Mechanical and electronic properties of monolayer MoS2 under elastic strain
Highlights
► We study the elastic and electronic properties of monolayer MoS2 under strain. ► The in-plane stiffness and Poissonʼs ratio are revealed. ► The band gap undergoes a descent trend as strain increasing. ► Direct-to-indirect and semiconductor-to-metal transitions are observed.
Introduction
Molybdenum disulfide, MoS2, unique semiconductor with honeycomb structure offers many remarkable mechanical, optical and electronic properties. The three-dimensional bulk MoS2 has been widely studied for promising application in tribology [1], [2], hydrogen production [3], [4], solar cells [5] and photocatalysis [6]. In recent years, motivated by the discovery of graphene [7], [8], and especially the report of monolayer MoS2 transistor [9], two-dimensional monolayer MoS2 has attracted more researcherʼs attention and been a topic of interest.
Experimentally, monolayer MoS2 can be produced using scotch tape [10] or chemical bath deposition method [11]. Superlubricity [12], [13] and photoluminescence [14] emerging from MoS2 sheet were observed. Theoretical researches on properties of monolayer MoS2 and its related structures either have been done using first-principles calculation, such as band gap [15], [16], functionalization through adatom adsorption and vacancy defect [17], [18] and stability of structures [19]. To date, lots of works about MoS2 have been gained, however some questions are still worth studying. For example, the electronic properties of monolayer MoS2 under strain have not been investigated. Current studies have confirmed that the properties of low-dimensional materials can be modified by strain [20], [21], [22], therefore, the response of electronic properties of monolayer MoS2 to the strain would be an interesting issue for discussion. Besides, Ref. [23] has reported relevant elastic constant of monolayer MoS2, but the Poissonʼs ratio which also exhibits the elastic property is not revealed. Hence, a repeated calculation is necessary.
In this Letter, we study the elastic and electronic properties of monolayer under elastic tensile strain from first-principles calculations. The elastic constants of monolayer are revealed using strain energy calculations in the harmonic elastic strain range. Band structure of monolayer MoS2 for the equilibrium case is discussed, both by GGA and hybrid functional method. Then, with the strain applied, it is shown that, the band gap of monolayer MoS2 is tuned as strain increasing. Meanwhile, direct-to-indirect and semiconductor-to-metal transitions are observed. Furthermore, the effective mass of carriers is also studied.
Section snippets
Computational method
First-principles plane-wave calculations within density-functional theory (DFT) using projector-augmented wave (PAW) potentials [24] were performed. The exchange correlation potential was approximated by generalized gradient approximation using Perdew–Wang 91 functional (GGA-PW91) [25]. After energy convergence analysis, a plane-wave basis set with kinetic energy cutoff of 400 eV and Brillouin zone (BZ) sampling with Monkhorst–Pack (MP) method [26] of k-points were chosen. The structures
Results and discussion
As is well known, the two-dimensional monolayer MoS2 consists of a monatomic Mo plane between two monatomic S planes like a sandwich structure. Mo and S atoms alternatively occupy corners of a hexagon. Each S atom is covalently bonded with three nearest Mo atoms, while Mo atom is bonded with six nearest S atoms [30]. Structure optimization shows that, the hexagonal lattice constant , the length of MoS bonds , and the thickness of MoS2 monolayer . Our
Conclusion
In this study, the elastic constants of two-dimensional monolayer MoS2 are revealed in the harmonic elastic strain range using strain energy calculation. The calculated in-plane stiffness and Poissonʼs ratio are determined to be 123 N/m and 0.25, indicating that the monolayer MoS2 is much softer than graphene. At the equilibrium state, monolayer MoS2 is found to have band gap of 1.65 and 2.12 eV, obtained both by the GGA-91 and HSE06 functionals, respectively. With tensile strain applied in the
Acknowledgements
J.L. gratefully acknowledges financial support from the “Hundred Talents Program” of Chinese Academy of Science and National Science Fund for Distinguished Young Scholar (grant No. 60925016). This work is supported by the National Natural Science Foundation of China (NSFC) (grant No. 11104347 and No. 11104349) and Advanced Research Foundation of National University of Defense Technology (grant No. JC-02-19).
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