Bond Relaxation and Electronic Properties of Two-Dimensional Sb/MoSe2 and Sb/MoTe2 Van der Waals Heterostructures

Van der Waals heterostructures have recently garnered interest for application in high-performance photovoltaic materials. Consequently, understanding the basic electronic characteristics of these heterostructures is important for their utilisation in optoelectronic devices. The electronic structures and bond relaxation of two-dimensional (2D) Sb/transition metal disulfides (TMDs, MoSe2, and MoTe2) van der Waals heterostructures were systematically studied using the bond-charge (BC) correlation and hybrid density functional theory. We found that the Sb/MoSe2 and Sb/MoTe2 heterostructures had indirect band gaps of 0.701 and 0.808 eV, respectively; further, these heterostructures effectively modulated the band gaps of MoSe2 (1.463 eV) and MoTe2 (1.173 eV). The BC correlation revealed four bonding and electronic contributions (electron-holes, antibonding, nonbonding, and bonding states) of the heterostructures. Our results provide an in-depth understanding of the Sb/TMD van der Waals heterojunction, which should be utilised to design 2D metal/semiconductor-based devices.


Introduction
Graphene has led to a research boom in the exploration of two-dimensional (2D) materials of various atomic layer thicknesses 1 , such as transition metal disulfides (TMDs) 1 , black phosphorus 2 , graphitic-C 3 N 4 3 . Due to their excellent optoelectronic properties, these materials have been extensively studied and their potential applications in next generation photovoltaic devices have been demonstrated. Because of its many advantages, including high thermal stability, high current carrying mobility, good thermal conductivity, and high conductivity 4, 5 , a 2D material of Sb metal of the VA group element recently caused a huge sensation 6,7 . These favourable characteristics make Sb monolayers a promising material for use in optoelectronic devices. 8 With a focus on a single 2D material of TMDs, van  We investigated the electronic properties of 2D Sb/TMDs heterojunctions using BOLS theory together with density functional theory (DFT) calculations and the bond-charge (BC) model. 17 The electronic performance of Sb/TMDs arises from the intrinsic relationship between related antibonding, nonbonding andbonding , quantitatively characterising the role of crystal potential. Our

DFT calculations
All structural relaxation and electronic properties of Sb/MoTe 2 and Sb/MoSe 2 vdW heterostructures were calculated with CASTEP, which used DFT with a plane-wave pseudopotential. 18,19 This was aimed at analysing the atomic structure, energetics, and electronic properties of 2D vdW heterojunctions. We used the HSE06 20 hybrid density function to describe the electron exchange and correlation potential; the cut-off energy of the plane-wave basis set was 440 eV. The k-point grids were 4×5×2 (Sb/MoTe 2 ) and 4×4×1(Sb/MoSe 2 ), as shown in Table 1. The vacuum thickness was 18 Å. We chose structures with lattice strains less than 1% in QuantumWise, and the lattice parameters of each structure that were determined using QuantumWise are shown in Table 1. Moreover, the Sb/MoTe 2 and Sb/MoSe 2 vdW heterostructures were as shown in Fig. 1a and b. Additionally, in order to consider the long-range vdW interaction, we used Grimme's DFT dispersion correction; this was because the standard HSE06 function does not describe the weak interaction well. 21 In the calculations, the energy converged to 10 −6 eV and the force on each atom converged to <0.01 eV/Å.

BC Model
In theory, we intended to extend the existing BOLS theory and combine it with DFT calculation to cover the local perturbation of the interfacial crystal potential and thereby overcome the nonbonding and antibonding electrons of other methods when dealing with electronic quantification of the heterojunction interface. The change in energy caused by external fields, such as pressure, temperature, electric fields, was used as a variable to determine the change in chemical bonds with the local electron density; thereby changing the crystal potential energy. The following formulae were used to describe the electronic state of a specific chemical bond:  and crystal potential functions based on the BOLS theory. 17 In Eq. 3,  V cry ® may become deeper ( > 1 for a potential well formation) or shallower ( < 1 for a potential barrier formation) than the corresponding V ® (r) of the specific constituent. 23 Eq. 4 describes the relationship between electronic binding energy and deformation charge density, and Eq. 5 shows the relationship between the crystal potential and the deformation charge density. From the above model, we obtained the functional relationship between bond-energy-electronic binding-energy-deformation-charge density and crystal potential energy through dimensional analysis and unit conversion. Fig. 2 shows a schematic of the BC model.

Formation energy and structures
The electronic structures and band gaps of Sb, MoTe 2 , MoSe 2 , Sb/MoTe 2 , and Sb/MoSe 2 were calculated. We considered the influence of lattice strain and vdW forces for the Sb/MoTe 2 and Sb/MoSe 2 heterostructures. The lattice strains in the Sb/MoTe 2 and Sb/MoSe 2 heterostructures were 0.52 % and 0.49 %, respectively, which was less than 1 % in both cases. The 2D heterostructures require spacing to maintain their stability, as shown in Fig. 2. The relaxed lattice parameters and interlayer distances are listed in Table 1. We set the initial distance in the z direction between the top Sb metallic layer and the bottom TMD layer to 3.20 Å; moreover, the relaxed interlayer distances in the Sb/MoTe 2 and Sb/MoSe 2 heterostructures were 3.94 and 3.75 Å, respectively.
We also calculated the formation energies (E form ) of the Sb/MoTe 2 and Sb/MoSe 2 heterostructures using the following equation 14 E form of the Sb/MoTe 2 and Sb/MoSe 2 heterostructures were -0.37 and 0.21 eV, respectively.
These negative formation energies indicate that the 2D heterostructure were structurally stable.

Band structure and density of states
In order to assess the validity of our calculation, we calculated the band structure of the monolayer Sb, MoTe 2 and MoSe 2 structures, as illustrated in Fig. 3. The calculated band gaps of

Deformation charge density resolved bond and electrons features
We believe that the formation of Sb/MoTe 2 and Sb/MoSe 2 vdW heterostructures is primarily  Table   3. These findings will be useful for calculation ing the bond states and crystal potentials of 2D vdW heterostructures.

Conclusions
Combining