First-principles study on enhancing the photocatalytic hydrogen evolution performance in Cs₃Bi₂I₉/MoS₂ heterostructure with interfacial defect engineering

Abstract

Hydrogen has been attracting continuously growing interest as a highly efficient and clean energy source for replacing fossil fuels in the future, and thus developing highly efficient photocatalytic materials for hydrogen evolution is much desirable. In this work, we study the structural, electronic and optical properties of heterostructures composed of the bismuth-based vacancy-ordered iodide double perovskite Cs₃Bi₂I₉ and a two-dimensional dichalcogenide 2H-MoS₂ monolayer without and with a vacancy defect using first-principles calculations. Our calculations demonstrate that the Cs₃Bi₂I₉/MoS₂ heterostructures are energetically stable and induce an interfacial dipole moment, which is beneficial for the prevention of charge carrier recombination. Due to the proper band-edge alignment and the smallest Gibbs free energy difference for hydrogen adsorption, the defective interface with a Cs-vacancy (V_Cs) is found to be the most promising for photocatalytic hydrogen evolution. Moreover, we find that the interfacial V_Cs defect can be formed favourably under the I-rich/Cs-poor condition, where V_I and V_S formations are suppressed. This work provides a way to develop high-performance photocatalysts based on heterostructures composed of the Bi-based halide perovskites and transition metal dichalcogenides for hydrogen evolution from solar-driven water splitting.

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1 Introduction

Superseding natural resources with clean sustainable energy sources has become an extremely urgent issue to meet the increasing demand for energy and achieve net-zero carbon emissions in light of the rapid exhaustion of fossil fuels and acute environmental problems. In this context, hydrogen has been attracting continuously growing interest as a highly efficient and clean energy source for the future.¹ Among various methods for producing hydrogen, solar-driven photocatalytic hydrogen evolution is the most attractive approach in terms of energy balance and clean production due to solar energy utilization.^2–4 Photocatalysts for hydrogen evolution reactions (HERs) reported so far include carbon nitrides,^5–7 metal oxides,^8,9 metal sulfides,^10–12 organic materials,^13,14 and heterojunctions.^15,16 When using those photocatalysts, however, the solar-to-hydrogen (STH) conversion efficiencies are still far below the target threshold of ∼10% required for commercialization.¹⁷ To increase the STH efficiency towards 10%, many strategies have been developed, including the search for new materials, heteroatom doping, interface engineering and phase engineering.¹⁸

Since their first use as light absorbers in solar cells in 2009,¹⁹ halide perovskites (HPs) have been attracting significant attention in the field of photovoltaics, with high power conversion efficiencies exceeding 27% being reported.^20–23 This is due to the superior optoelectronic properties of HPs, including strong light absorption,²⁴ tunable bandgap,²⁵ long carrier lifetime,²⁶ long carrier diffusion lengths^27,28 and high carrier mobility.²⁹ The best-known photocatalysts for HERs are lead-containing HPs,³⁰ which are usually used in the form of heterojunctions with other photocatalysts to prevent the serious recombination of photogenerated charge carriers. As reported by Zhao et al.,³¹ the organic–inorganic hybrid HP MAPbI₃ (MA = CH₃NH₃, methylammonium), when integrated with a MoS₂ monolayer, demonstrated a STH efficiency of 1.09% and prominent hydrogen generation activity (HGA) of 13.6 mmol g⁻¹ h⁻¹. By integrating a polyfluorene co-catalyst onto the surface of MAPbI₃, Pal et al.³² reported a HGA of up to 6.2 mmol g⁻¹ h⁻¹ in HI solution, almost 200-fold higher than that of pristine MAPbI₃. In spite of such outstanding photovoltaic and photocatalytic properties, the organic–inorganic hybrid HPs have suffered from poor stability due to the existence of the organic moiety.³³ Therefore, the organic species (e.g., MA) were replaced with inorganic ones; for instance, CsPb(Br_1−xI_x)₃ with a noble metal co-catalyst of Pt demonstrated a HGA value of 1.12 mmol g⁻¹ h⁻¹ in the HI/HBr mixed solution.³⁴

In the Pb-based HPs, toxicity of lead is another problem, causing environmental and health care concerns. To address these problems, several metals, such as Sn, Ge and Bi, can be used instead of Pb in the all-inorganic HPs.^35–37 Typically, Bi-based HPs have been utilized in photocatalytic and photovoltaic applications due to their optoelectronic properties being comparable with Pb-based ones, including good intrinsic stability and eco-friendliness.^38,39 For instance, Cs₃Bi₂Br₉ nanocrystals coupled with graphitic carbon nitride (g-C₃N₄) nanosheets were found to exhibit a good HGA of 4.6 mmol g⁻¹ h⁻¹.⁴⁰ Moreover, Pancielejko et al.⁴¹ have demonstrated a 24-fold improvement in HGA by combining Bi-based HPs of Cs₃Bi₂X₉ (X = I, Br, Cl) with different types of TiO₂. Tang et al.⁴² also reported an improved photocatalytic performance for a Cs₃Bi₂I₉/Ti₃C₂ composite due to the promoted charge transfer and separation. A stable composite of Cs₃Bi₂I₉ and MoS₂ quantum dots has also been reported to show great enhancement in photocatalytic performance,⁴³ achieving a HGA of 6.09 mmol g⁻¹ h⁻¹, which notably surpasses that of pristine Cs₃Bi₂I₉ and Pt/Cs₃Bi₂I₉ composite by 8.8 and 2.5 times, respectively. Such an impressive improvement, leading to a new record for Bi-based HP photocatalysts under visible light, was attributed to the type-II heterojunction between Cs₃Bi₂I₉ and MoS₂.

The experimental findings mentioned above highlight the importance of interface engineering in enhancing the photocatalytic performance of Bi-based HP photocatalysts. To fully understand the underlying mechanism of such an enhancement through interface formation, a first-principles study based on density functional theory (DFT) is necessary.¹⁶ Since the photocatalytic performance encompasses both the intrinsic properties and the efficiency of a photocatalyst, one should clarify the electronic and optical properties such as band structure, band-edge alignment against the water redox potential, photoabsorption coefficients and the Gibbs free-energy difference upon hydrogen adsorption on the catalysis surface to estimate the photocatalytic performance, which further determines the STH conversion efficiency or HGA. To the best of our knowledge, however, no theoretical studies on the Cs₃Bi₂I₉/MoS₂ heterostructure have been reported to date, meaning that the effects of interface and defect engineering on its photocatalytic performance remain unclear. In this work, we perform first-principles calculations of the Cs₃Bi₂I₉/MoS₂ heterostructure to gain atomistic insights into the interfacial and defect effects on the electronic and optical properties. In particular, we consider typical vacancy defects at the interface, evaluating their formation energies, various interfacial properties and HER performance.

2 Methods

2.1 Computational methods

In the early steps, the DFT calculations were performed by using the pseudopotential plane-wave method as implemented in the Quantum ESPRESSO (QE, version 7.2) package.⁴⁴ For describing the ion–electron interactions, we used the ultrasoft pseudopotentials provided in the GBRV library,⁴⁵ which were generated with scalar relativistic calculations by using the valence electron configurations of Cs-5s²5p⁶6s¹, Bi-6s²6p³5d¹⁰, I-5s²5p⁵, Mo-4s²4p⁶5s²4d⁴ and S-3s²3p⁴. The Perdew–Burke–Ernzerhof (PBE) formalism⁴⁶ within the generalized gradient approximation (GGA) was used for the exchange–correlation interaction. Since the interface systems under study include layered materials of MoS₂ and Cs₃Bi₂I₉, the van der Waals (vdW) interactions between the layers were taken into account by using the vdW-DF-ob86 functional.⁴⁷ As the major computational parameters, the kinetic cutoff energies were set to 40 and 400 Ry for wave functions and electron density, respectively, and the special k-point meshes for the Brillouin zone sampling were set to (4 × 4 × 2). All the atomic positions were relaxed until the residual force on the atom converged to 5 × 10⁻⁴ Ry per Bohr, while the crystalline lattice was optimized until the stress was less than 0.05 kbar.

For the supercell calculations to consider the interfacial defects, the pseudo-atomic orbital (PAO) basis sets method as implemented in the SIESTA (version 4.1) package⁴⁸ was used. We selected the double-ζ plus polarization (DZP) scheme for the PAO basis sets, which were generated using an energy shift of 300 meV for the orbital-confining cutoff radii and a split norm of 0.30 for the split-valence. The plane-wave cutoff energy was set to 100 Ry and the special k-points mesh was set to (4 × 4 × 1) for atomic relaxations and (6 × 6 × 1) for energetic and optical calculations. The atomic relaxations were performed until the atomic forces converged to 0.02 eV Å⁻¹. We note that such calculations using the combination of QE and SIESTA packages were found to give reasonable results for different interface systems, with an affordable computational cost.^16,49–51

The formation energy of a vacancy defect i with charge q was calculated as follows:^52,53

E_f(i,q) = E_tot(i,q) − E_perf + μ_i + q(E_F + E_VBM), (1)

where E_perf and E_tot(i,q) are the DFT total energies of the perfect supercell and the defective supercell containing one vacancy defect i with a charge state q, E_F is the Fermi energy referenced to the energy level of the valence band maximum (VBM) E_VBM, and μ_i is the chemical potential of the i-th species removed from the supercell. The chemical potential μ_i can be written as μ_i = E_i + Δμ_i, where E_i is the total energy per atom of the corresponding simple substance. Under the thermodynamic equilibrium condition, the existence of bulk Cs₃Bi₂I₉ and MoS₂ puts constraints on the chemical potentials as follows:^51,54,55

ΔE_Cs3Bi2I9 = 3Δμ_Cs + 2Δμ_Bi + 9Δμ_I, (2)

ΔE_MoS2 = Δμ_Mo + 2Δμ_S, (3)

where and are the formation energies of the Cs₃Bi₂I₉ and MoS₂ compounds, respectively. To prevent the formation of elemental bulk i, the condition Δμ_i < 0 should be satisfied. To ensure the formation of Cs₃Bi₂I₉ from the binary compounds CsI and BiI₃, the following constraints must be met:

Δμ_Cs + Δμ_I < ΔE_CsI (4)

Δμ_Bi + 3Δμ_I < ΔE_BiI3 (5)

For other binary compounds, such as CsI₃, CsI₄, Bi₉I₂, Cs₃Bi, CsBi and CsBi₂, similar constraints are satisfied. Moreover, chemical dissociation of Cs₃Bi₂I₉ into the binary constituents (CsI and BiI₃) should be prohibited and thus the following condition should be satisfied:

ΔE_Cs3Bi2I9 − 3ΔE_CsI < 2Δμ_Bi + 6Δμ_I < 2ΔE_BiI3 (6)

The hydrogen adsorption energy ΔE_H is determined as⁵⁶

where E_sub+H and E_sub are the total energies of the substrate systems with and without an adsorbed H atom on the surface, respectively, and E_H2 is the total energy of an isolated H₂ molecule placed in a supercell of the same size as the substrate system, which is large enough to neglect the artificial interactions between the molecule and its periodic images. Then, the Gibbs free energy of hydrogen adsorption ΔG_H* can be evaluated as follows:

ΔG_H* = ΔE_H + ΔE_ZPE − TΔS_H, (8)

where ΔE_ZPE is the difference between the zero-point energy (ZPE) of H₂ in the adsorbed state and that in the gas-phase state, and ΔS_H is the difference in entropy of H₂ between the gas phase and adsorbed state. Here, ΔS_H can be written as , where is the entropy of H₂ under standard conditions. We utilized 0.24 eV for ΔE_ZPE − TΔS_H, as reported in the previous work for hydrogen adsorption.⁵⁶

The imaginary and real parts of the frequency-dependent complex dielectric function, ε(ω) = ε₁(ω) + iε₂(ω), were calculated using the density functional perturbation theory (DFPT) as implemented in the SIESTA package.^48,57 Then, the optical absorption coefficients α(ω) were obtained as follows:^58–60

where c is the speed of light.

2.2 Interface modelling

As a layered vacancy-ordered double perovskite, Cs₃Bi₂I₉ is crystallized in a hexagonal lattice with a space group of P6₃/mmc under ambient conditions,⁶¹ as shown in Fig. 1(a). The structure of Cs₃Bi₂I₉ is characterized by two neighboring [Bi₂I₉]³⁻ octahedra, which are face-shared along the c-axis to form a [Bi₂I₉]³⁻ bioctahedral cluster, and the [Bi₂I₉]³⁻ clusters are separated by hexagonal channels filled with Cs⁺ cations, leading to the formation of a zero-dimensional molecular salt crystal structure. Within the [Bi₂I₉]³⁻ bioctahedral cluster, there exist three long bridging Bi–I bonds, which involve I atoms on the shared face, and six terminal short Bi–I bonds oriented away from the shared face. For MoS₂ bulk, we selected the 2H phase among its polymorphs, which is also in a hexagonal lattice with the space group of P6₃/mmc. With the optimized bulk structures, we built the interface slab models of Cs₃Bi₂I₉ (001) surface and MoS₂ (001) monolayer (ML). According to the experimental report for the structural characteristics,⁶² the Cs₃Bi₂I₉ (001) surface was suggested to have CsI₃ termination. To minimize the lattice mismatch between the Cs₃Bi₂I₉ (001) and MoS₂ (001) surfaces, we applied the coincidence lattice method.⁶³ As a result, we obtained the surface supercells along the lines of [310] and [230] for 2H-MoS₂ (Fig. 1(c)) and [100] and [110] for Cs₃Bi₂I₉ (Fig. 1(d)), with a significantly small lattice mismatch of 0.1% evaluated as follows:⁶⁴where a₁ and a₂ are the lattice constants of the Cs₃Bi₂I₉ and 2H-MoS₂ lattices. The resultant supercells correspond to (1 × 1) and (7 × 7) for Cs₃Bi₂I₉ (001) and 2H-MoS₂ (001) surfaces, respectively. The slab models of the interface contained ten atomic layers of Cs₃Bi₂I₉ and an S–Mo–S layer of MoS₂ (49 atoms) with a vacuum layer of 15 Å thickness, as shown in Fig. 1(e). We confirm that the 10 atomic layers for the Cs₃Bi₂I₉ is thick enough to guarantee convergence of the surface energy and the 15 Å vacuum thickness is sufficiently large to inhibit the artificial interactions between the top and bottom atoms of the neighbouring slabs. While fixing the lattice constants of the slab supercell and the atomic positions of the 6 atomic layers in the Cs₃Bi₂I₉ side, all other atomic positions were relaxed using the QE code. Here, we considered two different possible sliding structures between Cs₃Bi₂I₉ and MoS₂, denoted as Conf1 and Conf2 (Fig. S2, SI), and performed atomic relaxations for these sliding configurations. From the calculation, the Conf1 sliding structure, where one of the S atoms in the MoS₂ layer is placed on top of the Cs atom of the Cs₃Bi₂I₉, was found to have a lower total energy with a shorter interlayer binding distance than the Conf2 structure. Therefore, we only considered the Conf1 sliding structure for further calculations of the electronic and photocatalytic properties.⁶⁵

Fig. 1 (a) Polyhedral view of the unit cell for the Cs₃Bi₂I₉ crystal optimized with QE. (b) Electronic band structure of the bulk Cs₃Bi₂I₉ calculated in this study. Top view of the lattice-matched structure of (c) the MoS₂ (001) surface (7 × 7) supercell and (d) the Cs₃Bi₂I₉ (001) surface unit cell. (e) Side view of the Cs₃Bi₂I₉/MoS₂ ML interface supercell model relaxed with SIESTA.

In order to consider the vacancy defects, we built 2 × 2 × 1 supercells (196 atoms) with a very thick vacuum layer (70 Å) using the relaxed interface slabs with the QE code. The atomic relaxations were also performed using the SIESTA code, while fixing the lattice constants and the 6 atomic layers of the Cs₃Bi₂I₉ side. We confirm that the supercell sizes are large enough for defect calculations as used in the previous works.^16,66 Then, each of the three types of interfacial vacancy defect, such as caesium (V_Cs), iodine (V_I) and sulfur (V_S), was created at different positions around the interface, and the lowest energy configuration for each defect was identified by performing the atomic relaxation (see Fig. S3 and Table S1, SI). We considered different charge states for each vacancy defect in this work.

The formation energy of the interface is defined as follows:⁶⁷

where , and are the DFT total energies of the Cs₃Bi₂I₉/MoS₂ interface, the Cs₃Bi₂I₉ (001) surface and the MoS₂ (001) surface, respectively, and A is the interface area. The total energies for the surfaces were calculated by using the fully relaxed isolated surface systems with the same cell size with the interface. The interlayer binding energy is defined as follows:where E^int(d_eq) and E^int(d_∞) are the total energies of the interface systems with the equilibrium interlayer distance and the infinity distance, respectively, and N is the number of atoms in the MoS₂ layer. The spatial charge density difference was evaluated as follows:

Δρ = ρ_int − ρ_Cs3Bi2I9 − ρ_MoS2, (13)

where ρ_int, ρ_Cs3Bi2I9 and ρ_MoS2 are the charge densities of the interface, isolated Cs₃Bi₂I₉ and MoS₂ surface sides, respectively. Then, the planar-averaged charge density difference integrated on the x − y plane was calculated as follows:where A is the area of the x − y plane.^16,51

3 Results and discussion

3.1 Structural stability of the interface

Firstly, we scrutinized the geometrical and electronic properties of bulk Cs₃Bi₂I₉ and 2H-MoS₂. By performing the structural optimizations of the unit cells, we determined their lattice constants to be a = b = 8.371 Å, c = 21.132 Å for Cs₃Bi₂I₉ and a = b = 3.167 Å, c = 12.374 Å for 2H-MoS₂, which agree well with the previous experimental results.^61,68,69 Using the QE code with the PBE functional, we then calculated their electronic band structures. Fig. 1(b) shows the calculated band structure of Cs₃Bi₂I₉, demonstrating an indirect bandgap of 1.97 eV in good agreement with the previous results.^61,70 Meanwhile, the band structure of the 2H-MoS₂ monolayer shows a direct bandgap of 1.84 eV, also in good agreement with the previous DFT calculations⁶⁹ (see Fig. S1, SI). Such good agreements indicate that the computational settings employed in this work are reasonably acceptable. We note that the GGA-PBE functional was found to give bandgap values that agreed well with the experimental ones for lead halide perovskites, due to the fortuitous error compensation between the underestimation of PBE and overestimation by ignoring the spin–orbit coupling effect.^71,72

With these calculated lattice constants of the bulk materials, the cell dimensions of the Cs₃Bi₂I₉/MoS₂ interface were found to be 8.375 × 8.375 Å and those of the 2 × 2 supercells was 16.75 × 16.75 Å. To estimate the stability of the Cs₃Bi₂I₉/MoS₂ interface system, the formation energy E_f was calculated. The formation energy was found to be negative, indicating that the formation of the Cs₃Bi₂I₉/MoS₂ interface is exothermic and that binding between the constituent Cs₃Bi₂I₉ surface and MoS₂ monolayer is energetically favorable. In fact, the formation energy of the perfect heterostructure without any defects was calculated to be −0.70 J m⁻², being lower than that of the CsPbI₃/MoS₂ interface obtained in our previous work¹⁶ (−0.22 and −0.37 J m⁻² for CsI and PbI₂ terminations, respectively). This indicates the stronger binding between the constituent layers in the Cs₃Bi₂I₉/MoS₂ heterostructure than in the CsPbI₃/MoS₂ heterostructure.

To further assess the binding strength between the constituent layers of the interface, the interlayer binding energy was also calculated. Fig. 2 shows the resultant E_b as a function of interlayer distance d_int. Table 1 lists the calculated values for the interface formation energy, interlayer binding energies and interlayer equilibrium distances for the Cs₃Bi₂I₉/MoS₂ heterostructures considered in this work. Irrelevant to the existence of vacancy defects, the binding energy E_b values for the interface systems were found to be negative, indicating the attractive binding in the Cs₃Bi₂I₉/MoS₂ interface systems. The binding energy for the perfect system was estimated to be −127.81 meV per atom, which is comparable to that of the CsPbI₃/MoS₂ interface.^16,73 Among the different defective systems, the V_S interface system was found to have the lowest binding energy of −132.54 meV per atom and accordingly the shortest interlayer distance of 3.08 Å. For the cases of V_I and V_Cs, the E_b values were found to slightly increase to −125.81 and −117.95 meV per atom, while the d_int values decrease to 3.18 and 3.22 Å, respectively.

Fig. 2 The interlayer binding energy per atom E_b for the Cs₃Bi₂I₉/MoS₂ heterojunction as a function of interlayer binding distance d_int. The inset represents the magnified view around the equilibrium distance d_eq.

Table 1 The interface formation energy E_f, interlayer binding energy E_b and interlayer equilibrium distances d_int in the Cs₃Bi₂I₉/MoS₂ heterostructures without and with vacancy defects

System	Ef (J m^−2)	Eb (meV per atom)	dint (Å)
Perfect	−0.70	−127.82	3.13
VCs		−117.95	3.22
VI		−125.81	3.18
VS		−132.54	3.08

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3.2 Formation of interfacial vacancy defect

Defects play a decisive role in the photovoltaic and photocatalytic applications. To check the formation possibility of the interfacial vacancy defects under the synthesis conditions, we estimated their formation energies from the thermodynamic point of view. According to eqn (1), the defect formation energy varies with the chemical potentials of the elements, which reflect the synthesis conditions in the experiments. Therefore, we first determined the chemical potential ranges of all the species included in the interface system for ensuring the stable existence of bulk Cs₃Bi₂I₉ and MoS₂ by using the thermodynamic constraints given by eqn (2)–(6) and the formation energy values of the available compounds (see Table S2 and Fig. S4, SI). Note that none of the ternary compounds are available in the Cs-Bi-I system, except for Cs₃Bi₂I₉.

Fig. 3(a) presents the chemical potential diagram obtained in this work concerning the chemical potentials of Cs (Δμ_Cs) and Bi (Δμ_Bi), which are referenced to those of the corresponding elemental bulks. The thermodynamically stable region for the Cs₃Bi₂I₉ compound is marked as the grey-colored region shown as the pentagon ABCDE (see Table S3 for the chemical potential values at the five vertexes of the pentagon, ESI). Among the vertex points of the pentagon, point B has the maximum value of Δμ_Cs and the minimum value of Δμ_I (Δμ_Cs = −2.70 eV, Δμ_Bi = 0.02 eV, Δμ_I = −0.99 eV), while point E has the maximum value of Δμ_I and the minimum value of Δμ_Cs (Δμ_Cs = −3.74 eV, Δμ_Bi = −2.13 eV, Δμ_I = −0.17 eV). Therefore, point B is said to represent the Cs-rich/I-poor condition, while point E represents the I-rich/Cs-poor condition. The possible chemical potential ranges for Mo and S species were also evaluated (see Table S3, SI). Note that outside of the pentagon region, the undesirable binary compounds such as CsI, BiI₃, CsI₃ and CsI₄ are more stable than Cs₃Bi₂I₉. For instance, BiI₃ will form in the left-hand side of the A–E line, while the CsI compound is stable in the right-hand side of the B–C line. It is worth noting that the stable region has a rather wide shape in contrast to the very narrow shapes for the Pb-based HPs, such as MAPbI₃ and CsPbI₃.^16,51,73 This indicates that the Bi-based HP Cs₃Bi₂I₉ is more stable than the Pb-based HPs, for which instability is the main obstacle to their photovoltaic applications.

Fig. 3 (a) Chemical potential ranges of Cs and Bi for the stable Cs₃Bi₂I₉ compound, marked as grey-colored pentagon ABCDE. Outside the pentagon, the other binary compounds such as CsI, BiI₃, CsI₃, CsI₄, Bi₉I₂, CsBi, Cs₃Bi and CsBi₂ will form instead of the Cs₃Bi₂I₉ perovskite. Insets depict the magnified views around the vertexes of the pentagon. (b) Calculated formation energies of V_Cs and V_I defects at theCs₃Bi₂I₉ part of the interface as a function of the Fermi energy (E_F) at points A, B, C, D and E. (c) The formation energy of vacancy defect V_S at the MoS₂ part of the interface under S-poor and S-rich conditions.

We then calculated the band structures of the Cs₃Bi₂I₉ and MoS₂ surfaces having the same planar size as the interface to determine the Fermi levels E_F, bandgaps and VBM levels (E_VBM) (see Fig. S5, SI). To determine the E_VBM levels for the interface, we adopted the line-up-averaged electrostatic potential method^74,75 for the Cs₃Bi₂I₉/MoS₂ interface, and Cs₃Bi₂I₉ and MoS₂ surfaces (see Fig. S6, SI). From the obtained band structures and the work functions (calculated by ϕ = E_v − E_F, where E_v is the vacuum level), the VBM levels were corrected to be and for the Cs₃Bi₂I₉ and MoS₂ sides, respectively.

Fig. 3(b) shows the calculated formation energies of the vacancy defects V_Cs and V_I as functions of E_F at the points A, B, C, D and E. The formation energies of all the vacancy defects were found to be positive, indicating that their formation is endothermic. In most cases (points A, B, C, and D), V⁰_I has the lowest formation energy, suggesting that V⁰_I is easier to form than other vacancies and thus the dominant defect at the Cs₃Bi₂I₉/MoS₂ interface. In particular, this argument is more evident under the I-poor/Cs-rich condition (points A, B and C). Note that in the Pb-based HPs, the V_I defect was also found to be the major defect with the lowest formation energy.^54,55 When going to the I-rich/Cs-poor condition (points D and E), it is natural to observe that the formation energy of V_Cs decreases while that of V_I increases, and finally V_Cs has a lower formation energy than V_I at point E. On the other hand, V_S was also found to have a positive formation energy, as shown in Fig. 3(c), implying that its formation at the interface is not spontaneous but endothermic in accordance with the case of the MoS₂ bulk.⁷⁶ Moreover, the formation energy of the V⁰_S state was found to be lower than those of the V_S¹⁺ and V_S²⁺ states in the whole range of E_F. Interestingly, none of the thermodynamic transition levels between the differently charged defects, where the electrons could be donated or accepted, were observed, suggesting that these vacancy defects do not cause the undesirable charge recombination at the Cs₃Bi₂I₉/MoS₂ interface.

3.3 Interfacial charge redistribution and DOS analysis

We evaluated the charge density difference upon interface formation to gain intuitive insights into the binding strength and charge carrier transfer across the interface. Fig. 4(a) depicts the calculated planar-averaged charge density differences upon the formation of Cs₃Bi₂I₉/MoS₂ interfaces without and with the vacancy defects. At a glance, the charge redistribution occurs locally around the interface region, while being barely influenced by the defect formation. The charge accumulation was observed mostly in the interstitial region biased to the MoS₂ side, whereas the charge depletion was found mostly around the CsI₃ layer of the Cs₃Bi₂I₉ side. This observation is further clarified by the isosurface plot of the spatial electron density difference, as can be seen in Fig. 4(b), where the charge depletion (blue colour) is distributed around the I atoms of Cs₃Bi₂I₉, while charge accumulation (red colour) is seen around the S atoms of the MoS₂ layer (see Fig. S7 for the defective systems, SI). The observed charge redistribution indicates that the significant amount of electrons are transferred from the MoS₂ layer to the Cs₃Bi₂I₉ side, leading to the strong binding between them at the interface. Moreover, the interface dipole originating from this charge redistribution is expected to help the transfer of photogenerated electrons and holes as will be discussed later.

Fig. 4 (a) Planar-averaged charge density difference (Δ[small rho, Greek, macron]) integrated over the x–y plane along the z-axis upon the formation of Cs₃Bi₂I₉/MoS₂ interfaces without and with the vacancy defects under study. (b) Isosurface plot of the spatial charge density difference upon the formation of the perfect interface projected on the (100) planes passing the I atoms (top panel) and Cs atoms (bottom panel) of the Cs₃Bi₂I₉ surface, ranging from 0.001 to 0.001 |e| Å⁻³. Partial density of states (PDOS) and isosurface and isoline plots of local density of states (LDOS) for (c) the perfect interface, (d) V_Cs-, (e) V_I- and (f) V_S-containing interfaces.

For a quantitative insight into the charge redistribution, we integrated the planar-averaged electron density difference to obtain the total transferred charge as Δq = ∫Δ[small rho, Greek, macron](z)dz, which was further divided into the contributions from the Cs₃Bi₂I₉ (Δq_Cs3Bi2I9) and MoS₂ (Δq_MoS2) sides. Table 2 lists the calculated transferred charge contributions from two constituent layers in the perfect and defective interfaces. For all the cases, the Cs₃Bi₂I₉ part was found to have negative values whereas the MoS₂ side had positive ones. This indicates that charge is depleted at the terminal surface of Cs₃Bi₂I₉, while it is accumulated at the MoS₂ monolayer, resulting in the creation of an interfacial dipole moment oriented from the Cs₃Bi₂I₉ side to the MoS₂ side, which prevents the charge carriers from transferring across the interface. Among the different systems without and with the vacancy defects, the largest charge transfer was observed in the V_I-containing system, whereas the smallest charge transfer occurred in the V_Cs-containing interface.

Table 2 Transferred charge upon the formation of the Cs₃Bi₂I₉/MoS₂ heterostructures under study, which is divided into contributions from each of the subsystems (Δq_Cs3Bi2I9, Δq_MoS2), and the interfacial dipole moment Δμ

System	ΔqCs3Bi2I9 (|e|)	ΔqMoS2 (|e|)	Δμ (Debye)
Perfect	−0.306	0.308	4.23
VCs	−0.202	0.204	2.41
VI	−0.318	0.321	4.79
VS	−0.250	0.254	4.29

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Charge transfer often induces interface polarization, which plays an important role in the properties of a heterostructure and is quantified by the interfacial dipole moment. As mentioned above, the interfacial dipole moment, orienting from the Cs₃Bi₂I₉ side to the MoS₂ side, helps the photogenerated electrons and holes move across the interface in opposite directions, thereby being favourable for preventing the recombination of photogenerated charge carriers and enhancing the photocatalytic performance in the Cs₃Bi₂I₉/MoS₂ heterostructure. The interface polarization induces a step in the electrostatic potential across the interface, which results in changes in the band-edge alignment. The interfacial dipole moment also originates the downward and upward band bending with the formation of a charge accumulation layer at the interface. The interfacial dipole moment, induced at the interface from the charge redistribution, was evaluated by Δμ = −∫zΔ[small rho, Greek, macron]dz. The calculated Δμ values are listed in Table 2. The V_I-containing interface was also found to have the largest Δμ value of 4.79 D among the interface systems under study. Meanwhile, the V_Cs defect causes a reduction in Δμ to 2.41 D. Such tendencies are consistent with the previous calculations for CsPbI₃/2H-MoS₂ (ref. 16) and MAPbI₃/2H-MoS₂ interfaces,⁷⁷ where V_I defect systems have obviously larger Δμ values and V_Cs systems have smaller Δμ values. When compared with those of the Pb-based HP/MoS₂ heterostructures, however, Δμ values are relatively larger, suggesting further improvement of photocatalytic performance in the Cs₃Bi₂I₉/MoS₂ interface.

In order to understand the generation and transport processes of charge carriers induced by photon incidence, we calculated the electronic density of states (DOS) of the interface systems. Fig. 4(c)–(f) display the calculated atom-projected partial density of states (PDOS) of the Cs₃Bi₂I₉ and MoS₂ sides and the local density of states (LDOS) along the z-axis for all the interface systems. Our calculations revealed that the lower conduction bands (CBs) responsible for the transport of photo-induced electrons are contributed from Bi and I atoms on the Cs₃Bi₂I₉ side and both Mo and S atoms on the MoS₂ side. From the LDOS plots, the CB edge states of MoS₂ were found to be lower in energy than those of Cs₃Bi₂I₉, being beneficial to the transfer of electrons photo-generated in the Cs₃Bi₂I₉ side to the MoS₂ side. It was found that the V_Cs defect causes barely any change in the electronic properties of the perfect interface system, whereas the V_I and V_S defects induce shallow trap states near the CBM level. In particular, the V_S-containing interface exhibits the trap state relatively far below the CBM level. Since trap states inside the bandgap would behave as recombination centers, they can be detrimental to the photocatalytic performance. However, it can be said that the V_S defect is difficult to be formed due to its relatively high formation energy.

3.4 Photocatalytic performance

In understanding the photocatalytic performance for HER, the band edge alignment is an important criterion. For a high HER performance, it is required that the CBM level should be higher than the hydrogen reduction potential of H⁺/H₂, while the VBM level should be lower than the water oxidation potential of O₂/H₂O. Selecting the vacuum level as the reference, the hydrogen reduction potential and the water oxidation potential are calculated at different pH values as follows:^56,73

Once the Cs₃Bi₂I₉ surface is combined with the MoS₂ monolayer to build the heterostructure, some electrons are transferred to ensure the same Fermi level at the interface.⁶⁴ By using the calculated work function ϕ, we determined the Fermi levels of the Cs₃Bi₂I₉/MoS₂ interfaces, and then obtained the E_VBM and E_CBM values for the Cs₃Bi₂I₉ and MoS₂ parts, which are referenced to the vacuum level E_v (see Fig. S8 for the band structures, SI).

For the perfect interface system, the VBM and CBM levels were calculated to be −4.66 and −3.10 eV for the Cs₃Bi₂I₉ side and −5.18 and −3.40 eV for the MoS₂ side, respectively. Therefore, the interface was characterized as a type-II heterojunction, being significantly beneficial to the separation of electrons and holes in opposite directions, i.e., preventing the recombination of charge carriers. The interfacial dipole moment induced from the charge redistribution originates the downward and upward band bending with the formation of a charge accumulation layer at the interface.⁷⁵ Fig. 5(a) shows a scheme that illustrates the generation and transfer processes of charge carriers at the heterojunction. When photons are absorbed in the Cs₃Bi₂I₉/MoS₂ heterojunction, electrons are excited from the VBM to the CBM on each side of the interface, due to their proper bandgaps for light absorption. Then, the electrons placed on the CBM of Cs₃Bi₂I₉ are attracted toward the MoS₂ side by the interface dipole, while the holes left in the VBM of MoS₂ are drawn to the Cs₃Bi₂I₉ side.

Fig. 5 (a) Schematic diagram of band alignment in the Cs₃Bi₂I₉/MoS₂ interface with a type-II heterojunction. Here, E_v and E_F are the vacuum and Fermi energy levels, and E_VB and E_CB are the VBM and CBM levels of the Cs₃Bi₂I₉ and MoS₂ sides. (b) Band-edge alignments of Cs₃Bi₂I₉/MoS₂ interface systems, referenced to the vacuum level. Turquoise and magenta bars indicate VBs and CBs of the Cs₃Bi₂I₉ and MoS₂ parts, respectively. The Fermi level is depicted as a horizontal black line for each interface system. Blue and red horizontal long lines represent the hydrogen reduction and water oxidation potentials, respectively, at different pH values.

Fig. 5(b) illustrates the calculated band-edge alignments of the interface systems under study (see Table S4 for the corresponding numerical values, SI). In all cases, the CBM is higher than the H⁺/H₂ reduction potential, indicating that the Cs₃Bi₂I₉/MoS₂ heterostructure has the potential to reduce H⁺ to H₂. In the case of the V_I-containing interface, however, it was revealed that the band-edge alignment is not appropriate for water splitting, since the VBM is even higher than the H⁺/H₂ potential. For the perfect interface and V_S-defective systems, the CBMs are lower than the O₂/H₂O potential only at pH values higher than 8, i.e., in the basic environment. Therefore, they cannot produce O₂ by oxidizing H₂O under acidic conditions. With the proper band-edge alignment, the V_Cs-containing interface is likely to be the most promising photocatalyst for water redox reactions, especially in an acidic environment.

For further insights into the photocatalytic performance of the interface, we evaluated the Gibbs free energy for hydrogen adsorption (ΔG_H*).⁵⁶ From the viewpoint of HER activity, the absolute value of ΔG_H* should be as small as possible. We calculated ΔG_H* for the Cs₃BI₂I₉/MoS₂ heterojunctions, together with the isolated Cs₃BI₂I₉ surface and the MoS₂ monolayer. Considering the previous result,¹⁶ we proposed that the H atom could be adsorbed on the S atom in the top layer of the MoS₂ monolayer (see Fig. S9, SI). For the case of the Cs₃Bi₂I₉ surface, the adsorption site of the H atom was identified using energetic calculations. As shown in Fig. 6, the Cs₃Bi₂I₉ surface was found to show the highest ΔG_H* value of 2.20 eV, while the perfect heterostructure and MoS₂ monolayer have nearly the same value of 2.01 eV, which is consistent with the ΔG_H* value obtained for the graphene/MoS₂ heterostructure.⁷⁸ This indicates that the formation of the interface between Cs₃Bi₂I₉ and MoS₂ without any defects hardly affects on the Gibbs free energy for hydrogen adsorption on the MoS₂ layer. The vacancy defect formation at the interface was found to have a positive effect on HER activity due to the lower ΔG_H*, except for the V_I defect which was found to slightly increase the ΔG_H* value. For V_S- and V_Cs-containing systems, ΔG_H* was reduced to 1.48 and 0.50 eV, respectively, implying some improvement of HER performance.

Fig. 6 Gibbs free energy difference for hydrogen adsorption (ΔG_H*) on the Cs₃Bi₂I₉/MoS₂ interface systems without and with the vacancy defects such as V_Cs, V_I and V_S, together with those on the pristine Cs₃Bi₂I₉ surface and MoS₂ monolayer.

For the final step, we calculated the photoabsorption spectra of the Cs₃Bi₂I₉/MoS₂ heterostructures without and with the interfacial vacancy defect, bulk Cs₃Bi₂I₉ and the MoS₂ monolayer, as shown in Fig. 7. From these spectra, we could estimate the photoabsorption edge and intensity, which are crucial factors to achieve high photocatalytic activity (see Fig. S10 for dielectric functions and other optical properties, SI). For bulk Cs₃Bi₂I₉ and the MoS₂ monolayer, the absorption edges were found to be 1.54 and 1.84 eV, respectively. Meanwhile, those of the heterostructures were found to be significantly shifted to the lower-energy region varying from 1.18 to 1.48 eV. Moreover, the Cs₃Bi₂I₉/MoS₂ heterostructures exhibited higher absorption intensities than their constituents in the visible-light and near-ultraviolet regions, representing their superior photoabsorption capability. The perfect interface has greater absorption intensity than the defective interfaces in the visible-light region, while in the ultraviolet region the defective heterostructures have higher absorption coefficients than the perfect interface. It is worth noting that among the different vacancy defects, the V_Cs defect induces the greatest intensity in the visible-light region. This is mainly due to the reduced bandgaps and the built-in electric field originating from the charge redistribution at the interface.^79,80

Fig. 7 Photoabsorption spectra of bulk Cs₃Bi₂I₉, the MoS₂ monolayer and the Cs₃Bi₂I₉/MoS₂ interface systems without and with a vacancy defect. The vertical dashed lines indicate the visible-light region.

4 Conclusions

We have systematically investigated the structural, electronic and optical properties of Cs₃Bi₂I₉/MoS₂ heterostructures using first-principles calculations to give a comprehensive theoretical understanding on the enhancement of photocatalytic water splitting activity for hydrogen evolution. Using the (1 × 1) unit cell of the Cs₃Bi₂I₉ (001) surface and a (7 × 7) cell of the 2H-MoS₂ monolayer, we built a slab model of the Cs₃Bi₂I₉/MoS₂ interface with a very small lattice mismatch of 0.1% without and with a vacancy defect, such as V_Cs, V_I and V_S. The formation and binding energies of the interface systems were calculated, confirming that these heterostructures are energetically stable. We computed the defect formation energies in the defective Cs₃Bi₂I₉/MoS₂ interfaces under the different growth conditions through chemical potentials of the species, finding that the V_I defect could be generated with the lowest formation energy under the I-poor/Cs-rich condition, while the V_Cs defect would be dominant under the Cs-poor/I-rich condition. Through the analysis of charge redistribution upon interface formation, we demonstrated that some electrons are transferred from the MoS₂ side to the Cs₃Bi₂I₉ side, inducing the interfacial dipole moment beneficial to preventing the recombination of photogenerated charge carriers. Our calculations of DOS and photoabsorption spectra revealed that the perfect interface system and the V_Cs-containing interface could be favourable for photocatalytic activity compared with other defective systems, since they do not induce shallow trap states inside the bandgap range and exhibit higher absorption intensities than others. Finally, we found that the V_Cs-containing heterostructure is particularly promising for improving the photocatalytic activity for hydrogen generation due to the significant reduction of the Gibbs free energy for hydrogen adsorption to 0.5 eV and the most suitable band alignment for photo-induced overall water splitting, whose band edge positions straddle the water redox potentials.

Author contributions

Yun-Sim Kim and Chol-Jun Yu developed the original project. Kyong-Mi Kim and Yun-Sim Kim performed the calculations and drafted the first manuscript. Dok-Ho Hyon and Chol-Hyok Ri contributed to useful discussions. Chol-Jun Yu supervised the work. All authors reviewed the manuscript.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data are available in the supplementary information (SI) and further from the authors upon reasonable request. Supplementary information: Tables for defect position search, formation energies of the compounds, chemical potential values and band alignment, and figures for the band structure of the MoS₂ monolayer, two different sliding configurations, vacancy sites at the interfaces, the Cs-Bi-I ternary system, band structures and electrostatic potential of the interface systems, spatial charge density difference of the heterostructures with vacancy defects, adsorption geometries for hydrogen adsorption on different systems, real and imaginary parts of the dielectric function and other optical properties. See DOI: https://doi.org/10.1039/d5ra05294g.

Acknowledgements

This work is supported as part of the fundamental research project “Design of New Energy Materials” (no. 2021-12) funded by the State Commission of Science and Technology, DPR Korea. Computations in this work have been done on the HP Blade System C7000 (HP BL460c) that is owned and managed by Faculty of Materials Science, Kim Il Sung University.

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