Bandgap Engineering of Two-Dimensional Double Perovskite Cs4AgBiBr8/WSe2 Heterostructure from Indirect Bandgap to Direct Bandgap by Introducing Se Vacancy

Heterostructures based on layered materials are considered next-generation photocatalysts due to their unique mechanical, physical, and chemical properties. In this work, we conducted a systematic first-principles study on the structure, stability, and electronic properties of a 2D monolayer WSe2/Cs4AgBiBr8 heterostructure. We found that the heterostructure is not only a type-II heterostructure with a high optical absorption coefficient, but also shows better optoelectronic properties, changing from an indirect bandgap semiconductor (about 1.70 eV) to a direct bandgap semiconductor (about 1.23 eV) by introducing an appropriate Se vacancy. Moreover, we investigated the stability of the heterostructure with Se atomic vacancy in different positions and found that the heterostructure was more stable when the Se vacancy is near the vertical direction of the upper Br atoms from the 2D double perovskite layer. The insightful understanding of WSe2/Cs4AgBiBr8 heterostructure and the defect engineering will offer useful strategies to design superior layered photodetectors.


Introduction
Organic-inorganic metal halide perovskites demonstrate high performance, but still face one major challenge: a stability issue due to hydrophilic organic cations and displaying very low thermal decomposition temperatures. Recently, all-inorganic halide perovskites, especially the double perovskite, without molecules and lead-free perovskite showing excellent stability against moisture, heat, and light, have attracted extensive attention [1][2][3]. In general, since the 2D all-inorganic double perovskite Cs 4 AgBiBr 8 has a high exciton-binding energy, which is 3 times larger than that of the 3D all-inorganic double perovskite Cs 2 AgBiBr 6 , the charge carrier mobility and absorption coefficients of Cs 4 AgBiBr 8 (2D) in the visible spectrum are worse than those of Cs 2 AgBiBr 6 (3D) [4]. However, in 2021, Wang et al. reported the upconversion photovoltaic effect of WS 2 monolayer/(C 6 H 5 C 2 H 4 NH 3 ) 2 PbI 4 2D perovskite heterostructures by below-bandgap twophoton absorption via a virtual intermediate state, which enables heterojunction devices with good photoresponsivity and excellent current on/off ratio [5]. Therefore, heterostructure is considered an efficient way to enhance device performance, especially the charge mobility and light adsorption.
Furthermore, van der Waals heterostructures (vdWHs) based on 2DLMs (2D layered materials) with selectable material properties pave the way to build new structures at the Materials 2023, 16, 3668 2 of 10 atomic scale, which may lead to new heterostructures with novel physical properties and versatility [6,7]. Two-dimensional layered materials, such as graphene and transition metal dichalcogenides (TMDs), have attracted great attention due to their extraordinary properties in fundamental physics and potential applications [8,9]. Interestingly, MoX 2 and WX 2 (X = S, Se, Te) TMDs are indirect gap semiconductors in their bulk states, but some of them can become direct gap semiconductors when the film thickness is intentionally changed into a monolayer [10][11][12]. Due to the weakened dielectric shielding and layer-dependent electronic structure, monolayer TMDs such as MoS 2 and WSe 2 have direct band gaps with strong exciton characteristics in the visible or near-infrared range [13]. However, their relatively weak light absorption hinders their practical application. Fang et al. reported that integrating monolayer TMDs with 2D perovskites, which serve as the light-absorption layer, can be an efficient solution. Through the complementary effect of two-dimensional perovskites, heterostructure engineering based on TMD layers can effectively improve the performance of photodetectors with low-power optoelectronic applications [14].
A TMD, WSe 2 , has recently received more attention [15][16][17]. Two-dimensional WSe 2 thin films and Nanoflakes have been used for photoelectrochemical hydrogen production [18,19]. In this work, we used first-principles calculations to investigate the effect of WSe 2 layer defects on the heterostructure properties of a monolayer WSe 2 /monolayer Cs 4 AgBiBr 8 heterostructure. Our computational results show that the heterostructure exhibits an indirect band gap where the CBM (conduction band minimum) and VBM (valence band maximum) positions locate at different k points when the WSe 2 monolayer is combined with the Cs 4 AgBiBr 8 monolayer. Xia et al. reported that when the atom vacancy defect of vdWHs generates a flat defect energy level [20], we can employ the strategy of defect modification and successfully change the heterostructure from an indirect band gap to a direct band gap by introducing the defect energy level. Finally, the obtained heterostructure with a Se vacancy exhibits a direct band gap, and the heterostructure is more stable when the Se vacancy is near the vertical direction of the upper Br atoms from the 2D double perovskite layer.

Calculation Methods
Our first-principles calculations were performed using density functional theory (DFT) [21,22], which is implemented in the VASP code [23,24] with the standard frozencore projector-augmented wave (PAW) [25] method. We used the generalized gradient approximation (GGA) [26] by the Perdew-Burke-Ernzerhof (PBE) method [27] to relax the structure. The cut-off energy is set to 400 eV. We used a 2 × 3 × 1 k-points Γ-centered mesh for calculating total energy and the structure relaxations of the WSe 2 /Cs 4 AgBiBr 8 heterostructure, WSe 2 /Cs 4 AgBiBr 8 heterostructure with W vacancy, and WSe 2 /Cs 4 AgBiBr 8 heterostructure with Se vacancy. A Γ-centered mesh of 9 × 9 × 2 k-points was used for the calculations of the WSe 2 monolayer. All structures were relaxed until the energy was less than 10 −5 eV per atom and the force on each ion reduced below 0.03 eV Å −1 . Then the electronic properties were calculated with the optimized structures. Considering the underestimation of the GGA-PBE functional of the band gaps, we employed the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional [28] to calculate the electronic structure of the WSe 2 monolayer and Cs 4 AgBiBr 6 monolayer for accurate band gap value.

Construction and Stability of the Heterostructure
We first investigated the structure of the WSe 2 monolayer and Cs 4 AgBiBr 8 . The WSe 2 monolayer is built by the monolayer 2D structure separated from WSe 2 bulk (space group: P6 3 mmc and lattice parameters: a = 3.327 Å, c = 15.069 Å from [29,30]) and adding a vacuum layer of 15 Å. We analyzed the WSe 2 monolayer using the GGA-PBE method; the space group is P − 6m2, and the optimized lattice parameters are a = 3.315 Å and c = 18.031 Å. We constructed a single-layer two-dimensional double perovskite Cs 4 AgBiBr 8 by cutting the (0 1 1) surface of the double perovskite Cs 2 AgBiBr 6 (space group: Fm − 3m; lattice parameters: a = 8.123 Å). To ensure that the analysis object is the Cs 4 AgBiBr 8 monolayer, we added a vacuum layer of 15 Å [31] to the unit cell of Cs 4 AgBiBr 8 to avoid the effect of periodicity. We analyzed the WSe 2 monolayer with the GGA-PBE method; the space group is P4mmm, and the optimized lattice parameters are a = 8.123 Å c = 20.782 Å.
Heterostructures were built by the Structural Utilities (804) of 'vaspkit' [32] to find two representative heterostructures containing 73 atoms (containing 8 Cs, 2 Ag, 2 Bi, 16 Br, 15 W, and 30 Se atoms) with a suitable lattice shape and reasonable lattice mismatch respectively, named Heterostructure A and Heterostructure B (shown in Figure 1). The lattice mismatch rate σ (the lattice mismatch which can quantify structural match of crystals) is 2.027% and 4.048%, respectively, less than 5%. Heterostructure A is obtained by expanding the Following several attempts, the vacuum layer of the two species in the heterostructure is set to 3.5 Å. In order to avoid the influence of periodicity on the calculation results, a vacuum layer of 15 Å is set outside the heterostructure.

Construction and Stability of the Heterostructure
We first investigated the structure of the WSe2 monolayer and Cs4AgBiBr8. The WSe2 monolayer is built by the monolayer 2D structure separated from WSe2 bulk (space group: P63mmc and lattice parameters: a = 3.327 Å, c = 15.069 Å from [29,30]) and adding a vacuum layer of 15 Å. We analyzed the WSe2 monolayer using the GGA-PBE method; the space group is P6 m2, and the optimized lattice parameters are a = 3.315 Å and c = 18.031 Å. We constructed a single-layer two-dimensional double perovskite Cs4AgBiBr8 by cutting the (0 1 1) surface of the double perovskite Cs2AgBiBr6 (space group: Fm3 m; lattice parameters: a = 8.123 Å). To ensure that the analysis object is the Cs4AgBiBr8 monolayer, we added a vacuum layer of 15 Å [31] to the unit cell of Cs4AgBiBr8 to avoid the effect of periodicity. We analyzed the WSe2 monolayer with the GGA-PBE method; the space group is P4mmm, and the optimized lattice parameters are a = 8.123 Å c = 20.782 Å.
Heterostructures were built by the Structural Utilities (804) of 'vaspkit' [32] to find two representative heterostructures containing 73 atoms (containing 8 Cs, 2 Ag, 2 Bi, 16 Br, 15 W, and 30 Se atoms) with a suitable lattice shape and reasonable lattice mismatch respectively, named Heterostructure A and Heterostructure B (shown in Figure 1). The lattice mismatch rate σ (the lattice mismatch which can quantify structural match of crystals) is 2.027% and 4.048%, respectively, less than 5%. Heterostructure A is obtained by expanding the WSe2 single crystal according to the transformation matrix  The two types of heterostructure are very similar; Heterostructure B can be obtained from Heterostructure A when the W atom and the vertical two Se atoms are exchanged in the horizontal direction. Interestingly, in the vertical direction, the atoms position correspondences are different; the calculated results show that the properties of the two heterostructures are basically the same. In order to quantify the thermodynamic stability of the interaction between WSe 2 and Cs 4 AgBiBr 8 , the interface adhesion energy E ad , a good descriptor, is obtained according to Equation (1): where E hete. , E WSe 2 , and E Cs 4 AgBiBr 8 represent the total energies of the relaxed heterostructures WSe 2 /Cs 4 AgBiBr 8 , monolayer WSe 2 , and monolayer Cs 4 AgBiBr 8 , respectively. We calculated the adhesion energy of the two heterostructures to be −0.226 eV and −0.219 eV, respectively. Obviously, Heterostructure A has lower adhesion energy and lattice mismatch rate, so we decided to use Heterostructure A for follow-up research. After geometric optimization, the surface of WSe 2 did not exhibit significant deformation. The WSe 2 /Cs 4 AgBiBr 8 heterostructure has a typical vdW equilibrium spacing, which was calculated to be 3.67 Å (Figure 1a) between the WSe 2 and Cs 4 AgBiBr 8 layers. We noticed that when WSe 2 was adsorbed onto the surface of Cs 4 AgBiBr 8 (001), only physical adsorption occurred, but no chemical adsorption was observed.

Electronic Properties of WSe 2 /Cs 4 AgBiBr 8
To investigate the photocatalytic performance of the WSe 2 /Cs 4 AgBiBr 8 heterostructure, the energy band structures of the WSe 2 monolayer, Cs 4 AgBiBr 8 monolayer, and WSe 2 /Cs 4 AgBiBr 8 heterostructure were calculated, respectively. We employed GGA-PBE and HSE06 methods to acquire more exact electronic structure properties, as shown in  The two types of heterostructure are very similar; Heterostructure B can be obtained from Heterostructure A when the W atom and the vertical two Se atoms are exchanged in the horizontal direction. Interestingly, in the vertical direction, the atoms position correspondences are different; the calculated results show that the properties of the two heterostructures are basically the same. In order to quantify the thermodynamic stability of the interaction between WSe2 and Cs4AgBiBr8, the interface adhesion energy , a good descriptor, is obtained according to Equation (1): where . , , and represent the total energies of the relaxed heterostructures WSe2/Cs4AgBiBr8, monolayer WSe2, and monolayer Cs4AgBiBr8, respectively. We calculated the adhesion energy of the two heterostructures to be −0.226 eV and −0.219 eV, respectively. Obviously, Heterostructure A has lower adhesion energy and lattice mismatch rate, so we decided to use Heterostructure A for follow-up research.
After geometric optimization, the surface of WSe2 did not exhibit significant deformation. The WSe2/Cs4AgBiBr8 heterostructure has a typical vdW equilibrium spacing, which was calculated to be 3.67 Å (Figure 1a) between the WSe2 and Cs4AgBiBr8 layers. We noticed that when WSe2 was adsorbed onto the surface of Cs4AgBiBr8(001), only physical adsorption occurred, but no chemical adsorption was observed.

Electronic Properties of WSe2/Cs4AgBiBr8
To investigate the photocatalytic performance of the WSe2/Cs4AgBiBr8 heterostructure, the energy band structures of the WSe2 monolayer, Cs4AgBiBr8 monolayer, and WSe2/Cs4AgBiBr8 heterostructure were calculated, respectively. We employed GGA-PBE and HSE06 methods to acquire more exact electronic structure properties, as shown in Figure 2. The WSe2 monolayer has a direct bandgap of 1.55 eV with the GGA-PBE method, which agrees well with the 1.6 eV estimated by extrapolating, as shown in Figure 2a. For the WSe2 monolayer, CBM and VBM are located at the K point, while the Cs4AgBiBr8 monolayer has an indirect bandgap of 2.09 eV, as shown in Figure 2b. With the HSE06 method, the WSe2 monolayer has a direct bandgap of 2.03 eV, and the bandgap of Cs4AgBiBr8 monolayer is 3.23 eV. Thus, the GGA-PBE functional might underestimate the band gaps of the heterostructures that we built, by about 0.6 eV, at least.  The WSe 2 /Cs 4 AgBiBr 8 heterostructure is a type-II heterostructure which has better photocatalytic performance, owing to its effectiveness in spatially separating photogenerated electron-hole pairs by band alignment between two semiconductors [33]. By comparing the band structures of the Cs 4 AgBiBr 8 monolayer and the WSe 2 monolayer, we found that the band structure of the WSe 2 /Cs 4 AgBiBr 8 heterostructure is influenced by vdW interaction between Cs 4 AgBiBr 8 and WSe 2 interfaces, rather than an uncomplicated superposition of the WSe 2 monolayer and the Cs 4 AgBiBr 8 monolayer. The energy bands of WSe 2 /Cs 4 AgBiBr 8 heterostructures are staggered around the forbidden band, as shown in Figure 3a, in which the red and blue parts are contributed by Cs 4 AgBiBr 8 and WSe 2 , respectively. The band structure of the WSe 2 /Cs 4 AgBiBr 8 heterostructure has an indirect bandgap of 1.10 eV using the GGA-PBE method, which did not meet our expectations. The VBM and CBM of the heterostructure were located at Γ point and the point between the Γ point and X point, respectively. Obviously, the Cs 4 AgBiBr 8 monolayer contributes the VBM, and the CBM comes from the WSe 2 monolayer. Learning from the total and atom-projected density of states (TDOS and PDOS) between −1.5 eV and 1.5 eV, as shown in Figure 3a, the VBM is mainly composed of Ag d state and Br p state; at the same time, the CBM is mainly composed of W d state and Se p state.
The WSe2/Cs4AgBiBr8 heterostructure is a type-II heterostructure which has better photocatalytic performance, owing to its effectiveness in spatially separating photogenerated electron-hole pairs by band alignment between two semiconductors [33]. By comparing the band structures of the Cs4AgBiBr8 monolayer and the WSe2 monolayer, we found that the band structure of the WSe2/Cs4AgBiBr8 heterostructure is influenced by vdW interaction between Cs4AgBiBr8 and WSe2 interfaces, rather than an uncomplicated superposition of the WSe2 monolayer and the Cs4AgBiBr8 monolayer. The energy bands of WSe2/Cs4AgBiBr8 heterostructures are staggered around the forbidden band, as shown in Figure 3a, in which the red and blue parts are contributed by Cs4AgBiBr8 and WSe2, respectively. The band structure of the WSe2/Cs4AgBiBr8 heterostructure has an indirect bandgap of 1.10 eV using the GGA-PBE method, which did not meet our expectations. The VBM and CBM of the heterostructure were located at Γ point and the point between the Γ point and X point, respectively. Obviously, the Cs4AgBiBr8 monolayer contributes the VBM, and the CBM comes from the WSe2 monolayer. Learning from the total and atom-projected density of states (TDOS and PDOS) between −1.5 eV and 1.5 eV, as shown in Figure 3a, the VBM is mainly composed of Ag d state and Br p state; at the same time, the CBM is mainly composed of W d state and Se p state. The VBM of WSe2/Cs4AgBiBr8 heterostructure is provided by the Cs4AgBiBr8 layer, while the CBM is provided by the WSe2 layer. This demonstrates that the holes and excited The VBM of WSe 2 /Cs 4 AgBiBr 8 heterostructure is provided by the Cs 4 AgBiBr 8 layer, while the CBM is provided by the WSe 2 layer. This demonstrates that the holes and excited electrons are separately confined to different layers of the heterostructure, which promotes the formation of spatially indirect excitons.

Cs 4 AgBiBr 8 /WSe 2 with W Vacancy
It can be learned from Figure 3c that W atoms play a major role in the CBM, so the effect of adding W vacancies to the heterostructure is also considered. The WSe 2 layer consists of 15 WSe 2 molecules with a total of 15 W atoms and 30 Se atoms. We attempted to analyze 15 different heterostructures with W atom vacancies using the GGA-PBE method (one of which is shown in Figure S1a). Electronic properties of 15 W atom vacancy heterostructures are similar and not ideal. It can be learned from the energy band structures and the DOS (Figure 3c) that the defect states brought by the W vacancies are generated near the VBM and coincide with the VBM, which makes both sides of the forbidden band provided by WSe 2 and the band gap is still indirect, which is not conducive to improving the photocatalytic activity.

Stability of Cs 4 AgBiBr 8 /WSe 2 with Se Vacancy
WSe 2 /Cs 4 AgBiBr 8 heterostructure is an indirect band gap heterostructure, which is not conducive to improving the photocatalytic activity, and the positions of VBM and CBM are very close, so we tried to introduce defects in the heterostructure. The VBM provided by Cs 4 AgBiBr 8 is located at the Γ point, while the CBM provided by WSe 2 is located between the Γ point and the X point, not on the ordinary high symmetry point. Compared with the 2D double perovskite Cs 4 AgBiBr 8 layer, the WSe 2 layer has better ductility. Combining the above two points, we decided to study the WSe 2 layers in WSe 2 /Cs 4 AgBiBr 8 , namely the W vacancy and the Se vacancy defects.
Interestingly, we found that the introduction of Se atomic vacancy evidently affects the electronic properties of the heterostructures. We numbered the 30 Se atoms in the WSe 2 layer as 1 to 30 (as shown in Figure 4a), where the odd numbers are the upper layer, and the even numbers are the lower layer. The calculated results show that all 30 Cs 4 AgBiBr 8 /WSe 2 heterostructures with Se atom vacancies are very close in electronic properties and all have direct band gaps, two of which are shown in Figure S2. Compared to the original heterostructure, that with Se atom vacancies shows minimal structure change. We therefore calculated the adhesion energies of 30 heterostructures with Se atom vacancy (Figure 4b). We found that the adhesion energy of most of the 30 heterostructures with Se atom vacancy is around −0.225 eV, and the heterostructures have lower interfacial adhesion energy when the defects appear on the lower surface of the WSe 2 layer. Clearly, we observe that the heterostructures with No. 6 Se vacancy and the No. 14 Se vacancy have abnormally low adhesion energies. Both of the heterostructures with No. 6 Se vacancy and No. 14 Se vacancy are near the vertical direction of the upper Br atoms from the 2D double perovskite layer. The abnormally low interfacial adhesion energy may be caused by this Br atom.

Electronic Structure of Cs 4 AgBiBr 8 /WSe 2 with Se Vacancy
We analyzed Cs 4 AgBiBr 8 /WSe 2 heterostructures with No. 6 Se vacancy (shown in Figure S1b), which has the lowest adhesion energy. We found a defect level provided by WSe 2 between the Fermi level and the conduction band, which is quite flat and reaches a minimum at the Γ point (Figure 3b). Compared with the Cs 4 AgBiBr 8 /WSe 2 heterostructure energy band structure (Figure 3a), the Se atom vacancy has little effect on the valence band, and the VBM is still located at the Γ point. Therefore, we speculate that the Cs 4 AgBiBr 8 /WSe 2 heterostructure with Se atom vacancy has a direct band gap of 0.63 eV, and both VBM and CBM are located at the Γ point.  Table S1). The partial charge densities of the (c) CBM and (d) VBM of the Cs4AgBiBr8/WSe2 heterostructure, and that of the (e) CBM and (f) VBM of the Cs4Ag-BiBr8/WSe2 heterostructure with Se vacancy.

Electronic Structure of Cs4AgBiBr8/WSe2 with Se Vacancy
We analyzed Cs4AgBiBr8/WSe2 heterostructures with No. 6 Se vacancy (shown in Figure S1b), which has the lowest adhesion energy. We found a defect level provided by WSe2 between the Fermi level and the conduction band, which is quite flat and reaches a minimum at the Γ point (Figure 3b). Compared with the Cs4AgBiBr8/WSe2 heterostructure energy band structure (Figure 3a), the Se atom vacancy has little effect on the valence band, and the VBM is still located at the Γ point. Therefore, we speculate that the Cs4Ag-BiBr8/WSe2 heterostructure with Se atom vacancy has a direct band gap of 0.63 eV, and both VBM and CBM are located at the Γ point.
We calculated the partial charge densities for the CBM and VBM of the Cs4Ag-BiBr8/WSe2 heterostructure and of the heterostructure with Se vacancy (shown in Figure  4c-f, respectively). The electron orbitals of WSe2 and Cs4AgBiBr8 occupy the CBM and VBM of the Cs4AgBiBr8/WSe2 heterostructure, respectively, which is consistent with the earlier analysis about DOS. Comparing the partial charge densities of CBM between the original heterostructure and heterostructure with Se vacancy, it is evident that the charge centers on the Se vacancy, which is uniformly distributed in the original heterostructure. The partial charge density of VBM has no change when there is a Se vacancy in the Cs4Ag-BiBr8/WSe2 heterostructure.
To understand how charges are transferring at the interface, we calculated the work function, which is used as an intrinsic reference for band alignment, of the Cs4AgBiBr8 monolayer, WSe2 monolayer with Se vacancy, and Cs4AgBiBr8/WSe2 with Se vacancy using the GGA-PBE method. The work function is calculated according to Equation (2) [34]:  Table S1). The partial charge densities of the (c) CBM and (d) VBM of the Cs 4 AgBiBr 8 /WSe 2 heterostructure, and that of the (e) CBM and (f) VBM of the Cs 4 AgBiBr 8 /WSe 2 heterostructure with Se vacancy.
We calculated the partial charge densities for the CBM and VBM of the Cs 4 AgBiBr 8 /WSe 2 heterostructure and of the heterostructure with Se vacancy (shown in Figure 4c-f, respectively). The electron orbitals of WSe 2 and Cs 4 AgBiBr 8 occupy the CBM and VBM of the Cs 4 AgBiBr 8 /WSe 2 heterostructure, respectively, which is consistent with the earlier analysis about DOS. Comparing the partial charge densities of CBM between the original heterostructure and heterostructure with Se vacancy, it is evident that the charge centers on the Se vacancy, which is uniformly distributed in the original heterostructure. The partial charge density of VBM has no change when there is a Se vacancy in the Cs 4 AgBiBr 8 /WSe 2 heterostructure.
To understand how charges are transferring at the interface, we calculated the work function, which is used as an intrinsic reference for band alignment, of the Cs 4 AgBiBr 8 monolayer, WSe 2 monolayer with Se vacancy, and Cs 4 AgBiBr 8 /WSe 2 with Se vacancy using the GGA-PBE method. The work function is calculated according to Equation (2) [34]: where Φ, E vac , and E f ermi represent the work function, the electrostatic potential of the vacuum level, and the Fermi level, respectively. Based on Equation (2), the work functions of the Cs 4 AgBiBr 8 monolayer, WSe 2 monolayer with Se vacancy, and Cs 4 AgBiBr 8 /WSe 2 with Se vacancy are 4.33 eV, 5.07 eV, and 4.43 eV, respectively, as shown in Figure 5a-c.
where , , and represent the work function, the electrostatic potential of the vacuum level, and the Fermi level, respectively. Based on Equation (2), the work functions of the Cs4AgBiBr8 monolayer, WSe2 monolayer with Se vacancy, and Cs4AgBiBr8/WSe2 with Se vacancy are 4.33 eV, 5.07 eV, and 4.43 eV, respectively, as shown in Figure 5a-c. It can be seen from the electrostatic potentials that the electrons in the Cs4AgBiBr8 layer with low work function flow into the WSe2 layer, which has high work function after the electrostatic potential contact is formed. Therefore, the negative charges will accumulate at the interface of the WSe2 layer; at the same time, the positive charges will accumulate at the interface of the Cs4AgBiBr8 layer. Finally, the two Fermi levels of WSe2 and Cs4AgBiBr8 reach the same energy level; then, an internal electric field, which is generated by this spontaneous interfacial charge transfer, takes shape at the interface from the WSe2 layer to the Cs4AgBiBr8 layer. We plotted the energy level lineup diagrams and the charge separation schematic of the Cs4AgBiBr8 monolayer and WSe2 monolayer before and after contact, as shown in Figure 5d. It can be seen from the electrostatic potentials that the electrons in the Cs 4 AgBiBr 8 layer with low work function flow into the WSe 2 layer, which has high work function after the electrostatic potential contact is formed. Therefore, the negative charges will accumulate at the interface of the WSe 2 layer; at the same time, the positive charges will accumulate at the interface of the Cs 4 AgBiBr 8 layer. Finally, the two Fermi levels of WSe 2 and Cs 4 AgBiBr 8 reach the same energy level; then, an internal electric field, which is generated by this spontaneous interfacial charge transfer, takes shape at the interface from the WSe 2 layer to the Cs 4 AgBiBr 8 layer. We plotted the energy level lineup diagrams and the charge separation schematic of the Cs 4 AgBiBr 8 monolayer and WSe 2 monolayer before and after contact, as shown in Figure 5d.

Conclusions
We constructed van der Waals heterostructures using monolayer WSe 2 and monolayer 2D Cs 4 AgBiBr 8 . Considering a reasonable lattice mismatch rate and interface adhesion energy, we constructed a newWSe 2 /Cs 4 AgBiBr 8 heterostructure with a lattice mismatch rate of 2.027% and the lowest interface adhesion energy. Importantly, layered WSe 2 /Cs 4 AgBiBr 8 can form a type-II heterostructure. By introducing Se vacancy, we further successfully converted it into a direct band gap WSe 2 /Cs 4 AgBiBr 8 heterostructure. We also found the most stable WSe 2 /Cs 4 AgBiBr 8 heterostructure with Se vacancy, when Se vacancy appeared Materials 2023, 16, 3668 9 of 10 on the lower surface of WSe 2 and near the vertical direction of the upper Br atoms from the 2D double perovskite layer. These results indicate that it is possible to construct type-II van-der-Waals heterostructures composed of TMD monolayers and 2D double perovskites from indirect band gaps to direct band gaps based on bandgap engineering.