Boland, Jing Jing Wang, John F. Donegan, Jaime C. Grunlan, Gregory Moriarty, Aleksey Shmeliov, Rebecca J. Nicholls, James M. Perkins, Eleanor M. Grieveson, Koenraad Theuwissen, David W. McComb, Peter D. Nellist, and Valeria Nicolosi.
Two-dimensional nanosheets
produced by liquid exfoliation of layered materials. Science, 331(6017):568–571, 2011. [20] Jinhua Hong, Zhixin Hu, Matt Probert, Kun Li, Danhui Lv, Xinan Yang, Lin Gu, Nannan Mao, Qingliang Feng, Liming Xie, Jin Zhang, Dianzhong Wu, Zhiyong Zhang, Chuanhong Jin, Wei Ji, Xixiang Zhang, Jun Yuan, and Ze Zhang. Exploring atomic defects in molybdenum disulphide monolayers.
Nat Commun, 6:6293,
February 2015. [21] Wei-Bin Xu, Bao-Jun Huang, Ping Li, Feng Li, Chang-Wen Zhang, and Pei-Ji Wang. The electronic structure and optical properties of mn and b, c, n co-doped mos2 monolayers. Nanoscale Research Letters, 9(1):554, 2014. [22] Qu Yue, Zhengzheng Shao, Shengli Chang, and Jingbo Li.
14
Adsorption of gas
molecules on monolayer mos2 and effect of applied electric field. Nanoscale Research Letters, 8(1):425, 2013. [23] Xiaodan Li, Shunqing Wu, Sen Zhou, and Zizhong Zhu. Structural and electronic properties of germanene/mos2 monolayer and silicene/mos2 monolayer superlattices. Nanoscale Research Letters, 9(1):110, 2014. [24] Shang-Chun Lu and Jean-Pierre Leburton.
Electronic structures of defects and
magnetic impurities in mos2 monolayers. Nanoscale Research Letters, 9(1):676, 2014. [25] SW Han, Hyuksang Kwon, Seong Keun Kim, Sunmin Ryu, Won Seok Yun, DH Kim, JH Hwang, J-S Kang, J Baik, HJ Shin, et al. Band-gap transition induced by interlayer van der waals interaction in mos 2. Physical Review B, 84(4):045409, 2011. [26] S Lebegue and O Eriksson. Electronic structure of two-dimensional crystals from ab initio theory. Physical Review B, 79(11):115409, 2009. [27] Tianshu Li and Giulia Galli. Electronic properties of mos2 nanoparticles. The Journal of Physical Chemistry C, 111(44):16192–16196, 2007. [28] C. Ataca, M. Topsakal, E. Aktrk, and S. Ciraci. A comparative study of lattice dynamics of three- and two-dimensional mos2. The Journal of Physical Chemistry C, 115(33):16354–16361, 2011. [29] Yafei Li, Zhen Zhou, Shengbai Zhang, and Zhongfang Chen. Mos2 nanoribbons: High stability and unusual electronic and magnetic properties. J. Am. Chem. Soc., 130(49):16739–16744, December 2008. [30] Peter E Bl¨ochl. Projector augmented-wave method. Physical Review B, 50(24):17953, 1994. [31] G. Kresse and D Joubert. From ultrasoft pseudopotentials to the projector augmentedwave method. Physical Review B, 59(3):1758, 1999.
15
[32] Paolo Giannozzi, Stefano Baroni, Nicola Bonini, Matteo Calandra, Roberto Car, Carlo Cavazzoni, Davide Ceresoli, Guido L Chiarotti, Matteo Cococcioni, Ismaila Dabo, Andrea Dal Corso, Stefano de Gironcoli, Stefano Fabris, Guido Fratesi, Ralph Gebauer, Uwe Gerstmann, Christos Gougoussis, Anton Kokalj, Michele Lazzeri, Layla Martin-Samos, Nicola Marzari, Francesco Mauri, Riccardo Mazzarello, Stefano Paolini, Alfredo Pasquarello, Lorenzo Paulatto, Carlo Sbraccia, Sandro Scandolo, Gabriele Sclauzero, Ari P Seitsonen, Alexander Smogunov, Paolo Umari, and Renata M Wentzcovitch. Quantum espresso: a modular and open-source software project for quantum simulations of materials. Journal of Physics: Condensed Matter, 21(39):395502–, 2009. [33] Chuong V Nguyen, Victor V IIyasov, and Hieu N Nguyen. Tuning the electronic properties of armchair graphene nanoribbons by strain engineering. Physica Scripta, 90(1):015802–, 2015. [34] C. Ataca, H. ahin, E. Aktrk, and S. Ciraci. Mechanical and electronic properties of mos2 nanoribbons and their defects.
The Journal of Physical Chemistry C,
115(10):3934–3941, 2011. [35] Ashok Kumar and PK Ahluwalia. A first principle comparative study of electronic and optical properties of 1h–mos 2 and 2h–mos 2. Materials Chemistry and Physics, 135(2):755–761, 2012. [36] Yi Ding, Yanli Wang, Jun Ni, Lin Shi, Siqi Shi, and Weihua Tang. First principles study of structural, vibrational and electronic properties of graphene-like mx 2 (m= mo, nb, w, ta; x= s, se, te) monolayers. Physica B: Condensed Matter, 406(11):2254– 2260, 2011. [37] Priya Johari and Vivek B Shenoy. Tuning the electronic properties of semiconducting transition metal dichalcogenides by applying mechanical strains. 6(6):5449–5456, 2012.
16
ACS nano,
[38] Ya ping Miao, Fei Ma, Yu hong Huang, and Ke wei Xu. Strain effects on electronic states and lattice vibration of monolayer mos2. Physica E: Low-dimensional Systems and Nanostructures, 71:1 – 6, 2015. [39] JA Wilson and AD Yoffe.
The transition metal dichalcogenides discussion and
interpretation of the observed optical, electrical and structural properties. Advances in Physics, 18(73):193–335, 1969. [40] H.S.S. RamakrishnaMatte, A. Gomathi, ArunK. Manna, DattatrayJ. Late, Ranjan Datta, SwapanK. Pati, and C.N.R. Rao.
Mos2 and ws2 analogues of graphene.
Angewandte Chemie International Edition, 49(24):4059–4062, 2010. [41] A. Kuc, N. Zibouche, and T. Heine.
Influence of quantum confinement on the
electronic structure of the transition metal sulfide ts2 . Phys. Rev. B, 83:245213, Jun 2011. [42] Ali Hussain Reshak and S. Auluck. Calculated optical properties of 2h − mos2 intercalated with lithium. Phys. Rev. B, 68:125101, Sep 2003. [43] Ali Hussain Reshak and Sushil Auluck.
Band structure and optical response of
2h-MoX2 compounds (x = S, se, and te). Phys. Rev. B, 71:155114, Apr 2005. [44] C. Ataca and S. Ciraci. Functionalization of single-layer mos2 honeycomb structures. J. Phys. Chem. C, 115(27):13303–13311, July 2011.
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