Tunable band-structures of MSe2/C3N (M = Mo and W) van der Waals Heterojunctions

Van der Waals (vdW) heterojunctions constructed using two-dimensional (2D) materials have shown excellent properties for applications in various fields. In this study, the structural and electronic properties of 2D MoSe2/C3N and WSe2/C3N vdW heterojunctions have been investigated using first-principles calculations. The results show that the MoSe2/C3N heterojunction is an indirect bandgap semiconductor with a small bandgap 0.05 eV and the WSe2/C3N heterojunction is a type II heterojunction with an indirect bandgap of 0.26 eV. Strains and external electric fields can effectively modulate the electronic structure of these heterojunctions. The WSe2/C3N heterojunction can become a type III heterojunction under compressive strains, which also becomes a direct bandgap heterojunction with type I band alignment under a negative electric field. Our results may be useful for the design of electronic nanodevices.

Transition metal dichalcogenides (TMDs) have periodic layered stacked structures with layers coupled by weak van der Waals forces [9]. 2D TMDs materials exhibit better properties than graphene because their electronic properties can be tuned through the thickness, composition, external strain, and electric field [10][11][12]. It has been reported that monolayer (1 L) TMDs are all direct bandgap semiconductors with band gaps between 1.1 and 2.5 eV [13]. Therefore, 1L TMDs are suitable for high-speed, light-harvesting, and light-emitting devices [14][15][16][17]. 1L MoSe 2 is a 2D semiconductor with good thermal stability, and its high carrier mobility and ultrathin conduction layer make it suitable for micro-Hall sensors [18]. 1L WSe 2 has a wide direct energy gap of 2.02 eV [19] and many superior characteristics, such as good chemical stability, high switching ON/OFF ratio, and high carrier mobility [19], 1 L WSe 2 has captured a great deal of interest for its promising use in photosensors [20], phototransistors [21] and field-effect transistors [22].
The merits of 2D materials include the discovery of many other 2D materials such as Ca 2 N, Sr 2 N, WS 2 , Ge 3 P 2 and C 3 NH [12,[23][24][25]. Among them, C 3 N has attracted considerable attention since its successful fabrication in 2017 [26]. C 3 N is a carbon-based semiconductor with desirable physical characteristics compared with other 2D materials [27,28], which is an indirect semiconductor with band gap of 0.39 eV [27], and the bandgap is tunable up to 2.6 eV by manipulating the size [28]. The Field Effect Transistor(FET) made by C 3 N can reach an on-off current ratio of 5.5 × 10 10 [26], and the C 3 N monolayer is extremely high with electron mobility [29]. According to Mortazavi, the thermal conductivity of C 3 N can reach 815 ± 20 W m −1 · K −1 [28]. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
With the development of modern techniques, 2D materials with different electrical properties can be vertically stacked to obtain van der Waals heterojunctions [30,31]. 2D vdW heterojunctions are atomically thin, have perfect interfaces, and have no vertical depletion region. Weak vdW interactions can modify the band structures of the two stacked materials, thus exhibiting some interesting properties. 2D vdW heterojunctions are suitable for applications in next-generation electronic and optoelectronic devices owing to their excellent physical characteristics, low power consumption, and ideal bandgap. For example, the spectral photoresponse of a 2D WSe 2 /MoS 2 vdW heterojunction PN diode is between the ultraviolet and near-infrared regions [32], which can be used to detect visible-near infrared broadband. The Sb 2 Te 3 /MoS 2 vdW heterojunction has a photoresponsivity of 330 A W −1 , and its photo response speed is smaller than 500 μs [33] thus, it is superior for optoelectronic devices. MoSe 2 /SnS 2 , MoSe 2 /SnSe 2 and MoSe 2 /CrS 2 vdW heterostructures have been proven to be suitable photocatalysts for overall water splitting [34].
In this study, the structural and electronic properties of 2D MSe 2 /C 3 N (M = Mo and W) heterojunctions have been investigated using first-principles calculations. The results also show that the band structures are tunable by different stacking, mechanical strains, and electric fields. These results are useful for the design of electronic devices.

Computational methods
The calculations in this study were performed using density functional theory (DFT), as implemented in the VASP code [35].Perdew Burke-Ernzerhof (PBE) was used to describe the exchange-correlation interaction [36]. The projector augmented-wave (PAW) pseudopotential method was adopted [37]. The cut-off energy was set to 520 eV. Monkhorst-Pack k-points were set to 4 × 4 × 1 for structural relaxation and 10 × 10 × 1 for band structure calculations. Geometry relaxation was performed until the maximum force on each atom was less than 0.01 eV Å and the change in total energy was less than 10 −6 eV. vdW interactions were described using the DFT-D2 method [38].  previous studies [39,40]. The C 3 N monolayer is an indirect band semiconductor with the VBM at M point and the CBM at Γ point. Its band gap is 0.39 eV, equal to the former data [12].

Results and discussion
3.1. The structural and electronic properties of MSe 2 /C 3 N (M = Mo and W) heterojunctions MSe 2 /C 3 N (M = Mo and W) heterojunctions were constructed by stacking a 3 × 3 MSe 2 supercell (27 atoms) onto a 2 × 2 C 3 N supercell (32 atoms). In this way, the lattice mismatch of the MoSe 2 /C 3 N heterojunction is less than 2.7%, and 2.6% for the WSe 2 /C 3 N heterojunction.
Herein, according to the symmetry of MoSe 2 and C 3 N monolayers, ten different positions of 1 l MoSe 2 on top of C 3 N were considered (such as one of the Mo atoms directly above one of the C or N atoms in figures 2(a) and (b) [41]. The interlayer distance (d) between MoSe 2 and C 3 N monolayer in the heterojunctions is in the range from 3.34 to 3.37Å, which agrees well with other heterojunctions [42][43][44]. Each heterojunction with the different configurations shown in figure 2 has an indirect band gap with the conduction band minimum (CBM) at the M point and corresponding binding energies are listed in table 1.
(the binding energy of the heterojunction is defined as are the total energies of the heterojunctions, MSe 2 and C 3 N monolayer, respectively). The stacking configuration in figure 2(b) has the lowest binding energy, indicating that it is the most stable configuration. Our subsequent work on the MoSe 2 /C 3 N heterojunction was based on this configuration.
The projected band structure of the MoSe 2 /C 3 N heterojunction is shown in figure 3(a). The black dots represent the contribution of C 3 N and the red dots indicate the contribution of MoSe 2 . In the heterojunction,     the CBM is mainly contributed by MoSe 2 and the VBM is contributed by C 3 N. The MoSe 2 /C 3 N heterojunction is an indirect band semiconductor with a CBM between the K and M points, and a VBM at the Γ point. It had a small bandgap of 0.05 eV. The band gaps of C 3 N and MoSe 2 become 0.44 eV and 1.51 eV after contact, which may be the impact of the vdW force.
The band alignment of the MoSe 2 /C 3 N heterojunction is shown in figure 3(b). The heterojunction exhibited a type-II band alignment. The CBM is 0.02 eV for MoSe 2 and 0.41 eV for C 3 N, while the VBM is −1.49 eV for MoSe 2 and −0.03 eV for C 3 N. The conduction band offset (CBO) defined as follows:  The projected band structure of the heterojunction is shown in figure 5(a). The black dots represent the contribution of C 3 N and the blue dots indicate the contribution of WSe 2 . The CBM was mainly contributed by WSe 2 , and the VBM was mainly contributed by C 3 N. The WSe 2 /C 3 N heterojunction is an indirect band semiconductor with a CBM between the K and M points, and a VBM at the Γ point. The bandgap of WSe 2 /C 3 N heterojunction is 0.26 eV. Figure 5(b) shows the band alignment of the WSe 2 /C 3 N heterojunction. Clearly, the heterojunction exhibited type-II band alignment. The CBM is 0.09 eV for WSe 2 and 0.23 eV for C 3 N, while the VBM is −1.51 eV for WSe 2 and −0.17 eV for C 3 N. Thus the CBO is 0.14 eV and VBO were 1.34 eV.
where a eq is the equilibrium value of in-plane lattice parameters [48].    can achieve 0.38 eV when the compressive strain is −4%. Under tensile strain, the CBM between K point and M point approaches Γ point, whereas the VBM of heterojunctions remains at Γ point, making an indirect-direct transform in the heterojunction. The CBM of MoSe 2 decreases under tensile strain, thus the band gap of the heterojunction become smaller. When the tensile strain is larger than 4%, the band gap is decreased to zero. Figure 7a exhibits the project band structure of the WSe 2 /C 3 N heterojunction under the biaxial strain of −4%∼8%. Under compressive strain, the CBM of WSe 2 gradually decreases and VBM of C 3 N increases, the band gap of the heterojunction become smaller. Moreover, the heterojunction exhibits a type-III band alignment when the strain reaches −4%, and the band overlap is 0.13 eV. When the tensile strain is applied, the CBM of the heterojunction changes from K−M points to the Γ point, while the VBM remains in the Γ point, contributing to an indirect-direct band gap transition in the WSe 2 /C 3 N heterojunction. From figure 7(c), the CBM shifts downward, whereas the VBM shifts upward with the increase of tensile strain, making a smaller band gap in the heterojunction. The band gap of the WSe 2 /C 3 N heterojunctions decreases from 0.26 to 0 eV when tensile strain shifts from 0 to 8% as shown in figure 7(b).  The influences of electric fields on the band structures of the WSe 2 /C 3 N heterojunction are as shown in figure 9. Under a negative electric field, the CBM of C 3 N was lower than that of WSe 2 , and the heterojunction had a type-I band alignment. The heterojunction has a direct bandgap, with the CBM and VBM located at the Γ point. The band gap increases to 0.38 eV when an electric field of −0.1 V Å was applied, while further increase the strength of the negative electric field seems have little influence on its value. When a positive electric field was applied, the CBM of the heterojunction continued to decrease and the VBM increased; thus, the bandgap decreased. When the strength of electric field achieves to 0.4 V Å, the heterojunction even become type III with a band overlap of 0.02 eV.

Conclusion
In this study, first-principles calculations were used to determine the structural and electrical properties of MSe 2 /C 3 N (M = Mo and W) vdW heterostructures. The calculated band structures show that they are both indirect bandgap semiconductors with type-II band alignment. The band gap is 0.05 eV of the MoSe 2 /C 3 N heterojunction and is 0.26 eV of the WSe 2 /C 3 N heterojunction. In-plane biaxial strain and an electric field were used to tune the band gaps and band edges. The results show that the strain and electric field can remarkably modulate the band structures, resulting in interesting properties. Our study may contribute to the design of related electronic devices.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).
Author contributions Z X Liu collected data and wrote the article. Yaxiao Yang and Xiaoyu Yang conducted data analysis and interpretation. Guangqiang Yin contributed to the discussion of best practices for data analysis presented in this editorial. Z X Liu is a PhD student of Z G Wang, who provided the research concept and design.

Conflict of interest
All authors declare that they have no known competing financial interests or personal relationships that could influence this study.

Ethics statement
The study was approved by the Ethics Committee of University of Electronic Science and Technology of China.