Introduction

2D materials, such as graphene (Gr), hexagonal boron nitride (h-BN), graphitic carbon nitride (g-C3N4), and transition metal dichalcogenide (TMD) monolayers, have been intensively investigated in the recent decade [1,2,3,4,5,6]. Their unique properties suggest great potentials in a wide range of applications, such as catalyst [7,8,9], solar cells [10], lithium-ion battery [11,12,13], supercapacitors [14,15,16], liquid crystals [17,18,19], and superconductors [20, 21]. Hence, constructing heterostructures using different types of 2D materials has been one of the most important strategies to improve their properties and performances [22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39].

Graphene has attracted great attention owing to its fascinating properties [40,41,42,43,44,45,46], like its high low-temperature electron mobility, the possession of massless Dirac fermions, and other excellent physical properties. However, the lack of band gap hinders its application to many important fields, such as field-effect transistors, photocatalysts, and solar cell batteries [47]. Monolayer h-BN is a structural analog of graphene and has been referred to as the “white graphene.” Their superb chemical stability and intrinsic insulation have been attracting significant amount of research interests [48,49,50,51,52]. However, the wide band gap of unmodified h-BN sheets impedes their applications to visible light emission [47, 48]. 2D g-C3N4 also has a similar structure as graphene, consisting of building blocks of cyamelluric tri-s-triazine. Energetically, unlike pure single-layer graphene, g-C3N4 has a band gap of 2.7 eV [53], which results in an intrinsic semiconductor-like absorption in the blue region of the visible spectrum. However, there is a high recombination rate of the generated electrons and holes in 2D g-C3N4 [54], which hinders the performance of the application to photocatalyst and solar cell.

2D TMDs, which are usually denoted as MX2, where X represents the chalcogens (S, Se, Te), and M the transition metals (such as Mo, W), also exhibit excellent performances in optical and electrochemical applications. However, the low mobility of the fabricated 2D TMD device is far inferior to the expected intrinsic properties and greatly limits its practical applications. Because there is no dangling bond on the sulfur/selenium/tellurium-terminated surface [1], forming van der Waals’ (vdW) heterostructures with Gr, h-BN and g-C3N4 becomes an effective way to modify the properties of 2D materials, such as graphene/TMDs [55,56,57,58,59,60], h-BN/TMDs [61,62,63,64,65,66], and g-C3N4/TMDs [63,64,65,66]. There have been many experimental and theoretical studies [55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70] of tuning 2D materials properties by forming bilayer heterostructures with TMDs via vdW interaction.

Combing the advantages of both the building monolayers, although this type of heterostructures could bring improvements in terms of electronic or optical properties, the integrity of Dirac cone will be, unfortunately, damaged after interacting with the monolayer MX2, decreasing their carrier mobility. Covering graphene on both sides of TMD may overcome this shortcoming and result in increased mobility without changing the integrity of Dirac cone. On the other hand, sandwiched TMD would also result in an increase in active sites, which may bring extra advantages in catalysis applications.

Research of sandwich heterostructures [71,72,73] has been a focal point and study frontier in improving the properties of 2D materials. In 2012, an in situ simultaneous reduction–hydrolysis technique was used to fabricate 2D sandwich-like graphene-TiO2 hybrid nano-sheets in a binary ethylenediamine/H2O solvent, which proves to be an efficient photocatalyst for CO2 conversion in the presence of water vapor [74]. Recently, Nakano et al. [75] synthesized Si/CaF2/Si SHS and opened up its band gap to 1.08 eV. Wang et al. [76] have demonstrated high-quality h-BN/black phosphorus/BN sandwich heterostructures that show excellent stability in the atmospheric environment with a high mobility and a large on–off ratio exceeding 105. The research in the same group also indicates that sandwich h-BN/MS2/BN heterostructure holds high mobility [77]. Koppens et al. [78] found that Gr/WSe2/Gr sandwich devices offer the best compromise for optimizing the internal quantum efficiency as they exhibit both a fast photoresponse and a high internal quantum efficiency.

In this work, we have investigated the electronic-structural properties of three types of SHS, with Gr, h-BN, and g-C3N4 as covering materials and various 2D TMDs as intermediate layers to form sandwich-like structures by first-principle method. Our attention is focused on the following two questions: (1) Whether the band gap of the structure can be influenced and, furthermore, tuned by using different TMD interlayers? (2) If it is possible to achieve good response to visible light as well as having efficient charge separation by such kind of interlayer tuning? We hope that our results can provide a new design concept for a novel class of 2D heterostructures that can inspire further exploration of innovative nano-devices.

Models and methods

Geometric models of SHS used in this work are listed in Table S1 and illustrated in Figure S1. Our simulation box contains a single supercell of the interested SHS. Periodic boundary conditions are applied to all the three directions. At least a 20 Å layer of vacuum is applied in the z-direction, escaping the models from the vertical interactions. Sizes in the transversal dimensions of the supercell are obtained by performing geometrical optimizations on the chosen TMDs isolated from the SHS.

The lattice mismatches between the TMD interlayers and the cover layers in SHS are measured by \( \eta = (\alpha_{s} - \alpha_{c} )/\alpha_{c} \), where \( \alpha_{s} \) and \( \alpha_{c} \) denote the optimized lattice parameters for the isolated TMD and cover layer supercells, respectively. The equilibrium distances (\( R_{e} \)) of the optimized SHS are the average z-direction distance between the TMD layers and cover layers. Depending on the chosen model, the atoms in TMD layers can be S, Se, or Te atoms, and those in cover layers are C for Gr monolayer, B/N atoms for h-BN monolayer, and C/N atoms for g-C3N4 monolayer. The interfacial binding energy (\( E_{b} \)) can be computed according to the equation:

$$ E_{b} = E_{a} - \left( {2 \times E_{c} + E_{s} } \right) $$

where \( E_{a} \) represents total energy of the entire SHS, \( E_{c} \) the energy of the isolated cover layer, and \( E_{s} \) the energy of the isolated interlayers.

Geometrical optimizations and calculations of electronic structure were performed by first-principle DFT, where generalized gradient approximation in the parameterization of Perdew–Burke–Ernzerh (PBE) and the vdW correction proposed by Grimme are chosen [79], using VASP code [80,81,82,83]. The energy cutoff was set to 450 eV. Geometry structures were fully relaxed to the energy tolerance of 10−4 eV and force tolerance of 0.01 eV Å−1. The Monkhorst–Pack special mesh k-points are set to be 5 × 5 × 1 for geometry optimizations and to be 9 × 9 × 1 for the density of state (DOS) calculation in order to achieve higher accuracy.

Results and discussion

The Gr/MX2/Gr-SHS (M = Mo and W, X = S, Se, and Te)

As shown in Table S2, the calculated mismatches between Gr cover layers and MX2 interlayers, denoted as \( \eta \)(%), are within the range of 1.14–3.72. The values of \( R_{e} \) are within the range of 3.75–4.01 Å, which are in good agreement with previous results (Table S2) [70, 84,85,86] and also indicate that the formation of the SHS is through van der Waals’ (VDW) interactions between the cover layer and interlayers. The negative \( E_{b} \) values of − 0.12, − 0.72, − 0.24, − 0.74, − 0.25, and − 0.14 eV suggest high stability for MoS2, MoSe2, MoTe2, WSe2, and WTe2, respectively. But the value for WS2 interlayers is positive, excluding the possibility of forming stable structures. Structure diagram of the graphene heterostructures at the top right corner of Fig. 1 shows that Gr layers remain almost planar in the SHS. R e of MoX2 series is found to be larger than that of WX2 series (Table S1), while E b is found to be lower. However, the values of both \( R_{e} \) and \( E_{b} \) are observed to follow the specific orders: \( R_{e} \left( S \right) < R_{e} \left( {Te} \right) < R_{e} \left( {Se} \right) \) and \( E_{b} \left( S \right) > E_{b} \left( {Te} \right) > E_{b} \left( {Se} \right) \). And it indicates the physical interaction regularly changes with the chalcogen in SHS.

Figure 1
figure 1

Schematic for SHS based on TMD monolayers. Left: TMDs monolayer, middle: from top to down, graphene, h-BN, and g-C3N4 monolayer, right: the corresponding SHS. Bottom: supercells with optimized lattice constants (in red diamond): from left to right, graphene, h-BN, g-C3N4, MoS2, MoSe2, MoTe2, WS2, WSe2, and WTe2 supercell

Full size image

The calculated band structures of the (3 × 3 and 4 × 4) supercells of the Gr monolayer are shown in Figure S1. The lattice constant of graphene is calculated to be 2.47 Å, and the Dirac cone is at the Г and K point of the Brillouin zone of the 3 × 3 and 4 × 4 supercell due to the band folding, respectively, which are in good agreement with previous studies [70].

Calculated band structures of the Gr-SHS are shown in Fig. 2a. For MoS2 and WS2 interlayers, the valence band (VB) part (green curve) is the same as that of the isolated grapheme in 4 × 4 supercell, which has a “half” Dirac cone at the Κ point of the Brillouin zone, and a conduction band (CB) part (red curve) around the Γ point, similar to that of MoS2 or WS2 interlayers. In addition, the CB minimum (CBM) is under the VB maximum (VBM), indicating the SHS becomes metallic. For Mo(Se, Te)2 and W(Se, Te)2 interlayers, there is a whole Dirac cone at the Κ and Γ point of the Brillouin zone, which is the same as isolated graphene monolayer in both 3 × 3 and 4 × 4 supercells, and the contribution to both CB and VB of the entire SHS comes mainly from the graphene cover layers. Moreover, the band gaps of the SHS with Mo(Se, Te)2 and W(Se, Te)2 interlayers are all opened up, as shown in the inset of Fig. 2a.

Figure 2
figure 2

a Calculated band structures of the Gr-SHS. The inset shows the band gap of the Dirac cone near the Κ and Γ points; b calculated partial DOS of the Gr-SHS

Full size image

More details of the electronic structures are investigated by partial DOS calculation (Fig. 2b), which shows that the VB of SHS with MoS2 and WS2 interlayers is mainly contributed by 2p orbitals of C atoms in the Gr cover layer, whereas the main contribution to CB comes from Mo atoms in the MoS2 interlayer together with C_2p in the graphene. On the other hand, the CB and VB of SHS with (Mo, W)Se2 and (Mo, W)Te2 interlayers are both contributed by C_2p in graphene cover layers.

Even though the band structures of Gr-SHS are more similar to that of isolated Gr monolayers than to that of isolated TMD monolayers, the change caused by different TMD interlayers can still be observed, as shown in Fig. 2a, b. R e plays the critical role in tuning the band structure of SHS, while the \( R_{e} \) values of SHS with (Mo,W)S2 interlayers are small enough so that Mo or W atoms in the interlayer can contribute to the CB. However, for (Mo, W)(Se, Te)2 interlayers, the increase in R e indicates that the contributions to CB and VB are only from C_2p in the graphene cover layers.

In general, WX2 interlayers can produce larger band gap than MoX2 in Gr-SHS. The above observations indicate that the interaction between the transition metals in TMD interlayers and the graphene layers plays the most important role in the opening up of the band gap, with W atoms displaying a more significant effect than Mo atoms. Close examination of the inset in Fig. 2a reveals a series of tiny but distinguishable band gaps, which suggests a practical way to design nano-devices with both finite band gap and higher carrier mobility.

The (h-BN)/MX2/(h-BN)-SHS (M = Mo and W, X = S, Se, and Te)

Calculated lattice mismatches η(%) of h-BN-SHS are within the range of − 5 to 5, as listed in Table S3. h-BN cover layers are found to remain almost planar (second row, fourth column in Fig. 1), while the values of R e are found between 3.61 and 3.97 Å (Table 2), implying the formation of SHS through the VDW interaction between h-BN cover layers and TMD interlayers. The computed values of \( E_{b} \) are between − 0.17 and − 1.62 eV for all h-BN-SHS, respectively, suggesting high structural stability. The band gap of h-BN-SHS is found to stay in the range from 0.62 to 1.44 eV (Table S3), which is smaller than that of the isolated h-BN monolayer (4.07 eV), suggesting improved sensitivity to visible light. In addition, ordering relations can be observed for the variation of Re, Eb, and band gap with chalcogens as: R e (S) < R e (Se) < R e (Te), E b (Se) < E b (Te) < E b (S), and band gap(Te) < band gap(S) < band gap(Se) (Table S2), indicating regular change with chalcogens, similar to the trend discovered in Gr/MX2/Gr-SHS. This regularity can be effectively used in the optimization of materials tuned.

The calculated band structures of the (h-BN)-SHS (Figure S2) are similar to those of isolated TMD monolayers (Figure S3), indicating the contributions to CB and VB come mainly from atoms in TMD interlayers. It is worth noting that the h-BN-SHS become indirect-band-gap materials with (Mo, W)Te2 interlayers, while remaining direct band gap with other type of interlayers.

Local and partial DOS of the h-BN-SHS is plotted in Fig. 3a, b. The top of VB of h-BN-SHS with (Mo, W)S2 interlayers is very close to that of isolated (Mo, W)S2 monolayers, while the bottom of CB is to the left of the corresponding isolated TMD monolayers for about 0.7–0.8 eV. When (Mo, W)Se2 are used as interlayers, both the top of VB and the bottom of CB overlap with the corresponding bands of MSe2 monolayer. For (Mo, W)Te2 interlayers, the top of VB is to the right of that of h-BN monolayer and MTe2 monolayers for about − 0.2 eV, and the bottom of CB is to the left of that of MTe2 for about 0.4–0.5 eV. The above observation explains why band gap(Te) < band gap(S) < band gap(Se) from the perspective of band structures. In addition, Fig. 3b shows that CB and VB of the h-BN-SHS are both contributed by Mo_4d or W_ 5d orbitals in the interlayers.

Figure 3
figure 3

Calculated a local DOS and b partial DOS of the h-BN-SHS

Full size image

The g-C3N4/MX2/g-C3N4-SHS (M = Mo and W, X = S, Se, and Te)

The range of the lattice mismatch η(%) of g-C3N4-SHS is found between − 0.76 and 4.45 (Table S4). Relatively large fluctuation of cover layers can be observed for g-C3N4-SHS (third row, fourth column in Fig. 1), which causes reduction in Eb and therefore increases the stability of the structure. The values of E b are all found to be negative except for those (Mo, W)Se2 interlayers. R e is calculated within the range of 3.69–4.01 Å (Table S4), indicating that the formation of the SHS is also driven by the VDW interactions between cover layers and interlayers.

The calculated band structures of the g-C3N4-SHS are shown in Figure S4. With (Mo, W)(S, Se)2 interlayers, the VB structures are similar to that of isolated g-C3N4 monolayers at the Γ point. What is more, the CB structures are similar to that of isolated (Mo, W)(S, Se)2 monolayers around the Μ point, where the second minimum for the isolated monolayers reaches the lowest for the SHS. For the MoTe2 interlayer, the VB structure is similar to that of isolated g-C3N4 monolayers around the Γ point, and the CB structure is very close to the summation of those for isolated g-C3N4 and MoTe2 monolayers. At the end, the band structures (both CB and VB) of the g-C3N4 with WTe2-interlayers are similar to that of isolated WTe2 monolayer.

Strong interactions are found between the g-C3N4 cover layers and the TMD interlayers, as shown by the local DOS plotted in Figure S6, from which it can be observed that the locations of VB and CB of TMD and g-C3N4 monolayers within the SHS are very close. The calculated partial DOS (Figure S7) shows the VB of the SHS with (Mo, W)(S, Se)2 interlayers is all contributed by N_2p in g-C3N4 cover layers and the CB by S_2p, Mo_4d or W_ 5d orbitals in TMD interlayers. For (Mo, W)Te2 interlayers, the VB of the SHS is contributed by N_2p in g-C3N4 cover layers and Mo_4d or W_ 5d in TMD interlayers. While the contribution to the CB of the SHS with WTe2 interlayers comes from both the cover layers and the interlayers, it comes mainly from the interlayer when MoTe2 is used.

In order to obtain more detailed understanding of the interface in the g-C3N4-SHS, we plot the plane-averaged electron densities and electron density differences (Fig. 4d and Figure S8), where the collection of vast number of negative charges in g-C3N4 cover layers and positive charges in (Mo,W)S2 interlayers can be clearly observed, consistent with the partial DOS calculations (Fig. 4c). It is the direct evidence of polarization with −/± sequence electric dipole moment in the g-C3N4/TMD/g-C3N4 structures, which drives photogenerated electrons to TMD interlayers and holes to g-C3N4 cover layers, effectively promoting the separation of photoelectrons from vacancies and further improving the degradation efficiency.

Figure 4
figure 4

Calculated a band structures, b local DOS, c partial DOS, and d charge density difference of the g-C3N4/(Mo, W)S2/g-C3N4 SHS, as well as e the schematic diagram of a corresponding solar cell device (blue: g-C3N4 layers, pink: (Mo,W)S2 layers)

Full size image

Due to their structural stability, good thee-hole separations, and suitable band gap for visible light response, g-C3N4-SHS with MoS2 and WS2 interlayers have strong potential in applications such as photocatalysts and solar cells. Figure 4f illustrates the principle of a solar cell device of such kind. When the device is illuminated by the sunlight, electrons of the VB in g-C3N4 cover layers are driven to the CB in MoS2 or WS2 interlayers, generating electrical potential between the negatively charged interlayer and positively charged cover layers. Electrons in the interlayer are then driven to flow through external circuit, supplying electric power to loads and eventually neutralizing holes in g-C3N4 cover layers. According to the calculation in Ref. [87], considering their good thee-hole separations and suitable band gaps, the potential conversion efficiencies could reach about 28 and 29% with the photocurrent densities of about 26 and 31 mA cm−2 under illumination of air mass 1.5 for the device of g-C3N4-SHS with MoS2 and WS2 interlayers, respectively.

Conclusions

In summary, we designed three series of sandwich heterostructures with 2D TMDs (including MoS2, MoSe2, MoTe2, WS2, WSe2, and WTe2) as the intermediate layer, while graphene, h-BN, and g-C3N4 on each side as the cover, and performed systematical studies on their structural and electronic properties.

In the Gr-SHS, the (Mo, W)(Se, Te)2 interlayers can open the band gap, especially with intact Dirac cones. The negative values of E b and band gaps tuned to suit good visible light response indicate good structural stability and its application in semiconductor industry, respectively. In addition, the values of R e , E b , and gap of Dirac cone change in a fixed order (to elaborate) with the chalcogens (S, Se, Te) in TMD layers. Comparing to the Gr-SHS, all calculated band gaps of (h-BN)-SHS indicate good response to visible light. But both CB and VB are contributed by transition metal in TMDs, and therefore, the separation of photoelectrons from vacancies cannot be improved. In comparison with the previous two SHS, the fluctuation of the g-C3N4 cover can further improve the structural stability. When the two series of 2D layers constituting SHS own close band gaps and locations of VBM and CBM, CB and VB of the SHS would be contributed by the two 2D layers, respectively (for instance the g-C3N4-SHS). Instead, when band gaps of the two series of 2D layers vary considerably from each other, then CB and VB of the SHS would be both contributed by the 2D monolayer that owning the smaller band gap(for instance the Gr- and the h-BN-SHS). In view of our sandwich vdW heterostructure study, this study will be of great interest and will promote the relevant theoretical and experimental efforts to seek advanced materials for photocatalysts and nano-devices.