Bond states, moiré patterns, and bandgap modulation of two-dimensional BN/SiC van der Waals heterostructures†

The matched lattice strain of the graphene/hexagonal boron nitride (BN) heterojunction that is less than 2% is known to form a moiré pattern. However, in the BN/SiC heterojunction, the formation of a moiré pattern for a lattice strain more than 5% is a novel phenomenon. This study aims to determine moiré patterns on the BN/SiC heterojunction at lattice strains of 5% and 7% and different incident angles, which can be applied to photoelectric detection technology. The BN/SiC-1 and BN/SiC-2 heterojunctions formed in this study had bandgaps of 0.851 and 1.373 eV, respectively. Furthermore, we observed that when two BN/SiC heterojunctions have indirect bandgaps, the BN/SiC van der Waals heterojunction can be a potential photoelectric material. We analyze the bonding states using the bond-charge model and calculate the potential functions of the antibonding, bonding, and nonbonding states. This study provides a theoretical reference for the precise regulation of the charge density and chemical bonding states of the 2D material surface.


Introduction
The successful preparation of a two-dimensional (2D) atomic layer of the planar graphene structure has encouraged researchers to investigate 2D nanomaterials. [1][2][3][4] Owing to the similarities between the structures and bonding properties of hexagonal boron nitride (BN) and graphite, shortly after the preparation of graphene, a single layer of hexagonal honeycomb BN was successfully prepared by micromechanical stripping. 5 BN has a layered hexagonal honeycomb structure with a wide band gap of 4.6 eV. 6 However, to increase the efficiency of light absorption and convert the 2D hexagonal BN sheet to a highly efficient photocatalytic material, the band gap of BN needs to be reduced to approximately 1.5 eV. 7 Hu et al. found that the band gap can be reduced through lattice strain regulation of the BN sheet. 8 Tang et al. found that band gap reduction can be achieved through electric field regulation of the BN sheet. 9 He et al. achieved the regulation of electronic structures in two-dimensional transition metaldoped BN materials through hydrogen and fluorine chemical modification. 10 These studies provide the theoretical references for band gap regulation.
When manufacturing electronic devices, the majority of the 2D materials are grown on metals or semiconductor substrates, which causes strain in the crystal lattice. [11][12][13] There exists a difference of 1.84% between the lattice constants of graphene and hexagonal BN. 14 Additionally, the graphene/hexagonal BN system forms a moiré pattern. 15,16 Furthermore, Kang et al. studied the 2D MoS 2 /MoSe 2 heterojunction and found that the strength of the van der Waals interaction between the MoS 2 and MoSe 2 layers is not sufficient to eliminate this mismatch resulting in lattice strain. Zhang et al. studied the interlayer couplings, moiré patterns, and 2D electronic superlattices in MoS 2 /WSe 2 hetero-bilayers. 17 Rosenberger et al. studied the moiré pattern of a transition metal dichalcogenide heterostructure and found that the angle rotation is related. 18 Cao et al. found that the superconducting properties of two layers of graphene were exhibited at specific angles (approximately 1.11). 19 Therefore, matching lattice strains of interlayer couplings and angle rotation of the two atomic layer heterojunctions will form a moiré pattern. 20 The formation of the moiré pattern has led to the emergence of many novel physical and chemical properties. [21][22][23][24] In this study, we found that lattice strains of 5% and 7% will cause a moiré pattern on the BN/SiC heterojunctions. The band gaps of BN/SiC-1 and -2 heterojunctions are approximately 0.851 and 1.373 eV, respectively. Furthermore, these heterostructures effectively modulate the bandgaps of BN (4.661 eV) and SiC (2.108 eV). This provides a basis for designing 2D semiconductor heterojunction materials, where the lattice 2. Principles

DFT calculations
The two-dimensional material geometry structure was obtained from the crystal Material Projects database. Then, through the interface function of the QuantumWise's software, structural models of the heterojunction (B30-50 kinds of possible structures) are established, and the lattice strain value that matches the geometry structure from the database is the obtained lattice strain. The model of the initial structure only considers the lattice strain of the BN atomic layer. The average strain in the BN layer is listed in Table 1. The initial structure is geometrically optimized in the Vienna ab initio simulation package, and the relaxation model includes optimization of atomic positions and unit cells. We set the energy cut off of the plane wave at 400 eV and the Brillouin zone at 4 Â 4 Â 4 k-points. To acquire the optimized geometric structures, the energy convergence criterion is 10 À5 eV, and the atomic force convergence is 0.01 eV Å À1 . Next, the Cambridge Sequential Total Energy Package (CASTEP) was used to optimize the geometry and increase the accuracy of calculating chemical bonding and electronic properties.
The DFT calculations, using the norm-conserving potentials of the hybrid density functional, were implemented in the CASTEP software. We use the Heyd-Scuseria-Ernzerhof (HSE06) 25 hybrid density functional to describe the electron exchange and correlation potential. There are no constraints on the atomic layer. Also, we consider non self-consistent dipole correction in the calculation process. The thickness of the vacuum region is 14 Å. The energy convergence criterion is set to 1 Â 10 À6 eV, and the plane wave cut-off energy is set to 700 eV. To consider the long-range van der Waals interaction, we use the TS scheme for DFT-D calculation. Table 1 summarizes the parameters used in the DFT calculations.

BOLS-BC model
The following equations are used to describe the electronic state of a specific chemical bond, based on the bond-orderlength-strength (BOLS) notation: 26     where d i is the bond length of the atom, E i represents the single bond energy, V cry (r i ) is the crystal potential, m is the bond nature, B represents bulk atoms, and i counts from the outermost atomic layer inward up to the third indicator layer (i r 3). Eqn (1) describes the relationship between the chemical bonds (energy and length) and crystal potential functions based on the BOLS notation. 27 The potential function g V cry (r i ) may become deeper (g 4 1 for potential well formation) or shallower (g o 1 for potential barrier formation) than the corresponding V cry (r B ) of the specific constituent. 28 Eqn (2) describes the relationship between the bond energy E i , crystal potential V cry (r i ), bandgap E G , and the deformation charge density Dr(r i ). Fig. 1 illustrates the BC model with the BOLS notation.

Geometry structure
The geometry structure of the different strains is selected based on QuantumWise's interface modeling, and the geometry structure to be optimized is obtained. The lattice strain (45%) produces the BN/SiC heterostructures (orthorhombic ( Fig. 2a and c) or rhombohedral ( Fig. 2b and d)). Fig. 2c and d show that both BN/SiC-1 and BN/SiC-2 heterojunctions form a  wave-shaped geometry structure. The optimized heterostructures 1 and 2 are depicted in Table 1. We calculate the total energy of the BN, SiC, and BN/SiC stable structures, and the energy difference between them is calculated as the formation energy, 29 using the equation E form = E heterostructure total À E SiC total À E BN total , as presented in Table 2. The formation energies of the two BN/SiC heterojunctions 1 and 2 are À1.26 and À1.16 eV, respectively, and these values are within the range of our calculation accuracy. Therefore, we confirm that both structures are stable with BN/SiC heterojunctions.
Additionally, we obtain the wave shape height h 1 of the BN layer, as presented in Table 3 and Fig. 2. The height (h) between the BN and SiC layers is the distance between the BN and SiC layers in the thickness direction of the slab. We calculate the different initial heights (H) between the BN and SiC layers, and atomic distance of the BN layer, as shown in Table 4. The relaxation heights h for the BN and SiC heterostructures are 2.43 Å and 2.73 Å, respectively. The different initial heights change with the relaxation height h of heterostructures 1 and 2 for small ranges (B0.1 Å). After the relaxation, the distance between atom 1 and atom 2 of heterostructures 1 and 2 are within a small range (B0.02 Å). This shows that the different heights between the BN and SiC layers will not change the wave shape structure of the heterostructures 1 and 2. A moiré structure is spatially periodic with a long-range period (in nm scale). Therefore, we have supercells in the BN/SiC-1 (3 Â 3) and BN/SiC-2 (3 Â 3) heterojunctions.
Previous studies have found that the moiré pattern is obtained by rotating the angle of two atomic layers of 2D materials. 18 However, we found that the 2D material with a single layer of the wave shape structure can obtain moiré patterns at different incident angles. Fig. 3 shows the moiré pattern of BN/SiC-1 heterostructures with different incident angles of the BN layer. Therefore, the optical effect of the double-layer material geometry structure can be realized by the single layer shape wave geometry material. Furthermore, the wave shape structure of the h-BN surface is obtained by treating with H-plasma. In the experiment, the h-BN flakes appear as bubbles on the h-BN surface after H-plasma treatment. 30 Also, a large strain will be generated on the h-BN surface by gas treatment. Our results show that lattice strain 45% will cause a moiré pattern on the BN/SiC heterojunctions. The results obtained in the experiment are consistent with our calculations.

Band structure, work function, and density of states (DOS)
We determine the band structures of the atomic monolayers of BN and SiC, whose band gaps are listed in Table 3. It can be seen from Fig. 4 that the band gaps of the atomic layers of BN and SiC are 4.661 and 2.108 eV, respectively. The band gaps of the BN/SiC van der Waals heterojunction structures 1 and 2 are 0.851 and 1.373 eV, respectively. The band gap of BN is reduced to approximately 0.7B1.4 eV. We find that the BN strain of structure 1 (7.37%) is higher than that of structure 2 (5.93%), whereas the band gap of structure 1 (0.851 eV) is lesser than that of structure 2 (1.373 eV). The results indicate that the strain of BN/SiC increases, as the band gap decreases.
We calculate the work function of the BN/SiC heterostructures, as presented in Table 3. The work function is the initial energy of the Fermi level and can be defined as the minimum energy required by the electrons to escape into a vacuum from the inside of the metal. In semiconductors, the energy at the bottom of the conduction band and valence band is typically lower than the minimum energy required for the electrons to escape from the metal. The work functions of BN/SiC structures 1 and 2 are 4.512 and 4.912 eV, respectively. A lower work function implies that electrons can easily escape the surface of the BN/SiC heterostructure. It can be seen from Table 3 that the work function of BN/SiC structure 1 is smaller than that of structure 2, which implies that the electrons of BN/SiC structure 1 can easily escape the surface than those of structure 2. We calculate the local density of states (LDOS) of the BN/SiC heterojunction, as depicted in Fig. 6. From Fig. 6a and b, we can see that the electronic distributions of the conduction band minimum (CBM) of the BN/SiC structures 1 and 2 are 0.851 and 1.373 eV, respectively. The electrons in the valence band maximum (VBM) are mainly distributed in Fermi surface E F . The LDOS is mainly contributed by the p orbital in the range from À2 to 2 eV; therefore, we compared the contribution of C 2p, Si 2p, B 2p, and N 3p atoms to the band structure, as depicted in Fig. 6c and d. We found that the main orbital contribution to the CBM and VBM of the BN/SiC structures 1 and 2 originates from the Si 3p and C 2p orbitals. The results indicate that the SiC substrate has a significant influence on the BN band structure in the BN/SiC van der Waals heterojunction.
The band arrangement of the heterojunction relative to the potential of the hydrogen evolution reaction/oxygen evolution reaction (HER/OER) has an important influence on the photocatalytic decomposition of water. 31 The energies of the hydrogen (H + /H 2 ) and oxygen evolution (O 2 /H 2 O) are À4.44 and À5.67 eV, respectively. 32 Fig. 5 compares the band edge positions of the BN/SiC structures 1 and 2 of hydrogen evolution (H + /H 2 ) and oxygen evolution (O 2 /H 2 O). As seen in Fig. 6, the energies of the BN/SiC-2 structure of the CBM and VBM relative to the vacuum level are À3.539 and À4.912 eV, respectively. Our results reveal that the BN/SiC-2 heterostructure could be a promising material for hydrogen evolution and optoelectronic devices.

Chemical bonding states and deformation charge density
From the BOLS-BC model, we derived the following formula for calculating the atomic energy density E D (eV nm À3 ) of a 2D heterojunction: E D (z) = (1 À e) À(m+3) . The parameter m is the indicator of the nature of the bond. The lattice strain e of each atom determines the distribution of energy density; a high energy density causes a high lattice strain e. We believe that the formation of BN/SiC van der Waals heterostructures is primarily due to bond, electron, and charge contributions. Deformation charge density (e Å À3 ) is a tool used to study the electron transfer between atoms. In Fig. 7, we depict the electronic states of four chemical bonding states, namely, the antibonding, nonbonding, and bonding states and electron holes. 33 The blue area represents the loss of electrons, and the red area represents the acquisition of electrons.
Antibonding states indicate the electron density and bond energy decrease in the region. Nonbonding states indicate that the electron density increases in the region, but the surrounding electron density does not overlap with the electron density of the other atoms. Bonding states indicate that the electron density increases in the region, but the electron density overlaps with the other atomic electron densities, indicating that the atom is in the bonding state. Electron holes indicate that the electron density decreases in the region, with a high concentration around the nucleus. Furthermore, by defining the electronic states of the chemical bonding, we establish the expressions for the deformation charge density and potential function of the chemical bond states. The chemical bond potential function can be obtained by calculating the differential charge density. We used eqn (2) to calculate the potential functions of the antibonding, nonbonding, and bonding states. Comparing the potential functions, we obtain V bonding cry (r) 4 V nonbonding cry (r) 4 V Antibonding cry (r). We also calculate the potential function of the atomic bonding states, as presented in Table 5. These results improve the theoretical reference for analyzing the quantitative bond properties of materials.

Conclusions
In this study, we investigated the geometric, energetic, electronic, and photocatalytic properties of BN/SiC van der Waals heterostructures. A lattice strain 45% results from the waveshaped geometry structure of the BN/SiC heterojunctions. The wave shape can cause a moiré pattern with different incident angles. The BN/SiC van der Waals heterojunctions 1 and 2 will form moiré patterns at different incident angles, which can be applied in photoelectric detection technology. The BN/SiC van der Waals heterostructures 1 and 2 exhibit a band gap of 0.851 and 1.373 eV, respectively. The band arrangement shows that the BN/SiC van der Waals heterojunction is a potential photoelectric material candidate. The DFT calculation and BOLS-BC model reveal the characteristics of the charge density and chemical bonds on the heterojunction's material surface. These results improve the theoretical reference for the analysis of the quantitative bond and charge properties of 2D heterojunction materials.