#### 3.1. Structural Features of the Monolayer SiS_{2}, WSe_{2} and SiS_{2}/WSe_{2} Hetero-Bilayer

Before investigating the SiS

_{2}/WSe

_{2} hetero-bilayer systems, we first study the electronic properties of isolated monolayer SiS

_{2} and monolayer WSe

_{2} (the space group of monolayer SiS

_{2} and monolayer WSe

_{2} are P3m1 and P63/mmc, respectively). The corresponding optimized structures of monolayer SiS

_{2} and monolayer WSe

_{2} are shown in

Figure 1a,b. As shown in

Figure 1, both of them have the same primitive cell of hexagonal structure with three atoms per unit cell. The lattice constants of SiS

_{2} and WSe

_{2} monolayers are calculated to be 3.30 and 3.33 Å, respectively, which agree well with previous results [

33,

41,

42]. Compared with the hybrid systems investigated previously [

21,

22,

23,

24,

25,

26,

27,

28,

29,

30,

31,

32], such a lattice mismatch (only about 0.9%) between the SiS

_{2} and WSe

_{2} monolayers is very small. Thus, we have employed supercells composed of 1 × 1 unit cells of SiS

_{2} monolayer and 1 × 1 unit cells of WSe

_{2} monolayer in the x-y plane. To explore the possible stacking models of hetero-bilayers, we build six different stacking patterns of SiS

_{2}/WSe

_{2} hetero-bilayers (labeled as AA-1, AA-2; AB-1, AB-2; AC-1, AC-2), as expressed in

Figure 1c–h.

For AA-1 stacking, W atoms and Se atoms are located directly under the Si atoms and S (top sub-plane) atoms, respectively. For AB-1 stacking, W atoms and Se atoms are positioned just below the S atoms (bottom sub-plane) and Si atoms, respectively. For AC-1 stacking, W atoms and Se atoms are both positioned directly below the S atoms (top sub-plane and bottom sub-plane). The AA-2 (AB-2, AC-2) configuration is achieved by fixing the top layer of SiS

_{2} and rotating the WSe

_{2} layer of AA-1 (AB-1, AC-1) by 180 degrees with the “c” axis. The calculated binding energies for those configurations are shown in

Table 1. According to our results, the binding energy of the AB-2 stacking (−197 meV) is shown to be larger than the binding energies of the other stacking models, indicating that the AB-2 model is the most stable and has the strongest bonding. These binding energies have the same order of magnitude as other typical vdW heterostructures such as the WSe

_{2}/BP heterostructure (−141 meV) [

26] and the MoSe

_{2}/MoS

_{2} heterostructure (−158.1 meV) [

43]. In addition to the binding energy, we also investigated the bond length, the interlayer spacing (the distance between the sulfur layer of the SiS

_{2} monolayer and its nearest selenium layer) and the band gaps of the hetero-bilayer systems, as shown in

Table 1. Clearly, the calculated differences of lattice constants (around 2.33 Å) and bond lengths (around 2.54 Å) of Si-S and W-Se between the six hetero-bilayer models are very small. However, due to the change in relative position of atoms between the two layers, the interlayer spacings exhibit relatively larger deviations. As shown in

Table 1, the AB-2 stacking configuration has the shortest interlayer distance, showing again the strongest bonding in the hetero-bilayer system. Among all six of the SiS

_{2}/WSe

_{2} hetero-bilayers, at the PBE level, the AB-2 stacking model is the only semiconductor. Since the AB-2 stacking model is the most stable stacking pattern, we now further discuss the electronic structures of the AB-2 stacking hetero-bilayer.

#### 3.2. Electronic Properties of the SiS_{2}/WSe_{2} Hetero-Bilayer

Figure 2a,b demonstrates the band structures of monolayer SiS

_{2} and monolayer WSe

_{2} obtained by the GGA-PBE (black solid lines) and HSE06 (red dashed lines) method. It is clear that the pristine SiS

_{2} monolayer displays an indirect band gap semiconductor. The band gaps of monolayer SiS

_{2} obtained by the GGA-PBE and HSE06 method are 1.39 and 2.34 eV, respectively. Its valence-band maximum (VBM) is located between the high symmetry points

$\Gamma $ and M and the conduction-band minimum (CBM) is at the high symmetry M-point. In regard to the isolated monolayer WSe

_{2}, it possesses a direct band gap of 1.48 eV (PBE level) or 2.0 eV (HSE06 level) at the high symmetric K-point. These results are consistent with previous studies [

33,

44,

45]. After the 2D materials were constructed into hetero-bilayers, the band gaps narrowed or even disappeared. However, the electronic properties of origin SiS

_{2} and WSe

_{2} monolayers were well preserved. As mentioned above, at PBE level, the AB-2 stacking is the most stable configuration and it is the only semiconductor among the six configurations. For the AB-2 stacking configuration, as shown in

Figure 2c, the CBM and VBM of the SiS

_{2} layer are both lower than those of the WSe

_{2}, which forms a staggered type-II indirect band alignment. To further the discussion of the electronic structures of the SiS

_{2}/WSe

_{2} hetero-bilayer, we also investigate the density of states. The total density of states is demonstrated by the black line. The orbital occupancy of each atom is clearly demonstrated in the projected density of states (the state with a low orbital occupancy is not shown in the figure). It can be seen clearly that, near the VBM (from −1 to 0 eV), the occupied states are almost dominated by W atoms (

d orbitals) and Se atoms (

p orbitals). While the electronic states above the Fermi level are contributed by Si (

s orbitals) and S atoms (

p orbitals). These results again confirm the type II band alignment of the AB-2 SiS

_{2}/WSe

_{2} hetero-bilayer, which can effectively separate the photogenerated holes and electrons [

46,

47,

48,

49]. Owing to the narrower band gap (0.154 and 0.738 eV obtained by GGA-PBE and HSE06, respectively), the electrons are more susceptible to being excited from VBM to CBM when the SiS

_{2}/WSe

_{2} heterostructure is exposed to light [

50].

On the other hand, we also calculate the effective mass of AB-2 stacking model based on the formula as follows:

Here,

$\hslash $ is Plank’s constant,

E(

k) is the energy of CBM or VBM, and

k is the wave vector. The effective mass is a key parameter to measure the mobility of carriers. Under certain conditions, the mobility

$\mu $ is inversely proportional to the effective mass

${m}^{*}$. Our results show that the electron effective mass

${m}_{n}^{*}$ of CBM is 0.43

${m}_{0}$ (

${m}_{0}$ represents the mass of a free-electron), and the hole effective mass

${m}_{p}^{*}$ of VBM is 0.47

${m}_{0}$. A relatively small effective mass means higher carrier mobility [

51]. Moreover, due to effectively separating electron–hole pairs of type-II band alignment, the lifetime of photogenerated carriers is remarkably extended.

The work function, which is crucial for evaluating the internal electronic behavior of heterostructures, is also discussed to explain the relevant charge transfer phenomenon (

Figure 3a). The work functions of monolayer WSe

_{2} and monolayer SiS

_{2} are 5.15 and 6.49 eV respectively. Obviously, the work function of the WSe

_{2} sheet is smaller than that of the SiS

_{2} sheet, leading the electrons to spontaneously diffuse from WSe

_{2} to the SiS

_{2} layer in the SiS

_{2}/WSe

_{2} hetero-bilayer. After the interaction between atomic layers, the Fermi level of WSe

_{2} is further moved downward while the Fermi level of SiS

_{2} is moved upward and finally reaches the same level, which causes the work function of the hetero-bilayer to be 5.21 eV. The same behaviors can be found in the electrostatic potential of the SiS

_{2}/WSe

_{2} hetero-bilayer shown in

Figure 3b. Due to the higher potential energy of WSe

_{2}, the positive charges are accumulated in the WSe

_{2} layer, while the negative charges are accumulated in the SiS

_{2} layer. A built-in electric field directed from WSe

_{2} to SiS

_{2} is thus formed on the surface of the SiS

_{2}/WSe

_{2} hetero-bilayer, resulting in a drift movement of the internal carriers. In addition, the calculated valence band offset (VBO)

$\mathit{\u2206}{E}_{V}$ and conduction band offset (CBO)

$\mathit{\u2206}{E}_{C}$ between the SiS

_{2} and WSe

_{2} layers reach 1.31 and 1.40 eV (1.33 and 1.66 eV) obtained by GGA-PBE (HSE06) method, respectively, as shown in

Figure 3a. Such a huge band offsets can remarkably prolong the lifetime of interlayer carrier (electrons and holes) and improve the efficiency of carrier separation, which plays an indispensable role in the application of optoelectronic devices. Thus, most of the photogenerated electrons are transferred from the valence band of the WSe

_{2} layer to the conduction band of the SiS

_{2} layer. After a few photogenerated electrons jump to the conduction band of WSe

_{2} with higher energy, they will then transit to the conduction band of SiS

_{2} with lower energy. The photogenerated holes transfer process of the SiS

_{2}/WSe

_{2} hetero-bilayer functions in an opposite manner.

In order to obtain a more accurate energy band gap, we also perform HSE06 calculations for the AB-2 stacking configuration, as shown in

Figure 3c. The size of the red and blue dots respectively indicates the contribution of the SiS

_{2} layer and WSe

_{2} layer to the band structure. It is obvious that the the band at the CBM and VBM are contributed from the WSe

_{2} layer and the SiS

_{2} layer, respectively. The band gap of the SiS

_{2}/WSe

_{2} hetero-bilayer, calculated by the HSE06 method, is 0.738 eV.

#### 3.3. Effect of Biaxial Strain on Electronic Properties of SiS_{2}/WSe_{2} Hetero-Bilayer

As is well known, strain modulation is an effective way to alter the electronic properties of 2D vdW heterostructures [

52,

53,

54]. In this work, we applied the in-plane biaxial strain to the SiS

_{2}/WSe

_{2} hetero-bilayer by changing the lattice constant of the system in both the x and y directions (i.e., compressive or tensile stresses). As shown in

Figure 4a, blue and orange arrows represent the compressive and tensile strain, respectively. The degree of strain (

$\epsilon $) is defined as follows:

where

a and

${a}_{0}$ correspond to the strained and unstrained lattice constants of SiS

_{2}/WSe

_{2} hetero-bilayer, respectively. Tensile (compressive) stress is represented by

$\epsilon 0$ (

$\epsilon 0$). The biaxial stresses range from −11% to 11% with an interval of 2%. To avoid the structure collapse of SiS

_{2}/WSe

_{2} hetero-bilayer, we also calculate the strain energy

E, which is defined as follows:

where

${E}_{\mathrm{total}}$ and

${E}_{0}$ represent the total energy of the strained system and the strain-free system, respectively.

N is the number of atoms in the supercell. The results are shown in

Figure 4b; the strain energy increases monotonously with increasing stress (compressive stresses: from 0 to −7%, tensile stresses: from 0 to 7%). Noteworthy is the evolution curve of the strain energy in this interval is close to the quadratic function of the strain, indicating that the stresses applied on the hetero-bilayer are within the elastic deformation limit. However, the strain energy curve begins to deviate from the original trend if the tensile (compressive) stress continues to increase, showing that the hetero-bilayer is undergoing inelastic deformation.

We also calculate the evolution curve of the band gap and band offsets of the SiS

_{2}/WSe

_{2} hetero-bilayer as a function of the biaxial stress

ε, as expressed in

Figure 4c. In the range of elastic deformation (the stress changes from −7% to 7%), the band gap of the SiS

_{2}/WSe

_{2} hetero-bilayer decreases gradually with increasing tensile stress. When the applied strain exceeds the range of elastic deformation, the change trend of energy band is opposite. In regard to the band offsets of the SiS

_{2}/WSe

_{2} hetero-bilayer, the VBO increase continuously as the strain changes from −11% to 5%, then decreases with increasing tensile stress.

The change of band gap and band offsets of the SiS

_{2}/WSe

_{2} hetero-bilayer can be intuitively shown in

Figure 5, which is the projected band structure diagrams of the SiS

_{2}/WSe

_{2} hetero-bilayer, obtained by the HSE06 method under different biaxial strains. The red and blue dotted lines indicate the contribution of SiS

_{2} and WSe

_{2}, respectively. In the range of elastic deformation, the SiS

_{2}/WSe

_{2} hetero-bilayer maintains its type-II band alignment with an indirect band gap. When the compressive stress reaches −9%, the system turns into a direct band gap semiconductor with type-II band alignment. On the other hand, the SiS

_{2}/WSe

_{2} hetero-bilayer system changed the band alignment from type-II to type-I when the tensile stress reaches 11%, which is attractive for realizing the nano-scale multi-functional device applications.

#### 3.4. Effect of Electric Field on Electronic Properties of SiS_{2}/WSe_{2} Hetero-Bilayer

Applying an external electric field (

E_{ext}) has proven to be an effective method to tune the band gap [

55,

56]. In this section, we apply a vertical electric field (

E_{ext}) along the z direction to the SiS

_{2}/WSe

_{2} hetero-bilayer. The direction from the SiS

_{2} layer to the WSe

_{2} layer is defined as the positive direction of the

E_{ext}, which is opposite to the direction of the

E_{int} in the hetero-bilayer. The value of the band gap gradually increases with increasing negative

E_{ext}, and reduces continuously with the increasing positive

E_{ext}, as shown in

Figure 6. The band gap as a function of the external electric field shows a trend of completely linear decrease, while the changes of VBO and CBO show a linear increase trend. The projected band structures of the SiS

_{2}/WSe

_{2} hetero-bilayer under various

E_{ext} are displayed in

Figure 7. We find that the hetero-bilayer system could retain type-II band alignment features in the range of −0.1 V/Å to 0.5 V/Å for the external E-field, indicating that the

E_{ext} has little influence on the variations of the band structure of the systems. This is essential for the future application of the SiS

_{2}/WSe

_{2} hetero-bilayer-based electronic devices, such as the field-effect transistor.