Tunable band alignment and optical properties in van der Waals heterostructures based on two-dimensional materials Janus-MoSSe and C3N4

Van der Waals heterostructures with tunable band alignments are the promising candidates for the fabrication of high-performance multifunctional nano-optoelectronic devices. In this work, we investigate the band alignments and optical properties of two-dimensional MoSSe/C3N4 and C3N4/MoSSe heterostructures using first-principles methods. The two most stable MoSSe/C3N4 (C3N4-Se) and C3N4/MoSSe (C3N4-S) heterostructures (labeled as A2 and B2, respectively) out of the twelve possible heterostructures are selected for the corresponding properties research. It is found that the A2 exhibits type-I band alignment, making it suitable for light-emitting applications, while the B2 exhibits typical type-II band alignment, which is favorable for carrier separation. Moreover, the band alignment of the two heterostructures can be modulated by the external electric fields, that is, band alignment transition between type-I and type-II. In addition, the main absorption peaks of both heterostructures in their pristine state are located in the visible light region (approximately 2.9 eV), and the peak values of the absorption peaks can be enhanced (weaken) via applying positive (negative) external electric fields. Our findings demonstrate that the C3N4/C3N4 and C3N4/MoSSe heterostructures hold significant potential for applications in multifunctional electronic devices including light-emitting, carrier separation, optical modulators, etc.


Introduction
Two-dimensional (2D) semiconductor materials have attracted much attention by virtue of their unique optoelectronic properties and broad technological applications in recent years [1][2][3].Further, van der Waals (vdW) heterostructures that stack various types of 2D materials together are novel composite materials because they can generate new properties and quantum phenomena that are different from those of monolayer materials because of the interlayer interaction, thus breaking through the limitations of the single 2D material in multifunctional device applications [4,5].For example, some vdW heterostructures can experience different band alignments, including type-I (straddling), type-II (staggered), and type-III (broken-gap) via manipulation of external electric fields, biaxial stresses, etc.For type-I heterostructures, the rapid recombination of carrier is facilitated as electrons and holes are located in the same material, which has been widely used in light-emitting devices such as light-emitting diodes [6,7] and quantum-well lasers [8,9] .For type-II heterostructures, the electrons and holes are located in different materials, which provides them with unique properties to effectively separate carrier and prolong the exciton lifetime, making them suitable for application in fields such as optoelectronics [10,11], and photocatalysis [12,13].For type-III heterostructures, the overlap of valence and conduction band of different constituent layers leads to higher electron tunnelling probability, which is suitable for applications in tunneling field effect transistors [14,15] and wavelength photodetectors [16].Therefore, vdW heterostructures with tunable band alignments can be used in the fabrication of high-performance multifunctional nano-optoelectronic devices [17].In this work, we will investigate the type of band alignments and optical properties in 2D MoSSe/C 3 N 4 and C 3 N 4 /MoSSe heterostructures.
A new Janus-MoSSe 2D material, constructed by replacing one of the S atoms with Se atoms to break the planar symmetry of MoS 2 , has been successfully synthesized using the chemical vapor deposition (CVD) method [18,19].Compared with that of MX 2 2D materials (taking MoS 2 and MoSe 2 as examples as presented in table S1 in supplementary materials, the three 2D materials do not have any major differences in terms of bandgap) that have a D3h point group, MoSSe has a C3v point group.More importantly, from the atomic structure, the atoms on both sides of Mo atoms in MoS 2 and MoSe 2 are identical, both S atoms or Se atoms, respectively, while those in MoSSe are not identical, resulting in an out-of-plane asymmetry, which can generate an intrinsic built-in electric field and two distinct surfaces, thus MoSSe shows abundant functionalities and potentials in the fields of opto-electronics, water splitting, spintronic devices and so on [20,21].For example, Zheng et al found faster exciton formation and longer exciton radiative recombination lifetimes in the monolayer Janus-MoSSe material [22].In bilayer MoSSe, the presence of an intrinsic dipole results in a type-II band alignment, and the bandgap can be tuned by adjusting the interlayer distance and dipole moment [23].In addition, C 3 N 4 is a porous graphitic carbon nitride (g-CN) material that has been experimentally synthesized through CVD [24] or temperature-induced condensation [25].It has garnered significant attention due to its tunable band gap, excellent physicochemical stability, and heightened photosensitivity [26,27].However, the narrow visible spectral response, low light absorption coefficient, and high carrier recombination rate of C 3 N 4 currently limit its application in optoelectronic devices [28].Therefore, to address the limitations of C 3 N 4 in optoelectronic devices, researchers have explored various techniques, including non-metallic element replacement, metal atoms attachment, and defect engineering, to modulate the its optoelectronic properties [29,30].Besides, the construction of vdW heterostructures by combining monolayers of C 3 N 4 with other semiconductors is another promising approach to improve the optoelectronic properties of the material.For example, Xu et al acquired a type-II band alignment in the C 3 N 4 /AlN heterostructure and promoted the efficient separation of photo-generated holes and electron.Moreover, the strong electrostatic field formed at the heterostructure interface facilitates the transfer of photo-generated electrons from the AlN layer to the C 3 N 4 layer, enhancing device performance by facilitating electron injection [31].
Based on the above properties of Janus-MoSSe and g-C 3 N 4 , we construct 2D MoSSe/C 3 N 4 and C 3 N 4 /MoSSe heterostructures, aiming to realize the band alignment transition between band alignment types and corresponding fine optical properties.Six stacking patterns by considering the rotation angle of MoSSe relative to C 3 N 4 are considered for both heterostructures, and the two stable A2 (C 3 N 4 -Se) and B2 (C 3 N 4 -S) heterostructures, labeled as A2 and B2, respectively, are selected for the further study.The band alignment types of A2 and B2 are studied, and interestingly, the A2 heterostructure exhibits type-I band alignment while the B2 heterostructure exhibits typical type-II band alignment, moreover, the external electric fields can modulate the band alignment of the two heterostructures, inducing band alignment transition between type-I and type-II.Finally, we concern the optoelectronic properties of A2 and B2 heterostructures and find the main absorption peaks of both heterostructures in their pristine state are located in the visible light region, approximately 2.9 eV.At present, most of the related researches on modulating the type of band alignment are realized by methods such as strain and doping, which are difficult to be realized in experiments [32,33].Comparatively, our constructed MoSSe/C 3 N 4 or C 3 N 4 /MoSSe heterostructures can be switched between type-I and type-II heterostructures easily by manipulating the external electric fields, which is a much simpler method.In addition, this heterostructure improves the disadvantage of weak optical properties of C 3 N 4 in the visible region and expands the scope of application in optical devices.More importantly, monolayers MoSSe and monolayers C 3 N 4 have been prepared experimentally, which is helpful for the actual synthesis of MoSSe/C 3 N 4 or C 3 N 4 /MoSSe heterostructures.

Computational details
All calculations are performed by first principles based on density functional theory (DFT), implemented in the Quantum Atomistix ToolKit (ATK) package [34].In the structure optimization, all atoms are relaxed until the residual forces acting on atoms are reduced to less than 0.05 eV Å −1 and the stress is less than 0.1 GPa, ensuring the attainment of minimum-energy configurations.As the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof method used to underestimates the band gap of 2D materials, the exchange correlation potential in our calculations is described by the GGA of Heyd-Scuseria-Ernzerhof (HSE06) hybrid functions [35].The convergence criteria for both the density matrix and the Hamiltonian matrix are set to 10 −5 .The k point samples of 16 × 16 × 1 are used for integration in the first Brillouin zone, and the density grid truncation energy is set to 125 Hartree.Considering the vdW interaction between the multilayered materials, the dispersion correction is performed by the DFT-D2 method [36].To avoid interactions between adjacent layers, we introduce a vacuum space of over 20 Å along the the stacking direction in all structures.Alongside this, a frozen phonon method with a 5 × 5 × 1 supercell is employed to calculate phonon band structures and assess the structural stability.The dipole correction is applied in all calculations.

Structural and electronic properties
The geometry and electronic properties of the monolayer C 3 N 4 and MoSSe are studied firstly.figures 1(a) and (b) show the top and side views of monolayer C 3 N 4 and MoSSe, respectively.After structure relaxation, the lattice parameters are 4.78 Å and 3.25 Å for C 3 N 4 and MoSSe, respectively.Specifically, the monolayer C 3 N 4 possessed two distinct C-N bonds, one with a C-N 1 bond length of 1.35 Å and another with a C-N 2 bond length of 1.48 Å, and for monolayer MoSSe, the S-Mo bond length is 2.41 Å and the Se-Mo bond length is 2.53 Å, which are rather consistent with previous theoretical or experimental data [37][38][39].Figures 1(c) and (d) depict the electronic band structures of C 3 N 4 and MoSSe monolayers, both of which exhibit direct band gap semiconductor properties.Moreover, the calculated band gap values of 3.529 eV and 1.983 eV for monolayers C 3 N 4 and MoSSe, respectively, which are also consistent with previous results [40,41].In order to assess the structural stability monolayers C 3 N 4 and MoSSe, the phonon band structures of them are calculated as presented in figures 1(e) and (f).The phonon band structures for both of them have no imaginary frequencies in the Brillouin zone as can be seen from figures 1(e) and (f), demonstrating the dynamic stability properties for both monolayers.
The supercells of heterostructures are constructed by combining (2 × 2) C 3 N 4 unit cell and (3 × 3) MoSSe unit cell because of the difference in their lattice parameters.The lattice parameters of A2 and B2 heterostructures is calculated to be 9.75 Å, resulting in a lattice mismatch of only 1.98%, which is beneficial for building heterostructures.As shown in figure 2 S2.Here, the binding energy is calculated by the binding energy equation, E b = E MoSSe(C3N4)/C3N4(MoSSe) − E C3N4 − E MoSSe , where E MoSSe(C3N4)/C3N4(MoSSe) , E C3N4 , and E MoSSe correspond to the total energy of the MoSSe/C 3 N 4 (A2) or C 3 N 4 /MoSSe(B2) heterostructures, monolayer C 3 N 4 , and MoSSe respectively.According to the binding energies of heterostructures, nearly all heterostructures are stable, but rotating MoSSe 60 • relative to C 3 N 4 yields two more stable configurations, named A2 and B2.In addition, due to the larger atomic radius of Se, the interlayer distance of the C 3 N 4 -Se stacking mode Ax (about 3.33 Å) are larger than those of the S-C 3 N 4 stacking mode Bx (3.26 Å) in the same stacking configuration.Correspondingly, the C 3 N 4 -Se stacking mode possesses greater binding energy as can be seen from table S2, suggesting that Coulomb gravity will lead to enhanced interlayer binding.The interlayer distance 3.33 Å (3.26 Å) for the A2 (B2) heterostructures is in interlayer distance range of typical vdW heterostructure [42], thus, interfacial interactions between the two layers in both heterostructures are weak vdW interactions.
Figures 3(a The band gap values for the A2 and B2 are 1.916 eV and 1.712 eV, respectively, much smaller than that for layer C 3 N 4 (3.529eV) and layer MoSSe (1.983 eV), both falling within the visible light energy range of 1.6 to 3.2 eV.More interesting and important, in the A2 heterostructure, both CBM (conduction band minimum) and VBM (valence band maximum) are contributed by the MoSSe layer, which indicates that the heterostructure is type-I semiconductor, while in the B2 heterostructure, the CBM is still from the MoSSe layer, but the VBM is from the C 3 N 4 layer, so the B2 heterostructure is the type-II semiconductor.
In order to demonstrate the band alignment in the A2 and B2 more intuitively, the band alignment schematics (including the band edges and work functions of the A2 and B2 heterostructures as well as of the isolated monolayer C 3 N 4 and MoSSe) are presented in figure 4, where the band alignments are set to the energy of the stable electron within the vacuum level.The work function of the structures is considered by    in B2, which lead to the different band alignment types between A2 (type-I semiconductor) and B2 (type-II semiconductor).
To explain the different band alignment types in the A2 and B2 heterostructures, we calculated the effective potentials (V eff ) for the two heterostructures as presented in figures 3(e) and (f).The effective potentials at electrostatic equilibrium are calculated by the following equation: Here, V H [n] represents the Hartree potential resulting from mean-field electrostatic interaction, V XC [n] denotes the exchange-correlation potential, V ext [n] signifies the sum of the external electrostatic potential and the electrostatic potential of ions, and n denotes electron density.We can see in figures 3(e) and (f) that the potential energy at the C 3 N 4 layer is higher than that at the MoSSe layer in both A2 and B2, generating a built-in electric field that points from the C 3 N 4 monolayer to the MoSSe monolayer.So electrons move away from the MoSSe monolayer and approach the C 3 N 4 monolayer.However, the interfacial energy potential difference ∆V between the C 3 N 4 layer and the MoSSe layer for B2 (6.71 eV) is bigger than that for A2 (5.88 eV), thus more electrons move away from the MoSSe monolayer and approach C 3 N 4 monolayer in B2 than that in A2.The more electrons the C 3 N 4 layer gain, the more the valence band edge will be lifted, thus, valence band edge of C 3 N 4 layer in B2 is higher than that in A2, which leads to the above different band alignments in A2 (type-I semiconductor) and B2 (type-II semiconductor).

Electronic properties under external electric field
In vdW heterostructure, an external electric field can cause charge redistribution between the layers, which will change the electronic properties of the heterostructure.As shown in the insets of figures 5(a) and (b), the external electric fields are applied perpendicular to the surface of the A2 (B2) heterostructure and with direction from MoSSe (C 3 N 4 ) to C 3 N 4 (MoSSe) when the external electric fields are positive (shown by black arrows), and the direction of the intrinsic electric field of the two heterostructures are from C 3 N 4 to MoSSe (shown by red arrows).The projected electronic band structures of A2 and B2 under external electric field from −0.6 V Å −1 to 0.6 V Å −1 with an interval of 0.2 V Å −1 are presented in figure S1.It can be seen that, the band gaps of both heterostructures vary with the change of the external electric field, also changes are the band alignment types between type-I and type-II.To display the effect of external electric field on the electronic properties of both heterostructures more intuitively, the evolution of the band gap and band alignment of A2 and B2 heterostructures as a function of the external electric field is shown in figure 5.For the A2 heterostructure (see figure 5(a)), at the beginning, the band gap increases slowly with the increase of external electric field at the considered external electric field range [−0.5, 0.6] V Å −1 and reaches its maximum value 1.93 eV at the electric field 0.2 V Å −1 , and then decreases rapidly when the external electric field increases continuously.Therefore, the A2 heterostructure undergoes a sudden change in the band gap at the electric field 0.2 V Å −1 .Meanwhile, the band edges of MoSSe and C 3 N 4 undergo relative displacement under the external electric field, the VBM of C 3 N 4 increases continuously and that of MoSSe decreases continuously with the increase of the external electric field, and then the VBM of C 3 N 4 surpasses that of MoSSe at the electric field 0.2 V Å −1 , which make the band alignment type of the heterostructure transform from type-I to type-II (see figure 5(c)).In addition, when the electric field is lower than −0.5 V Å −1 , the CBM of C 3 N 4 surpasses that of MoSSe, which leads to a shift in the band alignment type from type-I to type-II.The band gap and band alignment of B2 under the external electric field are similar but somewhat different from that of A2 (see figures 5(b) and (d)) attributed to their different strengthen of the built-in electric field as have been provided in figures 3(c) and (d).There is also a turning point in the band gap and band alignment type in B2 at the positive electric field of 0.1 V Å −1 .The band gap increases quickly as the external electric field increases from −0.6 V Å −1 to 0.1 V Å −1 , while it increases slowly as the positive electric field increases from 0.1 V Å −1 to +0.6 V Å −1 (see figure 5(c)).When the external electric field is smaller than 0.1 V Å −1 , the CBM and VBM of the heterostructure are contributed by MoSSe and C 3 N 4 , respectively, so the heterostructures exhibit the type-II band alignment, while when the external electric field exceeds 0.1 V Å −1 , both the CBM and VBM of the heterostructure are contributed by MoSSe, so the band alignment type of the heterostructure is the type-I.Thus, the external electric field can modulate the band alignment type of the B2 between type-II and type-I.In addition, as can be noticed, due to the presence of the built-in electric field of the heterostructures, the effect of positive and negative external electric fields is different in modulating the electronic properties of the heterostructures when the applied external electric field is rather small.However, when the applied external electric field is much larger than the built-in electric field of the heterostructure, the effect of the built-in electric field on the electronic properties of the heterostructure can be negligible.Therefore, the large magnitude of external electric field can modulate the band structure and band alignment of heterostructures, which can ultimately expand their applications in high-performance multifunctional devices.

Optical properties
To investigate the optical properties of A2 and B2 heterostructures, the frequency-dependent complex dielectric function, ϵ r (ω) = 1 + χ(ω), where ω is the photon frequency.The dielectric susceptibility χ(ω) is calculated within the framework of the Kubo-Greenwood formalism implemented in the Quantum ATK package, , where V is the unit cell volume, f is the Fermi-Dirac function, Γ is the energy broadening, π i nm is the i-th dipole matrix element between the states n and m.In the linear response range, the complex dielectric response function for describing the optical properties of the material is ϵ r (ω) = ϵ 1 (ω) + iϵ 2 (ω), where ϵ 1 (ω) is the real part of the complex dielectric response function, and ϵ 2 (ω) is the imaginary part of the complex dielectric response function which can evaluate the optical properties of the material [45,46].Since each monolayer and both heterostructures are anisotropic, the imaginary parts of the dielectric functions in the in-plane (x-y) and out-of-plane (z) directions for monolayer C 3 N 4 , MoSSe, A2 and B2 heterostructures are considered, as can be seen in figures 6(a) and (b), respectively.In the x-y direction, monolayer C 3 N 4 has one comparatively wide photon absorption peak near the photon energy 4.05 eV (corresponding to the ultraviolet-B light), while monolayer MoSSe has three major photon absorption peaks at 2.9 eV (violet), 4.25 eV (UV-B), and 4.8 eV (UV-C) (see figure 6(a)).In stacked heterostructures, interlayer coupling and electron transfer can lead to overlapping electronic states in the valence band of the heterostructure, which produce optical properties different from those of the monolayer.The A2 heterostructure has four major photon absorption peaks at photon energies 2.6 eV  (cyan), 2.9 eV (blue), 3.65 eV (UV-A), and 4.05 eV (UV-B), and the B2 heterostructure has the same peaks in this direction.While in the z direction, monolayer C 3 N 4 has small fluctuations only at 1.05 eV (Infrared), and monolayer MoSSe has only one main absorption peaks located at energies 5.1 eV (UV-C).Thus, in the z direction, both the A2 and B2 heterostructures have only one absorption peak at 4.9 eV (UV-C).In a whole, the main (high and broad) absorption peaks of both heterostructures in the x-y direction are in the visible light region (approximately 2.9 eV) and in the z direction are at 4.9 eV (UV-C).As stated in the Introduction, although the pristine C 3 N 4 is not good for optoelectronic devices, it may still act as a good building block for constructing heterostructures with desired optical performance.
Under external electric field, the interlayer coupling and charge transfer in the heterostructure can be altered, which may induce distinct optical properties as compared to that in the original heterostructure.Thus, we investigated the imaginary part of the dielectric function ϵ 2 (ω) of A2 and B2 heterostructures under certain external electric fields.Figure 7 shows the trends of the imaginary part of the dielectric function ϵ 2 (ω) versus photon energy under the influence of certain given external electric fields [−0.6, 0.6, with an interval of 0.2 V Å −1 ] for both heterostructures in the in-plane ((a) x-y and out-of-plane (z) directions.The insert provides a magnified view of main photon absorption peaks in the shaded areas.Under the external electric field, the main photon absorption peaks of both heterostructures in the x-y and z directions increase with the increase of the positive external electric field, but decrease with the increase of the negative external electric field.Compared to graphene optical modulators [47] that have large bandwidths (1350 nm-1600 nm) only in the near-infrared region, large optical absorption peaks in the visible region can be observed along the x-y direction in our proposed heterostructures.

Conclusion
In summary, we have systematically investigated the structural, electronic and optical properties of MoSSe/C 3 N 4 and C 3 N 4 /MoSSe heterostructures and their corresponding properties under external electric fields based on first-principles calculations.The MoSSe/C 3 N 4 and C 3 N 4 /MoSSe heterostructures stable due to their negative binding energy and small lattice mismatch.Moreover, analysis of the effective potential along the z-axis reveals charge transfer from the monolayer MoSSe to C 3 N 4 , leading to an internal electric field from the C 3 N 4 layer to the MoSSe layer in both heterostructures and inducing different band gaps and band alignment types in the two heterostructures.In the MoSSe/C 3 N 4 heterostructure, the conduction band minimum and valence band maximum are contributed by MoSSe, resulting in typical type-I band alignment that is well-suited for luminescence applications.While in the C 3 N 4 /MoSSe heterostructure, the CBM and VBM are contributed by C 3 N 4 and MoSSe, respectively, resulting in a type-II band alignment that promotes efficient carrier separation.Furthermore, the MoSSe/C 3 N 4 heterostructure exhibits band alignment transitions between type-I and type-II at the external electric field points near −0.4 V Å −1 and 0.2 V Å −1 .In contrast, the C 3 N 4 /MoSSe heterostructure undergoes band alignment transition between type-II and type-I at external electric field of about 0.1 V Å −1 .In addition, we found the main absorption peaks of both heterostructures in the x-y direction located in the visible light region (approximately 2.9 eV) and in the z direction are at 4.9 eV (UV-C), and the peak values of the absorption peaks can be enhanced (weaken) via applying positive (negative) external electric fields.In experiment, both the monolayer MoSSe and monolayer C 3 N 4 have been successfully prepared by CVD method, and the wet transfer technique can be used to synthesise MoSSe/C 3 N 4 and C 3 N 4 heterostructures just as the preparation process of MoS 2 /WS 2 heterostructures proposed by Yuan et al [48] .The synthesis process can be: firstly, grown MoSSe and C 3 N 4 on a suitable substrate by the CVD method.The monolayer MoSSe is transferred to the new substrate using NaOH solution as an etchant and the monolayer C 3 N 4 is subsequently stacked on top of the monolayer MoSSe to yield Janus-MoSSe/C 3 N 4 heterostructures.Our research will contribute to the further development of multifunctional devices in the MoSSe/C 3 N 4 and C 3 N 4 /MoSSe vdW heterostructures.Additionally, we note that this phenomenon is not limited to C3N4.Any other materials with a suitable bandgap, work function, and low lattice mismatch rate with MoSSe will be good candidates for constructing a heterstructure with similar phenomenon.
, two distinct types of heterostructures (MoSSe/C 3 N 4 and C 3 N 4 /MoSSe heterostructures) based on the direction of the MoSSe electric dipole, with C 3 N 4 positioned both above (C 3 N 4 -Se, labeled as Ax, x = 1-6) and below (S-C 3 N 4 , labeled as Bx, x = 1-6) the MoSSe layer are considered.In addition, for each type of heterostructure, six different stacking modes by rotating MoSSe relative to C 3 N 4 at angles of 0 • , 60 • , 120 • , 180 • , 240 • , and 300 • are considered (where x = 1-6 correspond heterostructures by rotating MoSSe relative to C 3 N 4 with rotation angles 0 • -300 • at the angel interval 60 • , respectively).The binding energy for the above 12 type heterostructures are shown in table ) and (b) show the layer-dependent projected electronic band structures of the A2 and B2, respectively.The bands of the heterostructures contributed by layer C 3 N 4 and layer MoSSe move toward the Fermi level (see figures 3(a) and (b)) as compared with single layer C 3 N 4 and layer MoSSe (see figures 1(c) and (d)) because of the layer-layer interaction.

Figure 1 .
Figure 1.(a) and (b) Top and side views of the monolayer C3N4 and MoSSe, where the blue, grey, orange, cyan and yellow balls represent C, N, Se, Mo and S atoms, respectively.The black frame indicates a unit cell of the C3N4 or MoSSe.(c) and (d) The electronic band structures of monolayer C3N4 and MoSSe, respectively, where the Fermi level is set as zero.(e) and (f) The phonon band structures for C3N4 and MoSSe monolayers, respectively.

Figure 2 .
Figure 2. Top and side views of MoSSe/C3N4 and C3N4/MoSSe heterostructures under stacking patterns with C3N4 positioned above (labeled as Ax, x = 1 − 6) or below (labeled as Bx, x = 1 − 6) the MoSSe layer, where x = 1-6 denotes heterostructure by rotating MoSSe relative to C3N4 with rotation angles 0 • -300 • at the angel interval 60 • , respectively.d represents the relaxed equilibrium interlayer distances.The gray shading on A2 and B2 highlights the two more energetically favorable stacking configurations.

Figure 3 .
Figure 3. (a) and (b) The projected electronic band structure and (c)-(d) effective potential along the z-axis for heterostructures A2 and B2, respectively.The red and blue bands in (a) and (b) denote the bands contributed by MoSSe and C3N4, respectively.∆V is the interfacial potential difference between the effective potentials of the MoSSe side and the C3N4 side.

Figure 4 .
Figure 4. Schematic representation of band alignment in C3N4 and MoSSe monolayers as well as A2 and B2 heterostructures.ΦW, Evac and EF represent the work function, the vacuum energy level, and the Fermi energy level, respectively.The vacuum energy level set to zero.

Figure 5 .
Figure 5. (a)-(b) The band gap and (c)-(d) the CBM and VBM band edges of A2 and B2 heterostructures under external electric field.The inset in (a)-(b) represents the schematic model of electric fields perpendicularly to the heterostructure surface, the black arrow represents the direction of the external electric fields, while the red arrow indicates the direction of the built-in electric field in the heterostructures.E C3N4−CBM (E C3N4−VBM ) denotes the CBM (VBM) of C3N4 and E MoSSe−CBM (E MoSSe−VBM ) denote the CBM (VBM) of MoSSe in heterostructures.The Fermi level is set to zero.

Figure 6 .
Figure 6.The imaginary part of the dielectric function ϵ2(ω) as a function of the photon energy in (a) x-y and (b) z direction for monolayers C3N4 and MoSSe, and A2 and B2.

Figure 7 .
Figure 7.The imaginary part of the dielectric function ϵ2(ω) as a function of the photon energy in the (a) x-y and (b) z direction under certain given external electric fields for A2, (c)-(d) the same as (a)-(b) but for B2.