Electronic properties of a two-dimensional van der Waals MoGe2N4/MoSi2N4 heterobilayer: effect of the insertion of a graphene layer and interlayer coupling

van der Waals heterostructures (vdWHs) based on 2D layered materials with select properties are paving the way to integration at the atomic scale, and may give rise to new heterostructures exhibiting absolutely novel physics and versatility. Herein, we investigate the structural and contact types in a 2D vdW heterobilayer between MoGe2N4 and MoSi2N4 monolayers, and the monolayers in the presence of electrical graphene (GR) contact. In the ground state, the MoGe2N4/MoSi2N4 heterobilayer forms type-II band alignment, which effectively promotes the separation of electrons and holes and provides opportunity for further electrons and holes. Thus, the MoGe2N4/MoSi2N4 heterobilayer is promising for designing optoelectronic devices with significantly suppressed carrier-recombination. Interestingly, the insertion of the GR contact to a MoGe2N4/MoSi2N4 heterobilayer gives rise to the formation of a metal/semiconductor contact. Depending on the GR position relative to the MoGe2N4/MoSi2N4 heterobilayer, the GR-based heterostructure can form either an n-type or p-type Schottky contact. Intriguingly, the contact barriers in the GR contacted MoGe2N4/MoSi2N4 heterobilayer are significantly smaller than those in the GR contacted with MoGe2N4 or MoSi2N4 monolayers, suggesting that the GR/MoGe2N4/MoSi2N4 heterostructure offers an effective pathway to reduce the Schottky barrier, which is highly beneficial for improving the charge injection efficiency of the contact heterostructures. More interestingly, by controlling the interlayer coupling through stacking, both the Schottky barriers and contact types in the GR/MoGe2N4/MoSi2N4 heterostructure can be manipulated. Our findings could provide theoretical insight into the design of nanodevices based on a GR and MoGe2N4/MoSi2N4 heterobilayer.


Introduction
Two-dimensional (2D) materials 1-3 have received extensive interest owing to their intriguing physical and chemical properties and broad device application potential, including in electronics, 3,4 nanophotonics, 5 optoelectronics 6,7 and spintronics. 8,9 A plethora of 2D materials, including graphene (GR), 10 phosphorene, 11,12 transition metal dichalcogenides (TMDCs), 13,14 and graphitic carbon nitrides, [15][16][17] have been synthesized experimentally and predicted theoretically. These 2D materials exhibit outstanding properties and unique advantages over conventional bulk materials, and are particularly promising candidates for designing high-performance nanodevices, such as eld-effect transistors 18 and photodetectors. 19 Very recently, Hong et al. 20 discovered a new family of 2D materials, namely MoSi 2 N 4 monolayers, using chemical vapor deposition (CVD). The MoSi 2 N 4 monolayer is a layered structure, which can be viewed as a MoN 2 layer sandwiched between two Si-N bilayers. The MoSi 2 N 4 monolayer exhibits semiconducting characteristics with a band gap of about 1.94 eV, and possesses high carrier mobility up to 1200 cm 2 V À1 s À1 . This monolayer is also stable and mechanically stronger than most other 2D semiconductors such as MoS 2 monolayers. The successful synthesis of MoSi 2 N 4 monolayers has led to a new class of 2D materials with formula MA 2 Z 4 , 20 where M represents an early transition metal (Mo, W, Cr), A ¼ Si or Ge, and Z ¼ N, P, or As. Motivated by this nding, many theoretical investigations have been performed to explore the electronic, optical and transport properties of MA 2 Z 4 monolayers. For instance, Guo et al. 21 studied the electronic properties and transport coefficient of MoSi 2 N 4 monolayers alongside the strain effect, and showed that band gap and Seebeck coefficient of such a monolayer are strain-tunable. Wu and colleagues 22 also predicted that the band gap of MSi 2 N 4 (M ¼ Mo, W) monolayers can be altered by strain and electric eld, which result in the transformation from indirect to direct band gap semiconductors. Furthermore, MoSi 2 N 4 , WSi 2 N 4 and VSi 2 N 4 monolayers are also predicted to be a potential valleytronic materials. 23,24 These ever expanding rst-principle calculations of MA 2 Z 4 have continually revealed the enormous potential of MA 2 Z 4 monolayers for future high-performance device applications.
Currently, constructing 2D van der Waals (vdW) heterostructures between two or more 2D materials is known to be an effective strategy to explore more new properties and extend the potential applications of the corresponding 2D materials. These 2D vdW heterostructures have been predicted theoretically using rst-principles calculations, and synthesized experimentally via several methods, such as CVD and mechanical exfoliation. In addition, 2D vdW heterostructures have new desirable properties which could be used for fabricating high-efficiency nanodevices experimentally, such as for solar cells, eld-effect transistors (FFTs), and photodetectors. Recently, the combination between the layers of several MA 2 Z 4 monolayers to form MA 2 Z 4 bilayers, 22,25 and between the GR layer and MA 2 Z 4 monolayers, 26,27 has received much attention from the scientic community. For instance, Zhong et al. 25 investigated the electronic features of MA 2 Z 4 (M ¼ Ti, Cr, Mo; A ¼ Si and Z ¼ N, P) bilayers under the strain effect. They predicted that the electronic properties of the MA 2 Z 4 family are tunable with straininduced transitions from semiconductor to metal. This nding makes the MA 2 Z 4 family a potential candidate for fabricating electro-mechanical devices. Similarly, Wu and colleagues 22 showed that applying an electric eld can also tune the semiconductor-to-metal transition in both MoSi 2 N 4 and WSi 2 N 4 bilayers, they are therefore suitable for designing next generation nanoelectronics and optoelectronics. Nonetheless, the combination between MoSi 2 N 4 and MoGe 2 N 4 to form a heterobilayer, and between graphene and MoSi 2 N 4 /MoGe 2 N 4 heterobilayer to form a GR/MoSi 2 N 4 /MoGe 2 N 4 heterostructure, have not yet been explored thoroughly.
In this work, based on rst-principles calculations, we investigate the electronic structures of the MoSi 2 N 4 /MoGe 2 N 4 heterobilayer and explore its electronic properties and band alignment alongside the presence of the GR layer. Various combinations and stacking congurations of GR/MoSi 2 N 4 / MoGe 2 N 4 heterostructures are investigated. Our results reveal that the MoSi 2 N 4 /MoGe 2 N 4 heterobilayer exhibits an indirect band gap semiconductor and possesses type-II band alignment at the equilibrium state. With the presence of the GR layer in the MoSi 2 N 4 /MoGe 2 N 4 heterobilayer, we see the formation of the Schottky contact with narrow barrier height of about 0.26 eV, which increases the carrier injection efficiency.

Computational details
In this work, all the calculations, including geometric optimization, electronic properties and band alignment of the MoSi 2 N 4 /MoGe 2 N 4 heterobilayers and the heterostructures between GR and MoSi 2 N 4 /MoGe 2 N 4 heterobilayer, were performed from rst-principles calculations within density functional theory, which was implemented in Vienna Ab initio Simulation (VASP) 28 and Quantum Espresso 29,30 packages. The Perdew-Burke-Ernzerhof (PBE) in the framework of the generalized gradient approximation (GGA) 31 was used to describe the exchange-correlation energy. The projector augmented wave (PAW) 32 pseudopotentials were used to describe the electron-ion interaction. In addition, the DFT-D3 method of Grimme 33 was also selected for describing the presence of the weak vdW forces that always occur in layered vdW systems, including heterobilayers and heterostructures. Furthermore, it should be noted that the traditional DFT method always underestimates the band gap values of materials, especially 2D materials, we therefore used the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional to avoid this issue and obtain an accurate band gap of the considered materials. The Brillouin zone (BZ) was sampled using the Monkhorst-Pack scheme. A 12 Â 12 Â 1 (6 Â 6 Â 1) k-point mesh was used for all the calculations within the DFT-PBE (HSE06) method with a cutoff energy of 510 eV. To avoid the interactions between periodical slabs, we set a large vacuum thickness of 25Å along the z direction. The geometric optimization was fully obtained with the convergence threshold for energy of 10 À6 eV and for a force of 10 À3 eVÅ À1 . The spinorbit coupling (SOC) was also taken into account for the electronic properties of the heterobilayer.

Structural and electronic properties of MoGe 2 N 4 / MoSi 2 N 4 heterobilayer
The relaxed atomic structures of the MoGe 2 N 4 /MoSi 2 N 4 heterostructure for AA and AB stacking congurations are depicted in Fig. 1. In AA-stacking, both the Ge and N atoms in the MoGe 2 N 4 layer are located directly above the Si and N atoms of the MoSi 2 N 4 layer, as depicted in Fig. 1(a). Whereas, in AB-stacking, the Ge and N atoms in the MoGe 2 N 4 layer are staggered with respect to the Si and N atoms of the MoSi 2 N 4 layer, as depicted in Fig. 1(b). Aer geometric optimization, the interlayer spacings (D) between the MoGe 2 N 4 and MoSi 2 N 4 layers for the AA and AB stacking congurations are obtained as listed in Table 1. For the AA-stacking, the equilibrium interlayer spacing is 3.33 Å , and it is 3.35Å for the AB-stacking conguration. For checking the structural stability of such a heterostructure, we further calculate the binding energy as: where E H is the total energy of the combined MoGe 2 N 4 /MoSi 2 N 4 heterostructure. E Mi is the total energy of the constituent MoGe 2 N 4 and MoSi 2 N 4 monolayers. The binding energy of the MoGe 2 N 4 / MoSi 2 N 4 heterobilayer for AA and AB stacking congurations is calculated to be À0.11 and À0.16 eV, respectively. The negative binding energy conrms that the heterobilayer is dynamically stable. In addition, the binding energy of the MoGe 2 N 4 /MoSi 2 N 4 heterobilayer for the AB stacking conguration is lower than that for the AA stacking conguration, suggesting that the AB stacking conguration can be considered as the most energetically favorable stacking conguration.
The band structures of the MoGe 2 N 4 /MoSi 2 N 4 heterostructure for different stacking congurations are displayed in Fig. 2. We used different methods, including PBE, HSE and PBE + SOC to calculate the band gaps of the considered heterostructure. The obtained band gaps for the MoGe 2 N 4 /MoSi 2 N 4 heterostructure are listed in Table 1. For the AA-stacking, the band gaps of the MoGe 2 N 4 /MoSi 2 N 4 heterostructure are calculated as 0.88 eV, 1.29 eV and 0.87 eV. It is clear that the HSE06 method gives rise to a larger band gap value than the PBE and PBE + SOC methods. However, all three methods predict the same characters of the MoGe 2 N 4 /MoSi 2 N 4 heterostructure, which possesses the indirect band gap semiconductor. The valence band maximum (VBM) is located at the G point, while the conduction band minimum (CBM) is located at the M point. Interestingly, when the SOC effect is applied, it tends to split the valence bands at the M point of the MoGe 2 N 4 /MoSi 2 N 4 heterostructure into two different parts, as depicted in Fig. 2(c). The energy of band splitting for the rst and second valence bands of the AA-stacking is calculated to be 13.27 meV and 13.9 meV, respectively. However, the SOC effect splits only the valence bands at the M point, whereas the VBM of such heterostructure is located at the G point. Therefore, the SOC does not affect the band alignments of the heterostructures. Similar trends are also observed in the AB-stacking of the MoGe 2 N 4 /MoSi 2 N 4 heterostructure. The PBE, HSE06 and PBE + SOC band gaps of the MoGe 2 N 4 /MoSi 2 N 4 heterostructure for the AB-stacking are 0.90, 1.33 and 0.89 eV, respectively. The AB-stacking also predicts the indirect band gap semiconductor in the MoGe 2 N 4 /MoSi 2 N 4 heterostructure with the VBM at the G point and the CBM at the M point, as depicted in Fig. 2(d-f). Furthermore, the band offset is also critical for the optoelectronic application, we therefore calculate the band offsets for valence bands (D V ) and for conduction bands (D C ). The band offsets D V and D C for the AAstacking are calculated to be 0.43 eV and 0.47 eV, respectively. Whereas, these values for AB-stacking are 0.40 eV and 0.43 eV, respectively. In addition, comparing AA and AB stacking, the band structure and alignment seems to be almost unchanged. This is a very convenient behaviour for experimental fabrication since the electronic properties are less affected by stacking congurations.
More interestingly, device performance based on vdW heterostructures depends crucially on the band alignment, forming between two different 2D materials. Depending on the band edge positions of the constituent monolayers, vdW heterostructure can be divided into three different types of band alignment, including type-I (straddling gap), type-II (staggered gap) and type-III (broken gap). To investigate the band alignment, we further calculate weighted band structures of the MoGe 2 N 4 /MoSi 2 N 4 heterostructure, as depicted in Fig. 3. For both the AA-stacking and AB-stacking, one can nd that the CBM of the MoGe 2 N 4 /MoSi 2 N 4 heterostructure is mainly contributed by the Mo-orbital states of the MoGe 2 N 4 layer, as marked with green circles. Whereas, the VBM at the G point is mainly contributed by the Mo-orbital states of the MoSi 2 N 4 layer, as marked by the violet circles. The contributions by the different monolayers to the VBM and CBM demonstrate that the MoGe 2 N 4 /MoSi 2 N 4 heterostructure possesses type-II band alignment for both AA-and AB-stacking. The type-II band alignment promotes effective separation of electrons and holes and provides an opportunity for electrons and holes to separate in real space. Thus, the MoGe 2 N 4 /MoSi 2 N 4 heterostructure is promising for designing optoelectronic devices with signicantly suppressed carrier-recombination.
We further investigated the charge mechanism in the MoGe 2 N 4 /MoSi 2 N 4 heterobilayer by calculating the charge  Fig. 4. The yellow and cyan regions represent the positive and negative charges, respectively. We nd that the charges are mainly visualized at the interface. The yellow regions are located in the MoGe 2 N 4 side, while the cyan regions are in the MoSi 2 N 4 layer. This nding suggests that the charges are mainly accumulated in the MoGe 2 N 4 layer and depleted in the MoSi 2 N 4 layer.

Electrical graphene contact to a MoGe 2 N 4 /MoSi 2 N 4 heterobilayer
We now consider the formation of a triple-layered 2D-metal/2Dsemiconductor heterostructure by including a graphene layer into the MoSi 2 N 4 /MoGe 2 N 4 heterobilayer. The atomic structures of all vdW heterostructures between the GR and MoSi 2 N 4 / MoGe 2 N 4 heterobilayer are depicted in Fig. 5(a-c). Three stacking sequences can be obtained: GR layer placed on top of the MoSi 2 N 4 layer in the MoSi 2 N 4 /MoGe 2 N 4 heterobilayer ( Fig. 5(a)); GR layer between the MoSi 2 N 4 and MoGe 2 N 4 layers ( Fig. 5(b)); and GR layer located below the MoGe 2 N 4 layer in the MoSi 2 N 4 /MoGe 2 N 4 heterobilayer (Fig. 5(c)). It is clear that the lattice constant of single-layer GR is calculated to be 2.46Å, while the lattice constant of the MoSi 2 N 4 /MoGe 2 N 4 heterobilayer is calculated to be 2.98Å. Therefore, in order to avoid the effect of lattice mismatch, we use a supercell, consisting of (2 Â   2) unit cells of GR and ð ffiffiffi 3 p Â ffiffiffi 3 p Þ unit cells of MoSi 2 N 4 / MoGe 2 N 4 heterobilayer to build the triple-layered 2D-metal/2Dsemiconductors heterostructure. The lattice constant of the triple-layered 2D-metal/2D-semiconductors heterostructure is calculated to be 5.04Å. Thus, the lattice mismatch between GR and the MoSi 2 N 4 /MoGe 2 N 4 heterobilayer is 2.38%, which is reasonably small and does not affect the main results. The interlayer spacings between the GR, MoSi 2 N 4 and MoGe 2 N 4 are calculated and listed in Table 2. For the GR/MoSi 2 N 4 /MoGe 2 N 4 , the interlayer spacings D 1 , D 2 and D 3 are calculated to be 3.58, 13.80 and 3.33Å, respectively. These values indicate that the interactions between the GR, MoSi 2 N 4 and MoGe 2 N 4 are weak. In addition, we can see that the interlayer spacings of 3.33Å and 3.58Å are comparable with those in other 2D-layered heterostructures, which have typical vdW forces. [34][35][36][37] This nding suggests that the GR, MoSi 2 N 4 and MoGe 2 N 4 layers in their corresponding heterostructures are bonded together via weak vdW interactions. It should be noted that the systems that are characterized by the vdW interactions are feasible and thus they can be easily fabricated in experiments using several common strategies, such as mechanical exfoliation 38 and chemical vapor deposition (CVD). 39 Furthermore, considering the MoSi 2 N 4 /GR/ MoGe 2 N 4 and MoSi 2 N 4 /MoGe 2 N 4 /GR heterostructures, we also nd that they are characterized by weak vdW forces. Furthermore, in order to guarantee stability, we also perform the ab initio molecular dynamics simulations of such heterostructures at room temperature of 300 K, as depicted in Fig. 6. We nd that the heterostructures are stable at 300 K room temperature.
The projected band structures of the heterostructures combined between the GR and MoSi 2 N 4 /MoGe 2 N 4 heterobilayer are depicted in Fig. 5(d-f). Red and green circles represent the contributions of the GR and MoSi 2 N 4 /MoGe 2 N 4 layers, respectively. One can observe that the electronic band structures of these graphene-based heterostructures seem to be a combination between those of the constituent GR and MoSi 2 N 4 / MoGe 2 N 4 heterobilayer. A Dirac cone with linear dispersion of the GR layer is well preserved and located at the M point. The physical mechanism of the shi in Dirac point from the K to M point is due to the size effects in the GR supercell. 40 The semiconducting feature of the MoSi 2 N 4 /MoGe 2 N 4 heterobilayer is also maintained. The band gap of the MoSi 2 N 4 /MoGe 2 N 4 heterobilayer contacted to the GR layer is about 0.84 eV, which is smaller than that of the freestanding MoSi 2 N 4 /MoGe 2 N 4 heterobilayer. This nding suggests that the contact between GR and the MoSi 2 N 4 /MoGe 2 N 4 heterobilayer tends to reduce the band gap of the MoSi 2 N 4 /MoGe 2 N 4 heterobilayer semiconductor. This reduction gives rise to an enhancement in optical absorption of graphene-based heterostructures. Furthermore, the MoSi 2 N 4 /MoGe 2 N 4 heterobilayer contacted with the GR layer possesses a direct band gap semiconductor with both the VBM and CBM at the G point, as depicted in Fig. 5(d-f). The nature of such a transformation from an indirect to direct band gap in the MoSi 2 N 4 /MoGe 2 N 4 heterobilayer is due to a band folding effect. More interestingly, when GR contacts the MoSi 2 N 4 /MoGe 2 N 4 heterobilayer, a band gap of about  meV is opened in the GR layer. It is clear that the mechanism of this band gap opening in the GR layer is due to symmetry breaking of the A and B sub-lattices in GR. This appearance was also observed in other GR-based heterostructures. [35][36][37] More interestingly, the contact between metallic GR and the semiconducting MoSi 2 N 4 /MoGe 2 N 4 heterobilayer gives rise to the formation of a 2D metal/2D semiconductor interface. For the 2D metal/2D semiconductor interface, depending on the position of the Fermi level of metallic GR with respect to the band edges of the semiconductor, there is the formation of either Schottky contact (ShC) or Ohmic contact (OhC). One can nd from the band structures in Fig. 5 that the Fermi level of the GR layer lies in the band gap region of the MoSi 2 N 4 /MoGe 2 N 4 semiconductor, thus suggesting the formation of the ShC type in all three corresponding GR-based heterostructures. In addition, the Fermi level pinning is still weak in the heterostructures that are characterized by the weak vdW interactions. Therefore, we determine the contact barriers of such heterostructures using the Schottky-Mott rule. 41 The n-type and p-type ShC, respectively, can be dened as F n ¼ E C À E F and F p ¼ E F À E V , where E C , E V and E F , respectively, are the CBM, VBM and Fermi level of the GR-based heterostructure. The calculated F n and F p of the GR/MoGe 2 N 4 /MoSi 2 N 4 , MoGe 2 N 4 /GR/MoSi 2 N 4 and MoGe 2 N 4 /MoSi 2 N 4 /GR heterostructures are listed in Table 2. We nd that the F n in the GR/MoGe 2 N 4 /MoSi 2 N 4 heterostructure is still smaller than the F p , indicating that it forms an n-type ShC at the equilibrium state. Whereas, for the MoGe 2 N 4 /GR/ MoSi 2 N 4 and MoGe 2 N 4 /MoSi 2 N 4 /GR heterostructures, the F n is higher that the F p , implying that they form the p-type ShC. The F n of the MoGe 2 N 4 /GR/MoSi 2 N 4 heterostructure is calculated to be 0.33 eV, which is smaller than that of the GR/MoGe 2 N 4 / MoSi 2 N 4 and MoGe 2 N 4 /MoSi 2 N 4 /GR heterostructures, as illustrated in Fig. 7. The lower the contact barrier, the better the  Table 2. This suggests that the GR/MoGe 2 N 4 /MoSi 2 N 4 heterostructure offers an effective pathway to reduce the Schottky barrier, which is highly benecial for improving the charge injection efficiency of contact heterostructures. The tuning of the contact barriers and contact types in GRbased vdW heterostructures is an important factor of nanodevices based on the GR heterostructures. Controlling the interlayer coupling through stacking is one of the most efficient strategies in tuning both the contact barriers and contact types of GR-based heterostructures. The interlayer coupling can be manipulated by changing the interlayer spacings between the GR and semiconductors in their corresponding heterostructures. One can observe from Table 2 that the GR/ MoGe 2 N 4 /MoSi 2 N 4 has the lowest binding energy of À67.66 meV per C atom in comparison with that of other congurations, as it is the most stable conguration. Therefore, the effects of the interlayer couplings on the contact barriers and contact types of the GR/MoGe 2 N 4 /MoSi 2 N 4 heterostructure are investigated as an illustrative example. The projected band structures of the GR/MoGe 2 N 4 /MoSi 2 N 4 heterostructure as well as the variation in the contact barriers as functions of the interlayer couplings are displayed in Fig. 8. Red and black lines represent the contributions of the metallic GR and semiconducting MoGe 2 N 4 /MoSi 2 N 4 heterobilayer, respectively. Interestingly, we nd that changing interlayer couplings gives rise to a change not only in the Schottky barriers but also in the contact types of the GR/MoGe 2 N 4 /MoSi 2 N 4 heterostructure. The changes in the Schottky barriers and contact types in the GR/MoGe 2 N 4 /MoSi 2 N 4 heterostructure are illustrated in Fig. 8(a). The F n decreases with increasing interlayer spacing, while the F p increases accordingly. On the contrary, the F n increases with decreasing the interlayer spacing, while the F p decreases accordingly. When the DD is smaller than À0.45Å, the F n becomes larger than the F p , leading to the transition from n-type ShC to p-type. The physical mechanism of such transitions can be described by analyzing the change in the Fermi level relative to the band edges of the semiconducting MoGe 2 N 4 /MoSi 2 N 4 heterobilayer. With the applications of the compressive strain, i.e. DD < 0, the Fermi level of graphene moves towards the VBM of the semiconducting MoGe 2 N 4 / MoSi 2 N 4 heterobilayer, thus resulting in an/a increase/decrease in the F n /F p . On the other hand, with the application of the tensile strain, i.e. DD > 0, the Fermi level of graphene shis upwards from the VBM to the CBM of the semiconducting MoGe 2 N 4 /MoSi 2 N 4 heterobilayer. Thus, the F n is decreased and the F p is increased accordingly. In this case, the heterostructure remains as n-type ShC. It can be concluded that with the application of different strains, both the Schottky barriers and contact types in the GR/MoGe 2 N 4 /MoSi 2 N 4 heterostructure can be manipulated.

Conclusions
In summary, we have investigated the structural and contact types in a 2D vdW heterobilayer between MoGe 2 N 4 and MoSi 2 N 4 monolayers, as well as in the presence of electrical graphene. We found that the MoGe 2 N 4 /MoSi 2 N 4 heterobilayer forms type-II band alignment, which effectively promotes the separation of electrons and holes, and provides an opportunity for further electrons and holes. Interestingly, the insertion of the electrical graphene contact to a MoGe 2 N 4 /MoSi 2 N 4 heterobilayer gives rise to the formation of a metal/semiconductor contact, which is characterized by the contact type barriers. Depending on the graphene position relative to the MoGe 2 N 4 /MoSi 2 N 4 heterobilayer, the graphene-based heterostructure can form either an n-type or p-type Schottky contact. The graphene/MoGe 2 N 4 / MoSi 2 N 4 heterostructure exhibits an n-type Schottky contact, whereas the MoGe 2 N 4 /GR/MoSi 2 N 4 and MoGe 2 N 4 /MoSi 2 N 4 /GR heterostructures form a p-type one. Intriguingly, the contact barriers in the GR contacted MoGe 2 N 4 /MoSi 2 N 4 heterobilayer are signicantly smaller than those in the GR contacted MoGe 2 N 4 and MoSi 2 N 4 monolayers, suggesting that the GR/ MoGe 2 N 4 /MoSi 2 N 4 heterostructure offers an effective pathway to reduce the Schottky barrier, which is highly benecial for improving the charge injection efficiency of the contact heterostructures. More interesting, by controlling the interlayer coupling through stacking, both the Schottky barriers and contact types in the GR/MoGe 2 N 4 /MoSi 2 N 4 heterostructure can be manipulated.

Conflicts of interest
There are no conicts to declare.