The nanotechnology has allowed the researchers to work up to a nanoscale and offered extraordinary results which were never possible earlier. The nanotechnologies include highly sensitive sensors, high-performance nanoelectronics, nanocomposites, and innovative medicines and cancer therapy based on nanoparticles [1-4]. The development of nanotechnology has also proposed the different classes of dimensional systems which are zero-dimensional (0D, e.g., nanoparticles), one-dimensional (1D, e.g., nanowires), two-dimensional (2D, e.g., graphene), and three-dimensional (3D, e.g., bulk materials). The low dimensional systems play major role to differentiate the nanomaterials, as they explore the atomic structure of materials and properties of the low dimensional materials .
In 2004, the experimental discovery of graphene is one of the most important scientific revolution of the 20th century . The two-dimensional (2D) crystal of graphene is created by separating it from graphite material [7-9]. Graphene is a single layer structure of carbon atoms arranged in the honeycomb form. Graphene material has the potential for high-speed nanoelectronics applications because of its unique
features like extremely high carrier mobility and half-integer quantum effects. Because of high mechanical and chemical stability, we can use it in different working conditions [10,11]. Looking into the potential of 2D materials, graphene-like inorganic monolayer materials gallium nitride (GaN) , silicon carbide (SiC) [13,14], boron nitride (BN) , zinc oxide (ZnO) [16,17], aluminum nitride (AlN) [18-20] and transition-metal dichalcogenides (TMDs) [21,22] have been synthesized and analyzed for various parameters. Among these 2D materials, the TMDs have shown a broad range of mechanical, electronics, optical, thermal, and chemical properties [23,24]. The monolayer of TMDs (such as MX2 where M=Mo, W; and X=S, Se, Te, etc.) having a honeycomb structure where transition metal atoms (M) are switched between chalcogen atoms X. All the atoms in a monolayer of TMD are attached by the covalent force and the different layers are attached by van der Waals forces. For electronics applications, the TMDs like MoS2, MoSe2, MoTe2, WS2, and WSe2 have shown extraordinary features. In bulk form, TMDs are indirect bandgap semiconductors. By thinning down to a single layer, the indirect bandgap changes into a direct bandgap. The monolayer direct bandgap of TMD is in the range of (1.1-2.0eV) at the K-point in the Brillion zone [25-27]. In this work, we have focused on bandgap and effective mass of MoS2 monolayer for without strain and with strain structure. We also investigated the same for defected monolayer and silicon-doped (Si-doped) monolayer.
1.1 Related Work
S. Deng et al.,  have investigated the response of 2D TMDs on a mechanical strain by using first-principles methods. By studying the mechanical properties of 2D TMDs it has been found that the stable range of strain is determined by the young’s modulus. Moreover, it has been also analyzed that the strain also induces the electronic bandgap properties. X Wang e al.,  have presented a theoretical study report for the interaction of No2 molecule with the Mo-edge of MoS2 zigzag nanoribbon, and for its simulations, the density functional theory (DFT) method has been used. The effect of uniaxial tensile strain on the physical and structural properties of MoS2 Nanoribbon and the absorption process has been discussed in detail. It has been observed that there is increase in the magnitude of the adsorption energy and a more stable structure is obtained with strain. S. Yua et al.,  have presented the computational study of MoS2 monolayer under tensile strain. The transition from direct to indirect and semiconductor to metal has been investigated under the tensile strain along with both x-direction and y-direction. The phase transition, carrier mobility, and effective mass of MoS2 monolayer have been studied under tensile strain. The mobility increases when the biaxial strain Ɛx=Ɛy=9.5% has been applied. Additionally, the mobility parameter with an increase in temperature has been decreased monotonically. J. Ni et al.,  have demonstrated the modulation of bandgap transition of two heterostructures i.e. Blue P/GeC and Blue P/SiC with strain engineering. According to the authors, the electronic structure and optical properties of the Blue P/GeC and Blue P/SiC have changed under strain. R. Beiranvand  has investigated the electrical and optical properties of TMDs MoX2 (X = S, Se, Te) based on the DFT method. Also, the author has studied the optical absorption coefficient, real and imaginary parts of the dielectric functions, reflectivity, and energy loss functions for external electric fields along with two directions in detail. The high absorption coefficient value is the remarked property of the MoX2 monolayer which makes these materials best for optoelectronics applications. A. O. M. Almayyali et al.,  have investigated the optical and electronics of zinc iodide (ZnI2) material under the impact of the biaxial strain. For the ZnI2 material-based calculation of molecular dynamic simulations, binding energy, and phonon dispersion curve it has been observed that the ZnI2 has high stability. According to the results it has been observed that the ZnI2 monolayer behave as a semiconductor having an indirect bandgap under PBF and HSE06 methods and values of bandgaps are 2.018eV and 2.94eV, respectively. M. Y. Liu et al.  have proposed a new class of 2D materials XBi (where X=Si, Ge, Sn, and Pb) along with the metal monochalogenide structure to provide tunable orbital properties. It has been found that the spin-orbit coupling shifts the SnBi electronics properties from semiconductor to metal, and the applied strain can lead toward a novel Dirac electronic state. Surface chemical decoration has been confirmed to be an effective path to achieve the Bi-pz filtering effect and p-p inversion in the orbital. Y. Solyaev et al.,  have investigated the electric field, inertia gradient, and strain impact on anti-plane wave propagation of piezoelectric materials. It has been analyzed that the model represents a normal dispersion of short wave in piezoelectric materials. Another model parameter on the phase velocity, attenuation of shear horizontal, and coupled electromechanical factor have been investigated. It has been concluded that the results obtained in this article can be applied for the analysis of small-scale piezoelectric structures and high-frequency MEMS/NEMS. H. Li et al.,  have explored a novel 2D bonding heterostructure that consists of a hexagonal borophene monolayer attached with two blue phosphorene layers. The proposed heterostructure having good conductivity, high stability, and high in-plane stiffness. Later, the proposed novel 2D heterostructure has been investigated by using the DFT method as an acceptable material for lithium-sulfur batteries. The results have shown that the lithium-polysulfides based on the proposed structure having proper adsorption energies i.e., 0.60-2.68 eV, and moderate diffusion barrier i.e., 0.09-0.31 eV. D.M. Hoat et al.,  have investigated the electronic structure and optical properties of Hafnium disulfide (HfS2) under vertical strain using DFT calculations. By calculating the phonon dispersion curves the dynamical stability of the HfS2 monolayer has been examined. The HfS2 monolayer has shown a high absorption coefficient of 49.6000 (104 /cm) and 88.122 (104 /cm) in the visible and ultraviolet regions, respectively which display promising optoelectronic applicability.