icin

Nort

VacancyElectronic structureOptical properties

ctu-wtureand re

indirect band gap. Mo vacancies bring about acceptor-like levels and p-type conductivities, whereas S

ith hewith

riety otalysis

suspended monolayer with honeycomb structures. Moreover, agreat number of literatures had predicted the electronic, elastic,mechanical, and optical properties of monolayer MoS2 [1621].

Dhas and Suslick [22] have found that vacancies exist in mono-layer MoS2 when they synthesized the monolayer MoS2 throughsonochemical deposition method. It is well known that vacancy

at the knowledgetical appliand analycused on i

gating the effect of charged vacancies on structure relaxatiotronic structure and optical properties of monolayer MoSrst-principles calculations.

2. Computational details

In the present calculations, the exchange correlation of the generalized gradientapproximation (GGA) with the PerdewWang 1991 (PW-91) functional [32] asimplemented in CASTEP code [33] was employed. The ionic cores are representedby ultrasoft pseudopotential forMo and S atoms. The valence electron congurations

Corresponding author. Tel.: +86 29 88488013; fax: +86 29 88492642.E-mail address: lpfeng@nwpu.edu.cn (L.-p. Feng).

Journal of Alloys and Compounds 613 (2014) 122127

Contents lists availab

Journal of Alloys a

.e lsevier .com/locate / ja lcomexperimental studies, a lot of theoretical work has been performedto investigate the properties of monolayer MoS2. Ataca et al.[14,15] have studied the lattice dynamics and structure stabilityof monolayer MoS2, indicating that MoS2 can form stable and

are not well understood yet. It is well known thof vacancy defects is very important for the pracof monolayer MoS2 as well as for the designingoptoelectronic devices. Therefore, this work is fohttp://dx.doi.org/10.1016/j.jallcom.2014.06.0180925-8388/ 2014 Elsevier B.V. All rights reserved.cationszing ofnvesti-n, elec-2 usingphotovoltaic and super-lubricity [110]. Most recently, the mono-layer MoS2 has been used to construct eld-effect transistors(FETs), which can offer lower power consumption than classicaltransistors [11,12]. New phototransistor based on monolayerMoS2 has been fabricated and exhibits a better photoresponsivityas compared with the graphene-based device [13]. Except for

the formation energy of neutral vacancies in monolayer MoS2and studied the inuence of vacancies on magnetic properties ofmonolayer MoS2, implying that vacancy creation appears to be apromising way to extend the applications of MoS2.

To the best of our knowledge, the effects of charged vacancieson electronic structure and optical properties of monolayer MoS21. Introduction

Molybdenum disulde (MoS2) wimportant semiconductor materialchemical properties, and it has a vahydrogen production, solar cells, cavacancies lead to donor-like levels and n-type conductivities. With the increasing charge states of vacan-cies, the band gaps get smaller and the defect energy levels become deeper. Moreover, as the chargestates of vacancies increase, the static dielectric constants of monolayer MoS2 with Mo vacanciesdecrease, whereas the static dielectric constants of monolayer MoS2 with S vacancies increase.

2014 Elsevier B.V. All rights reserved.

xagonal structure is anunique physical and

f applications including, biomedicine, sensing,

defects have a strong inuence on geometric structures, electronicstructures, magnetic properties, optical characteristics and so on[2328]. However, few literatures have reported the effect ofvacancies on properties of monolayer MoS2. Makarova et al. [29]have investigated selective adsorption of thiol molecules atS-vacancies on MoS2 (0001). Ataca et al. [30,31] have calculatedKeywords:Monolayer MoS2

relaxation. Electronic analysis implies that the band gaps of defective monolayer MoS2 are smaller thanthat of perfect one. After introduction of neutral S-vacancy, monolayer MoS2 has changed from direct toEffect of vacancies on structural, electronproperties of monolayer MoS2: A rst-pr

Li-ping Feng , Jie Su, Zheng-tang LiuState Key Lab of Solidication Processing, College of Materials Science and Engineering,

a r t i c l e i n f o

Article history:Received 7 January 2014Received in revised form 22 May 2014Accepted 3 June 2014Available online 11 June 2014

a b s t r a c t

Effects of vacancies on struusing rst-principles planeshow that the band structhe available experimentalvacancies show an outwar

journal homepage: wwwand opticalciples study

hwestern Polytechnical University, Xian, Shaanxi 710072, China

ral, electronic and optical properties of monolayer MoS2 were investigatedave pseudopotential method based on density functional theory. Resultsand band gap of perfect monolayer MoS2 are in good agreement with

d theoretical data. Structural analysis indicates that ions surrounding Molaxation, while that ions surrounding S vacancies exhibit slightly inwardle at ScienceDirect

nd Compounds

include Mo 4p6 4d5 5s1 electrons and S 3s2 3p4 electrons. The plane-wave cutoffenergy was set to be 380 eV after extensive convergence analysis. The Brillouin-zoneintegration was performed over the 5 5 2 grid sizes using the MonkorstPackmethod, where the self-consistent convergence of the total energy is5.0 106 eV/atom. The optimized primitive lattice constants a = 3.17 andc = 12.32 for bulk MoS2 are in good agreement with other theoretical data(a = 3.17 , c = 12.58 [34], a = 3.16 , c = 12.29 [35]) and experimental values(a = 3.20 , c = 12.29 [36]). A 4 4 supercell of 48 atoms was constructed fordefect-free monolayer MoS2 (shown in Fig. 1(a)). A 12 vacuum region was usedto separate the two dimensional single layers ofMoS2 along the c axis to hinder inter-layer coupling [37]. To introduce an isolated vacancy, an Mo or S atoms is removedfrom the host supercell, respectively. The large supercell size separates the two adja-cent defects over 10 , which is sufcient to neglect the articial Coulomb interac-tion between the defects [38,39]. The charge states of vacancies were controlled byadjusting the background charge of crystals. Defective monolayer MoS2 with singleMo and S vacancy was presented in Fig. 1(b) and (c), respectively.

3. Results and discussion

still remains direct band gap. Fig. 3 presents the calculated bandgaps for monolayer MoS2 with neutral and charged vacancies. Itcan be seen that the band gaps of defective monolayer MoS2 are

Table 1Distances from charged vacancy (Vyx , x is Mo or S atom, y represents the charge statesof vacancy) to the neighboring atoms for monolayer MoS2 before and after thestructural relaxation. Neighboring atomic species, their coordination numbers and therelaxations in % are also shown in parentheses.

Vacancies Distance in (atomic species coordination number)First NN Second NN

Mo (perfect) 2.41 (S 6) 3.16 (Mo 6)V0Mo 2.45 (1.6%) 3.18 (0.6%)

V1Mo 2.45 (1.6%) 3.18 (0.6%)

V2Mo 2.46 (1.9%) 3.18 (0.6%)

V3Mo 2.45 (1.6%) 3.19 (0.9%)

V4Mo 2.45 (1.6%) 3.20 (1.3%)

S (perfect) 2.41 (Mo 3) 3.16 (S\caxis 6,Skcaxis 1)V0S 2.40 (0.4%) 3.11 (1.5%)1

L.-p. Feng et al. / Journal of Alloys and Compounds 613 (2014) 122127 1233.1. Structural properties

Vacancies in monolayer MoS2 can lead to its structural relaxa-tion. Table 1 lists the distances from charged vacancy to the neigh-boring ions for monolayer MoS2 before and after structuralrelaxation. For Mo vacancy, ions surrounding the Mo-vacancyshow an outward relaxation because of the ionic size and chargeeffects [40]. Additionally, the outward relaxations of the rst near-est neighbor (NN) S ions are larger than those of the second NN Moions. For example, the outward relaxation of the rst NN S ions andthe second NNMo ions for V0Mo is about 1.6% and 0.6%, respectively.When the charge states of Mo vacancies increase, the second NNMo ions exhibit more outward relaxations due to the increasingelectrostatic interactions between the vacancy and the secondNN Mo ions [41]. In the case of V4Mo, the second NN Mo ions(1.3%) undergo almost twice higher relaxation than that of V0Mo(0.6%). However, the distances from the rst NN S ions to Mo-vacancy almost maintain 2.45 with the increasing charge statesof Mo-vacancy because of the signicant electrostatic repulsionsbetween the rst NN S ions [40]. For S vacancy, the ions surround-ing the S-vacancy exhibit slightly inward relaxation. That was alsoobserved in many materials when whose big size ion is removed toform vacancy [4043]. In addition, the inward relaxations of thesecond NN S ions are larger than those of the rst NN Mo ionsdue to the decreased electrostatic repulsions between the secondNN S ions and the S-vacancy [43]. For example, the inward relaxa-tion of the rst NN Mo ions and the second NN S ions for V0S isabout 0.4% and 1.5%, respectively. Moreover, both the rst and sec-ond NN ions undergo more inward relaxation with the increasingcharge states of S vacancies. In the case of V2S , the relaxation ofthe rst and second NN ions reaches 1.2% and 2.2%, respectively.Fig. 1. Atomic congurations of monolayer MoS2. (a) Defect-free monolayer MoS2, (The above phenomena are further conrmed by the following Mul-liken atomic population analysis.

3.2. Electronic properties

Fig. 2 shows the band structures and density of states (DOS) ofperfect and defective monolayer MoS2. As shown in Fig. 2(a), thecalculated direct band gap for perfect monolayer MoS2 is about1.78 eV, which is in good agreement with other theoretical values(1.80 eV [35,16], 1.70 eV [44]) and experimental data (1.98 eV [45],1.90 eV [37]). Additionally, bottom of conduction bands and top ofvalence bands for perfect monolayer MoS2 mainly consist of thehybridization from Mo 4d and S 3p orbitals, which is consistentwith previous calculational results [30,46,47]. The band structuresfor monolayer MoS2 with neutral S- and Mo-vacancy are shown inFig. 2(b) and (c), respectively. The conduction and valence bands ofmonolayer MoS2 with vacancies are composed predominantly ofthe strong hybridization from Mo 4d and S 3p orbitals. The calcu-lated band gaps for monolayer MoS2 with neutral Mo and Svacancy are 1.63 and 1.74 eV, respectively. It should be noted thatmonolayer MoS2 has changed from direct to indirect band gap afterthe introduction of neutral S-vacancy because the relaxation ofadjacent surrounding atoms of S-vacancy induces the variation ofthe Mo 4d symmetry and the trigonal crystal eld around Mo[39,48,49]. In contrast, monolayer MoS2 with neutral Mo-vacancy

VS 2.38 (1.2%) 3.10 (1.8%)

V2S 2.38 (1.2%) 3.09 (2.2%)b) monolayer MoS2 with Mo vacancy and (c) monolayer MoS2 with S vacancy.

Fig. 3. The calculated band gaps for perfect monolayer MoS2 and defective

and Compounds 613 (2014) 122127124 L.-p. Feng et al. / Journal of Alloyssmaller than that of perfect monolayer MoS2. With the increasingcharge states of vacancies, the band gap of monolayer MoS2 withMo-vacancy decreases rapidly, while the band gap of monolayerMoS2 with S-vacancy decreases comparatively slowly.

Moreover, as shown in Fig. 2(b) and (c), the vacancy defects alsointroduce defect energy levels in the band gap. The calculateddefect energy levels for the neutral and charged vacancies inmonolayer MoS2 are shown in Fig. 4. For Mo vacancies, the defectenergy levels of 0, 1-, 2-, 3-, and 4- charge states lie at 0.11, 0.23,0.37, 0.46, and 0.69 eV, respectively. It is clear that the defectenergy levels become deeper with the increasing charge states ofMo vacancies. All the defect energy levels generated by Mo vacan-cies locate near the valence band maximum, suggesting that Movacancies induce acceptor-like levels in the band gap. Hence, Movacancies might trap the electrons from the valence bands. For Svacancies, the defect energy levels of 0, 1+, and 2+ charge stateslie at 0.40, 0.60, and 0.67 eV, respectively. As the charge states ofS vacancies increase, the defect energy levels become deeper. Addi-tionally, all the defect energy levels caused by S vacancies are closeto the conduction band minimum, implying that donor-like levelsare formed and that the electrons of S vacancies might tunnel intothe conduction bands.

Fig. 2. The band structures and DOS for perfect monolayer MoS2 (a), monolayerMoS2 with neutral Mo-vacancy (b), and monolayer MoS2 with neutral S-vacancy (c).To further investigate the electronic structure, Mulliken popula-tion of SMo bonding in monolayer MoS2 was analyzed. Mullikenpopulation can determine the type of bond and its magnitude, ahigh positive value of bond population means the type of the bondis dominated by covalency, and a value of zero presents a perfectionic bond [50]. Mulliken population of SMo bonding in bulk2HMoS2 was reported to be about 0.25, which indicates a cova-lent character of SMo bonding [51]. For perfect monolayerMoS2, the calculated Mulliken population of SMo bonding isabout 0.37 which is bigger than the value of 0.25 of bulk 2HMoS2 [51], showing that the SMo bonding also has a covalentcharacter. Moreover, the excess charge on each S atom and thedepletion of electrons on each Mo atom were calculated to be0.17 and 0.34e, respectively, implying that the SMo bonding inperfect monolayer MoS2 also exhibits partially ionic character,which is consistent with previous theoretical report [30]. TheMulliken population and bond length of SMo bonding aroundvacancies are shown in Fig. 5. The overlap population becomesgreater and the bond length becomes shorter for the rst NNSMo bonding around vacancies compared with those of SMobonding in perfect monolayer MoS2, indicating that vacanciesenhance the covalent character of the SMo bonding. Obviously,the variations for SMo bondings aroundMo-vacancy are more sig-nicant than those for SMo bondings around S-vacancy, which

monolayer MoS2 with charged vacancies.may relate to the large relaxation of geometric structure whenthe Mo-vacancy forms. Nevertheless, as the distance from SMo

Fig. 4. Calculated defect energy levels for the neutral and charged vacancies inmonolayer MoS2. The positions of the energy levels are given with respect to theVBM in the case of VMo, while those from the CBM in the case of VS. The value of theperfect monolayer MoS2 is set to zero.

bonding to vacancy increases, the variations of the SMo bondingbecome weak.

Charge densities can further examine the change of chemicalbonding around vacancies. Fig. 6 presents the charge densities ofSMo bonding in perfect and defective monolayer MoS2. Comparedwith the charge densities of SMo bonding in perfect monolayerMoS2, the charge densities of the rst NN SMo bonding aroundvacancies become higher, suggesting that the covalent charactersof the SMo bondings are strengthened when vacancies formed[52]. Additionally, it can be seen that the charge densities ofSMo bondings around Mo-vacancy have more signicant changesthan those of SMo bondings around S-vacancy. Furthermore, thecharge densities of the SMo bondings decrease when the distancefrom SMo bonding to vacancy increases. These results are consis-

3.3. Optical properties

The optical properties of perfect and defective monolayer MoS2have been calculated in the polarization direction of (100). 12unoccupied states and the Gaussian broadening with a width of0.5 eV were used for the optical spectra calculations after extensiveanalysis. The imaginary parts of complex dielectric function ofmonolayer MoS2 with Mo and S vacancies are shown in Fig. 7(a)and (b), respectively. For the imaginary part of perfect monolayerMoS2, there are three peaks in the energy regions from 0 to20 eV, which are the absorptive transitions from the valence bandsto the conduction bands. These peaks are labeled A, B and C,respectively. According to the analysis of the electronic structure,peak A originates mainly from the transitions of S 3p into Mo 4d

Fig. 5. Mulliken population and bond length of SMo bonding around Mo-vacancy (a) and S-vacancy (b). The atoms serial number is indexed in Fig. 1(b) and (c).

L.-p. Feng et al. / Journal of Alloys and Compounds 613 (2014) 122127 125tent with the above Mulliken population analysis.Fig. 6. The charge density contour prole of SMo bondings. (a) The SMo bonding in perg) the adjacent SMo bondings around S-vacancy. The atoms serial number is indexedconduction bands [53]. Peak B originates mainly from thefect monolayer MoS2, (bd) the adjacent SMo bondings aroundMo-vacancy and (ein Fig. 1(b) and (c).

f m

andFig. 7. The imaginary parts of complex dielectric function o

126 L.-p. Feng et al. / Journal of Alloyshybridization orbitals between S 3p and Mo 4d into Mo 4d conduc-tion bands [21,54]. And peak C originates mainly from r bondingbetween S 3p and Mo 5s into Mo 4d conduction bands [55]. Theimaginary parts of defective monolayer MoS2 have similar proleswith that of perfect one, but they move slightly toward lowerenergies because of the localized effects of vacancies [28,56]. Addi-tionally, extra peaks appear at low energy in the imaginary parts ofdefective monolayer MoS2, which may be ascribed to the danglingbonds and defective states formed after the removal of atom.

The real parts of complex dielectric function and static dielec-tric constants of prefect and defective monolayer MoS2 are shownin Fig. 8. The calculated static dielectric constant of perfect mono-layer MoS2 is about 1.50, which is consistent with other theoreticalvalue of 1.26 [14] calculated by GGA but a little smaller than thetheoretical value of 3.0 [57] calculated by LDA. It is obvious fromFig. 8(a) that the static dielectric constants of monolayer MoS2 withMo vacancies are larger than that of perfect one. Moreover, mono-layer MoS2 with neutral Mo vacancy has the largest static dielectricconstant of about 2.45. As the charge states of Mo vacanciesincrease, the static dielectric constants of defective monolayerMoS2 decrease, and the variation of the static dielectric constantsis satised to Penns model [58]. In Fig. 8(b), the static dielectricconstant of monolayer MoS2 with neutral S vacancy is found tobe about 1.50, which is the same as that of perfect monolayerMoS2. Nevertheless, the static dielectric constants of monolayerMoS2 with charged S vacancies are higher than that of perfectone. In contrast to monolayer MoS2 with Mo vacancies, the staticdielectric constants of monolayer MoS2 with S vacancies show a

Fig. 8. The real parts of complex dielectric function of monolayer MoS2 with Mo vacancieMoS2 and defective monolayer MoS2 with different charge states.onolayer MoS2 with Mo vacancies (a) and S vacancies (b).

Compounds 613 (2014) 122127growing tendency with the increasing positive charge states of Svacancies.

4. Conclusion

In summary, the structural, electronic and optical properties ofmonolayer MoS2 with charged vacancies have been investigatedusing the rst-principles calculations. Results show that the bandstructure and band gap of perfect monolayer MoS2 consist wellwith experimental and previous calculational data. Structuralrelaxation is found in the monolayer MoS2 with vacancies. Ionssurrounding Mo vacancies show an outward relaxation while ionssurrounding S vacancies exhibit slightly inward relaxation. Bandstructure, band gap, Mulliken population, and charge density ofperfect and defective monolayer MoS2 were analyzed. The bandgaps of monolayer MoS2 with vacancies are smaller than that ofperfect monolayer MoS2. After introduction of neutral S-vacancy,monolayer MoS2 has changed from direct to indirect band gap.Mo vacancies induce acceptor-like levels and p-type conductivi-ties, whereas S vacancies introduce donor-like levels and n-typeconductivities. With the increasing charge states of vacancies, theband gaps become smaller and the defect energy levels becomedeeper. The complex dielectric functions of perfect and defectivemonolayer MoS2 were obtained. Vacancies induce extra peaks atlow energy in the real and imaginary parts of complex dielectricfunctions of defective monolayer MoS2. The calculated staticdielectric constant of perfect monolayer MoS2 is about 1.50. Themonolayer MoS2 with neutral Mo vacancy has the largest static

s (a) and S vacancies (b). Inset is the static dielectric constant for perfect monolayer

dielectric constant of about 2.45, while the monolayer MoS2 withneutral S vacancy has the same static dielectric constant with per-fect monolayer MoS2. Furthermore, with the increasing chargestates of vacancies, the static dielectric constants of monolayerMoS2 with Mo vacancies decrease, whereas the static dielectricconstants of monolayer MoS2 with S vacancies increase.

Acknowledgements

We acknowledge the National Natural Science Foundation ofChina under grant No. 61376091, the Natural Science Foundationof Shaanxi Province under grant No. 2012JM6012, the Fundamen-tal Research Funds for the Central Universities under grant No.3102014JCQ01033 and the 111 Project under grant No. B08040.

Reference

[1] B. Hinnemann, P. Moses, J. Bonde, K. Jorgensen, J. Nielsen, S. Horch, I.Chorkendorff, J. Norskov, J. Am. Chem. Soc. 127 (2005) 5308.

[2] T.F. Jaramillo, K.P. Jorgensen, J. Bonde, J.H. Nielsen, S. Horch, I. Chorkendorff,Science 317 (2007) 100.

[3] G. Kline, K. Kam, R. Ziegler, B. Parkinson, Sol. Energy Mater. 6 (1982) 337.[4] Y. Li, H. Wang, L. Xie, Y. Liang, G. Hong, H. Dai, J. Am. Chem. Soc. 133 (2011)

[20] Q. Yue, J. Kang, Z.Z. Shao, X.A. Zhang, S.L. Chang, G. Wang, S.Q. Qin, J.B. Li, Phys.Lett. A 376 (2012) 1166.

[21] A. Kumar, P.K. Ahluwalia, Mater. Chem. Phys. 135 (2012) 755.[22] N.A. Dhas, K.S. Suslick, J. Am. Chem. Soc. 127 (2005) 2368.[23] D. Kurbatov, V. Kosyak, A. Opanasyuk, V. Melnik, Physica B 404 (2009) 5002.[24] X.J. He, T. He, Z.H. Wang, M.W. Zhao, Physica E 42 (2010) 2451.[25] A.G.M. Das, C. Nyamhere, F.D. Auret, M. Hayes, Surf. Coat. Technol. 203 (2009)

2628.[26] I.A. Buyanova, B. Monemat, J.L. Lindstrom, T. Hallberg, L.I. Murin, V.P.

Markevich, Mater. Sci. Eng. B 72 (2000) 146.[27] D.P. Zhang, J.D. Shao, H.J. Qi, M. Fang, K. Yi, Z.X. Fan, Opt. Laser Technol. 38

(2006) 654.[28] J.J. Thevaril, S.K. Oleary, Solid State Commun. 150 (2010) 1851.[29] M. Makarova, Y. Okawa, M. Aono, J. Phys. Chem. C 116 (2012) 22411.[30] C. Ataca, S. Ciraci, J. Phys. Chem. C 115 (2011) 13303.[31] C. Ataca, H. Sahin, E. Akturk, S. Ciraci, J. Phys. Chem. C 115 (2011) 3934.[32] J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, C.

Fiolhais, Phys. Rev. B 46 (1992) 6671.[33] M.D. Segall, P.J.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, J.

Phys.: Condens. Matter 14 (2002) 2717.[34] T.S. Li, G. Galli, J. Phys. Chem. C 111 (2007) 16192.[35] T. Boker, R. Severin, A. Muller, C. Janowitz, R. Manzke, Phys. Rev. B 64 (2001)

235305.[36] K.F. Mak, C.G. Lee, J. Hone, J. Shan, T.F. Heinz, Phys. Rev. Lett. 105 (2010)

136805.[37] Q. Yue, S. Chang, S. Qin, J. Li, Phys. Lett. A 377 (2013) 162.[38] L.N. Kantorovich, Phys. Rev. B 60 (1999) 15476.[39] D. Liu, Y. Guo, L. Fang, J. Robertson, Appl. Phys. Lett. 103 (2013) 183113.

L.-p. Feng et al. / Journal of Alloys and Compounds 613 (2014) 122127 1277296.[5] H. Wu, R. Yang, B. Song, Q. Han, J. Li, Y. Zhang, Y. Fang, R. Tenne, C. Wang, ACS

Nano 5 (2011) 1276.[6] M. De, S. Rana, H. Akpinar, O.R. Miranda, R.R. Arvizo, U.H.F. Bunz, V.M. Rotello,

Nat. Chem. 1 (2009) 461.[7] N. Yaacobi-Gross, M. Soreni-Harari, M. Zimin, S. Kababya, A. Schmidt, N.

Tessler, Nat. Mater. 10 (2011) 974.[8] H. Holscher, D. Ebeling, U.D. Schwarz, Phys. Rev. Lett. 101 (2008) 246105.[9] C.G. Lee, Q.Y. Li, W. Kalb, X.Z. Liu, H. Berger, R.W. Carpick, J. Hone, Science 328

(2010) 76.[10] E. Gourmelon, O. Lignier, H. Hadouda, G. Couturier, J.C. Bermede, J. Tedd, J.

Pouzet, J. Salardenne, Sol. Energy Mater. 46 (1997) 115.[11] B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti, A. Kis, Nat. Nanotechnol.

6 (2011) 147.[12] W.Z. Bao, X.H. Cai, D. Kim, K. Sridhara, M.S. fuhrer, Appl. Phys. Lett. 102 (2013)

042104.[13] Z.Y. Yin, H. Li, H. Li, L. Jiang, Y.M. Shi, Y.H. Sun, G. Lu, Q. Zhang, X.D. Chen, H.

Zhang, ACS Nano 6 (2012) 74.[14] C. Ataca, M. Topsakal, E. Akturk, S. Ciraci, J. Phys. Chem. C 115 (2011) 16354.[15] C. Ataca, H. Sahin, S. Ciraci, J. Phys. Chem. C 116 (2012) 8983.[16] S. Lebegue, O. Eriksson, Phys. Rev. B 79 (2009) 115409.[17] E.S. Kadantsev, P. Hawrylak, Solid State Commun. 152 (2012) 909.[18] X.D. Li, S. Yu, S.Q. Wu, Y.H. Wen, S. Zhou, Z.Z. Zhu, J. Phys. Chem. C 117 (2013)

15347.[19] X.D. Li, J.T. Mullen, Z.H. Jin, K.M. Borysenko, M.B. Nardelli, K.W. Kim, Phys. Rev.

B 87 (2013) 115418.[40] K. Matsunaga, T. Tanaka, T. Yamamoto, Phys. Rev. B 68 (2003) 085110.[41] T. Tanaka, K. Matsunaga, Y. Ikuhara, T. Yamamoto, Phys. Rev. B 68 (2003)

205213.[42] F.F. Ge, W.D. Wu, X.M. Wang, H.P. Wang, Y. Dai, H.B. Wang, J. Shen, Physica B

404 (2009) 3814.[43] X. Luo, B. Wang, Y. Zheng, Phys. Rev. B 80 (2009) 104115.[44] J.V. Lauritsen, J. Kibsgaard, H. Topsoe, B.S. Clausen, E. Laegsgaard, F.

Besenbacher, Nat. Nanotechnol. 2 (2007) 53.[45] A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C.Y. Chim, G. Galli, F. Wang, Nano

Lett. 10 (2010) 1271.[46] A. Kumar, P.K. Ahluwalia, Eur. Phys. J. B 85 (2012) 186.[47] N. Singh, G. Jabbour, U. Schwingenschlgl, Eur. Phys. J. B 85 (2012) 392.[48] J.R. Hahn, H. Kang, Phys. Rev. B 60 (1999) 6007.[49] J.R. Hahn, H. Kang, Phys. Rev. B 53 (1996) 1725.[50] R.S. Mulliken, J. Chem. Phys. 23 (1955) 1833.[51] T. Toforova, V. Alexiev, R. Prins, T. Weber, Phys. Chem. Chem. Phys. 6 (2004)

3023.[52] J.H. Yao, Y.W. Li, N. Li, S.R. Le, Physica B 407 (2012) 3888.[53] H. Shi, H. Pan, Y.W. Zhang, B.I. Yakobson, Phys. Rev. B 87 (2013) 155304.[54] A.H. Reshak, S. Auluck, Phys. Rev. B 68 (2003) 125101.[55] J.V. Acrivos, W.Y. Liang, J.A. Wilson, J. Phys. C: Solid State Phys. 4 (1971) L18.[56] H. Qiu, T. Xu, Z. Wang, W. Ren, H. Nan, Z. Ni, et al., Nat. Commun. 4 (2013)

2642.[57] A. Kumar, P.K. Ahluwalia, Physica B 407 (2012) 4627.[58] D.R. Penn, Phys. Rev. B 128 (1962) 2091.

Effect of vacancies on structural, electronic and optical properties of monolayer MoS2: A first-principles study1 Introduction2 Computational details3 Results and discussion3.1 Structural properties3.2 Electronic properties3.3 Optical properties

4 ConclusionAcknowledgementsReference