MoS₂ and Janus (MoSSe) based 2D van der Waals heterostructures: emerging direct Z-scheme photocatalysts

Abstract

Two-dimensional (2D) materials, viz. transition metal dichalcogenides (TMD) and transition metal oxides (TMO), offer a platform that allows the creation of heterostructures with a variety of properties. The optoelectronic industry has observed an upheaval in the research arena of MoS₂ based van der Waals (vdW) heterostructures (HTSs) and Janus structures. Therefore, interest towards these structures is backed by the ability to select their electronic and optical properties. The present study investigates the photocatalytic abilites of bilayer, MoS₂ and Janus (MoSSe) based vdW HTSs, viz. MoS₂/TMO, MoS₂/TMD, MoSSe/TMO and MoSSe/TMD, by a first-principles based approach under the framework of (hybrid) density functional theory (DFT) and many body perturbation theory (GW approximation). We have considered HfS₂, ZrS₂, TiS₂ and WS₂, and HfO₂, T-SnO₂ and T-PtO₂ from the families of TMDs and TMOs, respectively. The photocatalytic properties of these vdW HTSs are thoroughly investigated and compared with their respective individual monolayers by visualizing their band edge alignments, electron–hole recombination and optical properties. Strikingly, we observe that, despite most of the individual monolayers not performing optimally as photocatalysts, type II band edge alignment is noticed in vdW HTSs and they appear to be efficient photocatalysts via the Z-scheme. Moreover, these vdW HTSs have also shown promising optical responses in the visible region. Finally, electron–hole recombination, H₂O adsorption and hydrogen evolution reaction (HER) results establish that MoSSe/HfS₂, MoSSe/TiS₂, MoS₂/T-SnO₂ and MoSSe/ZrS₂ are probable highly efficient Z-scheme photocatalysts.

---

1 Introduction

At present, solar energy is the superior resource to combat energy and environment related issues. With an aim to enhance the utilization of solar energy, the field of photocatalysis for water splitting and pollutant degradation has gained interest.^1–4 Further, the demand for exciting materials that are selective, have directed the focus towards 2D materials. Amongst these, MoS₂ is one of the widely studied 2D materials that belongs to the transition metal dichalcogenides (TMDs) family. Other classifications of 2D materials include the graphene family, transition metal oxides (TMOs) and MXenes.⁵ These materials have been widely studied in the areas of defect study,^6,7 photovoltaics^8,9 and optoelectronics.^10,11 The widely studied (both theoretically and experimentally) TMDs are MoS₂, MoSe₂, WS₂ and WSe₂. However, other TMDs such as HfS₂, ZrS₂ and TiS₂ have also been a matter of research for their salient electronic, vibrational and optical properties.^12–14 Conversely, a similar level of experimental data has not been established for TMOs as that for TMDs. Lebègue et al.¹⁵ have indicated that the synthesis of TMOs is challenging due to the rare occurrence of their stable bulk phases. Only a few of these materials have been synthesized experimentally.¹⁶ In this scenario, theoretical studies of TMOs have showcased a huge potential, which helps in opening the scope of further research.^17,18 Another class of 2D materials that has recently drawn a lot of interest is Janus materials.^19,20 These materials, having the form of MXY (M = Mo and X, Y = O, S, Se and Te; X ≠ Y), lack mirror symmetry and have a vertical dipole.^21,22 They exhibit superior photocatalytic activities amongst their counterparts.^23,24 Engineering them for constructing van der Waals (vdW) heterostructures (HTSs) has established novel physics such as interlayer screening effects^25–27 and valley physics,^28–30etc. Therefore, the existing literature indicates that the aforementioned materials are promising in the present research context.^31–36

Here, we select vdW HTSs for the study of photocatalytic water splitting. Now, the MoS₂ monolayer with a direct band gap and apt redox potentials is a good photocatalyst.^37,38 However, its performance is affected by electron (e⁻) and hole (h⁺) recombination as the carriers are generated in the same spatial region.³⁹ Therefore, an attempt to mitigate this issue is to consider making vdW HTSs, where due to the separation of e⁻–h⁺ carriers in different layers (i.e. different spatial regions), they are considered to be a successful alternative for photocatalytic water splitting.^40,41 Here we have considered the class of vdW HTSs with type II band alignment for this application. Note that there are two types of photocatalysts in the case of vdW HTSs: (a) simple heterojunction photocatalysts and (b) Z-scheme systems. In the former, the conduction band minimum (CBM) and the valence band maximum (VBM) of the vdW HTSs straddle the redox potential.^42,43 Here, the CBM and VBM are on two different monolayers, thereby facilitating spatial charge separation with the reduction and oxidation reactions on different monolayers. But, to achieve sufficient redox ability for a specific reaction to occur on a single photocatalyst, a larger bandgap that simultaneously inhibits e⁻–h⁺ recombination and correlates with a higher oxidation/reduction ability is required. However, to enhance the efficiency, a smaller bandgap is desirable for light harvesting. Therefore, this is of paramount importance for improving the photocatalytic performance, and Z-scheme photocatalysts^44–46 provide a solution by manipulating the photogenerated e⁻–h⁺ pairs, as shown in the Z-scheme model (see Fig. 1). Like before, here having type II alignment is mandatory, but the CBM and VBM of the vdW HTSs do not straddle the redox potentials in the same manner as before. The layer with the CBM straddling the reduction level and the other layer with the VBM straddling the oxidation level are involved in the hydrogen evolution reaction (HER) and the oxygen evolution reaction (OER), respectively (see Fig. 1). The higher interlayer recombination of e⁻–h⁺ as compared to that of intralayer is a necessary step in the process. Thus, photoabsorption is improved due to the two different band gaps, leading to HER and OER occurring on different layers.^47–49 The weak vdW interlayer interactions in vdW HTSs facilitate lubrication or interlayer movement that further assists the Z-scheme photocatalysis.⁴¹ Although, some vdW HTSs have been studied in this area,^41,44,50,51 no extensive study on MoS₂ based vdW HTSs consisting of TMDs (viz. HfS₂, ZrS₂, TiS₂) and TMOs (viz. HfO₂, T-PtO₂, T-SnO₂) as a second layer has been conducted so far. On a similar note, the data for Janus (MoSSe) based vdW HTSs for photocatalytic application is at an initial stage.^20,24 Hence, there is a justified interest to explore their applicability as photocatalysts. MoSSe based vdW HTSs have further given rise to two possible stacking arrangements. Contrary to the structure of MoS₂, MoSSe lacks mirror symmetry. Hence, it is crucial to compare the possible stacking configurations of MoSSe based vdW HTSs with those of MoS₂ based vdW HTSs, for photocatalytic application.

Fig. 1 Schematic of Z-scheme photocatalysis.

In this article, we have presented an exhaustive comparative study of MoS₂ and MoSSe based vdW HTSs, where the second layer is from the family of (i) TMDs, viz. WS₂, HfS₂, ZrS₂, TiS₂ and (ii) TMOs, viz. HfO₂, T-PtO₂, T-SnO₂. The existing literature so far has not discussed the above listed vdW HTS configurations for Z-scheme photocatalysis. Up to this date, earlier reports exist only on monolayers of type II vdW HTSs of TMDs and TMOs for photocatalytic applications.⁵² Here, using state-of-the-art theoretical methodologies within the framework of hybrid density functional theory (DFT) and many body perturbation theory (MBPT) (viz. G₀W₀) we have systematically studied the important parameters for photocatalytic applications. First, we introduce the different possible stable configurations of vdW HTSs. Next, we discuss the band edge alignment of 2D monolayers and their corresponding vdW HTSs. Subsequently, their recombination path is thoroughly analyzed to check their capabilities as Z-scheme photocatalysts. Finally, their accurate optical responses are computed and understood using the MBPT technique for considering them for photocatalytic devices. Strikingly, we observe that, despite most of the individual monolayers not performing optimally as photocatalysts, their vdW HTSs with type II band edge alignment appear to be efficient Z-scheme photocatalysts.

2 Methodology

We have employed a first-principles based methodology under the framework of DFT.^53–58 PAW pseudopotentials are used in our calculations using the plane wave basis set as employed in the Vienna ab initio simulation package (VASP).^59–61 The exchange–correlation (xc) interactions amongst electrons are accounted for by the generalized gradient approximation (GGA) with the functional form as proposed by Perdew–Burke–Ernzerhof (PBE).^62,63 The hybrid density functional has also been employed to account for the same with the functional proposed by Heyd–Scuseria–Ernzerhof (HSE06).⁶⁴ The hybrid functional (HSE06) considers 25% mixing (α) of the short range Hartree–Fock (HF) exchange. Its long range part is described by the GGA-PBE functional.

The vdW HTSs are optimized using the PBE functional and HSE06 is used to determine the single point energy. The conjugate gradient minimization is performed with the Brillouin zone (BZ) sampling of a 2 × 2 × 1 K-grid and the energetics are obtained by the BZ sampling of a 16 × 16 × 1 K-grid. An energy tolerance of 0.001 meV and a force tolerance of 0.001 eV Å⁻¹ have been used for optimization. In the ground state calculations, the plane wave cut-off energy is set to 600 eV. The vdW HTSs are modelled with a 20 Å vacuum in order to avoid electrostatic interactions between the periodic images. The two-body vdW interaction as devised by Tkatchenko–Scheffler has been employed.^65,66 The correction parameter is based on Hirshfeld partitioning of the electron density. Note that we have not included spin–orbit coupling (SOC) in our calculations, since the previous literature has reported only a slight change in the band gap due to this.^44,67,68 The optical properties are calculated using the GW approach.^69,70 We have performed hybrid calculations (HSE06) as an initial step for single shot GW calculations (i.e. G₀W₀@HSE06).

3 Results and discussion

3.1 Heterostructure stacking

We have constructed commensurate bilayer vdW HTSs⁷¹ with minimum lattice mismatch between the layers. The vdW HTSs have been formed with a monolayer of MoS₂ (or MoSSe) and a monolayer of WS₂, ZrS₂, HfS₂, TiS₂, HfO₂, T-PtO₂ or T-SnO₂, in vertical alignment. The specifications of the monolayers (see the lattice parameters in ESI†) corroborate with the existing literature.^52,72,73 All of the monolayers constitute a 2 × 2 × 1 supercell (24 atoms) except ZrS₂ and HfS₂, where the supercell consists of 21 atoms. Here, the stacking styles between the two monolayers have not been varied in each vdW HTS. This is due to the fact that a binding energy change of merely a few meV is observed with the change in stacking styles of the two monolayers in a particular vdW HTS.^74,75

We have calculated the binding energy of vdW HTSs by the expression,⁷⁴

E_b = E(vdW HTSs) − E(MoS₂ or MoSSe) − E(BX₂) (1)

where E_b is the binding energy of the vdW HTS MoS₂/BX₂ (or MoSSe/BX₂), E(MoS₂) is the energy of monolayer MoS₂, E(MoSSe) is the energy of monolayer MoSSe and E(BX₂) is the energy of monolayer BX₂ (where B = W, Hf, Zr, Pt or Sn and X = S or O).

Fig. 2 shows the three configurations of vdW HTSs considered in the present work. Configuration I is of the type MoS₂/BX₂. The stacking type of MoS₂/T-SnO₂, MoS₂/ZrS₂ and MoS₂/WS₂(or HfO₂) are the same as that of MoS₂/T-PtO₂, MoS₂/HfS₂ and MoS₂/TiS₂, respectively. By replacing MoS₂ with MoSSe, we have created configurations II and III. The former consists of a Se atomic layer from MoSSe at the interface, whereas the latter has a S atomic layer at the interface. Configurations II and III also follow the same pattern as configuration I. Table 1 contains the lattice mismatches and the binding energies of all of the vdW HTS configurations. We define the mismatch as (l(MoS₂) − l(BX₂))/l(BX₂), where l(MoS₂) and l(BX₂) are the lattice constants of MoS₂ and BX₂, respectively.

Fig. 2 vdW HTSs with configurations I, II and III. MoS₂/BX₂ (configuration I), MoSSe/BX₂ (configuration II), where the Se atomic layer is at the interface, and MoSSe/BX₂ (configuration III), where the S atomic layer is at the interface.

Table 1 The corresponding bilayer vdW HTS lattice mismatches and binding energies of the different configurations (MoS₂/BX₂(I), MoSSe/BX₂(II and III))

BX2	Lattice mismatch (%)	Binding energy (eV)
		I	II	III
WS2	0.0	−1.04	−1.05	−1.02
ZrS2	2.5	−0.49	−0.54	−0.52
HfS2	3.9	−0.30	−0.35	−0.33
TiS2	2.5	−0.45	−1.00	−0.94
HfO2	1.2	−0.40	−0.54	−0.47
T-PtO2	0.4	−0.83	−0.63	−0.68
T-SnO2	1.8	−2.19	−2.24	−2.22

---

3.2 Band edge alignment

Photocatalytic applications require the understanding of the band gaps and absolute band edge positions. We have calculated these with both the PBE and HSE06 functionals. Fig. 3(a) shows the band edge alignments of the monolayers. We observe here that the chosen monolayers for the vdW HTSs have type II heterojunctions. In Fig. 3, H⁺/H₂ and O₂/H₂O correspond to the reduction and oxidation potentials of water splitting, respectively, for both pH(0) (solid line) and pH(7) (dashed line). Fig. 3(a) shows that HSE06 and PBE have some discrepancies in estimating the band edge positions. Calculations with the HSE06 functional incorporate the HF exact exchange term resulting due to the self-interaction error of e⁻, which is not well taken care of in the case of the PBE functional. Hence, the results presented in further plots are carried out using the HSE06 functional.

Fig. 3 Band edge alignment with respect to water redox potentials of (a) the individual monolayers, (b) MoS₂/BX₂ vdW HTSs (configuration I), (c) MoSSe/BX₂ vdW HTSs (configuration II and III), where BX₂ refers to WS₂, ZrS₂, HfS₂, TiS₂, HfO₂, PtO₂ or SnO₂.

Fig. 3(b) and (c) depict the absolute band edge positions of the MoS₂ and MoSSe based vdW HTSs, respectively. Fig. 3(b) indicates that individual band alignment approximately predicts the combined alignment of the vdW HTSs. The weak vdW interactions between the 2D monolayers is attributed to the aforementioned prediction. Here, type II alignment can be seen with the VBM of the MoS₂ (or MoSSe) monolayer and the CBM of HfS₂, ZrS₂, TiS₂, HfO₂, T-PtO₂ and T-SnO₂ monolayers. The band gaps of the monolayers and vdW HTSs are listed in the ESI† (Table II). The CBM and VBM should lie a few eVs above and below the redox potentials of water for the material to be suitable for photocatalysis. However, in our case the vdW HTSs band gaps do not straddle the photocatalytic water splitting potentials. Hence, we analyze these bilayer vdW HTSs for their applicability as Z-scheme photocatalysts. The vdW HTSs selected for further analysis from Fig. 3 are the configurations consisting of HfS₂, ZrS₂, TiS₂, HfO₂, T-PtO₂ and T-SnO₂. Note that the MoS₂ (or MoSSe) monolayer (CBM) does form type II alignment with WS₂ (VBM) as well and the HTS is observed to be capable of photocatalysis (but not via the Z-scheme). However, we have included this in our manuscript as a reference, with an intention to showcase a clear distinction with regards to Z-scheme photocatalysts. Moreover, from observing Fig. 3(c) a unanimously similar trend suggests that the band gaps of the vdW HTSs with configuration II are significantly different than those with configuration III.

It should be noted that the absolute band edge alignment is obtained with respect to the zero vacuum level. The associated E_Vac (vacuum level) of each calculation is obtained from the electrostatic potential of the system. As is evident from the term, the plot explains the electrostatic potential corresponding to each atomic layer (see Fig. 4). It is pertinent to understand the plot as it informs us about the work function and potential difference between the monolayers. Thus, we are able to analyze the interlayer charge transfer that indicates the photocatalytic ability. Fig. 4 presents the electrostatic potential plot of MoS₂/WS₂. From left to right in Fig. 4(a), we observe the potential of the S, Mo and S atomic layers of the MoS₂ monolayer and the S, W and S atomic layers of the WS₂ monolayer. We see a clear difference in the potentials of the cationic layers with regards to the Mo and W atomic layers. The gradient between the monolayers facilitates the charge separation between them. Fig. 4(b) shows the corresponding MoS₂/WS₂ vdW HTS, describing the respective atomic layers.

Fig. 4 Electrostatic potential plot of MoS₂/WS₂ depicting (a) potential difference in configuration I, (b) schematic of configuration I; (c) potential difference in configuration II and (d) potential difference in configuration III.

Fig. 4(c) and (d), show the plots for MoSSe/WS₂ configuration II and III, respectively. We observe that in configuration II (Fig. 4(c)) there is an additional potential gradient between the Se atomic layer of MoSSe and the S atomic layer of the WS₂ at the interface, along with the cationic potential difference. In the case of configuration III, the interface has no anionic gradient (due to the presence of S in both of the layers facing each other) and hence, charge separation is mainly the result of the cationic gradient. Therefore, we see different band gaps in configuration III and configuration II. Further, one should always remember, that these configurations are type II and the band edge levels are on two different layers. Therefore, any potential gradient at the interface will definitely effect the corresponding band edge levels. Fig. S1–S6 in ESI† discuss the electrostatic potentials for other vdW HTSs. Fig. S4† explains the change in the band gap on the basis of the dipole direction. The dipole direction is seen from S to Se i.e. from the lower to the higher potential. So, we observe opposite dipole directions in configurations II and III, thereby affecting the interfacial interactions. Thus, the vdW HTSs with TMOs are also in line with the above discussion and inference.

We have also calculated the associated charge densities on the layers and the work functions of the vdW HTSs. The work function (ϕ) is a significant parameter to understand the charge separation or transfer at the interface. It is defined as follows:

ϕ = E_Vac − E_Fermi, (2)

where E_Vac and E_Fermi are the electrostatic potentials corresponding to the vacuum level and Fermi level, respectively (see Fig. 4). Table 2 gives the total Hirshfeld charges (of all of the atoms in the monolayers of the HTSs) and the work functions of vdW HTSs. The estimated values of the work functions of the free standing monolayers (ϕ_M as in Table 3), corroborate with the existing literature.⁷³‡ The Hirshfeld charge in the case of configuration II shows greater charge transfer than those of configuration I and III. This is attributed to the anionic and cationic potential difference at the interface. The smaller charge transfer corresponds to the lower work function in configurations I and III. The plane averaged charge density difference Δρ has been calculated (see Section V in the ESI†) by:

Δρ = ρ(vdW HTSs) − ρ(MoS₂ or MoSSe) − ρ(BX₂) (3)

where ρ(vdW HTSs), ρ(MoS₂), ρ(MoSSe) and ρ(BX₂) are the charge densities of the vdW HTS, monolayer MoS₂, monolayer MoSSe and monolayer BX₂, respectively.

Table 2 The Hirshfeld charges and work functions of the different configurations (I: MoS₂/BX₂, II: MoSSe/BX₂ (Se interfacial layer), III: MoSSe/BX₂ (S interfacial layer))

BX2	Hirshfeld charge (e)			Work function (ϕ) (eV)
	I	II	III	I	II	III
WS2	0.64	0.19	3.00	5.19	5.34	4.76
ZrS2	−0.26	−0.25	−0.16	5.98	6.02	5.56
HfS2	−0.08	−0.14	−0.07	5.98	6.01	5.58
TiS2	−0.09	−0.25	−0.12	6.02	6.15	5.69
HfO2	−0.04	−0.12	−0.09	6.12	6.13	5.70
T-PtO2	0.03	−0.08	−0.04	5.78	5.75	5.53
T-SnO2	−0.10	−0.16	−0.06	5.91	5.79	5.46

---

We can understand the charge transfer by calculating the band bending (ΔE_BB) as well. This parameter is estimated by the Fermi-level difference between the vdW HTSs and the corresponding free-standing monolayer, with the expression as follows:⁷⁶

ΔE_BB = ϕ − ϕ_M (4)

where ϕ is the work function of the vdW HTS and ϕ_M is the work function of the free standing monolayer. A ΔE_BB < 0 indicates charge transfer from the vdW HTSs to the monolayer. All of the vdW HTSs display ΔE_BB < 0 i.e. charge is gained by the monolayer (Table 3). The observation is in agreement with the calculated Hirshfeld charges as noted in Table 2. It is to be noted that in the case of WS₂, ΔE_BB is more negative, with ϕ_M(MoS₂) = 5.82 eV compared to ϕ_M(WS₂). Hence, the associated Hirshfeld charge on the WS₂ monolayer is positive. The above observations indicate that the MoSSe based configurations (II and III) can play a crucial role in photocatalytic applications.

Table 3 The estimated band bending between vdW HTSs and the free-standing monolayer (ϕ_M is the work function of the free standing monolayer, I: MoS₂/BX₂, II: MoSSe/BX₂ (Se interfacial layer), III: MoSSe/BX₂ (S interfacial layer))

BX2	ϕ M (eV)	ΔEBB (eV)
		I	II	III
WS2	5.53	−0.34	−0.19	−0.77
ZrS2	6.95	−0.97	−0.93	−1.39
HfS2	7.13	−1.15	−1.12	−1.55
TiS2	7.01	−0.99	−0.86	−1.32
HfO2	8.86	−2.74	−2.73	−3.16
T-PtO2	7.86	−2.08	−2.11	−2.33
T-SnO2	9.06	−3.15	−3.27	−3.60

---

The aforementioned discussions, along with Fig. 3(a), have showcased the spatial charge separation due to the work function difference. Therefore, with the e⁻–h⁺ pair generation in the individual monolayers of the vdW HTSs, the MoS₂ (or MoSSe) monolayer will be positively charged as it contributes to the VBM of the vdW HTS, which will restrict the flow of e⁻ to the other layer (BX₂). Moreover, the BX₂ monolayer that contributes to the CBM of the vdW HTS does not straddle the reduction potential. Hence, the MoS₂ (or MoSSe) monolayer will have restricted e⁻ motion from its CBM to the BX₂ CBM, thereby facilitating the e⁻–h⁺ recombination path of the BX₂ CBM to the MoS₂ VBM and promoting the standard Z-scheme mechanism.

3.3 Recombination in vdW HTSs

Considering the case of photocatalysts that straddle the potentials, less recombination is synchronous with effective photocatalytic capability. However, for their applicability as Z-scheme photocatalysts, higher recombination is required in the vdW HTSs compared to their constituent monolayers. Hence, the layer with a CBM above the reduction potential can facilitate HER, while the layer with a VBM below the oxidation potential can facilitate OER. In view of this, we have analyzed the recombination rate, which is indicated by the effective mass of the electrons and holes. The effective mass have been calculated by the parabolic fitting at the CBM and VBM in the band structures obtained by the hybrid calculations.⁷⁷ The band structures of MoS₂/ZrS₂ have been previously reported⁷⁸ and are in agreement with those reported in the present work. The same data for the other vdW HTSs discussed here are previously unreported.

The recombination in the system can be estimated by relative ratio (D) that is defined as follows:⁷⁹

The higher the variance of D from 1, the less the recombination. Since, D refers to the relative ratio of the effective mass of holes and electrons a value closer to 1 (i.e. a low variance) is ideal for high recombination in the system . This is obvious as a value closer to 1 indicates similar electron and hole effective mass, resulting in easier recombination. On the contrary, a large difference in the effective mass leads to significant differences in the carrier mobilities, leading to the separation of carriers and hindrance of their recombination. Consider Tables 4 and 5 that gives the value of D for the monolayers and their corresponding vdW HTSs, respectively. The effective mass of carriers at the CBM (i.e.) and VBM (i.e.) have been obtained along the designated direction in the high symmetry path Γ–M–K–Γ (see the band structures i.e. Fig. S7 in the ESI†). Also, it should be noted that the parameter is calculated from the band structures of the supercells rather than the primitive cells. Since the supercell is small, the density of the bands near the VBM and CBM is not very high and hence the band folding is not an issue here.

Table 4 The effective mass ratios (D) of the monolayers (BX₂) except for MoS₂ and MoSSe (both have same value of D = 1.21)

BX2	WS2	ZrS2	HfS2	TiS2	HfO2	T-PtO2	T-SnO2
D	1.29	1.58	1.17	0.03	5.88	4.66	9.00

---

Table 5 The effective mass ratios (D) of the vdW HTSs (I: MoS₂/BX₂, II: MoSSe/BX₂ (Se interfacial layer), III: MoSSe/BX₂ (S interfacial layer))

BX2	Effective mass ratio (D)
	I	II	III
WS2	2.50	0.85	10.19
ZrS2	0.13	0.64	0.62
HfS2	0.65	0.87	0.71
TiS2	0.50	0.20	0.80
HfO2	0.32	0.34	0.34
T-PtO2	0.49	0.50	0.49
T-SnO2	0.91	1.15	1.14

---

Furthermore, since we are considering Z-scheme photocatalysis, we require monolayers with less recombination compared to that of their corresponding vdW HTSs. In order to review this, we have checked the variance of the D values for the monolayers and the vdW HTSs. Therefore, the vdW HTSs with D values which have a smaller variance compared to those of their respective monolayers can be considered probable Z-scheme photocatalysts. As per the discussed approach, we have deduced MoSSe/ZrS₂ (configuration II and III), MoSSe/HfS₂ (configuration II), MoSSe/TiS₂ (configuration III), MoS₂/SnO₂ and MoSSe/SnO₂ (configuration II and III) as probable Z-scheme vdW HTSs. Amongst these, the D values for MoS₂/SnO₂, MoSSe/HfS₂ (configuration II) and MoSSe/TiS₂ (configuration III) show the smallest variance. Their respective carrier mobilities⁸⁰ are computed as 46 × 10² cm² V⁻¹ s⁻¹, 21 × 10² cm² V⁻¹ s⁻¹ and 2 × 10² cm² V⁻¹ s⁻¹. Additional details are provided in the ESI.† Note that, we have also estimated their exciton binding energies (E_B), and the vdW HTSs showed comparatively smaller E_B as compared to those of the MoS₂ and MoSSe monolayers (see Section VII in the ESI†). It should be mentioned here that the value of D is an indicative approach and should not be considered as the sole criterion for e⁻–h⁺ recombination. This yields future scope to explore the carrier dynamics more to understand the excitonic physics in these materials. We have, nevertheless, supported the inferences with the study of the optical responses, carrier mobilities, H₂O adsorption and HER.

3.4 Absorption spectra

Optical response is amongst the important parameters involved in constructing photocatalytic devices. Therefore, we have obtained the absorption spectra for the previously discussed vdW HTSs that can be considered for photocatalytic applications. Fig. 5 gives the absorption spectra obtained from the imaginary part of the dielectric function as computed by the GW method (G₀W₀@HSE06). The dielectric function is a frequency dependent complex function (ε(ω) = Re(ε) + Im(ε)) where the real part (Re(ε)) is computed from the Kramers–Kronig relation, and the imaginary part (Im(ε)) is obtained from the interband matrix elements in the momentum space.⁸¹ Since the interband process consists of transitions to the unoccupied orbitals, the Im(ε) gives the absorption spectra. The first peak will, therefore, indicate the onset of the absorption process. We observe that the vdW HTSs of MoS₂/TMD and MoS₂/TMO have responses in the visible region. The spectra corresponding to the MoSSe vdW HTSs (configuration II and III) have shown minute blue shifts compared to those of the MoS₂ vdW HTSs. Furthermore, we observe from Fig. 5 that the vdW HTSs with ZrS₂ (Fig. 5b) and TiS₂ (Fig. 5d) monolayers show red shifts compared to the other vdW HTSs (i.e., Fig. 5(a), (c), (d)–(f)). The spectra thus indicate the use of MoS₂/ZrS₂, MoSSe/ZrS₂, MoS₂/TiS₂ and MoSSe/TiS₂ for harnessing the overlap region of Im(ε) with the solar spectrum in order to construct photocatalytic devices.

Fig. 5 Imaginary part of the dielectric function vs. energy plot depicting the optical responses of the vdW HTS configurations I, II and III by G₀W₀@HSE06. Here, the arrows indicate the initial peak positions that are associated with the absorption onset.

3.5 H₂O adsorption

We have further calculated the H₂O adsorption in these vdW HTSs to confirm that the adsorption is supported for further redox reactions. The associated expression is given as:

E_ads = E(adsorbed H₂O) − E(vdW HTSs) − E(H₂O) (6)

where E_ads is the adsorption energy (see Table 6) of the H₂O on the vdW HTSs, E(adsorbed H₂O) is the energy of the vdW HTSs with adsorbed H₂O, E(vdW HTSs) is the energy of the vdW HTSs and E(H₂O) is the energy of the water molecule. From Table 6 we observe that H₂O is physisorbed in the system and its binding strength in all of the monolayers is higher than that of WS₂. Also, the transition metal oxides show higher binding strengths than the transition metal dichalcogenides. The data supplements the previous analysis which supports considering the monolayers for Z-scheme photocatalysis.

Table 6 H₂O adsorption on the monolayer surfaces

BX2	Adsorption energy (eV)	Distance (Å)
WS2	−0.09	2.88
ZrS2	−0.24	2.59
HfS2	−0.23	2.75
TiS2	−0.25	2.74
T-PtO2	−0.28	2.08
T-SnO2	−0.29	2.31

---

In addition, we have calculated the Gibbs free energy changes (ΔG) of the intermediate in the HER as per the expression:

ΔG = ΔE + ΔE_zpe − TΔS (7)

where ΔE is the intermediate adsorption energy on the vdW HTSs, ΔE_zpe is the change in zero-point energy and ΔS is the difference in entropy. The temperature, T, is taken as 300K. We have calculated the E_zpe and TS by the following expression using density functional perturbation theory (DFPT):where ℏ is Planck’s constant, ν_i is the vibrational frequency and k_B is the Boltzmann constant. The HER diagram along the reaction pathway H⁺ + e⁻ → H* → 1/2H₂ is illustrated in Fig. 6. Here, H* represents the adsorbed intermediate. Under the conditions of pH = 0 and a standard hydrogen electrode (SHE) potential of 0 V, H⁺ + e⁻ is equivalent to the 1/2H₂.

Fig. 6 The HER reaction free energy diagrams on the monolayers and vdW HTSs at an electrode potential E_SHE = 0 V and pH = 0. At zero potential, (H⁺ + e⁻) can be expressed as 1/2H₂.

Now, upon systematically revisiting all of the aforementioned factors, we have observed vdW HTSs to have type II band alignment with their work function being affected by the interfacial potential difference. This further influences the charge separation. Another point is that the smaller conduction band offset between the two monolayer systems would promote efficient charge separation at the interface.⁸² Therefore, in reference to Fig. 3, with the comparatively large differences in the two conduction band levels along with type II alignment, the possibility of interlayer recombination in vdW HTSs for the Z-scheme process seems very plausible. Effective mass is also an important factor for this, and we have indicated the recombination probability by the effective mass ratio (D). However, since this approach is qualitative, we have explicitly included the results of the optical responses, H₂O adsorption and HER as direct evidence to validate MoSSe/HfS₂, MoSSe/TiS₂, MoS₂/T-SnO₂, MoSSe/T-SnO₂ and MoSSe/ZrS₂ as probable Z-scheme photocatalysts.

4 Conclusion

An exhaustive study has been undertaken for understanding different MoS₂ and MoSSe based vdW HTSs. As per the band edge alignment, it is observed that these vdW HTSs do not facilitate the normal photocatalytic process as the band edges do not straddle the redox potential. However, they are predicted to show Z-scheme photocatalysis. The band edge alignments of the MoSSe vdW HTSs infer larger band gaps in configuration III than in configuration II. This has been attributed to the additional anionic potential gradient due to the Se atomic layer at the interface in configuration II. The probability of recombination, as suggested by the effective mass ratio (D), has corroborated MoSSe/HfS₂, MoSSe/TiS₂, MoS₂/T-SnO₂, MoSSe/T-SnO₂ and MoSSe/ZrS₂ as favourable Z-scheme photocatalysts. The absorption spectra further confirm the visible light response of these vdW HTSs and hence, their applicability in photocatalytic devices. Finally, the H₂O adsorption and HER indicate their interactions with water to help the photocatalytic process.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

AS thanks IIT Delhi for the financial support. AS and MJ thank Pooja Basera for the helpful discussions. MJ acknowledges CSIR, India, for the senior research fellowship [grant no. 09/086(1344)/2018-EMR-I]. SB acknowledges the financial support from SERB under the Core Research Grant [CRG/2019/000647]. We thank the High Performance Computing (HPC) facility at IIT Delhi for computational resources.

Notes and references

1. M. Ni, M. K. Leung, D. Y. Leung and K. Sumathy, Renewable Sustainable Energy Rev., 2007, 11, 401–425.
2. H. Yao, M. Fan, Y. Wang, G. Luo and W. Fei, J. Mater. Chem. A, 2015, 3, 17511–17524.
3. F. Opoku, K. K. Govender, C. G. C. E. van Sittert and P. P. Govender, New J. Chem., 2017, 41, 11701–11713.
4. C. Yu, F. Chen, D. Zeng, Y. Xie, W. Zhou, Z. Liu, L. Wei, K. Yang and D. Li, Nanoscale, 2019, 11, 7720–7733.
5. A. Gupta, T. Sakthivel and S. Seal, Prog. Mater. Sci., 2015, 73, 44–126.
6. A. Singh, P. Basera, S. Saini, M. Kumar and S. Bhattacharya, J. Phys. Chem. C, 2020, 124, 1390–1397.
7. Y. Chen, S. Huang, X. Ji, K. Adepalli, K. Yin, X. Ling, X. Wang, J. Xue, M. Dresselhaus and J. Kong, et al. , ACS Nano, 2018, 12, 2569–2579.
8. C. Rao, K. Gopalakrishnan and U. Maitra, ACS Appl. Mater. Interfaces, 2015, 7, 7809–7832.
9. E. Singh, P. Singh, K. S. Kim, G. Y. Yeom and H. S. Nalwa, ACS Appl. Mater. Interfaces, 2019, 11, 11061–11105.
10. H. Zeng, G.-B. Liu, J. Dai, Y. Yan, B. Zhu, R. He, L. Xie, S. Xu, X. Chen and W. Yao, et al. , Sci. Rep., 2013, 3, 1608.
11. C.-Y. Wang and G.-Y. Guo, J. Phys. Chem. C, 2015, 119, 13268–13276.
12. N. Glebko, I. Aleksandrova, G. C. Tewari, T. S. Tripathi, M. Karppinen and A. J. Karttunen, J. Phys. Chem. C, 2018, 122, 26835–26844.
13. K. W. Lau, C. Cocchi and C. Draxl, Phys. Rev. Mater., 2019, 3, 074001.
14. M. Mattinen, G. Popov, M. Vehkama ki, P. J. King, K. Mizohata, P. Jalkanen, J. Ra isa nen, M. Leskela and M. Ritala, Chem. Mater., 2019, 31, 5713–5724.
15. S. Lebègue, T. Björkman, M. Klintenberg, R. M. Nieminen and O. Eriksson, Phys. Rev. X, 2013, 3, 031002.
16. J. Yang, Z. Zeng, J. Kang, S. Betzler, C. Czarnik, X. Zhang, C. Ophus, C. Yu, K. Bustillo and M. Pan, et al. , Nat. Mater., 2019, 18, 970–976.
17. C. C. Leong, H. Pan and S. K. Ho, Phys. Chem. Chem. Phys., 2016, 18, 7527–7534.
18. P. Liao and E. A. Carter, Chem. Soc. Rev., 2013, 42, 2401–2422.
19. L. Ju, M. Bie, J. Shang, X. Tang and L. Kou, J. Phys.: Mater., 2020, 3, 022004.
20. Y. Sun, Z. Shuai and D. Wang, Nanoscale, 2018, 10, 21629–21633.
21. B. Song, L. Liu and C. Yam, J. Phys. Chem. Lett., 2019, 10, 5564–5570.
22. M. Sun and U. Schwingenschlogl, Chem. Mater., 2020, 32, 4795–4800.
23. X. Ma, X. Wu, H. Wang and Y. Wang, J. Mater. Chem. A, 2018, 6, 2295–2301.
24. Y. Luo, S. Wang, H. Shu, J.-P. Chou, K. Ren, J. Yu and M. Sun, Semicond. Sci. Technol., 2020, 35, 125008.
25. A. Kuc and T. Heine, Chem. Soc. Rev., 2015, 44, 2603–2614.
26. R. Kumar, I. Verzhbitskiy, F. Giustiniano, T. P. Sidiropoulos, R. F. Oulton and G. Eda, 2D Mater., 2018, 5, 041003.
27. Y. Huang, X. Chen, C. Wang, L. Peng, Q. Qian and S. Wang, Nanoscale, 2017, 9, 8616–8622.
28. H. Terrones, F. López-Urías and M. Terrones, Sci. Rep., 2013, 3, 1549.
29. Q. Zhang and U. Schwingenschlögl, Phys. Rev. B: Condens. Matter Mater. Phys., 2018, 97, 155415.
30. P. Rivera, K. L. Seyler, H. Yu, J. R. Schaibley, J. Yan, D. G. Mandrus, W. Yao and X. Xu, Science, 2016, 351, 688–691.
31. P. Li, W. Zhang, D. Li, C. Liang and X. C. Zeng, ACS Appl. Mater. Interfaces, 2018, 10, 19897–19905.
32. P. Li, W. Zhang, C. Liang and X. C. Zeng, Nanoscale, 2019, 11, 19806–19813.
33. Y. Luo, K. Ren, S. Wang, J.-P. Chou, J. Yu, Z. Sun and M. Sun, J. Phys. Chem. C, 2019, 123, 22742–22751.
34. Y. Luo, S. Wang, K. Ren, J.-P. Chou, J. Yu, Z. Sun and M. Sun, Phys. Chem. Chem. Phys., 2019, 21, 1791–1796.
35. K. Ren, S. Wang, Y. Luo, J.-P. Chou, J. Yu, W. Tang and M. Sun, J. Phys. D: Appl. Phys., 2020, 53, 185504.
36. S. Wang, C. Ren, H. Tian, J. Yu and M. Sun, Phys. Chem. Chem. Phys., 2018, 20, 13394–13399.
37. Y. Li, Y.-L. Li, C. M. Araujo, W. Luo and R. Ahuja, Catal. Sci. Technol., 2013, 3, 2214–2220.
38. E. Parzinger, B. Miller, B. Blaschke, J. A. Garrido, J. W. Ager, A. Holleitner and U. Wurstbauer, ACS Nano, 2015, 9, 11302–11309.
39. Z.-K. Tang, W.-J. Yin, L. Zhang, B. Wen, D.-Y. Zhang, L.-M. Liu and W.-M. Lau, Sci. Rep., 2016, 6, 32764.
40. X. Gao, Y. Shen, Y. Ma, S. Wu and Z. Zhou, Appl. Phys. Lett., 2019, 114, 093902.
41. R. Zhang, L. Zhang, Q. Zheng, P. Gao, J. Zhao and J. Yang, J. Phys. Chem. Lett., 2018, 9, 5419–5424.
42. K. Ren, C. Ren, Y. Luo, Y. Xu, J. Yu, W. Tang and M. Sun, Phys. Chem. Chem. Phys., 2019, 21, 9949–9956.
43. B.-J. Wang, X.-H. Li, R. Zhao, X.-L. Cai, W.-Y. Yu, W.-B. Li, Z.-S. Liu, L.-W. Zhang and S.-H. Ke, J. Mater. Chem. A, 2018, 6, 8923–8929.
44. C.-F. Fu, Q. Luo, X. Li and J. Yang, J. Mater. Chem. A, 2016, 4, 18892–18898.
45. Y. Liu, X. Zeng, C. D. Easton, Q. Li, Y. Xia, Y. Yin, X. Hu, J. Hu, D. Xia and D. T. McCarthy, et al. , Nanoscale, 2020, 12, 8775–8784.
46. X. Xia, M. Song, H. Wang, X. Zhang, N. Sui, Q. Zhang, V. L. Colvin and W. Y. William, Nanoscale, 2019, 11, 11071–11082.
47. K. Maeda, ACS Catal., 2013, 3, 1486–1503.
48. H. Li, W. Tu, Y. Zhou and Z. Zou, Adv. Sci., 2016, 3, 1500389.
49. A. J. Bard, J. Photochem., 1979, 10, 59–75.
50. J. Lang and Y. H. Hu, Phys. Chem. Chem. Phys., 2020, 22, 9250–9256.
51. L. Ju, Y. Dai, W. Wei, M. Li and B. Huang, Appl. Surf. Sci., 2018, 434, 365–374.
52. F. A. Rasmussen and K. S. Thygesen, J. Phys. Chem. C, 2015, 119, 13169–13183.
53. R. M. Martin, Electronic structure: basic theory and practical methods, Cambridge university press, 2004.
54. R. M. Martin, L. Reining and D. M. Ceperley, Interacting Electrons, Cambridge University Press, 2016.
55. C. Freysoldt, B. Grabowski, T. Hickel, J. Neugebauer, G. Kresse, A. Janotti and C. G. Van de Walle, Rev. Mod. Phys., 2014, 86, 253.
56. L.-p. Feng, J. Su, S. Chen and Z.-t. Liu, Mater. Chem. Phys., 2014, 148, 5–9.
57. P. Hohenberg and W. Kohn, Phys. Rev., 1964, 136, B864.
58. W. Kohn and L. J. Sham, Phys. Rev., 1965, 140, A1133.
59. G. Kresse and J. Furthmüller, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 54, 11169.
60. P. E. Blöchl, Phys. Rev. B: Condens. Matter Mater. Phys., 1994, 50, 17953.
61. V. Blum, R. Gehrke, F. Hanke, P. Havu, V. Havu, X. Ren, K. Reuter and M. Scheffler, Comput. Phys. Commun., 2009, 180, 2175–2196.
62. C. Stampfl and C. Van de Walle, Phys. Rev. B: Condens. Matter Mater. Phys., 1999, 59, 5521.
63. J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865.
64. J. Heyd, G. E. Scuseria and M. Ernzerhof, J. Chem. Phys., 2003, 118, 8207–8215.
65. A. Tkatchenko and M. Scheffler, Phys. Rev. Lett., 2009, 102, 073005.
66. A. Tkatchenko, R. A. DiStasio Jr, R. Car and M. Scheffler, Phys. Rev. Lett., 2012, 108, 236402.
67. J. Weng and S.-P. Gao, Phys. Chem. Chem. Phys., 2018, 20, 26453–26462.
68. K. Ren, W. Tang, M. Sun, Y. Cai, Y. Cheng and G. Zhang, Nanoscale, 2020, 12, 17281–17289.
69. G. Onida, L. Reining and A. Rubio, Rev. Mod. Phys., 2002, 74, 601.
70. H. Jiang, P. Rinke and M. Scheffler, Phys. Rev. B: Condens. Matter Mater. Phys., 2012, 86, 125115.
71. A. U. Rahman, J. M. Morbec, G. Rahman and P. Kratzer, Phys. Rev. Mater., 2018, 2, 094002.
72. C. M. Bastos, R. Besse, J. L. Da Silva and G. M. Sipahi, Phys. Rev. Mater., 2019, 3, 044002.
73. S. Haastrup, M. Strange, M. Pandey, T. Deilmann, P. S. Schmidt, N. F. Hinsche, M. N. Gjerding, D. Torelli, P. M. Larsen and A. C. Riis-Jensen, et al. , 2D Mater., 2018, 5, 042002.
74. C. Xia, W. Xiong, W. Xiao, J. Du, L. Fang, J. Li and Y. Jia, Phys. Rev. Appl., 2018, 10, 024028.
75. X. Hu, L. Kou and L. Sun, Sci. Rep., 2016, 6, 31122.
76. J. Padilha, A. Fazzio and A. J. da Silva, Phys. Rev. Lett., 2015, 114, 066803.
77. A. Ganose, A. Jackson and D. Scanlon, J. Open Source Softw., 2018, 3, 717.
78. A. K. A. Lu, M. Houssa, M. Luisier and G. Pourtois, Phys. Rev. Appl., 2017, 8, 034017.
79. H. Zhang, L. Liu and Z. Zhou, RSC Adv., 2012, 2, 9224–9229.
80. J. Dai and X. C. Zeng, Angew. Chem., 2015, 127, 7682–7686.
81. P. Basera, S. Saini and S. Bhattacharya, J. Mater. Chem. C, 2019, 7, 14284–14293.
82. S. Khanchandani, P. K. Srivastava, S. Kumar, S. Ghosh and A. K. Ganguli, Inorg. Chem., 2014, 53, 8902–8912.

---

Footnotes

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d1na00154j

‡ Note that the mentioned reference has considered a 15 Å vacuum, whereas we have used a 20 Å vacuum. The slight differences (i.e. the not exact matches) may be due to this change.

---