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Manipulation of electronic structure in WSe2 monolayer by strain
Author’s Accepted Manuscript Manipulation of electronic structure in WSe2 monolayer by strain Cong-xia Yang, Xu Zhao, Shu-yi Wei
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S0038-1098(16)30149-1 http://dx.doi.org/10.1016/j.ssc.2016.07.003 SSC12979
To appear in: Solid State Communications Received date: 28 February 2016 Revised date: 29 June 2016 Accepted date: 4 July 2016 Cite this article as: Cong-xia Yang, Xu Zhao and Shu-yi Wei, Manipulation of electronic structure in WSe2 monolayer by strain, Solid State Communications, http://dx.doi.org/10.1016/j.ssc.2016.07.003 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 galley proof before it is published in its final citable 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.
Manipulation of electronic structure in WSe2 monolayer by strain Cong-xia Yang1, Xu Zhao1,*, Shu-yi Wei1 (1 College of Physics and Materials Science, Henan Normal University, Xinxiang 453007, China) E-mail: [email protected] Abstract: In this paper, we study the electronic properties of WSe2 monolayer with biaxial tensile strain and compressive strain by using first principles based on the density function theory. Under the biaxial tensile strain, WSe2 monolayer retains direct band gap with increasing strain and the band gap of WSe2 continuously decreases with increasing strain, eventually turn to metal when strain is equal to or more than 13℅. Under the biaxial compressive strain, WSe2 monolayer turns to indirect gap and the band gap continuously decreases with increasing strain, finally turn to metal when strain is up to -7℅. The strain can reduce the band gap of the WSe2 monolayer regardless of the strain direction. By comparison, we can see that the tensile strain appears to be more effective in reducing the band gap of pristine WSe2 monolayer than the compressive strain from -5% to 5%. But the band gap turns to zero quickly from -6% to -7% under compressive strain, however for tensile strain from 5% to 13%, the band gap decreases slowly. Based on the further analysis of the projected charge density for WSe2 monolayer, the fundamental reason of the change of band structure under biaxial tensile strain is revealed. Keywords: A. Transition-metal dichalcogenides; D. Electronic band structure; E. First-principles I. Introduction In recent years, tremendous efforts of researches have been focused on the layered transition-metal dichalcogenides (TMDCs, such as WS2, MoS2) due to their potential applications in some areas such as optoelectronic, lubricant, catalysis and so on [1-12]. 1
Transition metal dichalcogenides are semiconductors with potential applications in solar cells. WSe2 has a band gap of ~1.35 eV with a temperature dependence of -4.6×10−4eV/K [13]. WSe2 photoelectrodes are stable in both acidic and basic conditions, making them potentially useful in electrochemical solar cells [14-16]. The properties of WSe2 monolayer differ from those of the bulk state, as is typical for semiconductors. Mechanically exfoliated monolayer of WSe2 is transparent photovoltaic materials with LED properties [17]. Belonging to the family of layered transition metal dichalcogenides, Tungsten diselenide (WSe2 has a crystal structure consisting of weakly coupled sandwich layers Se−W−Se, where a W atom layer is enclosed within two Se layers, the atoms in layers are hexagonally packed, and these layers are held together by van der Walls interaction. Bulk WSe2 which is a semiconductor with an indirect gap, the monolayer WSe2 is a semiconductor with a direct band gap of 1.6 ~ 1.7eV [18].The direct band gap character opens the possibility for application of WSe2 monolayer as light-emitting diodes (LEDs), photoelectric detector and solar cells. For MoS2 monolayer subjected to isotropic tensile strain, the direct band gap of MoS2 changes to indirect gap and the band gap decreases monotonically with increasing strain [6]. The previous work by combining chemical functionalization and strain engineering provides a route to harness the magnetic properties of two-dimensional transition metal dichalcogenides for spintronic applications [19-23]. And previous results have shown that elastic strain is an effective pathway to induce and control the electronic and magnetic properties of materials [24-29]. Previous studies show that there exists a huge asymmetry in the compressive strains that can be applied to graphene: while it can be stretched by more than 20%, it is almost incompressible (at most 0.1% for typical sample size) because it would always undulate to relax the compressive strain by out-of-plane buckling [30]. However, the systematical study of the electronic characteristics in WSe2 monolayer so far is still limited. Here we perform first-principles calculations to investigate the structural properties of WSe2 monolayers and modulate the electronic properties of WSe2 monolayer with biaxial tensile strain and compressive strain. We find that the strain can reduce the band gap of the WSe2 monolayer regardless of the strain 2
direction and compressive strain is more effective than tensile strain in modulating electronic structure of WSe2 monolayer. This band gap engineering by strain may be applied to optical devices. II. Theoretical models and methods The layered WSe2 consists of stacked Se–W–Se layers. WSe2 layers have a P63/mmc space group symmetry with the W atoms having a trigonal prismatic coordination with the Se atoms. Our calculations were performed within first-principles DFT using the projector augmented wave (PAW) method [31] was used within the Vienna ab initio simulation package (VASP) [32]. Electron exchange and correlation effects were described within the generalized gradient approximation (GGA) in the Perdew–Burke–Ernzerhof (PBE) parametrization [33]. The layered WSe2 is modeled using a supercell method with 2D periodic boundary conditions. Two adjacent WSe2 layers are separated by a vacuum region of 20 Å in the direction normal to the layers. An energy cutoff of 550eV for the plan-wave expansion of the wavefunctions was used. For the Brillouin zone integration, a 9×9×1 centered Monkhorst-Pack-K-point mesh is used for a 3×3×1 WSe2 monolayer (As shown in Fig.1)supercell. The system minimize total energy is reached to 10-5 for all the structure relaxed. And the atomic positions and lattice parameters are optimized until the residual forces fall below 0.01 eV/Å. III. Results and discussion WSe2 monolayers have a hexagonal lattice with honeycomb structure, where W is bonded to 6 neighboring Se atoms. Our optimization yields for WSe2 a lattice parameter of a= 3.29Ǻ, which agrees with previous theoretical findings [34]. We apply compressive and tensile strain from -7% to 13% and relax the atomic positions. For WSe2 the bond length of 2.541Ǻ without strain agrees well with ref. [34]. Compressive/tensile strain reduces/increases the W–Se bond length, see Table 1, due to an increasing/decreasing coupling between the W and Se atoms, which also modifies the electronic structure. From Table 1, we found that the band gap gradually decreases with increasing isotropic strain including compressive and tensile isotropic strain. Moreover, the tensile strain appears to be more effective in reducing the band 3
gap of pristine WSe2 monolayer than the compressive strain from -5% to 5%, which is similar to ref. [35-36]. The band gap changes linearly with applied isotropic strain. The band gap turns to zero quickly from -6% to -7% under compressive strain, however for tensile strain from 5% to 13%, the band gap decreases slowly. So, we can find that -7% is critical compressive strain, in this case, the WSe2 monolayer turns to metal. This band gap engineering by strain may be applied to optical devices. Through these analysis, we find that the change in electronic properties for pristine WSe2 monolayer is determined by the strength of the W - Se bond. In this work, we are interested in the electronic structure of the WSe2 monolayer with biaxial tensile strain and compressive strain. To study the electronic structures of the WSe2 monolayer, we consider firstly 3×3×1 WSe2 monolayer supercell. Fig. 2(a) gives the electronic band structure of prinstine WSe2 monolayer without strain. Numerical results show that the monolayer WSe2 is direct semiconductor with an energy gap of 1.609 eV without strain, in agreement with the ref. [18]. And the valence band maximum (VBM) and conduction band minimum (CBM) are located at ΓH and ΓL points, respectively. But the band structure under different strain is changed obviously. The band gap of WSe2 continuously decreases, in some instances, the metallic nature of the bands can be obtained. We give the band structure with strain, as show in Fig. 2(b-e). Numerical results show that the WSe2 monolayer retains direct band gap with increasing strain under the biaxial tensile strain. The band gap of WSe2 continuously decreases with increasing strain, eventually turn to metal when strain is equal to or more than 13℅. Under the compressive biaxial strain, the VBM is still located at ΓH point and the CBM turn to A point which is located at between M point and K point. The band gap of WSe2 continuously decreases with increasing strain, finally turn to metal when strain is up to -7℅, as show in Fig. 2(e). As show in Fig.2, the WSe2 monolayer retains direct band gap with increasing biaxial tensile strain. Under the biaxial compressive strain, the direct band gap of WSe2 monolayer becomes an indirect gap. The reason for the phenomenon was that theΓL point energy in the CBM has changed. Fig. 3 gives the band gap (Eg) of WSe2 monolayer 4
and the conduction band minimum energy difference (Ec(Γ）- Ec(A)) between Γ and A with the different compressive biaxial strain. We find that the band gap is easily changed. It is clear that the energy value shifts upward to 0.652 eV from -0.077 eV under the biaxial compressive strain which is from 0% to -6% in Fig. 3. In order to further understand the band structure variation, we give that the energy of Γ and A points in the CBM under different biaxial compressive strains in Fig. 4. As show in Fig. 4, the energy change of AL that reduced from 0.892 eV to 0.635 eV is very small. And the energy change of ΓL is enhanced from 0.798 eV to 1.287 eV. These results indicate that strain changes the atoms relative position, so that the bond lengths is different and the band gap is changed. To reveal the mechanism of the electronic characteristics in WSe2 monolayer with strain, the total density of states and partial density of stats (PDOS) are shown in Fig. 5. As can be seen from Fig. 5, W d orbital dominates in -6—4eV, Se s orbital dominates in -16— -12eV, Se p orbitals dominate in -6—4eV. It forms a strong covalent bond between W d orbital and Se p orbital. we can see that W d orbital and Se p orbital have similar DOS in -6—2eV and the hybridization between the localized W d and Se p is strong. The DOS is mainly contributed by the W atom d orbital and feebly by the Se atom p orbital in 2— 3.5 eV, which indicates the π bond-like is formed. The results show that the high sensitivity of the π bond to strain to lead to the effect of strain on its band structure is relatively large. Finally, we plot the charge densities at A and Γ of the conduction band minimum without strain to describe the effect of this π bond-like in Fig. 6. Its isosurface is 0.04 e/Å3, it is clear to describe the effect of bond between the electrons. Moreover, we can see that the distance of Se-W （recorded as d） decreases from 2.541 to 2.514 Å when strain increases linearly (Table 1), leading to the σ bond which formed between W atom d orbital and the Se atom p orbital increases for the monolayer WSe2. And the corresponding band dispersion curves strengthen slightly and the total energy of the system decreases. It will emerge significant relaxation between atoms for increasing the total energy of the system with compressive strain. And relaxation will increase the distance between Se layer and the W layer, distance of Se layer to W layer (h/2) 5
increases monotonically from 1.688 to 1.769 Å show in Table 1.The contact area between Se and W is increased in the plane which is perpendicular to the atom layer, leading to the π bond-like significantly increase. As shown in Fig. 6(a), (c), and Fig. 4 the band energy is changed by the π bond-like and decreased in the vicinity of the A point under with increasing strain. In contrast, the energy of Γ point is mainly from the W-dz 2 orbital in Fig. 6(b), (d). The W-dz2 orbital is the highest occupied state in the whole system and electronic is very active, which similar to dz2 orbital of isolated atom. Thus, the energy of Γ point is increased with increasing compressive strain. IV. Conclusion In this work, the electronic properties are studied in WSe2 monolayer by biaxial tensile strain and compressive strain using the first-principles methods based on density functional theory. We find out that the WSe2 monolayer retains direct band gap with increasing strain under the biaxial tensile strain. The band gap of WSe2 continuously decreases with increasing strain, eventually turn to metal when strain is equal to or more than 13℅. The direct gap of WSe2 monolayer becomes an indirect gap under the compressive biaxial strain and WSe2 monolayer retains indirect band gap with increasing strain. The band gap of WSe2 continuously decreases with increasing strain, finally turn to metal when strain is up to -7℅. It is clear that the strain can reduce the band gap of the WSe2 monolayer regardless of the strain direction and tensile strain appears to be more effective in reducing the band gap of pristine WSe2 monolayer than the compressive strain from -5% to 5%. But the band gap turns to zero quickly from -6% to -7% under compressive strain, however for tensile strain from 5% to 13%, the band gap decreases slowly. Through analysis of partial charge density distribution and partial density of states of WSe2 monolayer, we find that the the high sensitivity of the π bond to strain, leading to the effect of compressive strain on its band structure is relatively large. The conduction band minimum Energy at Γ point is mainly contributed by the localized dz2 orbital in the same plane of W atoms, so its energy is increased with increasing compressive strain.. These theoretical results may have a certain reference value for the design and production of nanodevices based WSe2. 6
This work is supported by a Grant from the National Natural Science Foundation of China (NSFC) under the Grant No. 11504092, Natural science foundation research project of education department of Henan province (No. 2011A140018), and Science and technology research key project f education department of Henan province (No. 14A140012), and High Performance Computing Center of Henan Normal University.
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[2] K. Chang, W. X. Chen, Chemical communications, 47(2011) 4252-4254. [3] S. Lebegue, O. Eriksson, Physical Review B, 79(2009) 115409(1)-115409(4). [4] H. S. S. R. Matte, A. Gomathi, A. K. Manna, ea tl. Angew Chem Int Ed, 49(2010)4059–4062. [5] M.S. Wu, B. Xu, G. Liu, C. Y. OuYang, Acta Physica Sinica,61 (2012) : 227102(1) - 2277102(5). [6] P. Lu, X. J. Wu, W. L. Guo, X. C. Zeng, Phys. Chem. Chem. Phys., 14(2012) 13035–13040. [7] X. F. Zhang, A. H. Wang, X. l. Zhang,ea tl. The Chinese Journal of Nonferrous Metals ,18（2008)215-220. [8] X. Zhao, X.Q. Dai, C.X. Xia, T.X. Wang, Y.T. Peng olid State Communications 215-216 (2015) 1–4. [9] X. Zhao, X. Q. Dai, C. X. Xia, T. X. Wang, Superlattices and Microstructures, 85 (2015) 339-347. [10] S. Tongay, W. Fan, J. Kang, J. Park, U. Koldemir, J. Suh, D. S. Narang, K. Liu, J. Ji, J.B. Li, R. Sinclair, J.Q. Wu, NANO LETTERS, 14 (2014) 3185−3190. [11] Qu Yue a, Shengli Chang a, Shiqiao Qina, Jingbo Li, Physics Letters A, 377 (2013) 1362–1367. [12] A. Kumar, P.K.Ahluwalia, Physica B, 419(2013)66–75. [13] L. C. UPADHYAYULA, J. J. LOFERSKI, A. WOLD, ea tl. Journal of Applied Physics, 39(1968) 353–358. 7
[14] J. Gobrecht, H. Gerischer, H. Tributsch. Berichte der Bunsengesellschaft für physikalische Chemie, 82 (1978) 1331–1335. [15] F. Xia, H. Wang, D. Xiao, M. Dubey, A. Ramasubramaniam. Nature Photonics, 8(2014)899-907. [16] X. Zhang, X. F. Qiao, W. Shi, J. B. Wu, D. S. Jiang, P. H. Tan , Chemical Society Reviews, 44 (2015) 2757-2785. [17] D. Johnson, IEEE Spectrum. 2014. [18] H. Zeng, G. B. Liu, J. Dai, et al, Scientific Reports, 3(2013)1608. [19] H. L. Shi, H. Pan, Y. W. Zhang, I. Boris. Yakobson PHYSICAL REVIEW B 88 (2013) 205305. [20] Y. D. Ma, Y. Dai, M. Guo, C. W. Niu, Y. T. Zhu and B. B. Huang, ACS Nano, 6 (2012) 1695. [21] E. J. G. Santos, A. Ayuela and D. Sanchez-Portal, J. Phys. Chem. C, 116 (2012) 1174. [22] L. Z. Kou, C. Tang, W. L. Guo and C. F. Chen, ACS Nano, 5 (2011) 1012. [23] Y. G. Zhou, Q. L. Su, Z. G. Wang, H. Q. Deng X. T. Zu, Phys.Chem.Chem.Phys., 15 (2013) 18464. [24] Y. D. Ma, Y. Dai, M. Guo, C. W. Niu, Y. T. Zhu and B. B. Huang, ACS Nano. 6 (2012) 1695. [25] E. J. G. Santos, A. Ayuela and D. Sanchez-Portal, J. Phys. Chem. C, 116 (2012) 1174. [26] L. Z. Kou, C. Tang, W. L. Guo and C. F. Chen, ACS Nano. 5 (2011) 1012. [27] Z. Liu, J. Wu, W. Duan, Max G. Lagally, and F. Liu, Physical Review Lett., 2010, 105, 016802. [28] F. Liu et al., Nature (London) (2002) 416, 498. [29] Z. F. Wang, M. Zhou, M. Yoon and F. Liu, Nano Lett. (2016) 16, 404. [30] Y. Zhang and F. Liu, Appl. Phys. Lett. 99 (2011) 241908. [31] P. E. Blonchl, Physical Review B, 1994, 50(24) 17953. [32] . resse, . Furthm̈ uller, Physical Review B,54(1996)11169. [33] J. P. Perdew, K. Burke,M. Ernzerhof,Physical Review Letters, 77(1996)3865. 8
[34]B. Amin, T. P. Kaloni and U. Schwingenschl¨ogl, RSC Adv., 2014, 4, 34561. [35] Peng Lu, Xiaojun Wu, Wanlin Guo and Xiao Cheng Zeng, Phys. Chem. Chem. Phys., 2012, 14, 13035–13040. [36]E. Scalise, M. Houssa, G. Pourtois, V. Afanasev, and A. Stesmans, Nano Research 5, 43 (2012).
Figure captions Fig. 1
Schematic of WSe2 monolayer crystal structure (a) Top view of WSe2
supercell; (b) Side view of WSe2 supercell (The green and grey balls represent Se and W atoms, respectively.) Fig. 2 The band structures of WSe2 monolayer with isotropic strain, the Fermi level is set at 0 eV. (a)ε=0% (b)ε=5% (c) ε=13% （d）ε= - 4% （e）ε= - 7%. Fig. 3 The band gap (Eg) of WSe2 monolayer and the conduction band minimum energy difference (Ec(Γ）- Ec(A)) between Γ and A with the different compressive biaxial strain. Fig. 4 The conduction band minimum Energy at Γ and A on of WSe2 monolayer with different compressive biaxial strain. Fig. 5 Total density of stats (TDOS) and partial density of states (PDOS) of monolayer WSe2. Fig. 6 Charge densities at A and Γ of the conduction band minimum without strain (a)Top view of A;(b) Top view of Γ;(c) Side view of A;(d)Side view of Γ.
9
Table caption Table 1. The optimized W-Se bond length, dW-Se, and the band gap, △Egap, and total energy of system, Etot in different strain.
Table 2. Structure of WSe2 monolayer changed by strain. ε represents lattice strain, h/2 represents distance of Se layer to W layer, W–Se bond length (d ).
Highlights WSe2 monolayer retains direct band gap when tensile strain is less than 13%. WSe2 monolayer turns to indirect gap semiconductor with compressive strain (less than -7%). Strain can reduce the band gap of the WSe2 monolayer.
10
B
A
O （a）
（b）
Figure
(a)
3
2
Energy/ev
1 = 0%
0
-1
-2
-3
(b)
3
2
Energy/ev
1 = 5%
0
-1
-2
-3
(c)
3
2
Energy/ev
1 = 13%
0
-1
-2
-3
(d)
3
2
Energy/ev
1 = -4%
0
-1
-2
-3
(e)
3 2
Energy/eV
1 0
= -7%
-1 -2 -3
Figure
Figure
1.3 1.2
Energy /eV
1.1 1.0
A 0.9 0.8 0.7 0.6
-6
-5
-4
-3
-2
%
-1
0
40 WSe2
30 20
DOS(states/ev)
10 0 0.6
Se--s Se--p Se--d
0.4 0.2 0.0 2
W--s W--p W--d
1 0 -15
-10
-5
Energy(ev)
0
5
10
Table
ε/%
0
-1
-2
-3
-4
-5
-6
（h/2）Å 1.688
1.700
1.714
1.727
1.740
1.755
1.769
d/Å
2.535
2.530
2.525
2.520
2.516
2.514
2.541
Table
Table 1 Strain (%)
dW-Se (Å)
△Egap (eV)
Etot(eV)
13
2.648
0
-185.86
12
2.638
0.071
-187.13
11
2.628
0.160
-188.32
10
2.619
0.264
-189.42
9
2.610
0.385
-190.45
7
2.592
0.655
-192.22
5
2.603
0.989
-193.27
3
2.561
1.298
-194.44
1
2.547
1.518
-194.78
0
2.541
1.609
-194.73
-1
2.535
1.557
-194.53
-3
2.525
1.457
-193.59
-4
2.520
1.396
-192.85
-5
2.516
1.332
-191.89
-6
2.514
1.268
-190.70
-7
2.511
0
-184.53
www.elsevier.com/locate/ssc
PII: DOI: Reference:
S0038-1098(16)30149-1 http://dx.doi.org/10.1016/j.ssc.2016.07.003 SSC12979
To appear in: Solid State Communications Received date: 28 February 2016 Revised date: 29 June 2016 Accepted date: 4 July 2016 Cite this article as: Cong-xia Yang, Xu Zhao and Shu-yi Wei, Manipulation of electronic structure in WSe2 monolayer by strain, Solid State Communications, http://dx.doi.org/10.1016/j.ssc.2016.07.003 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 galley proof before it is published in its final citable 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.
Manipulation of electronic structure in WSe2 monolayer by strain Cong-xia Yang1, Xu Zhao1,*, Shu-yi Wei1 (1 College of Physics and Materials Science, Henan Normal University, Xinxiang 453007, China) E-mail: [email protected] Abstract: In this paper, we study the electronic properties of WSe2 monolayer with biaxial tensile strain and compressive strain by using first principles based on the density function theory. Under the biaxial tensile strain, WSe2 monolayer retains direct band gap with increasing strain and the band gap of WSe2 continuously decreases with increasing strain, eventually turn to metal when strain is equal to or more than 13℅. Under the biaxial compressive strain, WSe2 monolayer turns to indirect gap and the band gap continuously decreases with increasing strain, finally turn to metal when strain is up to -7℅. The strain can reduce the band gap of the WSe2 monolayer regardless of the strain direction. By comparison, we can see that the tensile strain appears to be more effective in reducing the band gap of pristine WSe2 monolayer than the compressive strain from -5% to 5%. But the band gap turns to zero quickly from -6% to -7% under compressive strain, however for tensile strain from 5% to 13%, the band gap decreases slowly. Based on the further analysis of the projected charge density for WSe2 monolayer, the fundamental reason of the change of band structure under biaxial tensile strain is revealed. Keywords: A. Transition-metal dichalcogenides; D. Electronic band structure; E. First-principles I. Introduction In recent years, tremendous efforts of researches have been focused on the layered transition-metal dichalcogenides (TMDCs, such as WS2, MoS2) due to their potential applications in some areas such as optoelectronic, lubricant, catalysis and so on [1-12]. 1
Transition metal dichalcogenides are semiconductors with potential applications in solar cells. WSe2 has a band gap of ~1.35 eV with a temperature dependence of -4.6×10−4eV/K [13]. WSe2 photoelectrodes are stable in both acidic and basic conditions, making them potentially useful in electrochemical solar cells [14-16]. The properties of WSe2 monolayer differ from those of the bulk state, as is typical for semiconductors. Mechanically exfoliated monolayer of WSe2 is transparent photovoltaic materials with LED properties [17]. Belonging to the family of layered transition metal dichalcogenides, Tungsten diselenide (WSe2 has a crystal structure consisting of weakly coupled sandwich layers Se−W−Se, where a W atom layer is enclosed within two Se layers, the atoms in layers are hexagonally packed, and these layers are held together by van der Walls interaction. Bulk WSe2 which is a semiconductor with an indirect gap, the monolayer WSe2 is a semiconductor with a direct band gap of 1.6 ~ 1.7eV [18].The direct band gap character opens the possibility for application of WSe2 monolayer as light-emitting diodes (LEDs), photoelectric detector and solar cells. For MoS2 monolayer subjected to isotropic tensile strain, the direct band gap of MoS2 changes to indirect gap and the band gap decreases monotonically with increasing strain [6]. The previous work by combining chemical functionalization and strain engineering provides a route to harness the magnetic properties of two-dimensional transition metal dichalcogenides for spintronic applications [19-23]. And previous results have shown that elastic strain is an effective pathway to induce and control the electronic and magnetic properties of materials [24-29]. Previous studies show that there exists a huge asymmetry in the compressive strains that can be applied to graphene: while it can be stretched by more than 20%, it is almost incompressible (at most 0.1% for typical sample size) because it would always undulate to relax the compressive strain by out-of-plane buckling [30]. However, the systematical study of the electronic characteristics in WSe2 monolayer so far is still limited. Here we perform first-principles calculations to investigate the structural properties of WSe2 monolayers and modulate the electronic properties of WSe2 monolayer with biaxial tensile strain and compressive strain. We find that the strain can reduce the band gap of the WSe2 monolayer regardless of the strain 2
direction and compressive strain is more effective than tensile strain in modulating electronic structure of WSe2 monolayer. This band gap engineering by strain may be applied to optical devices. II. Theoretical models and methods The layered WSe2 consists of stacked Se–W–Se layers. WSe2 layers have a P63/mmc space group symmetry with the W atoms having a trigonal prismatic coordination with the Se atoms. Our calculations were performed within first-principles DFT using the projector augmented wave (PAW) method [31] was used within the Vienna ab initio simulation package (VASP) [32]. Electron exchange and correlation effects were described within the generalized gradient approximation (GGA) in the Perdew–Burke–Ernzerhof (PBE) parametrization [33]. The layered WSe2 is modeled using a supercell method with 2D periodic boundary conditions. Two adjacent WSe2 layers are separated by a vacuum region of 20 Å in the direction normal to the layers. An energy cutoff of 550eV for the plan-wave expansion of the wavefunctions was used. For the Brillouin zone integration, a 9×9×1 centered Monkhorst-Pack-K-point mesh is used for a 3×3×1 WSe2 monolayer (As shown in Fig.1)supercell. The system minimize total energy is reached to 10-5 for all the structure relaxed. And the atomic positions and lattice parameters are optimized until the residual forces fall below 0.01 eV/Å. III. Results and discussion WSe2 monolayers have a hexagonal lattice with honeycomb structure, where W is bonded to 6 neighboring Se atoms. Our optimization yields for WSe2 a lattice parameter of a= 3.29Ǻ, which agrees with previous theoretical findings [34]. We apply compressive and tensile strain from -7% to 13% and relax the atomic positions. For WSe2 the bond length of 2.541Ǻ without strain agrees well with ref. [34]. Compressive/tensile strain reduces/increases the W–Se bond length, see Table 1, due to an increasing/decreasing coupling between the W and Se atoms, which also modifies the electronic structure. From Table 1, we found that the band gap gradually decreases with increasing isotropic strain including compressive and tensile isotropic strain. Moreover, the tensile strain appears to be more effective in reducing the band 3
gap of pristine WSe2 monolayer than the compressive strain from -5% to 5%, which is similar to ref. [35-36]. The band gap changes linearly with applied isotropic strain. The band gap turns to zero quickly from -6% to -7% under compressive strain, however for tensile strain from 5% to 13%, the band gap decreases slowly. So, we can find that -7% is critical compressive strain, in this case, the WSe2 monolayer turns to metal. This band gap engineering by strain may be applied to optical devices. Through these analysis, we find that the change in electronic properties for pristine WSe2 monolayer is determined by the strength of the W - Se bond. In this work, we are interested in the electronic structure of the WSe2 monolayer with biaxial tensile strain and compressive strain. To study the electronic structures of the WSe2 monolayer, we consider firstly 3×3×1 WSe2 monolayer supercell. Fig. 2(a) gives the electronic band structure of prinstine WSe2 monolayer without strain. Numerical results show that the monolayer WSe2 is direct semiconductor with an energy gap of 1.609 eV without strain, in agreement with the ref. [18]. And the valence band maximum (VBM) and conduction band minimum (CBM) are located at ΓH and ΓL points, respectively. But the band structure under different strain is changed obviously. The band gap of WSe2 continuously decreases, in some instances, the metallic nature of the bands can be obtained. We give the band structure with strain, as show in Fig. 2(b-e). Numerical results show that the WSe2 monolayer retains direct band gap with increasing strain under the biaxial tensile strain. The band gap of WSe2 continuously decreases with increasing strain, eventually turn to metal when strain is equal to or more than 13℅. Under the compressive biaxial strain, the VBM is still located at ΓH point and the CBM turn to A point which is located at between M point and K point. The band gap of WSe2 continuously decreases with increasing strain, finally turn to metal when strain is up to -7℅, as show in Fig. 2(e). As show in Fig.2, the WSe2 monolayer retains direct band gap with increasing biaxial tensile strain. Under the biaxial compressive strain, the direct band gap of WSe2 monolayer becomes an indirect gap. The reason for the phenomenon was that theΓL point energy in the CBM has changed. Fig. 3 gives the band gap (Eg) of WSe2 monolayer 4
and the conduction band minimum energy difference (Ec(Γ）- Ec(A)) between Γ and A with the different compressive biaxial strain. We find that the band gap is easily changed. It is clear that the energy value shifts upward to 0.652 eV from -0.077 eV under the biaxial compressive strain which is from 0% to -6% in Fig. 3. In order to further understand the band structure variation, we give that the energy of Γ and A points in the CBM under different biaxial compressive strains in Fig. 4. As show in Fig. 4, the energy change of AL that reduced from 0.892 eV to 0.635 eV is very small. And the energy change of ΓL is enhanced from 0.798 eV to 1.287 eV. These results indicate that strain changes the atoms relative position, so that the bond lengths is different and the band gap is changed. To reveal the mechanism of the electronic characteristics in WSe2 monolayer with strain, the total density of states and partial density of stats (PDOS) are shown in Fig. 5. As can be seen from Fig. 5, W d orbital dominates in -6—4eV, Se s orbital dominates in -16— -12eV, Se p orbitals dominate in -6—4eV. It forms a strong covalent bond between W d orbital and Se p orbital. we can see that W d orbital and Se p orbital have similar DOS in -6—2eV and the hybridization between the localized W d and Se p is strong. The DOS is mainly contributed by the W atom d orbital and feebly by the Se atom p orbital in 2— 3.5 eV, which indicates the π bond-like is formed. The results show that the high sensitivity of the π bond to strain to lead to the effect of strain on its band structure is relatively large. Finally, we plot the charge densities at A and Γ of the conduction band minimum without strain to describe the effect of this π bond-like in Fig. 6. Its isosurface is 0.04 e/Å3, it is clear to describe the effect of bond between the electrons. Moreover, we can see that the distance of Se-W （recorded as d） decreases from 2.541 to 2.514 Å when strain increases linearly (Table 1), leading to the σ bond which formed between W atom d orbital and the Se atom p orbital increases for the monolayer WSe2. And the corresponding band dispersion curves strengthen slightly and the total energy of the system decreases. It will emerge significant relaxation between atoms for increasing the total energy of the system with compressive strain. And relaxation will increase the distance between Se layer and the W layer, distance of Se layer to W layer (h/2) 5
increases monotonically from 1.688 to 1.769 Å show in Table 1.The contact area between Se and W is increased in the plane which is perpendicular to the atom layer, leading to the π bond-like significantly increase. As shown in Fig. 6(a), (c), and Fig. 4 the band energy is changed by the π bond-like and decreased in the vicinity of the A point under with increasing strain. In contrast, the energy of Γ point is mainly from the W-dz 2 orbital in Fig. 6(b), (d). The W-dz2 orbital is the highest occupied state in the whole system and electronic is very active, which similar to dz2 orbital of isolated atom. Thus, the energy of Γ point is increased with increasing compressive strain. IV. Conclusion In this work, the electronic properties are studied in WSe2 monolayer by biaxial tensile strain and compressive strain using the first-principles methods based on density functional theory. We find out that the WSe2 monolayer retains direct band gap with increasing strain under the biaxial tensile strain. The band gap of WSe2 continuously decreases with increasing strain, eventually turn to metal when strain is equal to or more than 13℅. The direct gap of WSe2 monolayer becomes an indirect gap under the compressive biaxial strain and WSe2 monolayer retains indirect band gap with increasing strain. The band gap of WSe2 continuously decreases with increasing strain, finally turn to metal when strain is up to -7℅. It is clear that the strain can reduce the band gap of the WSe2 monolayer regardless of the strain direction and tensile strain appears to be more effective in reducing the band gap of pristine WSe2 monolayer than the compressive strain from -5% to 5%. But the band gap turns to zero quickly from -6% to -7% under compressive strain, however for tensile strain from 5% to 13%, the band gap decreases slowly. Through analysis of partial charge density distribution and partial density of states of WSe2 monolayer, we find that the the high sensitivity of the π bond to strain, leading to the effect of compressive strain on its band structure is relatively large. The conduction band minimum Energy at Γ point is mainly contributed by the localized dz2 orbital in the same plane of W atoms, so its energy is increased with increasing compressive strain.. These theoretical results may have a certain reference value for the design and production of nanodevices based WSe2. 6
This work is supported by a Grant from the National Natural Science Foundation of China (NSFC) under the Grant No. 11504092, Natural science foundation research project of education department of Henan province (No. 2011A140018), and Science and technology research key project f education department of Henan province (No. 14A140012), and High Performance Computing Center of Henan Normal University.
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Figure captions Fig. 1
Schematic of WSe2 monolayer crystal structure (a) Top view of WSe2
supercell; (b) Side view of WSe2 supercell (The green and grey balls represent Se and W atoms, respectively.) Fig. 2 The band structures of WSe2 monolayer with isotropic strain, the Fermi level is set at 0 eV. (a)ε=0% (b)ε=5% (c) ε=13% （d）ε= - 4% （e）ε= - 7%. Fig. 3 The band gap (Eg) of WSe2 monolayer and the conduction band minimum energy difference (Ec(Γ）- Ec(A)) between Γ and A with the different compressive biaxial strain. Fig. 4 The conduction band minimum Energy at Γ and A on of WSe2 monolayer with different compressive biaxial strain. Fig. 5 Total density of stats (TDOS) and partial density of states (PDOS) of monolayer WSe2. Fig. 6 Charge densities at A and Γ of the conduction band minimum without strain (a)Top view of A;(b) Top view of Γ;(c) Side view of A;(d)Side view of Γ.
9
Table caption Table 1. The optimized W-Se bond length, dW-Se, and the band gap, △Egap, and total energy of system, Etot in different strain.
Table 2. Structure of WSe2 monolayer changed by strain. ε represents lattice strain, h/2 represents distance of Se layer to W layer, W–Se bond length (d ).
Highlights WSe2 monolayer retains direct band gap when tensile strain is less than 13%. WSe2 monolayer turns to indirect gap semiconductor with compressive strain (less than -7%). Strain can reduce the band gap of the WSe2 monolayer.
10
B
A
O （a）
（b）
Figure
(a)
3
2
Energy/ev
1 = 0%
0
-1
-2
-3
(b)
3
2
Energy/ev
1 = 5%
0
-1
-2
-3
(c)
3
2
Energy/ev
1 = 13%
0
-1
-2
-3
(d)
3
2
Energy/ev
1 = -4%
0
-1
-2
-3
(e)
3 2
Energy/eV
1 0
= -7%
-1 -2 -3
Figure
Figure
1.3 1.2
Energy /eV
1.1 1.0
A 0.9 0.8 0.7 0.6
-6
-5
-4
-3
-2
%
-1
0
40 WSe2
30 20
DOS(states/ev)
10 0 0.6
Se--s Se--p Se--d
0.4 0.2 0.0 2
W--s W--p W--d
1 0 -15
-10
-5
Energy(ev)
0
5
10
Table
ε/%
0
-1
-2
-3
-4
-5
-6
（h/2）Å 1.688
1.700
1.714
1.727
1.740
1.755
1.769
d/Å
2.535
2.530
2.525
2.520
2.516
2.514
2.541
Table
Table 1 Strain (%)
dW-Se (Å)
△Egap (eV)
Etot(eV)
13
2.648
0
-185.86
12
2.638
0.071
-187.13
11
2.628
0.160
-188.32
10
2.619
0.264
-189.42
9
2.610
0.385
-190.45
7
2.592
0.655
-192.22
5
2.603
0.989
-193.27
3
2.561
1.298
-194.44
1
2.547
1.518
-194.78
0
2.541
1.609
-194.73
-1
2.535
1.557
-194.53
-3
2.525
1.457
-193.59
-4
2.520
1.396
-192.85
-5
2.516
1.332
-191.89
-6
2.514
1.268
-190.70
-7
2.511
0
-184.53