ELECTRONIC PROPERTIES OF BULK AND SINGLE-LAYER MOS 2 USING AB INITIO DFT: APPLICATION OF SPIN-ORBIT COUPLING (SOC) PARAMETERS

Two dimensional (2D) materials are currently gaining a lot of interest due to excellent properties that are different from their bulk structures. Single and few-layered of Transition metal dichalcogenides (TMDCs) have a bandgap that ranges between 1-2 eV, which is used for FET devices or any optoelectronic devices. Within TMDCs, a ton of consideration is focused on Molybdenum Disulfide (MoS2) because of its promising band gap-tuning and transition between direct to indirect bandgap properties relies upon its thickness. The density functional theory (DFT) calculations with different functionals and spin-orbit coupling (SOC) parameters were carried out to study the electronic properties of bulk and monolayer MoS 2 . The addition of SOC brought about a noteworthy change in the profile of the band energy, explicitly the splitting of the valence band maximum (VBM) into two sub-bands. The indirect bandgap in bulk MoS 2 ranges from 1.17-1.71 eV and that of the monolayer bandgap was 1.6-1.71 eV. The calculated parameters were compared to the obtained experimental and theoretical results. The obtained density of states (DOS) can be used in explaining the nature of bandgap in both the bulk and monolayer MoS 2. These electronic characteristics are important for applications in material devices and energy-saving applications. 2 the bulk is 1.17-1.27 consistent the available experimental and theoretical results. The structure and density of states indicate many similarities between the monolayer and bulk MoS 2 . The main contribution to the valence and conduction band are 4d states of Mo and 3p orbitals of s atom in both monolayer and bulk MoS 2 We have discovered that the incorporation of spin-orbit coupling influences the band structures and the splitting of degenerate valence band occurs on high symmetry K-point.

Two dimensional (2D) materials are currently gaining a lot of interest due to excellent properties that are different from their bulk structures. Single and few-layered of Transition metal dichalcogenides (TMDCs) have a bandgap that ranges between 1-2 eV, which is used for FET devices or any optoelectronic devices. Within TMDCs, a ton of consideration is focused on Molybdenum Disulfide (MoS2) because of its promising band gap-tuning and transition between direct to indirect bandgap properties relies upon its thickness. The density functional theory (DFT) calculations with different functionals and spin-orbit coupling (SOC) parameters were carried out to study the electronic properties of bulk and monolayer MoS2. The addition of SOC brought about a noteworthy change in the profile of the band energy, explicitly the splitting of the valence band maximum (VBM) into two sub-bands. The indirect bandgap in bulk MoS2 ranges from 1.17-1.71 eV and that of the monolayer bandgap was 1.6-1.71 eV. The calculated parameters were compared to the obtained experimental and theoretical results. The obtained density of states (DOS) can be used in explaining the nature of bandgap in both the bulk and monolayer MoS2. These electronic characteristics are important for applications in material devices and energysaving applications. KEYWORDS: Electronic properties, Density functional theory, Spin-orbit coupling, Density of states, MoS2, bandgap One of the greatest discoveries in science is the successful flaking of graphene into a 2D sheet of carbon in 2004 by Novoselov et al [1]. Graphene exhibits excellent mechanical, electronic, and physical properties. It's unanticipated Zero bandgap limits its applications [2,3]. The introduction of graphene has resulted in a great interest in other 2D materials such as phosphorene [4], silicone [5], TMDCs [6], and monochalcogenides [7,8], creating huge attention in Nanoelectronic and optoelectronic devices [9][10][11]. From the various available 2D materials, 2D TMDCs exhibits superb physical properties like large bandgap which is needed in Photocatalytic water splitting [12,13].
Layered TMDCs materials are the best candidates for 2D materials because their bandgap lies between 1 to 2 eV [14]. Within the TMDCs, MoS 2 is the most sought for due to its industrial application starting from the use in lubricant [15], energy storage [16], photovoltaics [17], and catalyst [18]. Bulk MoS 2 is a semiconductor having an indirect bandgap of 1.23 eV, with its monolayer possessing a direct energy bandgap of 1.8 eV [19]. The electronic structure undergoes an excellent transition upon exfoliation from the bulk [1,[19][20][21][22][23]. Currently, field-effect transistor (FET) based on singlelayer MoS 2 using HfO 2 as a gate insulator has been experimentally implemented [21]. These extraordinary properties have made monolayer MoS 2 an interesting material in optoelectronic devices and next-generation FET. Also, the transition from indirect to direct bandgap upon thinning shows excellent photoluminescence in 2D monolayer [24]. Albeit various brilliant investigations have been performed on the basic and electronic properties of MoS 2 [25][26][27][28]. The size-subordinate tunability of the electronic properties makes MoS 2 a novel material for nanoscale field-effect transistors and optical sensors [29][30][31]. However, as far as we could possibly know, the impact of SOC on both bulk and monolayer MoS 2 band structure has not been widely examined.
In this study, the band structure of bulk and monolayer MoS 2 were numerically investigated by the plane-wave based CASTEP, and local density approximation (LDA) and generalized gradient approximation (GGA) exchange-correlation functional were used. The influence of the spin-orbit coupling (SOC) effect on the electronic energy band structure of both monolayer and bulk MoS 2 has also been calculated in this study. Our results indicate that both bulk and monolayer MoS 2 materials are very good candidates for Opto-and spintronic device applications.

COMPUTATIONAL METHOD
First principle's calculation based on the pseudopotential plane-wave method [32] is executed in the Cambridge serial total energy package (CASTEP) [33]. This method has been used to study the electronic properties of monolayer GeI [34] and bulk and monolayer WSe 2 . The generalized gradient approximations (GGA) of Perdew-Burke-Ernzerhof (PBE) and Local density approximations (LDA) functional [35,36] including the spin-orbit coupling (SOC) [37] for exchange-correlation interactions. Furthermore, norm-conserving pseudopotential was used in the treatment of ionelectron exchange. The energy cut off for all calculations in this work was 700 eV, for both bulk and monolayer MoS 2 , a k-points separation of 0.015/angstrom and SCF tolerance of 6 1.0 10   eV/atom were employed. The electronic minimizer was set to all bands/EDFT. Generally, the density mixing is the proposed choice for electronic minimizer, but to perform the calculation with SOC effect, the required electronic minimizer is set to all bands/EDFT in order to make a meaningful

Structural parameters
Molybdenum disulfide has a hexagonal crystal structure linked to space group P 6_3/mmc (194). The structure is made up of the stacking of three atomic layers S-Mo-S layer. Monolayer MoS 2 has a single S-Mo-S layer as shown in Fig. 1b, whiles the bulk MoS 2 has a two-layer monolayer MoS 2 with one-layer Mo atoms place on top of the Sulphur atoms of the other layer, illustrated in Fig. 1b. From geometry optimization, the lattice constants for bulk MoS 2 are 3.192A in a and b axis and 12.478 in the c-axis. The monolayer slab was cleaved in 001 direction and a vacuum layer of 20A. Electronic properties and density of states A series of calculations were performed on the bulk and monolayer MoS 2 with LDA CAPZ and GGA PBE functionals incorporated with or without SOC. The electronic band pattern of monolayer MoS 2 as shown in Fig. 2 has a direct bandgap situated at K K  of k point.

EEJP. 4 (2020)
This transition in bandgap makes monolayer MoS 2 applicable to different devices. Interestingly, all the calculations either with or without SOC captures the direct bandgap feature for monolayer MoS 2 . Also, the application of SOC for monolayer MoS 2 affects the band gap value. Furthermore, the valence band maximum and that of the conduction band both occur at high symmetric K point indicating a direct bandgap semiconductor as shown in Fig. 2(a-d) above. The bandgap value for monolayer MoS 2 ranges from 1.60 to 1.71eV. The experimental result indicates a slight shift from the theoretical result. The theoretical work gives a slight difference in bandgap than the experiment as illustrated in Table.  Fig. 2(a-d), the valence band maximum (VBM) and the conduction band minimum (CBM) lie below and above the Femi level respectively along with the K-symmetry. For the monolayer MoS 2 , there is a reasonable band splitting as seen in Fig 2 (c) and (d), this band splitting is brought about by the utilization of SOC and can likewise help in the application of spintronic and valleytronics [43][44][45][46][47]. The band splitting is observed distinctly in the valence band (VB) of the high symmetry K-direction. This result is good agreement with previously reported literature [28,43,48].  [19,27] shown in Table. From the obtained results of the electronic structures, we realized that there are slight changes in the energy band with or without SOC. Also, it was observed that the bandgap value 0f the compound with SOC is smaller than the one without SOC. Fig. 3 (c) and (d) show a slight Valence band (VB) splitting on a high symmetry K direction. This splitting can be ascribed to the utilization of SOC [43,[49][50][51][52][53]. The SOC influences the valence band of the compound as appeared in Fig. 3(c,d). Fig. 4. (a-d) represents the partial density of states of bulk and monolayer MoS 2 using two different functionals i.e. PBE and LDA. MoS 2 exhibits a neutral charge due to the presence of +4 in the valence of Mo and a charge of -2 for the S-atom. From Fig. 4(a-d), the partial density of states can be divided into three classes of states. For the first class, the density around -14eV is due to 3s orbital of S atom which is separated by a wide gap. The second class is the one below the Fermi level in which the contributing orbitals the 3p orbitals of S atom and 4d orbitals of Mo. This class possesses a strong hybridization. The third class is the one above the Fermi-level, here the contributing orbital is the 4d orbitals of Mo and is separated by the second class with a narrow gap. For both functionals, the bandgap occurs due to the 4d orbitals of Mo and 3p orbitals of S atoms in monolayer and bulk MoS 2 .

CONCLUSION
The electronic properties of bulk and monolayer MoS 2 have been studied using first-principle calculations based on the pseudopotential plane-wave method. Our results show that monolayer MoS 2 is a direct semiconductor whiles bulk MoS 2 has an indirect bandgap. Also, our calculations show that the bandgap of monolayer MoS 2 ranges from 1.6-1.73 eV whereas the bulk is 1.17-1.27 eV which is consistent with the available experimental and theoretical results. The electronic structure and density of states indicate many similarities between the monolayer and bulk MoS 2 . The main contribution to the valence and conduction band are 4d states of Mo and 3p orbitals of s atom in both monolayer and bulk MoS 2 . We have discovered that the incorporation of spin-orbit coupling influences the band structures and the splitting of degenerate valence band occurs on high symmetry K-point.

Conflict of interest
The authors declare that they have no conflict of interest.

Funding
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.