# The effect of strain on the electronic properties of MoS2 monolayers

• Park, Soon-Dong ;
• Kim, Sung Youb
• Accepted : 2015.11.04
• Published : 2016.01.25
• 21 0

#### Abstract

We utilize first-principles calculations within density-functional theory to investigate the possibility of strain engineering in the tuning of the band structure of two-dimensional $MoS_2$. We find that the band structure of $MoS_2$ monolayers transits from direct to indirect when mechanical strain is applied. In addition, we discuss the change in the band gap energy and the critical stains for the direct-to-indirect transition under various strains such as uniaxial, biaxial, and pure shear. Biaxial strain causes a larger change, and the pure shear stain causes a small change in the electronic band structure of the $MoS_2$ monolayer. We observe that the change in the interaction between molecular orbitals due to the mechanical strain alters the band gap type and energy.

#### Keywords

molybdenum disulfide;density functional theory;mechanical strain;band gap engineering

#### References

1. Novoselov, K.S. (2004), "Electric field effect in atomically thin carbon films", Science, 306(5696), 666-669. https://doi.org/10.1126/science.1102896
2. Novoselov, K.S. and Geim, A.K. (2005), "Two-dimensional gas of massless dirac fermions in graphene", Nature, 438(7065), 197-200. https://doi.org/10.1038/nature04233
3. Zhang, Y.B., Tan, Y.W. and Stromer, H.L. (2005), "Experimental observation of the quantum hall effect and berry's phase in graphene", Nature, 438(7065), 201-204. https://doi.org/10.1038/nature04235
4. Lee, C., Wei, X.D. and Kysar, J.W. (2008), "Measurement of the elastic properties and intrinsic strength of monolayer graphene", Science, 321(5887), 385-388. https://doi.org/10.1126/science.1157996
5. Dan, Y.P., Lu, Y. and Kybert, N.J. (2009), "Intrinsic response of graphene vapor sensors", Nano Lett., 9(4), 1472-1475. https://doi.org/10.1021/nl8033637
6. Kim, S.Y. and Park, H.S. (2010), "On the utility of vacancies and tensile strain-induced quality factor enhancement for mass sensing using graphene monolayers", Nanotech., 21(10), 105710. https://doi.org/10.1088/0957-4484/21/10/105710
7. Mak, K.F., Lee, C. and Hone, J. (2010), "Atomically thin $MoS_2$: a new direct-gap semiconductor", Phys. Rev. Lett., 105(13), 136805. https://doi.org/10.1103/PhysRevLett.105.136805
8. Radisavljevic, B. Radenovic, A. and Giacometti, V. (2011), "Single-layer $MoS_2$ transistor", Nature Nanotech., 6(3), 147-150. https://doi.org/10.1038/nnano.2010.279
9. Obradovic, B., Kotlyar, R. and Heinz, F. (2006), "Analysis of graphene nanoribbons as a channel material for field-effect transistors", Appl. Phys. Lett., 88(14), 142102. https://doi.org/10.1063/1.2191420
10. Kress, G. and Hafner, J. (1993), "Ab initio molecular dynamics for open-shell transition metals", Phys. Rev. B, 48(17), 13115. https://doi.org/10.1103/PhysRevB.48.13115
11. Kress, G. and Furthmuller, J. (1996a), "Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set", Mat. Sci., 6(1), 15-50.
12. Kress, G. and Furthmuller, J. (1996b), "Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set", Phys. Rev. B, 54(16), 11169. https://doi.org/10.1103/PhysRevB.54.11169
13. Perdew, J.P. and Zunger, A. (1981), "Self-interaction correction to density-functional approximations for many-electron systems", Phys. Rev. B, 23(10), 5048. https://doi.org/10.1103/PhysRevB.23.5048
14. Perder, J.P. and Chevary, J.A. (1992), "Atoms, molecules, solids, and surfaces: applications of the generalized gradient approximation for exchange and correlation", Phys. Rev. B, 46(11), 6671. https://doi.org/10.1103/PhysRevB.46.6671
15. Vanderbit, D. (1990), "Soft self-consistent pseudopotentials in a generalized eigenvalue formalism", Phys. Rev. B, 41(11), 7892. https://doi.org/10.1103/PhysRevB.41.7892
16. Bloch, P.E. (1994), "Projector augmented-wave method", Phys. Rev. B, 50(24), 17953. https://doi.org/10.1103/PhysRevB.50.17953
17. Monkhorst, H.J. and Pack, J.D. (1976), "Special points for brillouin-zone integrations", Phys. Rev. B, 13(12), 5188. https://doi.org/10.1103/PhysRevB.13.5188
18. Ataca, C. and Ciraci, S. (2011), "Functionalization of single-layer $MoS_2$ honeycomb structures", J. Phys. Chem. C, 115(27), 13303-13311. https://doi.org/10.1021/jp2000442
19. Joensen, P. and Crozier, E.D. (1987), "A study of single-layer and restacked $MoS_2$ by x-ray diffraction and x-ray absorption spectroscopy", J. Phys. C: Solid State Phys., 20(26), 4043-4053. https://doi.org/10.1088/0022-3719/20/26/009
20. Kam, K.K. and Parkinson, B. (1982), "Detailed photocurrent spectroscopy of the semiconducting group VIB transition metal dichalcogenides", J. Phys. Chem., 86(4), 463-467. https://doi.org/10.1021/j100393a010
21. Yun, W.S., Han, S.W. and Hong, S.C. (2012), "Thickness and strain effects on electronic structures of transition metal dichalcogenides: 2H-$MX_2$ semiconductors (M=Mo, W; X=S, Se, Te)", Phys. Rev. B, 85(3), 033305. https://doi.org/10.1103/PhysRevB.85.033305

#### Cited by

1. Strain-Induced Optimization of Nanoelectromechanical Energy Harvesting and Nanopiezotronic Response in a MoS2 Monolayer Nanosheet vol.121, pp.17, 2017, https://doi.org/10.1021/acs.jpcc.7b01970
2. Nanoscale-Barrier Formation Induced by Low-Dose Electron-Beam Exposure in Ultrathin MoS2 Transistors vol.10, pp.10, 2016, https://doi.org/10.1021/acsnano.6b05952
3. The effects of strain on DC transverse and spin-valley Hall conductivity of ferromagnetic MoS 2 and silicene vol.426, 2017, https://doi.org/10.1016/j.jmmm.2016.10.158

#### Acknowledgement

Supported by : National Research Foundation (NRF)
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