- NANO EXPRESS
- Open Access
Dispersion-Corrected Density Functional Theory Investigations of Structural and Electronic Properties of Bulk MoS_{2}: Effect of Uniaxial Strain
- Chuong V. Nguyen^{1, 2}Email authorView ORCID ID profile,
- Nguyen N. Hieu^{1} and
- Duong T. Nguyen^{3}
- Received: 23 August 2015
- Accepted: 28 September 2015
- Published: 4 November 2015
Abstract
Strain-dependent structural and electronic properties of MoS_{2} materials are investigated using first principles calculations. The structural and electronic band structures of the MoS_{2} with relaxed unit cells are optimized and calculated by the dispersion-corrected density functional theory (DFT-D2). Calculations within the local density approximation (LDA) and GGA using PAW potentials were also performed for specific cases for the purpose of comparison. The effect of strain on the band gap and the dependence of formation energy on strain of MoS_{2} are also studied and discussed using the DFT-D2 method. In bulk MoS_{2}, the orbitals shift towards the higher/lower energy area when strain is applied along the z/x direction, respectively. The energy splitting of Mo4d states is in the range from 0 to 2 eV, which is due to the reduction of the electronic band gap of MoS_{2}.
Keywords
- Molybdenum disulphide
- Uniaxial strain
- Electronic property
- Dispersion-corrected density functional
Background
Molybdenum disulphide (MoS_{2}) is an interesting material for applications in nanoelectronic applications due to its unique mechanical, electronic, and optical properties [1, 2]. It is a typical layered inorganic material, which is similar to graphite. MoS_{2} triple layers are held together by weak van der Waals (vdW) interactions. It is a typical example of layered transition-metal dichalcogenides family, which has been studied in recent years. The MoS_{2} attracts investigation due its distinctive industrial applications from use as a lubricant [3] and a catalyst [4] as well as in photovoltaics. By chemical bath deposition method and the mechanochemical route, MoS_{2} films have been obtained in the experiments [5]. Due to the interlayer vdW interaction, the bulk MoS_{2} tends to form a bilayer which is known to be an indirect semiconductor. It has indirect energy band gap of 1.23 eV [6]. The bulk MoS_{2} has been used in conventional industries as an intercalation agent and a dry lubricant for many years. In addition, a two-dimensional MoS_{2} is expected for applications in nanoelectronic devices [7].
In recent years, properties of MoS_{2} and its related structures have been theoretically studied [8–13] such as stability of structure, band gap, functionalization through adatom adsorption, and vacancy defects. By means of density functional theory computations, Chen et al. have been systematically investigated the stability and magnetic and electronic properties of MoS_{2} nanoribbons [14, 15]. The defect structure of MoS_{2} has also been studied [16]. Besides, the creation of magnetic and metallic characteristics in low-width MoS_{2} nanoribbons has been studied by the first principles calculations [17]. The electronic structure of MoS_{2} has been also studied[3]. Up to date, many works about MoS_{2} have been done, but some questions are still worth studying. For example, the electronic properties of bulk MoS_{2} under strain have not been enough investigated. Current studies have confirmed that the properties of low-dimensional materials can be modified by strain, therefore, the response of electronic properties of bulk MoS_{2} to the strain would be an interesting issue for discussion.
In the present work, we investigate the strain-dependent structural and electronic properties of low-dimensional MoS_{2} materials using first principles calculations. We apply uniaxial strain onto the bulk MoS_{2}. The structural and electronic band structures of MoS_{2} with relaxed unit cells are optimized and calculated by the dispersion-corrected density functional theory (DFT-D2). The effects of strain on the band gap and the dependence of formation energy on strain of MoS_{2} are also studied and discussed.
Methods
The present calculations are performed within density functional theory using accurate frozen-core full-potential projector augmented-wave (PAW) pseudopotentials [19, 20], as implemented in the Quantum Espresso code [21]. We use the generalized gradient approximation (GGA) with the parametrization of Perdew-Burke-Ernzerhof (PBE) with added van der Waals (vdW) corrections. They are important for describing the interaction between Mo S _{2} layers. Beside DFT-D2 method, calculations within the local density approximation (LDA) and GGA using PAW potentials were also performed for specific cases. This combination is for the comparison with DFT-D2 calculations when the vdW interactions were introduced. These vdW interactions were included using the method of Grimme (DFT (PBE)-D2) [22]. This approach has been successful in describing graphene-based structures [23]. For the plane waves used in the expansion of the pseudowave functions, the cutoff energy varies in the range from 450 to 545 eV. The results of the calculations for convergence in the surface energy and interplanar distances confirmed that the cutoff energy of higher than 400 eV and the planar grid with dimensions of 6×6×1 are quite sufficient. For the different layers of the MoS_{2}, the supercells are constructed with a vacuum space of 20 Å along the z direction. The Brillouin zones are sampled with the Γ-centered K point grid of 18×18×1. The strain is simulated by setting the lattice parameter to a fixed larger value and relaxing the atomic positions. The magnitude of strain is defined as: ε=(a−a _{0})/a _{0}, where a _{0} and a are the lattice parameters of the unstrained and strained systems, respectively.
Results and Discussion
Structural and Electronic Properties of the Bulk MoS_{2}
Calculated structural parameters and band gap of the bulk MoS_{2} using LDA, GGA, and DFT-D2 methods
Lattice constant | E _{ g }, eV | d _{ M o−S }, eV | ||
---|---|---|---|---|
a, Å | c/a | |||
LDA | 3.115 | 3.85 | 0.72 | 2.36 |
GGA | 3.172 | 3.95 | 0.96 | 2.43 |
DFT-D2 | 3.176 | 3.85 | 1.22 | 2.41 |
Theory (LDA) | 3.13 [29] | 3.84 [29] | 0.75 [29] | 2.39 [29] |
3.11 [30] | - | 0.72 [30] | 2.37 [30] | |
Theory (GGA) | 3.23 [29] | 4.01 [29] | 1.05 [29] | 2.45 [29] |
3.20 [30] | - | 0.85 [30] | 2.42 [30] | |
Experiment | 3.16 [18] | 3.89 [18] | 1.23 [6] | 2.41 [18] |
We calculate the electronic band gap of the bulk MoS_{2} by using different methods (LDA, GGA, and DFT-D2). We see that the band gap value calculated by the LDA and GGA methods is smaller than that of the experimental study. Our result for the band gap of the bulk MoS_{2} form is 0.72 eV (0.96 eV) using LDA (GGA) functionals, which is in good agreement with the available theoretical data of 0.72 eV (0.85 ev) using the same LDA-PAW (GGA) funtionals [30, 31]. These values are smaller than that of the experimental study (1.23 eV) [6]. This difference is due to the inherent drawback of standard LDA/GGA functionals. However, the DFT-D2 calculations for the band gap give results (1.20 eV) that are in good agreement with the experimental data (1.23 eV) [6]. Besides, our DFT-D2 calculations give the bond length d _{ M o−S } being 1.41 Å. That is the same value as in the experimental study. The match between the DFT-D2 method and the experimental study can be explained by the existence of the vdW interaction in MoS_{2}. Our DFT-D2 calculations is including the vdW interaction. We believe that the DFT-D2 method is a suitable method for the structural and electronic properties of the bulk MoS_{2}.
Effect of Uniaxial Strain on the Structural and Electronic Properties of MoS_{2}
In this part, we consider the influence of uniaxial strain on the structural and electronic properties of the bulk MoS_{2}. Uniaxial strain along both x and z directions is considered in our study (see, Fig. 1). The components of strain along the x and z directions are noted as ε _{ x } and ε _{ z }, respectively. The strains are evaluated as the lattice stretching percentage. We defined ε _{ x }=(a−a _{0})/a _{0} and ε _{ z }=(c−c _{0})/c _{0}, where a _{0} and c _{0} are the lattice constants at the equilibrium state, and a and c are strained lattice constants. A wide range of strain along (up to 10 %) both directions with step Δ ε=2 % has been employed in the present study.
Figure 3 b, c shows the dependence of Fermi level E _{ F } and bond length d _{ M o−S } in the bulk MoS_{2} on the strain along x and z directions. Under uniaxial strain, the Fermi energy and the Mo-S bond length change linearly with strain. As the uniaxial strain increases, the Fermi energy is decreased and the bond length d _{ M o−S } increases. We can see that the total energy, Fermi energy, and bond length depend not only on strain strength but also depend strongly on the direction of the applied strain.
At equilibrium, the lowest energy of the conduction band \(\left (E_{K}^{\text {CBM}}\right)\) and the highest energy of the valence band \(\left (E_{K}^{\text {VBM}}\right)\) are 0.903 and −0.736 eV, respectively. These values of energy are decreased due to increasing the strain strength. Especially, when the strain increases from 0 to 10 %, \(E_{K}^{\text {CBM}}\) decreases from 0.903 to 0.08 eV.
Figure 5 depicts the energy band gap as a function of the applied ε _{ xz } strain. Under ε _{ x } strain, the band gap decreases monotonically with strain. We can see that at ε _{ x }=2 %, the band gap is equal to 0.78 eV. This band gap decreases to 0.13 eV when ε _{ x }=10 %. The effect of the ε _{ z } on the band gap of the MoS_{2} is negligible (in comparison to the case of strain applied along the x direction). We see that when the ε _{ z }<6 %, the point in k-space corresponding to the highest energy of the valence band is located at the Γ point and it will be shifted to the K point in the first Brillouin zone when the ε _{ z }>6 %. The band gap of the bulk MoS_{2} is strongly dependent on the applied strain along the x direction and we expect that a phase transition will occur in the case of larger deformation.
In addition, we also calculate band gap of bulk MoS_{2} under uniaxial strain along the armchair direction (y direction). Similar to the case of strain along the zigzag direction, band gap of MoS_{2} reduces concurrently with strain. Our calculations show that the change in band gap of MoS_{2} under uniaxial strain along the zigzag and armchair directions is almost the same. This result is in good agreement with the previous works [32, 33].
Conclusions
In this paper, we studied the effect of uniaxial strain on the structural and electronic properties of the bulk MoS_{2} using first principles calculations. Methodologically, we pointed out that the DFT-D2 calculations are a suitable method for calculations of structural and electronic properties of the bulk MoS_{2}. Our calculations showed that the electronic properties of the bulk MoS_{2} are very sensitive to the uniaxial strain, especially when the strain is applied along the x direction. The band gap of the bulk MoS_{2} decreases linearly with an increase of the strain strength and we can control the energy splitting and band gap of the bulk MoS_{2} by the strain. This makes MoS_{2} becoming a promising material for application in nanoelectronic device such as nanosensors.
Declarations
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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