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Open AccessArticle

Tunable Electronic Properties of Type-II SiS2/WSe2 Hetero-Bilayers

1
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
2
School of Physics, Northeast Normal University, Changchun 130024, China
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Nanomaterials 2020, 10(10), 2037; https://doi.org/10.3390/nano10102037
Received: 25 September 2020 / Revised: 12 October 2020 / Accepted: 13 October 2020 / Published: 15 October 2020
(This article belongs to the Special Issue 2D Materials and Their Heterostructures and Superlattices)

Abstract

First-principle calculations based on the density functional theory (DFT) are implemented to study the structural and electronic properties of the SiS2/WSe2 hetero-bilayers. It is found that the AB-2 stacking model is most stable among all the six SiS2/WSe2 heterostructures considered in this work. The AB-2 stacking SiS2/WSe2 hetero-bilayer possesses a type-II band alignment with a narrow indirect band gap (0.154 eV and 0.738 eV obtained by GGA-PBE and HSE06, respectively), which can effectively separate the photogenerated electron–hole pairs and prevent the recombination of the electron–hole pairs. Our results revealed that the band gap can be tuned effectively within the range of elastic deformation (biaxial strain range from −7% to 7%) while maintaining the type-II band alignment. Furthermore, due to the effective regulation of interlayer charge transfer, the band gap along with the band offset of the SiS2/WSe2 heterostructure can also be modulated effectively by applying a vertical external electric field. Our results offer interesting alternatives for the engineering of two-dimensional material-based optoelectronic nanodevices.
Keywords: first principle; hetero-bilayer; type-II band alignment; tunable band gap first principle; hetero-bilayer; type-II band alignment; tunable band gap

1. Introduction

In the past two decades, the emergence of two-dimensional layered materials [1,2,3,4] has attracted tremendous attention of researchers due to their novel electronic properties, such as high carrier mobility [5,6], high thermal conductivity [7] and excellent on/off ratio [8], which ensure their potential application prospects in the field of photoemission, photodetection and field effect transistors (FETs). However, under the growing demands of material multifunction, the electronic properties of one single 2D material are far from enough [9,10]. For example, graphene, silicene and germanene, as the most promising materials, all have linear dispersion at the Fermi level at the K-point in the Brillouin zone. To our knowledge, one of the key factors for the development of 2D materials is dependent on its tunable band gap [11,12]. Thus, being a gapless semiconductor, graphene, silicene and germanene cannot be directly used in electronic optoelectronic devices [13,14]. However, if we introduce a hetero-bilayer system by stacking two single-layer materials vertically, the tunable band gaps could be realized by employing in-plane biaxial stress or changing the interlayer distance [15,16,17,18].
Recently, the heterostructures based on transition metal dichalcogenides (TMDs) [19,20], especially the WSe2 [21,22,23] material, have attracted extensive research due to their excellent electronic and optoelectronic properties [24,25]. For example, Ren et al. established several TMDs-based van der Waals heterostructures (MoS2/BP, MoSe2/BP, WS2/BP and WSe2/BP) with bandgaps of 1.29, 1.37, 1.22 and 1.21 eV, respectively. Among them, MoSe2/BP and WSe2/BP possess type-II band alignment with a direct band gap, which can separate the photogenerated electron–hole pairs effectively [26]. Engin Torun et al. predicted the existence of interlayer excitons (0.15 and 0.24 eV below the absorption onset of intralayer excitons) in MoS2/WS2 and MoSe2/WSe2 heterostructures, indicating that the excitonic ground states of these systems spontaneously separate the electron and the hole in different layers [27]. Si et al. also investigated the photoelectronic properties of MoS2/WSe2 heterojunction via the combination of theoretical prediction and experimental verification. They deduced that the enhancement of the photoelectric response should be attributed to the construction of the MoS2/WSe2 type-II heterostructure, which not only promotes the photogenerated electron–hole pair separation, but also suppresses their recombination [28]. Aretouli et al. found that SnSe2/WSe2 heterostructure possesses a broken gap configuration, indicating that band-to-band tunneling through an ultrathin van der Waals gap can be switched on and off easily via applying a small bias across the interface, which implies promising applications in 2D-2D vertical TFETs [29]. Thus, the heterostructures not only provide a new way to enrich the novel properties of the system but also to well preserve the electronic properties of the original freestanding two single-layer 2D components [30,31,32].
In this study, we perform ab initio calculations to investigate the electronic properties of hetero-bilayers composed of WSe2 monolayer and SiS2 monolayer (a new group of VI-IV 2D material [33]). Six possible stacking models are considered here. The geometries, relative stabilities and band structures of the considered models are discussed. Our results show that the most stable SiS2/WSe2 hetero-bilayer possesses the type-II band alignment with a narrow band gap, which contributes to the separation of electron–hole pairs. Furthermore, by applying a certain range of biaxial strain and external electric field, the band gap of the SiS2/WSe2 hetero-bilayer can be effectively tuned while maintaining the type-II band alignment. Our calculations and analysis demonstrate that the SiS2/WSe2 heterostructure may become a promising candidate material in the application of photoelectric devices.

2. Computational Method

To systematically investigate the structural and electronic properties of SiS2/WSe2 heterobilayers, we performed all calculations using the Vienna ab initio simulation package (VASP 5.4.1., Vienna, Austria) based on density functional theory (DFT) with the plane-wave pseudopotential methods [34,35]. The generalized gradient approximation (GGA), with the Perdew–Burke–Ernzerhof (PBE) function, was employed to describe the exchange and correlation potential [36,37]. Additionally, the hybrid Heyd–Scuseria–Eenzerhof (HSE06, Houston, TX, USA) functional was also used to obtain a more accurate bandgap [38]. In consideration of the weak van der Waals (vdW) interactions in all calculations, we used the DFT-D2 method of Grimme to correct the long-range weak vdW interlayer interactions [39]. A plane-wave kinetic energy cutoff of 500eV was adopted. The Monkhorst–Pack K-points [40] were set to 35 × 35 × 1. A large vacuum zone of 20 Å was used to make the interaction between two adjacent 2D sheets in the periodic arrangement (along the “z” axis) negligible. The structure relaxations were carried out until the change of the energy and the force was less than 10−5 and 10−2 eV/Å per atom, respectively.
To quantitatively characterize the stability of the heterostructure, the binding energy of SiS2/WSe2 is defined as: E b = E S i S 2 / W S e 2 E S i S 2 + E W S e 2 , where E S i S 2 / W S e 2 , E S i S 2 and E W S e 2 represent the total energies of the SiS2/WSe2 hetero-bilayer, free-standing SiS2 monolayer and isolated WSe2 monolayer, respectively. E S i S 2 is calculated by using a 1 × 1 unit cell of the SiS2 monolayer, and E W S e 2 is calculated by using a 1 × 1 unit cell of the WSe2 monolayer (i.e., the size of the unit cells are the same as the supercell of the hetero-bilayer). To evaluate the interlayer electronic property and behavior of the SiS2/WSe2 heterobilayer, we also calculated the work function, defined as ϕ =   E 0 E F , where E 0 and E F are the energy of the stationary electron in the vacuum and the Fermi level, respectively.

3. Results and Discussion

3.1. Structural Features of the Monolayer SiS2, WSe2 and SiS2/WSe2 Hetero-Bilayer

Before investigating the SiS2/WSe2 hetero-bilayer systems, we first study the electronic properties of isolated monolayer SiS2 and monolayer WSe2 (the space group of monolayer SiS2 and monolayer WSe2 are P3m1 and P63/mmc, respectively). The corresponding optimized structures of monolayer SiS2 and monolayer WSe2 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 SiS2 and WSe2 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 SiS2 and WSe2 monolayers is very small. Thus, we have employed supercells composed of 1 × 1 unit cells of SiS2 monolayer and 1 × 1 unit cells of WSe2 monolayer in the x-y plane. To explore the possible stacking models of hetero-bilayers, we build six different stacking patterns of SiS2/WSe2 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 SiS2 and rotating the WSe2 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 WSe2/BP heterostructure (−141 meV) [26] and the MoSe2/MoS2 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 SiS2 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 SiS2/WSe2 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 SiS2/WSe2 Hetero-Bilayer

Figure 2a,b demonstrates the band structures of monolayer SiS2 and monolayer WSe2 obtained by the GGA-PBE (black solid lines) and HSE06 (red dashed lines) method. It is clear that the pristine SiS2 monolayer displays an indirect band gap semiconductor. The band gaps of monolayer SiS2 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 Γ and M and the conduction-band minimum (CBM) is at the high symmetry M-point. In regard to the isolated monolayer WSe2, 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 SiS2 and WSe2 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 SiS2 layer are both lower than those of the WSe2, which forms a staggered type-II indirect band alignment. To further the discussion of the electronic structures of the SiS2/WSe2 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 SiS2/WSe2 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 SiS2/WSe2 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:
m * =   ( 2 E ( k ) / k 2 ) 1
Here, 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 μ 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 WSe2 and monolayer SiS2 are 5.15 and 6.49 eV respectively. Obviously, the work function of the WSe2 sheet is smaller than that of the SiS2 sheet, leading the electrons to spontaneously diffuse from WSe2 to the SiS2 layer in the SiS2/WSe2 hetero-bilayer. After the interaction between atomic layers, the Fermi level of WSe2 is further moved downward while the Fermi level of SiS2 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 SiS2/WSe2 hetero-bilayer shown in Figure 3b. Due to the higher potential energy of WSe2, the positive charges are accumulated in the WSe2 layer, while the negative charges are accumulated in the SiS2 layer. A built-in electric field directed from WSe2 to SiS2 is thus formed on the surface of the SiS2/WSe2 hetero-bilayer, resulting in a drift movement of the internal carriers. In addition, the calculated valence band offset (VBO) E V and conduction band offset (CBO) E C between the SiS2 and WSe2 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 WSe2 layer to the conduction band of the SiS2 layer. After a few photogenerated electrons jump to the conduction band of WSe2 with higher energy, they will then transit to the conduction band of SiS2 with lower energy. The photogenerated holes transfer process of the SiS2/WSe2 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 SiS2 layer and WSe2 layer to the band structure. It is obvious that the the band at the CBM and VBM are contributed from the WSe2 layer and the SiS2 layer, respectively. The band gap of the SiS2/WSe2 hetero-bilayer, calculated by the HSE06 method, is 0.738 eV.

3.3. Effect of Biaxial Strain on Electronic Properties of SiS2/WSe2 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 SiS2/WSe2 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 ( ε ) is defined as follows:
ε   =   a a 0 a 0   ×   100 %
where a and a 0 correspond to the strained and unstrained lattice constants of SiS2/WSe2 hetero-bilayer, respectively. Tensile (compressive) stress is represented by ε   >   0 ( ε   <   0 ). The biaxial stresses range from −11% to 11% with an interval of 2%. To avoid the structure collapse of SiS2/WSe2 hetero-bilayer, we also calculate the strain energy E, which is defined as follows:
E   =   ( E total     E 0 ) / n
where E 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 SiS2/WSe2 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 SiS2/WSe2 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 SiS2/WSe2 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 SiS2/WSe2 hetero-bilayer can be intuitively shown in Figure 5, which is the projected band structure diagrams of the SiS2/WSe2 hetero-bilayer, obtained by the HSE06 method under different biaxial strains. The red and blue dotted lines indicate the contribution of SiS2 and WSe2, respectively. In the range of elastic deformation, the SiS2/WSe2 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 SiS2/WSe2 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 SiS2/WSe2 Hetero-Bilayer

Applying an external electric field (Eext) has proven to be an effective method to tune the band gap [55,56]. In this section, we apply a vertical electric field (Eext) along the z direction to the SiS2/WSe2 hetero-bilayer. The direction from the SiS2 layer to the WSe2 layer is defined as the positive direction of the Eext, which is opposite to the direction of the Eint in the hetero-bilayer. The value of the band gap gradually increases with increasing negative Eext, and reduces continuously with the increasing positive Eext, 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 SiS2/WSe2 hetero-bilayer under various Eext 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 Eext has little influence on the variations of the band structure of the systems. This is essential for the future application of the SiS2/WSe2 hetero-bilayer-based electronic devices, such as the field-effect transistor.

4. Conclusions

In summary, the structural and electronic properties of the SiS2/WSe2 hetero-bilayers are investigated in detail through first principles calculations. Our results show that the SiS2/WSe2 hetero-bilayer is an indirect band gap semiconductor (0.154 and 0.738 eV obtained by GGA-PBE and HSE06, respectively) with an intrinsic type-II band alignment. Meanwhile, the heterostructure perfectly retains the electronic properties of the pristine 2D monolayer components. Moreover, the SiS2/WSe2 hetero-bilayers have been shown to possess a relatively low effective mass, which enhances carrier mobility of the heterostructure. The type-II band alignment, narrow band gap, together with low effective mass conduce effective separation of photogenerated carriers, which is promising for application in optoelectronic devices. On the other hand, under biaxial strain, the heterostructure can withstand the biaxial strain from −7% (compressive) to 7% (tensile) while maintaining the type-II band alignment. Moreover, through changing the effective electric field crossing the interface of the heterostructure, the band gap and band offset of the SiS2/ WSe2 hetero-bilayers can be effectively modulated by applying the external electric field. Our results offer promising alternatives for the engineering of two dimensional material-based optoelectronic nanodevices.

Author Contributions

Y.G.—writing, review, editing, writing original draft, conceptualization; X.L.—project administration, validation, resources, supervision, writing original draft, review and editing; R.N.—investigation, formal analysis; N.Z.—investigation, formal analysis; T.H.—investigation; L.Z.—investigation, editing. All authors have read and agreed to the published version of the manuscript.

Funding

This work is supported by the Fundamental Research Funds for the Central Universities, China under grant No. 2412019FZ037.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Top and side views of (a) monolayer SiS2, (b) monolayer WSe2 and (ch) SiS2/WSe2 hetero-bilayers.
Figure 1. Top and side views of (a) monolayer SiS2, (b) monolayer WSe2 and (ch) SiS2/WSe2 hetero-bilayers.
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Figure 2. Energy band structures of (a) monolayer SiS2 and (b) monolayer WSe2. (c) Projected band structure and partial density of the state of AB-2 stacking SiS2/WSe2 hetero-bilayer; red and blue lines are bands contributed by SnS2 and WSe2 respectively.
Figure 2. Energy band structures of (a) monolayer SiS2 and (b) monolayer WSe2. (c) Projected band structure and partial density of the state of AB-2 stacking SiS2/WSe2 hetero-bilayer; red and blue lines are bands contributed by SnS2 and WSe2 respectively.
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Figure 3. (a) Band alignment and (b) electrostatic potential of AB-2 SiS2/WSe2 hetero-bilayer obtained by GGA-PBE method. (c) Projected band structure of AB-2 SiS2/WSe2 hetero-bilayer obtained by the HSE06 method’ red and blue lines are bands contributed by SnS2 and WSe2 respectively.
Figure 3. (a) Band alignment and (b) electrostatic potential of AB-2 SiS2/WSe2 hetero-bilayer obtained by GGA-PBE method. (c) Projected band structure of AB-2 SiS2/WSe2 hetero-bilayer obtained by the HSE06 method’ red and blue lines are bands contributed by SnS2 and WSe2 respectively.
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Figure 4. (a) Schematic diagram of tensile (orange arrows) and compressive (blue arrows) stresses on the SiS2/WSe2 hetero-bilayer. (b) Strain energy (E) as a function of strain of the biaxial stress ε. (c) Band gap and band offsets of the SiS2/WSe2 hetero-bilayer as a function of the biaxial stress ε.
Figure 4. (a) Schematic diagram of tensile (orange arrows) and compressive (blue arrows) stresses on the SiS2/WSe2 hetero-bilayer. (b) Strain energy (E) as a function of strain of the biaxial stress ε. (c) Band gap and band offsets of the SiS2/WSe2 hetero-bilayer as a function of the biaxial stress ε.
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Figure 5. Projected band structures obtained by the HSE06 method under different in-plane biaxial stresses; red and blue lines are bands contributed by SnS2 and WSe2, respectively.
Figure 5. Projected band structures obtained by the HSE06 method under different in-plane biaxial stresses; red and blue lines are bands contributed by SnS2 and WSe2, respectively.
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Figure 6. Band gap and band offsets of the SiS2/WSe2 hetero-bilayer as a function of the external electric field.
Figure 6. Band gap and band offsets of the SiS2/WSe2 hetero-bilayer as a function of the external electric field.
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Figure 7. Projected band structures of the SiS2/WSe2 hetero-bilayers under different external electric fields obtained by the HSE06 method; red and blue lines are bands contributed by SnS2 and WSe2 respectively.
Figure 7. Projected band structures of the SiS2/WSe2 hetero-bilayers under different external electric fields obtained by the HSE06 method; red and blue lines are bands contributed by SnS2 and WSe2 respectively.
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Table 1. The optimized structural parameters of SiS2/WSe2 heterostructures with different configurations, including the binding energy ( E b ), lattice constant (a), bond length ( d Si - S , d W - Se ), the interlayer spacing (s), and the band gap (Eg) of the system obtained by GGA-PBE and hybrid HSE06.
Table 1. The optimized structural parameters of SiS2/WSe2 heterostructures with different configurations, including the binding energy ( E b ), lattice constant (a), bond length ( d Si - S , d W - Se ), the interlayer spacing (s), and the band gap (Eg) of the system obtained by GGA-PBE and hybrid HSE06.
Stacking
Mode
E b ( meV ) a
(Å)
d Si - S ( Å ) d W - Se ( Å ) s
(Å)
E g PBE ( eV ) E g HSE 06 ( eV )
AA-1−182.53.3152.3252.5413.192metal/
AA-2−125.13.3152.3262.5423.784metal/
AB-1−194.23.3152.3252.5403.144metal/
AB-2−197.03.3152.3242.5413.1250.1540.738
AC-1−125.03.3142.3252.5413.788metal/
AC-2−175.03.3172.3252.5423.234metal/
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