A first principles study of a van der Waals heterostructure based on MS2 (M = Mo, W) and Janus CrSSe monolayers

The strategy of stacking two-dimensional materials for designing van der Waals heterostructures has gained tremendous attention in realizing innovative device applications in optoelectronics and renewable energy sources. Here, we performed the first principles calculations of the geometry, optoelectronic and photocatalytic performance of MS2–CrSSe (M = Mo, W) vdW heterostructures. The mirror asymmetry in the Janus CrSSe system allows the designing of two models of the MS2–CrSSe system by replacing S/Se atoms at opposite surfaces in CrSSe. The feasible configurations of both models of the MS2–CrSSe system are found energetically, dynamically and thermally stable. The studied heterobilayers possess an indirect type-I band alignment, indicating that the recombination of photogenerated electrons and holes in the CrSSe monolayer is hence crucial for photodetectors and laser applications. Remarkably, a red-shift in the optical absorption spectra of MS2–CrSSe makes them potential candidates for light harvesting applications. More interestingly, all heterobilayers (except W(Mo)S2–CrSSe of model-I(II)) reveal appropriate band edge positions of the oxidation and reduction potentials of the photocatalysis of water dissociation into H+/H2 and O2/H2O at pH = 0. These results shed light on the practical design of the MS2–CrSSe system for efficient optoelectronic and photocatalytic water splitting applications.


Introduction
The isolation of single layer graphene has led to the emergence of novel two-dimensional (2D) materials for designing novel next-generation nanoelectronic and photonic devices. 1,2 A majority of ultra-thin atomic layer materials such as hexagonal boron nitrides (h-BNs), transition metal dichalcogenide (TMDCs), and MXenes have been fabricated and widely studied due to their exceptional physical properties. [2][3][4] In this sense, TMDCs with the general formula MX 2 (M ¼ Mo, W; X ¼ S, Se) exhibit an extraordinary physical behavior compared to their bulk counterpart and have gained tremendous attention among the scientic community. 5 The feasible fabrication, high thermal and mechanical structural stability, direct semiconducting band gap nature and unique optical properties of MX 2 make them promising for optoelectronics, 6 energy storage, 7 gas sensing, 8 eld effect transistors, 9 photocatalysis, 10 and photovoltaic 11 device applications.
In parallel with the search for new 2D materials, the formation of Janus congurations of TMDCs has been recently achieved as an alternative technique to tune the intrinsic behavior of already existing 2D TMDC systems. For instance, the Janus TMDC MoSSe monolayer has been practically realized through the chemical vapor deposition (CVD) technique by replacing sulfur with selenium in the MoS 2 monolayer 12 and replacing selenium with sulfur in the MoSe 2 monolayer. 13 Recently, Janus WSSe monolayers have been fabricated through the CVD method. 14 The MXY (M ¼ Mo, W; X, Y ¼ S, Se) monolayers have proven excellent electronic and optical properties, realizing them potential candidates for designing optoelectronic, 15 piezoelectric, 16 photocatalysis, 17 and spintronic devices. 18 More recently, it has been demonstrated that all single layer Janus CrXY (X, Y ¼ S, Se, Te) are energetically and thermally stable, and display semiconducting band gap nature (in the range of 1.10-1.57 eV), have good optical absorption in the near infra-red region and hold a suitable band edge for fully photocatalytic water splitting. 19 The interest in tailoring the properties of 2D materials has gained tremendous attention in designing novel devices with enhanced tunable functionalities. The vertical assembling of 2D materials via weak van der Waals (vdW) interactions allows for the tailoring of the physical properties of the constituents, provides a feasible path for photogenerated charge separation and facilitates maximum optical absorption. 20 The vdW heterostructures possess different types of band alignment. In the type-I band alignment, the valence band maximum (VBM) and conduction band minimum (CBM) are localized in one constituent, resulting in the fast recombination of photogenerated charge carriers and hence making them favorable for laser or light emitting diode (LED) applications. 21 A type-II heterostructure holds both VBM and CBM localized in different constituents reducing the photogenerated charge separation, making them promising for solar cells and photovoltaics. 22 Moreover, the continuous separation of photogenerated electrons and holes in different layers of the vdW heterojunction is utilized for water decomposition under solar irradiation. 23 The photocatalytic water splitting reaction is driven by photoexcited electron-hole pairs, which are generated in a semiconducting photocatalyst as solar illumination and spatially separated by band bending at the semiconductor surface layer. Water at the photocatalyst surface can be reduced to H 2 by photoexcited electrons that reach the surface, while holes at the surface would induce oxidation of water to produce O 2 gas. [24][25][26] Recently, several efforts have been dedicated to explore enhanced optoelectronic and photocatalytic properties in GeC-MXY, 27 Janus TMDC-Janus TMDCs, MoSSe-WSSe, 28 MoSSe-graphene, 29 MoSSe-WSe 2 (ref. 30) and MoSSe-XN. 31 Despite these attempts, the theoretical or experimental study of a feasible design of the MS 2 -CrSSe vdW heterostructure remains unexplored.
In accordance with outstanding physical properties and satisfactory lattice mismatch, in the present study, we designed and investigated the unprecedented properties of the vdW heterostructure based on MS 2 (M ¼ Mo, W) and Janus CrSSe monolayers by rst-principles calculations. The mirror asymmetry in the CrSSe monolayer allows for considering two different models of the MS 2 -CrSSe heterostructure with six possible stacking patterns. The most feasible stacking conguration of both models reveals energetic, dynamic and thermal stability. Finally, the electronic, optical and photocatalytic behavior of the feasible conguration is explored. Our ndings predict MS 2 -CrSSe heterostructures as promising candidates for future optoelectronic and photovoltaic devices.

Computational details
In present study, rst principles calculations on the MS 2 -CrSSe heterostructure are performed using the projector augmented wave (PAW) method 32 as implemented in the Vienna ab initio simulation package (VASP). [33][34][35] The generalized gradient approximation (GGA) combined with the Perdew-Burke-Ernzerhof (PBE) functional 36 with an energy cut-off of 600 eV was adopted to optimize the geometric structure and the HSE06 (Heyd-Scuseria-Ernzerhof) functional 37 was used to correct the underestimated electronic band structures. The weak dispersion forces between the adjacent layers were described by the DFT-D2 scheme proposed by Grimme. 38 A 6 Â 6 Â 1 Monkhorst-Pack k-point grid 39 was used for geometric relaxation and further rened to 12 Â 12 Â 1 in the whole Brillouin zone (BZ) for the optimized geometry and electronic structure calculations. The interactions between the adjacent layers of the MS 2 -CrSSe heterostructure are avoided by using a vacuum slab of 25Å along the z-axis. The convergence criteria of energy and force are set as 10 À6 eV and 0.01 eVÅ À1 , respectively. The phonon band spectra are calculated using the density functional perturbation theory (DFPT) within the PHONOPY code. 40 Ab initio molecular dynamics (AIMD) calculations of the feasible structures are performed for a 6 Â 6 Â 1 supercell at room temperature. Bader charge analysis is adopted to demonstrate the charge transfers between the atom. 41,42 Results and dissection The pristine single layers MS 2 (M ¼ Mo, W) and CrXY (X ¼ S, Y ¼ Se) exhibit a graphene-like hexagonal honeycomb structure. The calculated bond length for Mo-S, W-S, Cr-S and Cr-Se are 2.402 A, 2.408Å, 2.302Å and 2.423Å, respectively. Also, the optimized lattice constant (band gap) values for parent MoS 2 , WS 2 and CrSSe monolayers are 3.16Å (2.01 eV), 3.15Å (1.95 eV) and 3.13 A (2.11 eV), respectively. These results are consistent with previously available theoretical and experimental literature [43][44][45][46][47][48][49][50][51] and conrm our theoretical approach for the study of TMDCs and Janus CrSSe monolayers.
In general, the orientation of contacted atoms in individual layers or local congurations strongly affects the interfacial properties of the heterostructures. Since the lattice mismatch between Mo(W)S 2 and CrSSe monolayers is 0.95 (0.63) %, the MS 2 and CrSSe monolayers exhibit a satisfactory lattice mismatch, revealing the experimental construction of MS 2 -CrSSe heterostructures through van der Waals (vdW) interaction. As Janus CrSSe with mirror asymmetry possesses different chalcogen (X/Y) atoms, we consider two different models (model-I and model-II) with alternate chalcogen atoms at the opposite surface of single layer CrSSe placed above the MS 2 monolayer to construct the MS 2 -CrSSe vdW-heterobilayer system, as displayed in Fig. 1 To further conrm the energetic stability of the most feasible conguration, the binding energy is calculated for each conguration of both models of MS 2 -CrSSe vdW heterostructures. The binding energy is dened as: where E b shows the binding energy of the system, E hetero , E TMDC and E CrSSe represent the total energy of MS 2 -CrSSe, isolated MS 2 and CrSSe monolayers, respectively. The calculated lattice constants, bond length, binding energy (E b ) and interlayer spacing (d) of the most feasible conguration for model-I and model-II are presented in Table 1. It is clear from Table 1 that an increase/decrease in the bond length of the Mo(W)S 2 /CrSSe system indicates intrinsic tensile/compressive strain in Mo(W) S 2 /CrSSe, respectively. The calculated intrinsic compressive/ tensile strain are 0.47%/0.48% for MoS 2 /CrSSe in MoS 2 -CrSSe and 0.32%/0.32% for WS 2 /CrSSe in WS 2 -CrSSe, which is attributed to vdW interactions between Mo(W)S 2 and CrSSe vertically stacked systems. Evidently, the disparity of local congurations leads to different magnitudes of binding energy and corresponding distance between the layers. The smaller interlayer spacing of the conguration (b) of both models reveals energetic stability and tailors the physical behavior of MS 2 (M ¼ Mo, W) and CrSSe monolayers.
To assess the dynamical stability of MS 2 -CrSSe heterobilayers, the phonon band spectra is calculated using the phonopy code, as shown in Fig. 2. There are six atoms per primitive unit cell therefore, each phonon band dispersion is composed of three acoustic zero frequency modes and 15 optical branches. As it is clear from Fig. 2 that all phonon modes with positive eigenfrequencies at the G-point of the Brillouin zone indicates dynamical stability of MS 2 -CrSSe heterobilayers. This conrms the synthesis of all MS 2 -CrSSe heterobilayers. Further, the thermal stability of a material is important to study the molecular vibrations or uctuation in energy with time at different temperatures. 52,53 The thermal stability of MS 2 -CrSSe systems, presented in Fig. 3(a-d), is carried out by performing ab initio molecular dynamics (AIMD) calculations. Since it determines the amount of energy per vibrational degree of freedom and the oscillation amplitudes are dependent on the temperature. Both models of MS 2 -CrSSe systems comprise pure harmonic oscillators, revealing no prominent change in the energy spectra, as shown in Fig. 3(a-d). This indicates the absence of broken bonds or the reconstruction of geometric structures aer heating the system at 300 K for 3000 fs, hence conrming the thermodynamical stability of the MS 2 -CrSSe systems. This behavior has also been demonstrated in P-SiS, P-SiC and P-Janus structures. 54 In general, the electronic properties of 2D materials can be modulated by the interaction between the stacked monolayers. The electronic band structure of MS 2 -CrSSe systems is investigated using PBE and HSE06 functionals, as displayed in Fig. 4(a-d). All understudy systems possess an indirect band gap semiconducting nature with the valence band maximum (VBM) located at K-point and the conduction band maximum (CBM) found at G-point of the Brillouin zone. In this case, the excited electrons could jump from the valence band to the conduction band at K-point and then the holes move from G-point, which can effectively retard the combination of photogenerated electrons and holes and enhance the photocatalytic performance 55 TMDCs. 56,57 This is consistent with other 2D In 2 X 3 (X ¼ S, Se, Te) monolayers 58 and Nb 2 XTe 4 . 59 The band gap values of MS 2 -CrSSe (model-I and model-II) systems using PBE and HSE06 functionals are listed in Table 1. Evidently, an enlarged band gap value using the HSE06 level can be seen. This trend has been demonstrated in GeC-MS 2 and SiC-MX 2 systems. 24,60,61 Further, the MS 2 -CrSSe vdW heterostructures with indirect type-I band gaps are comparatively more promising for photodetectors and photocatalysis as compared to MX 2 -Zr 2 CO 2 , 62 PbI 2 -a-Te 63 and GaS-g-C 3 N 4 (ref. 64) vdWs heterostructures.
In order to illuminate the orbital character for understanding the nature of the band alignment of heterostructures, the weighted band structure of all heterobilayers is calculated, as displayed in Fig. 5. For both models of MS 2 -CrSSe systems,   The absence of mirror-symmetry in Janus 2D materials results in different polarization effects, which helps to understand the intrinsic electronic and extrinsic photocatalytic behavior of the materials. [70][71][72][73] The plane-averaged electrostatic potential of all MS 2 -CrSSe heterobilayers for both models is calculated and plotted in Fig. 6(a-d). It can be clearly seen that    The optical response of materials to incident solar light is crucial in identifying the promising materials for the water splitting mechanism. The optical parameter particularly the imaginary part of the dielectric function 3 2 (u) of understudy systems is calculated to understand the transition between the occupied and unoccupied states, as displayed in Fig. 7(a-d). The electronic band structure is modied in the MS 2 -CrSSe system due to the weak coupling and interlayer charge transfer between the pristine monolayers. Moreover, the excitons dominate the optical transition from the valence band (VB) to the conduction band (CB) in all understudy heterostructures. Interestingly, the excitonic transition occurs in the range of 1.07-1.60 eV for MoS 2 -CrSSe, 2.05-2.80 eV for WS 2 -CrSSe, 2.01-2.80 eV for MoS 2 -CrSeS and 3.0-3.5 eV for WS 2 -CrSeS. In contrast to pristine monolayers, a red-shi is evidently observed in the optical absorption spectra of MS 2 -CrSSe, highlighting them as potential candidates for optoelectronic devices to capture the visible solar spectrum. Other 2D materials have followed the same trend. [75][76][77][78] To explore water dissociation into hydrogen production under solar irradiation, the valence band (VB) edge and conduction band (CB) edge position align with the standard reduction (H + /H 2 ) and oxidation (O 2 /H 2 O) potentials of water dissociation are calculated at pH ¼ 0 using the HSE06 level, as displayed in Fig. 8. In general, the standard potentials for the redox reactions of water splitting are as follows E red (H + /H 2 ) ¼ À4.44 eV + pH Â 0.059 eV and E Ox (O 2 /H 2 O) ¼ À5.67 eV + pH Â 0.059 eV. 79 In photocatalysis, photogenerated electrons and holes are separated and transported to H + /H 2 or to O 2 molecules. For the water splitting reaction, the photocatalyst should possess a semiconducting band gap with a value greater than 1.23 eV. Evidently, for W(Mo)S 2 -CrSSe of model-I(II), the valence band (VB) edge is found above the oxidation potential and the conduction band (CB) edge fails to reside above the reduction potential. In contrast, for other Mo(W)S 2 -CrSSe systems of model-I(II), the CBM lies higher than the reduction potential (À4.50 eV) and the VBM is located lower than the oxidation potential (À5.70 eV). This exciting trend of the band edge position has been demonstrated for other materials. 80,81 Hence, both VB and CB edges straddle the redox potentials, Fig. 7 The absorption spectra of (a-d) MS 2 -CrSSe heterostructures.
rendering these systems as suitable candidates for producing low cost hydrogen gas at a commercial scale.

Conclusion
To summarize, we theoretically investigated the structural, electronic, optical and photocatalytic behavior of two different models of MS 2 -CrSSe (M ¼ Mo, W) heterostructures by performing the density functional theory calculations. The feasible binding energy, absence of imaginary frequencies in phonon branches and no considerable uctuation of the energy curve at room temperature verify the energetic and dynamical stability of all understudy heterobilayers. All MS 2 -CrSSe (M ¼ Mo, W) systems possess an indirect type-I band alignment with VBM and CBM localized in the CrSSe layer, indicating the recombination of photogenerated electrons and holes in the CrSSe layer, hence making them suitable for light detection applications. The broadening of light absorption in the visible region coupled with red-shi in absorption spectra reveals MS 2 -CrSSe systems promising for light conversion purposes. The Mo(W)S 2 -CrSSe of model-I(II) heterobilayers are capable of performing redox reactions of water splitting under solar irradiation, whereas the WS 2 (MoS 2 )-CrSSe system of model-I(II) fails to perform redox reactions. These ndings lead to the practical utilization of MS 2 -CrSSe systems in future optoelectronic and photocatalytic water splitting applications.