Stability of direct band gap under mechanical strains for monolayer MoS2, MoSe2, WS2 and WSe2
Introduction
The transition-metal dichalcogenides (TMDs), such as MoS2, MoSe2, WS2 and WSe2 have attracted much attention owing to their superior electronic, optical, mechanical and catalytic properties [[1], [2], [3], [4], [5], [6], [7], [8]]. It has been found that the monolayer TX2 type (T, transition-metal atom; X, chalcogen atom) have several distinctive electronic and optical properties including a direct band gap (the band gap is in the range of 1.1–2.0 eV) at the K point in the Brillouin zone [[9], [10], [11]], strong photoluminescence effects [[12], [13], [14], [15]] and the possibility of full optical control of the valley and spin occupation [[16], [17], [18], [19]]. These properties will significantly enhance the potential of using them in various applications such as pressure sensors [20], fast photodetection [21], and nanoelectromechanical systems (NEMS) devices [22].
Due to their important semiconducting properties, the band structures were extensively investigated in the past. A vast number of first-principles calculations [11,[23], [24], [25], [26], [27]] and experiments [28] have been reported that under large mechanical strains, the band gap of the monolayer TX2 changes from direct type to indirect type, more specifically the band gap has been narrowed, eventually leading to the CBM (conduction band minimum) plunge to below the Fermi level, which implicates that the material becomes exhibiting metal properties. Applying mechanical strains is one of the most promising ways to tune the band gap of the monolayer TX2. However, a few theoretical groups reported the relationship between the Young's modulus and the deformation region of direct band gap [26,29]. The study on the directional dependence of the mechanical strain has not been conducted so far [11,26]. Hence the critical issue is to conduct a thorough investigation to unveil the relation between their mechanical properties and electronic properties.
In this work, we simulate the Young's modulus of monolayer TX2 cells and investigate the band structures of hexagonal and orthorhombic monolayer TX2 cells under a wide range of strain amplitudes in different directions using first-principles methods. This theoretical method has been used in many previous studies in TMDs [[23], [24], [25], [26], [27]]. Our aim is to theoretically explore the relationship between the Young's modulus and the width of the direct band gap region. Furthermore, the directional properties of strains acting on the orthorhombic monolayer TX2 cells will also be explored. The effect of Young's modulus and various directions of strains on the monolayer TX2 will be detailed in the following sections of this paper. The phonon spectral properties of these four materials have been studied in Ref. [11], and our focus was not on studying this property. We also neglect other properties which could be extracted from DFT, as it was simulated, for examples, in Refs. [30,31] for similar zigzag sheet monolayers with high Young's modulus and strong mechanical anisotropy.
Section snippets
Computational method
We start modelling the monolayer TX2. By creating two types of crystal cells using the Atomistix ToolKit (ATK) [32] simulation tools, the lattice constants and key bond lengths/angles calculated are listed in Table 1. Based on the lattice constant of Table 1, the initial model of monolayer TX2 are established. Shown in Fig. 1, the monolayer TX2 can be viewed as composed of two-dimensional (2D) X-T-X sheets stacked on top of one another. Each T atom is bonded to six X atoms located in the top
Simulation results and discussion
We calculated band structures for various amplitudes of biaxial symmetric compressive and tensile strains on the monolayer TX2 hexagonal cell, as show in Fig. 3, Fig. 4, respectively. The bold black lines are the band when no strain is applied. At equilibrium, the monolayer TX2 are direct band gap semiconductors with the conduction band minimum (CBM) and valence band maximum (VBM) at K point. Under strains (Fig. 3, Fig. 4), the conduction band is decreasing and the valence band is increasing as
Conclusion
To summarize, the first-principles methods have been used to investigate the electronic and mechanical properties of four monolayer TMD materials - MoS2, MoSe2, WS2 and WSe2. Hexagonal and orthorhombic cell structures of all these materials have been built and subsequently simulated when subjecting to tensile and compressive strains. Main conclusion is deduced that the region of the direct band gap in the CBM-strain curves exhibiting a trend of Rd-WS2 < Rd-MoS2 < Rd-WSe2 < Rd-MoSe2, which has
Acknowledgement
Authors would like to acknowledge China Scholarship Council for support.
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