Intriguing electronic, optical and photocatalytic performance of BSe, M₂CO₂ monolayers and BSe–M₂CO₂ (M = Ti, Zr, Hf) van der Waals heterostructures

Abstract

Using density functional (DFT) theory calculations, we have investigated the electronic band structure, optical and photocatalytic response of BSe, M₂CO₂ (M = Ti, Zr, Hf) monolayers and their corresponding BSe–M₂CO₂ (M = Ti, Zr, Hf) van der Waals (vdW) heterostructures. Optimized lattice constant, bond length, band structure and bandgap values, effective mass of electrons and holes, work function and conduction and valence band edge potentials of BSe and M₂CO₂ (M = Ti, Zr, Hf) monolayers are in agreement with previously available data. Binding energies, interlayer distance and Ab initio molecular dynamic simulations (AIMD) calculations show that BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures are stable with specific stacking and demonstrate that these heterostructures might be synthesized in the laboratory. The electronic band structure shows that all the studied vdW heterostructures have indirect bandgap nature – with the CBM and VBM at the Γ–K and Γ-point of BZ for BSe–Ti₂CO₂, respectively; while for BSe–Zr₂CO₂ and BSe–Hf₂CO₂ vdW heterostructures the CBM and VBM lie at the K-point and Γ-point of BZ, respectively. Type-II band alignment in BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures prevent the recombination of electron–hole pairs, and hence are crucial for light harvesting and detection. Absorption spectra are investigated to understand the optical behavior of BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures, where the lowest energy transitions are dominated by excitons. Furthermore, BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures are found to be potential photocatalysts for water splitting at pH = 0, and exhibit enhanced optical properties in the visible light zones.

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1. Introduction

After the successful synthesis of graphene,^1–4 great attention has been paid to other 2D materials, such as hexagonal boron nitrides (h-BN),⁵ blue and black phosphorene,⁶ transition metal dichalcogenides (TMDCs),⁷ silicene,⁸ germanene,⁹ MXenes,¹⁰ and Janus transition metal dichalcogenides (JTMDCs).¹¹ Among these materials, MXenes (M_n+1X_n), synthesized by eliminating the A-layer from their bulk counterpart the MAX phase (M_n+1AX_n, M refers to early transition metals, “A” represents the group of sp elements, “X” represents C or N atoms, and n is 1, 2, 3), has received wide research attention¹² due to a wide range of applications in Li-ion batteries,¹³ catalysis,¹⁴ electrochemical capacitors¹⁵ and also in fuel cells.¹⁶ The M–X bond in the MAX crystals is stronger than the M–A bond, making it possible to etch “A” atoms between the M_n+1X_n layer.¹⁷ All the MXenes are metals, while appropriate surface termination (M_n+1X_nT_x, T_x denotes surface terminations, i.e. O, F, OH) makes them semiconductors.¹⁸

Tuning the properties of 2D materials has led to a new field that assembles 2D materials (isolated) into hybrid heterostructures in a precisely controlled sequence of layer by layer stacking, called vdW heterostructures.¹⁹ It provides a versatile platform for exploring new phenomena and designing novel nanoelectronic devices.^20,21 To date, a great deal of vdW heterostructures have been studied theoretically^22–27 and perceived experimentally.^28–31 These vdW heterostructures are also utilized to create electronic and optoelectronic devices with novel physical properties and applications.^32–37

MXenes-based vdW heterostructures, such as MXenes–MXenes,³⁸ MXene and nitrogen-doped graphene,³⁹ MXenes–TMDCs,⁴⁰ MXene–blue phosphorene,⁴¹ MXenes and B-doped graphene,⁴² have already been fabricated and investigated in detail. BSe, another 2D material, has been proposed and predicted to be thermally stable with indirect bandgap nature.^43,44

Motivated by the fascinating optoelectronic and photocatalytic performance of MXenes with other monolayers in the form of vdW heterostructures, we have fabricated BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures. Indeed small lattice mismatch and the same hexagonal symmetry of the BSe and M₂CO₂ (M = Ti, Zr, Hf) monolayer allow the creation of BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures. It is also surprising that there is no previous work on the BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures. We have investigated the structural and electronic properties, band alignments, average and planar electrostatic potentials, Bader charge analysis, optical and photocatalytic response of BSe, M₂CO₂ (M = Ti, Zr and Hf) monolayers and their vdW heterostructure. Our results show that BSe–M₂CO₂ (M = Ti, Zr) vdW heterostructures are a promising novel material for visible light photocatalysis, electronic and optoelectronic devices.

2. Computational details

We used DFT⁴⁵ with empirical dispersion correction of Grimme⁴⁶ and Perdew–Burke–Ernzerhof (PBE)⁴⁷ functional in Vienna ab initio simulation package (VASP).^48,49 In the first Brillouin zone, a Γ-point centered 6 × 6 × 1 Monkhorst–Pack k-point grid and 500 eV cutoff energy were used. A vacuum layer thickness of 25 Å is established to avoid the interaction of the adjacent layers of atoms. The geometric relaxations are carried out until we achieve the convergence criterion of 10⁻⁴ eV Å⁻¹ (10⁻⁵ eV) for forces (energy). Commonly, the PBE functional underestimates the band gap values of semiconductors, therefore, we have also performed a computationally expensive HSE06 (Heyd–Scuseria–Ernzerhof)⁵⁰ functional for the precise calculation of the electronic structure and band gap values.

Ab initio molecular dynamic simulations (AIMD)⁵¹ are used to investigate the thermal stabilities of BSe–M₂CO₂ (M = Ti, Zr) vdW heterostructures. AIMD simulations are performed through the Nose thermostat algorithm at a temperature of 300 K for a total of 6 ps with a time interval of 1 fs.

Furthermore, we have solved the Bethe–Salpeter equation (BSE) in GW calculations using the Quantum-Espresso program package,⁵² to explore the optical spectra estimated by the imaginary part of the dielectric function (ε₂(ω)) of the BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures.^53–55

3. Results and discussion

Optimized lattice constant, bond length, bandgap values, effective mass of electrons and holes, work function and conduction and valence band edge potentials (E_CB and E_VB) of BSe and M₂CO₂ (M = Ti, Zr, Hf) monolayers in Table 1, are in agreement with ref. 56–58. Optimized geometry (top view) and electronic band structure (using PBE and HSE06 functional) are presented in Fig. 1, and show that both BSe and M₂CO₂ (M = Ti, Zr, Hf) monolayers are indirect bandgap semiconductors with CBM(VBM) at the M(Γ)-point of BZ. The calculated effective mass for both holes and electrons in Table 1, show that BSe and Hf₂CO₂ monolayers would have high carrier mobility.⁵⁹ Difference in the work functions in Table 1, show that in the case of the interface of these materials, electrons will spontaneously flow from M₂CO₂ to the BSe monolayer, which is further explained in detail later in the vdW heterostructure of BSe and M₂CO₂ (M = Ti, Zr, Hf) monolayers.⁶⁰ Furthermore, the imaginary part of the dielectric function in Fig. 1, shows that the first excitonic peak at 3.851 for BSe, 0.286 for Ti₂CO₂, 1.79 for Zr₂CO₂, and 2.416 eV for the Hf₂CO₂ monolayer, lies in the visible range of the spectrum, consistent with ref. 61–63. In the case of the photocatalytic response at pH = 0, BSe and Hf₂CO₂ cross both the conduction and valence band edge potentials, while Ti₂CO₂ and Zr₂CO₂ cross the valence band edge potential only and fail to cross the conduction band edge, in agreement with ref. 56, 59 and 64, hence showing the potential of these systems in electronic, optoelectronic and photocatalytic applications. The above discussed consistencies for BSe and M₂CO₂ (M = Ti, Zr, Hf) monolayers, show the authenticity of the present approach for the calculation of BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures.

Table 1 Lattice constant (a in Å), bond length (B–Se, M–O and M–C in Å), band gap (E_g in eV), effective mass ( and ), work function (ϕ in eV) and conduction and valence band edge potentials (E_CB and E_VB in eV) for BSe monolayer and M₂CO₂ (M = Ti, Zr, Hf) MXenes

Monolayers	BSe	Ti2CO2	Zr2CO2	Hf2CO2
a	3.26	3.01	3.31	3.27
B–Se	2.10	—	—	—
M–O	—	1.970	2.119	2.091
M–C	—	2.210	2.359	2.332
Eg-PBE	2.635	0.300	0.865	0.99
Eg-HSE06	3.56	0.920	1.590	1.70
d1ra07569a-t3	0.42	0.87	0.69	0.61
d1ra07569a-t3	0.93	1.32	1.05	1.27
Φ	3.953	5.536	4.835	4.450
ECB	−1.255	0.354	0.069	−0.005
EVB	2.304	1.248	1.659	1.695

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Fig. 1 Geometrical structure (top view), electronic band structure (PBE(blue), HSE06(red)), and imaginary part of dielectric function (ε₂(ω)), of BSe ((a), (e), (i) and (m)), Ti₂CO₂ ((b), (f), (j) and (n)), Zr₂CO₂ ((c), (g), (k) and (o)), and Hf₂CO₂ ((d), (h), (l) and (p)), and their photocatalytic response.

Lattice mismatch of BSe, with Ti₂CO₂ of 4.9%, with Zr₂CO₂ of 1.2% and with Hf₂CO₂ of 0.03%, are experimentally achievable⁶⁵ and the same hexagonal symmetry realizes the fabrication of BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures. The electronic band structure is very sensitive to layer stacking,⁶⁶ therefore we have chosen five possible stacking configurations of BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures, see Fig. 2. In stacking (a) the M(O) atom of M₂CO₂ is placed on top of the Se(B) atom of the BSe monolayer; in stacking (b) the M(C) atom of M₂CO₂ is placed on top of the B(Se) atom of the BSe monolayer; in stacking (c) the O(C) atom of M₂CO₂ is placed on top of the Se(B) atom of the BSe monolayer; in stacking (d) the O(M) atom of M₂CO₂ is placed on top of the Se(B) atom of the BSe monolayer; and in stacking (e) the O(M) atom of M₂CO₂ is placed on top of the (B) atom of the BSe monolayer, while the C is on a hexagonal site.

Fig. 2 Possible stacking configurations of the BSe–M₂CO₂ (M = Ti, Zr, Hf) van der Waal heterostructures.

Binding energy; E_b = E_BSe–M2CO2 − E_M2CO2 − E_BSe, where E_BSe–M2CO2 is the total energy of the BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructure, E_M2CO2 is the total energy of the isolated M₂CO₂ (M = Ti, Zr, Hf) MXene, and E_BSe is the total energy of the isolated BSe monolayer along with interlayer distance of the stacking as presented in Table 2. Smaller interlayer distance and binding energies represent the most stable stacking configuration, therefore, stacking (a) of the BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures is the most stable configuration. Obviously, negative binding energies show that the formation of all heterostructures are exothermic, see Table 2. These values are in the range of binding energies for other vdW heterostructures,^67,68 hence suggest the possible experimental fabrication of BSe–M₂CO₂ vdW heterostructures. The calculated interlayer distance (see Table 2) also confirms weak vdW interactions in the stacked layers of these heterostructures. Optimized lattice constants of the most stable stacking configurations are presented in Table 3.

Table 2 Binding energies (E_b in eV) and inter layer distance (d in Å) of the BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures in different stacking configurations

Stacking	BSe–Ti2CO2	BSe–Zr2CO2	BSe–Hf2CO2
Eb (a)	−0.429	−0.395	−0.297
d	3.33	3.32	3.33
Eb (b)	−0.326	−0.316	−0.268
d	3.42	3.41	3.39
Eb (c)	−0.331	−0.337	−0.284
d	3.39	3.38	3.35
Eb (d)	−0.409	−0.305	−0.277
d	3.37	3.41	3.39
Eb (e)	−0.398	−0.327	−0.281
d	3.46	3.39	3.36

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Table 3 Lattice constant (in Å), bandgap values (E_g in eV), effective mass ( and ), work function (ϕ in eV), potential difference (ΔV) conduction and valence band edges (E_VB and E_CB in eV) of BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures

Heterostructure	BSe–Ti2CO2	BSe–Zr2CO2	BSe–Hf2CO2
a	3.15	3.29	3.27
Eg-PBE	0.107	0.837	0.970
Eg-HSE06	0.61	1.536	1.79
ΔV	4.280	2.300	2.050
ϕ	6.537	5.764	5.808
	0.39	0.73	0.51
	0.76	1.08	0.97
EVB	0.477	−0.0046	−0.0617
ECB	1.0876	1.575	1.657

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To further verify the thermal stability of the stacking of (a) BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures, we have used the AIMD simulation. We have chosen a 3 × 3 supercell with top view, see Fig. 3. It is clear from the figure that after heating for 5 ps at 1 fs time steps at 300 K, the BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures show no broken bonds (remain stable), while the free energy oscillates slightly (see Fig. 3, middle row), which confirms the thermal stability of these systems at 300 K. Therefore, the stacking of the (a) BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures is the most stable structure configuration and will be further examined in detail.

Fig. 3 Geometrical structure before heating (first row), with fluctuating energy (second row) and after heating (third row) of: (a) BSe–Ti₂CO₂, (b) BSe–Zr₂CO₂, and (c) BSe–Hf₂CO₂ vdW heterostructures using AIMD simulation.

Using both PBE and HSE06 functionals, we have calculated the electronic band structures of BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures, see Fig. 4, while the calculated bandgap values are presented in Table 3. The electronic band structure shows that all the studied vdW heterostructures have an indirect band nature with the CBM and VBM at the Γ–K and Γ-point of BZ for BSe–Ti₂CO₂, (see Fig. 4(a)), while both BSe–Zr₂CO₂ and BSe–Hf₂CO₂ vdW heterostructures are indirect bandgap semiconductors with CBM at the K-point and VBM at the Γ-point of the first BZ (see Fig. 4(b) and (c)). In the case of the BSe–Ti₂CO₂ vdW heterostructure direct recombination of photogenerated electrons and holes hence play a crucial rule in optoelectronic devices.⁶⁹ In the case of the BSe–Zr₂CO₂ and BSe–Hf₂CO₂ vdW heterostructures, the recombination of photogenerated electrons and holes is slow because firstly the CBM and VBM momenta align themselves and then recombination occurs, which is useful for laser applications.^70–72 The variation in bandgap values (given in Table 3) and the band structures of BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures from their parent monolayers, reveals the bandgap engineering making the vdW heterostructures.⁷³ The contribution of the different atomic states to the Fermi level is further explored by investigating the partial density of states (PDOS), see Fig. 4 (b), (d) and (f). One can see that the CBM is mainly due to the d state of Ti/Zr/Hf atoms of the M₂CO₂ layer, while the VBM is due to the p state of the Se atom of BSe layer.

Fig. 4 PBE (blue) and HSE06 (yellow) band structures (left column) and partial density of states (right column) of the BSe–Ti₂CO₂ ((a) and (b)), BSe–Zr₂CO₂ ((c) and (d)), BSe–Hf₂CO₂ ((e) and (f)) vdW heterostructures.

To verify the contribution of different atomic states in the VBM and CBM, and nature of the band structure for type-I and type-II, we have calculated the weighted band structure of BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures, plotted in Fig. 5. One can clearly see that in the case of BSe–Ti₂CO₂ vdW heterostructures (Fig. 5(a)) at the Γ-point of BZ, the main contribution in the CBM is due to the Ti-d_xy atom of Ti₂CO₂ monolayers while the VBM is due to the Se-p_xy state of BSe monolayers, hence confirming type-II band alignment.^74,75 In the case of the BSe–Zr₂CO₂ and BSe–Hf₂CO₂ vdW heterostructures (see Fig. 5(b) and (c), respectively) the main contribution in the CBM(VBM) is due to the Zr/Hf-d_xy (Se-p_xy) states of the Zr₂CO₂, Hf₂CO₂ (BSe) monolayers at the K(Γ)-point of BZ, which also shows type-II band alignment. The localization of the VBM and CBM from different layers are obtained without any external electric field, as the intrinsic electric field induces bond bending in making the vdW heterostructures.^76,77 This induced field drive photogenerated electrons and holes in different directions. Type-II band alignment is an effective tool to enhance electron–holes pairs which reduce the recombination time, applicable for light harvesting and detection.^74,75 The spontaneous apprehension about the charge transfer is obtained from the deportation charge density (DCD) isosurface, presented in Fig. 5(d–f) for BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures. In Fig. 5(d–f) the cyan(yellow) color shows the charge electrons depletion(accumulation), hence confirming that charge is transferred from M₂CO₂ (M = Ti, Zr, Hf) to BSe monolayers at the interface of the BSe–M₂CO₂ vdW heterostructures, which leads to p-doping in Ti₂CO₂, Zr₂CO₂ and Hf₂CO_2, and n-doping in the BSe monolayer. For further verification and quantification of charge transfer we have investigated the Bader charge analysis, which shows that the charge of about 0.17, 0.09 and 0.11 e/unitcell is transferred from the Ti₂CO₂, Zr₂CO₂ and Hf₂CO₂ to the BSe monolayer, respectively.⁷⁸ This transfer of charge confirms that due to long range vdW forces, the interlayer bonding of Ti₂CO₂, Zr₂CO₂, Hf₂CO₂ and BSe monolayers can be weak and diminishes with increasing bond length.

Fig. 5 Weighted band structure (left column) and 3D isosurface 0.001 eV Å ⁻³ of the charge density difference (right column) of BSe–Ti₂CO₂ ((a) and (d)), BSe–Zr₂CO₂ ((b) and (e)) and BSe–Hf₂CO₂ ((c) and (f)) vdW heterostructures. The cyan(yellow) color shows the charge electrons depletion(accumulation).

Furthermore, we have verified the transfer of charge and potential difference by calculating the average and planar electrostatic potential difference along the z-axis, see Fig. 6. One can easily see that the BSe monolayer has a deeper potential then Ti₂CO₂, Zr₂CO₂ and Hf₂CO₂ monolayers in BSe–M₂CO₂ vdW heterostructures (see Fig. 6), confirming the transfer of charge from Ti₂CO₂, Zr₂CO₂ and Hf₂CO₂ to the BSe layer. Also, the potential drop (DV) across the vdW heterostructures, given in Table 3, facilitates the separation of electrons and holes at the interface. Making vdW heterostructures may effect the work function, which leads to enhanced electronic properties of the vdW heterostructures. Therefore, we have calculated the work function of monolayers and their vdW heterostructures, as presented in Table 1 and 3. One can easily see that the work function of vdW heterostructures is almost the average of the corresponding monolayers, efficient for charge transfer.

Fig. 6 Average and planar electrostatic potential of (a and b) BAse–Ti₂CO₂, (c and d) BSe–Zr₂CO₂ and (e and f) BSe–Hf₂CO₂. The work function (ϕ) and potential drop (ΔV) are highlighted.

Furthermore, we have calculated the effective mass of electrons and holes in the BSe–M₂CO₂ vdW heterostructures. Smaller effective mass leads to higher carrier mobility which is useful for high performance nanoelectronic devices.⁷⁹ We used parabolic fitting for the VBM and CBM and investigated the effective mass of electrons and holes of the BSe–M₂CO₂ vdW heterostructures. The value for effective mass of the holes and electrons are given in Table 3. One can see that the effective mass of vdW heterostructures (for holes and electrons) is smaller than that of the corresponding monolayers in Table 1, hence are suitable for application in high-performance nanoelectronic devices.

We have also calculated the optical performance in terms of imaginary parts of the dielectric function (ε₂(ω)) of BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures as a function of photon energy, given in Fig. 7. One can see that optical transitions are dominated by excitons at 2.59 eV for Ti₂CO₂, at 2.27 eV for Zr₂CO₂ and at 2.43 eV for Hf₂CO₂. The calculated exciton binding energies are 0.77, 0.048 and 0.143, respectively (see Fig. 7). All these BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures show substantial absorption in visible and UV regions of the spectrum. This can be attributed to the fact that the charge transfer and interlayer coupling, which can result in the overlap of electronic states in the valence bands of the heterostructure, and which enhances the optical absorption (see Fig. 1 and 7).^80–82

Fig. 7 Optical absorption of (a) BSe–Ti₂CO₂, (b) BSe–Zr₂CO₂ and (c) BSe–Hf₂CO₂.

We have also investigated the photocatalytic^83–86 properties of BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures using the Mulliken electronegativity.^87,88 Appropriate bandgap size, valence and conduction band edges must straddle the redox potentials of water, as reported in our previous work⁸⁹ for use in the water splitting reaction. The standard water redox potentials are −4.50 eV for the reduction (H⁺/H₂) and −5.73 eV for the oxidation (H₂O/O₂).⁹⁰ The calculated band edge potentials E_VBM and E_CBM of the heterostructures by the HSE06 functional are summarized in Table 3 and presented in Fig. 8. Valence band edge potential and conduction band edge potential, (E_VBM and E_CBM) for BSe–Hf₂CO₂ and BSe–Zr₂CO₂ vdW heterostructures are higher than that of H⁺/H₂ and H₂O/O₂. These results signify that, BSe–Hf₂CO₂ and BSe–Zr₂CO₂ vdW heterostructures can oxidize H₂O/O₂ and reduce H⁺/H₂,⁹⁰ which is suitable for the production of clean and renewable energy equipment applications.⁹¹ Although, the Zr₂CO₂ monolayer fails to oxidize water (see Fig. 1 and Table 1), the BSe–Zr₂CO₂ vdW heterostructure shows a good response to water redox potential, hence making the vdW heterostructure suitable for the production of clean and renewable energy device applications.⁹¹ Similar to the corresponding monolayer, in the case of BSe–Ti₂CO₂, the E_VB(E_CB) cross(fail to cross) the reduction level. All these findings demonstrate that the BSe–M₂CO₂ heterostructures can be considered as potential photocatalysts for water splitting and provide theoretical guidance for designing high-performance nano-electronic and optoelectronic devices based on the BSe–M₂CO₂ heterostructures.^92–94

Fig. 8 Band alignment for the valence band (VB) and conduction band (CB) edge of BSe–Ti₂CO₂, BSe–Zr₂CO₂ and BSe–Hf₂CO₂, at pH = 0. The standard oxidation (−5.67 eV, O₂/H₂O) and reduction (−4.44 eV, H⁺/H²) potentials are also labeled.

4. Conclusion

In summery, using first principles DFT calculations, we have investigated the electronic band structure, optical and photocatalytic response of BSe, M₂CO₂ (M = Ti, Zr, Hf) monolayers and their corresponding BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures. The calculated lattice parameters, electronic band structure, bandgap values and valence and conduction band edge potentials of BSe and M₂CO₂ (M = Ti, Zr, Hf) monolayers are in good agreement with previous available data, showing the authenticity of the present approach for the calculations of BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures. Based on the binding energy and interlayer distance calculations, stacking (a) of the five different stacking of BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures is the most stable stacking configuration. Furthermore, AIMD simulations also show that stacking (a) for all studied systems, is thermally stable at 300 K. Surprisingly, in contrast to the parent monolayers, BSe–Ti₂CO₂ (BSe–Zr₂CO₂ and BSe–Hf₂CO₂) vdW heterostructures are direct (indirect) band gap semiconductor(s). All studied vdW heterostructures have type-II band alignment, hence play a major role in light harvesting and detection. Bader charge analysis shows transfer of charge from M₂CO₂ (M = Ti, Zr, Hf) to the BSe layer, hence N(P)-type doping is achieved in the M₂CO₂(BSe) monolayer at the interface of BSe–M₂CO₂ vdW heterostructures. The imaginary part of the dielectric function is also investigated to understand the optical absorption of BSe–M₂CO₂ (M = Ti, Zr, Hf) vdW heterostructures, where the lowest energy transitions are dominated by excitons. The calculated photocatalytic response signifying that BSe–Zr₂CO₂ and BSe–Hf₂CO₂ vdW heterostructures can oxidized H₂O/O₂ and reduce H⁺/H₂, while the Zr₂CO₂ monolayer fails to oxidize water, hence making BSe–M₂CO₂ vdW heterostructures viable for the production of clean and renewable energy device applications. Similar to the corresponding monolayer, in the case of BSe–Ti₂CO₂, the E_VBM(E_CBM) cross(fail to cross) the reduction level.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Authors thank the Center for Computational Materials Science, the University of Malakand Chakdara, Pakistan, for their computing support.

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