Two-dimensional trilayer heterostructures with cascade dual Z-schemes to achieve efficient hydrogen evolution reaction

Abstract

Cascade dual Z-schemes for photocatalytic overall water splitting for hydrogen production are constructed for trilayer Bi/HfSeTe/ZrSe₂, Bi/HfSeTe/ZrSe₂, and InAs₃/HfSeTe/ZrSe₂ heterostructures. Electronic properties are studied by first-principles calculations, and the photoexcited carrier pathway is explored by nonadiabatic molecular dynamics simulations. The arrow-up, arrow-down, and cascade arrangement of band alignments for the Bi/HfSeTe/ZrSe₂ and InAs₃/HfSeTe/ZrSe₂ heterostructures are explored, and those for the HfSe₂/ZrSe₂/HfSe₂ and ZrSe₂/HfSe₂/ZrSe₂ sandwich heterostructures are also considered for comparison. The solar-to-hydrogen efficiency of 22.08% for the bilayer HfSeTe/ZrSe₂ heterostructure can be raised to 40.52%, 39.47%, and 41.04% by the cascade dual Z-schemes with Bi/HfSeTe/ZrSe₂, Bi/HfSeTe/ZrSe₂, and InAs₃/HfSeTe/ZrSe₂. They can further be boosted to 41.53%, 41.12%, and 43.57% under 1%, 1%, and −2% biaxial strains, respectively. The nonadiabatic molecular dynamics simulations reveal that the activity of the photogenerated carriers can be well protected. Moreover, the Gibbs free energy changes demonstrated that the hydrogen and oxygen evolution reactions driven by Bi/HfSeTe/ZrSe₂ can spontaneously proceed. Therefore, the cascade dual Z-scheme provides an effective way to develop highly efficient photocatalysts for hydrogen generation from overall water splitting.

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1. Introduction

Serious environmental and energy problems have arisen with the rapid economic development of countries around the world.¹ The method of photocatalytic water splitting to produce hydrogen is gaining considerable attention due to its advantages of being inexpensive and non-polluting.² Photocatalyst performance is promoted by a high carrier separation efficiency, wide light absorption range, and strong redox ability.³ Extensive efforts have been devoted to improving the photocatalytic ability of materials by enhancing the above factors. For example, constructing Janus monolayers with electrostatic potential difference (Δφ) on two surfaces is one of the most effective methods of facilitating internal carrier separation,^4–6 such as group III chalcogenides,⁷ III₂–VI₃ groups,⁸ and group VI chalcogenides.⁹ Establishing heterostructures also has the above advantages and can further improve the overpotential of the hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) compared with the monolayers composing them.^10,11 Bilayer heterostructures can be classified into three types according to their different band structures. Type-I heterostructures have the straddling band structure characteristic, accumulating electrons and holes into the same components under light irradiation.¹² For type-III heterostructures, the bandgap of one monolayer is broken by the other component.¹³ However, type-II heterostructures with staggered band structures are beneficial for efficient photocatalyst performance.¹⁴ Based on the different carrier migration pathways, type-II heterostructures can be divided into conventional type-II and direct Z-schemes. The conventional type-II scheme has excellent photogenerated carrier utilization capacity, but diminished redox capacity.¹⁵ Conversely, the direct Z-scheme can improve the redox capacity and have excellent light absorption performance that can drive HERs in the higher conduction band minimum (CBM) of two components and the OERs in the lower valence band maximum (VBM).¹⁶ Thus, constructing direct Z-scheme heterostructures is a smart choice to obtain efficient photocatalyst materials. For example, ZnIn₂S₄/MoSe₂ ¹⁷ with a direct Z-scheme fabricated through an experiment exhibits an optimized apparent quantum yield and a high hydrogen-production rate. In₂O₃/ZnInSe₄,¹⁸ TiO₂/ZnIn₂S₄,¹⁹ and Cd_0.5Zn_0.5S/BiVO₄F ²⁰ heterostructures display a more excellent photocatalyst performance than the monolayers composing them. The theoretically proposed PtTe₂/Sb₂S₃,²¹ C₇N₆/Sc₂CCl₂,²² and C₇N₆/GaSnPS ²³ with direct Z-schemes further demonstrate outstanding light absorption and carrier separation abilities. Dual Z-scheme heterostructures constructed from three monolayers with a narrow bandgap can achieve a wide light absorption range, which is one of the crucial factors for enhancing the photocatalyst performance. Generally, the dual Z-scheme of trilayer heterostructures is divided into arrow-up,²⁴ arrow-down,²⁵ and cascade^26,27 according to the characteristics of band alignments. Considering that the HER and OER can occur in nonadjacent monolayers in dual Z-scheme heterostructures, the lifetime of photogenerated carriers in a trilayer heterostructure is prolonged, which is conducive to suppressing the recombination of carriers.^28,29 Meanwhile, the shape and size of different materials can be controlled, resulting in the large specific surface area and the high photocatalytic activity of a trilayer heterostructure. Carrier migration mechanisms with different types of band alignments have been suggested in some experimental reports, such as the V₂O₅/CdS/CoS₂,³⁰ BiSi/Bi₂WO₆/g-C₃N₄,³¹ and AgI/g-C₃N₄/Bi₂WO₆ ³² trilayer heterostructures. However, they have not been confirmed theoretically. Therefore, intensive theoretical studies of the carrier migration mechanism of trilayer heterostructures are urgently needed.

Two-dimensional (2D) transition metal dichalcogenide HfSe₂ and ZrSe₂ monolayers reportedly have attractive electronic and optical properties.^33–35 For example, the HfSe₂/ZrSe₂ heterostructure has been reported to have a type-I band alignment, and the potential of CBMs cannot straddle the hydrogen reduction potential (−4.44 eV).³⁶ We have first constructed sandwich heterostructures by stacking^37,38 and doping^11,39 methods, which have turned out to be effective measures to regulate band alignment. However, the working CBM of HfSe₂/ZrSe₂/HfSe₂ and ZrSe₂/HfSe₂/ZrSe₂ configurations cannot match the HER condition. The band alignment of the HfSe₂/ZrSe₂ heterostructure can be changed to type II by doping Te atoms into the HfSe₂ monolayer. We have also considered two different configurations of the HfSeTe/ZrSe₂ heterostructures. However, we have found that only the HfSeTe/ZrSe₂-I heterostructure can straddle the potentials of the HER and OER, whereas the overpotential for the HER is only 0.03 eV even though the η′_STH is 22.08%. Subsequently, four sandwich configurations constructed from the HfSeTe and ZrSe₂ monolayers have also been explored, whereas their band alignment types are arrow-up or arrow-down. The CBMs and VBMs cannot fully match the potential conditions of HERs or OERs. In the present study, we constructed eight different configurations of 2D trilayer heterostructures by adding the Bi or InAs₃ monolayer on the bilayer HfSeTe/ZrSe₂ heterostructure. As expected, the Bi/HfSeTe/ZrSe₂-I, Bi/HfSeTe/ZrSe₂-II, and InAs₃/HfSeTe/ZrSe₂-I configurations had cascade band alignment, by which we constructed cascade dual Z-schemes. The obtained schemes also satisfied the potential requirements of the HER and OER. The η′_STH's on Bi/HfSeTe/ZrSe₂-I, Bi/HfSeTe/ZrSe₂-II, and InAs₃/HfSeTe/ZrSe₂-I can reach 40.52%, 39.47%, and 41.04%, respectively. The η′_STH was further boosted to 41.53%, 41.12%, and 43.57% under 1%, 1%, and −2% biaxial strain, respectively. Additionally, the protection of the redox ability in cascade dual Z-scheme heterostructures is demonstrated using the carrier transfer speeds through non-adiabatic molecular dynamics (NAMD)⁴⁰ simulations. The Gibbs free energy changes (ΔG) indicated that HERs and OERs were thermodynamically feasible. Remarkably, the HER and OER with Bi/HfSeTe/ZrSe₂-II can proceed spontaneously in a neutral environment because the potential energies of the photogenerated electrons and holes were larger than the ΔG's in the HER and OER, respectively. Therefore, these trilayer heterostructures had competitive potential to achieve high STH efficiency through the cascade dual Z-scheme.

2. Computational methods

The HfSeTe monolayer was constructed by replacing all Se atoms on the same side of the HfSe₂ monolayer with Te atoms. The present HfSeTe, ZrSe₂, and InAs₃ monolayers were with the symmetry of the p3m1 space group, and the Bi monolayer belonged to the p6m2 space group, as shown in Fig. S1.† Trilayer heterostructures were constructed by adding the third monolayer to the top or bottom of HfSe₂/ZrSe₂ or HfSeTe/ZrSe₂ bilayer heterostructures. For all heterostructures containing the HfSeTe monolayer, we also considered two different configurations (HfSeTe monolayer rotating 180° along the y direction), which were represented by HfSeTe/ZrSe₂-I, HfSeTe/ZrSe₂-II, ZrSe₂/HfSeTe/ZrSe₂-I, HfSeTe/ZrSe₂/HfSeTe-II, HfSeTe/ZrSe₂/HfSeTe-III, ZrSe₂/HfSeTe/ZrSe₂, Bi/HfSeTe/ZrSe₂-I, Bi/HfSeTe/ZrSe₂-II, HfSeTe/ZrSe₂/Bi-I, HfSeTe/ZrSe₂/Bi-II, InAs₃/HfSeTe/ZrSe₂-I, InAs₃/HfSeTe/ZrSe₂-II, HfSeTe/ZrSe₂/InAs₃-I, and HfSeTe/ZrSe₂/InAs₃-II. The interlayer distances (d) and formation energies (E_f) for 16 configurations are listed in Table S1.†

All calculations for the geometrical optimization and electronic and optical properties were realized in the Vienna ab intitio simulation package (VASP).⁴¹ The projector augmented wave⁴² pseudopotentials in combination with the generalized gradient approximation with Perdew–Burke–Ernzerhof⁴³ and Heyd–Scuseria–Ernzerhof (HSE06)⁴⁴ hybrid functionals were used. The dipole correction was added along the z direction in all calculations to correct the potential and force because of the asymmetric monolayers in the heterostructures. The cutoff energy was used at 550 eV for the plane wave. The density functional dispersion correction (DFT-D4)^45,46 was used to describe the van der Waals interactions. The energy and force convergence standards were selected as 10⁻⁶ eV and 0.01 eV Å⁻¹, respectively. Geometric structures were optimized and static calculations of electronic properties were performed using HSE06 with a 3 × 3 × 1 and 5 × 5 × 1 k-mesh, respectively. Ab initio molecular dynamics (AIMD) simulations for the screened structures lasting 10 ps at 300 K based on the Nose–Hoover thermostat and a canonical ensemble (NVT)^47,48 were conducted to confirm the thermodynamic stability of the heterostructures. NAMD simulations combined with decoherence-induced surface hopping (DISH)⁴⁹ methods implemented in the Hefei-NAMD code⁴⁰ were used to study the migration pathway and lifetimes of the photogenerated carriers. For the DISH simulation, we selected 100 random initial configurations and sampled 2000 trajectories, expanding the simulation time to 10 ps.

The calculation methods and details for the η′_STH's, optical absorption, carrier mobility, ΔG's in the HER and OER, and NAMD simulation are presented in the ESI.†

3. Results and discussion

3.1 Bilayer heterostructures composed of HfSe₂ and ZrSe₂ monolayers

HfSe₂ and ZrSe₂ monolayers were prepared in the experiment and showed excellent thermal and optical properties,^33,50 whereas the HfSe₂/ZrSe₂ heterostructure³⁶ was found to have a type-I band alignment. The CBM and VBM contributed by the ZrSe₂ monolayer did not match the overall water splitting conditions. To manipulate the photocatalyst performance, we constructed HfSe₂/ZrSe₂/HfSe₂ and ZrSe₂/HfSe₂/ZrSe₂ sandwich configurations, as shown in Fig. 1a and d. The negative formation energies (E_f's) of −35.74 and −37.82 meV Å⁻² indicated that they were stable in energy. The band structures and projected density of states (PDOS) are presented in Fig. 1b and e. They showed that the band of the sandwich configurations changed into a dual type-I arrangement. The charge transfer between the adjacent monolayers was decided by the direction of the built-in electron field (E_in)⁵¹ through Bader charge analysis⁵² and plane-integrated charge density difference (Δρ). As shown in Fig. S1a,† the charge transfer of 0.0012 and 0.0016 |e| occurs from the bottom and top HfSe₂ to the ZrSe₂ monolayer, together with the accumulated electrons on both sides of the ZrSe₂ monolayers, given by Δρs, indicating that the E_in directions between the two interfaces of the HfSe₂/ZrSe₂/HfSe₂ heterostructure were from the HfSe₂ to the ZrSe₂ monolayers. As shown in Fig. 1c, the photogenerated electrons in the CBM of ZrSe₂ transferred into the CBM of HfSe₂ monolayers, whereas the holes in the VBM of HfSe₂ transferred into the VBM of the ZrSe₂ monolayer. Therefore, the HER occurred in the CBMs of the two HfSe₂ monolayers, and the OER was driven by the middle ZrSe₂ monolayer.

Fig. 1 The geometric structures, band alignments, projected density of states, and the schemes for HERs and OERs. (a)–(c) HfSe₂/ZrSe₂/HfSe₂, and (d)–(f) ZrSe₂/HfSe₂/ZrSe₂.

For ZrSe₂/HfSe₂/ZrSe₂, Fig. S1b† demonstrates that 0.0015 and 0.0014|e| transferred from the two ZrSe₂ monolayers into the HfSe₂ one. Combining the band alignment and E_in at the two interfaces, the photogenerated electrons in the CBMs of the two ZrSe₂ monolayers were found to spontaneously transfer into the CBM of the HfSe₂ monolayer, whereas the holes in the VBM of the HfSe₂ monolayer transferred into the VBMs of the two ZrSe₂ monolayers (Fig. 1f). Therefore, the electrons in the CBM of the HfSe₂ and the holes in the VBM of the ZrSe₂ monolayers proceeded to undergo the HER and OER, respectively.

The absolute band edges can be evaluated by the following equations:

E^Abs_CBM = E^HSE06_CBM − V_vac (1)

E^Abs_VBM = E^HSE06_VBM − V_vac (2)

where E^HSE06_CBM/ E^HSE06_CBM represent the energies of the CBM and VBM calculated by the HSE06 functional, respectively, and V_vac represents the values obtained from the electrostatic potential plots, as shown in Fig. S2 and S3.† Unfortunately, the E^Abs_CBM's cannot match the HER condition, although the E^Abs_VBM's of the HfSe₂/ZrSe₂/HfSe₂ and ZrSe₂/HfSe₂/ZrSe₂ configurations can satisfy the OER requirement.

3.2 Bilayer HfSeTe/ZrSe₂ and trilayer HfSeTe/ZrSe₂/HfSeTe and ZrSe₂/HfSeTe/ZrSe₂ sandwich heterostructures

The electronic properties of monolayers and heterostructures can be significantly controlled by doped atoms.^39,53 Thus, the heterostructure comprising the Te-doped HfSe₂ monolayer, i.e., HfSeTe, was explored. The geometric structure, band alignment, and PDOS of the HfSeTe monolayer are shown in Fig. S4a and b.† The present direct bandgap of 0.39 eV of the HfSeTe monolayer was close to the previous ones of 0.44 ⁵⁴ and 0.47 eV,⁵⁵ confirming that the present theoretical level was reliable. The HfSeTe monolayer can also be synthesized by chemical vapor deposition or conventional flux methods experimentally, such as the fabrication of MoSSe ⁵⁶ and MoSeTe.⁵⁷ Accordingly, we constructed bilayer and trilayer heterostructures by using the HfSeTe and ZrSe₂ monolayers. Nowadays, the MoSSe/MoS₂,⁵⁸ MoS₂/WSe₂,⁵⁹ and ZrSe₂/MoSe₂ ⁶⁰ heterostructures are synthesized by mechanical exfoliation, chemical vapor deposition, and dry transfer methods, so the bilayer heterostructure of HfSeTe/ZrSe₂ may be synthesized in the same ways because of the similar structures. We considered two configurations of the HfSeTe/ZrSe₂ heterostructure, as shown in Fig. 2a and d. The negative E_f's of −21.65 and −19.48 meV Å⁻² meant that the HfSeTe/ZrSe₂ heterostructures can be synthesized through an exothermic process. The insignificant deformation of the geometric structures in the AIMD simulations in Fig. S5a and b† indicated that they were thermodynamically stable. Staggered band alignments were observed for the HfSeTe/ZrSe₂-I and HfSeTe/ZrSe₂-II configurations, as shown in Fig. 2b and e. The E_in directions from HfSeTe to the ZrSe₂ monolayer in the heterostructures can propel the electrons transferring from the ZrSe₂ into the HfSeTe monolayer, as shown in Fig. S1c and d.† Therefore, the photogenerated electrons in the CBM of the ZrSe₂ monolayer recombined with the holes in the VBM@HfSeTe. As a result, direct Z-schemes formed with the HER proceeding on the CBM@HfSeTe and the OER on the VBM@ZrSe₂, respectively. However, as presented in Fig. 2c and f, the CBM of HfSeTe/ZrSe₂-II cannot satisfy the HER condition, whereas the HER overpotential of 0.03 eV for HfSeTe/ZrSe₂-I implied a weak reduction ability.

Fig. 2 The geometric structures, band alignments, project density of states, and the schemes for HERs and OERs. (a)–(c) HfSeTe/ZrSe₂-I, (d)–(f) HfSeTe/ZrSe₂-II, (g)–(i) HfSeTe/ZrSe₂/HfSeTe-I, (j)–(l) HfSeTe/ZrSe₂/HfSeTe-II, (m)–(o) HfSeTe/ZrSe₂/HfSeTe-III, and (p)–(r) ZrSe₂/HfSeTe/ZrSe₂.

Furthermore, three sandwich configurations of HfSeTe/ZrSe₂/HfSeTe-I, HfSeTe/ZrSe₂/HfSeTe-II, and HfSeTe/ZrSe₂/HfSeTe-III were considered, as shown in Fig. 2g, j and m. The band alignments in Fig. 2h, k and n showed a staggered and arrow-down feature, whereas the directions of E_in between the adjacent monolayers were from the HfSeTe to the ZrSe₂ monolayers. As shown in Fig. 2i, l and o, all three configurations were suitable for constructing a dual Z-scheme with HERs proceeding on the HfSeTe monolayers and OERs on the middle ZrSe₂ monolayer. Unlike the single V_vac's for HfSeTe/ZrSe₂/HfSeTe-I and HfSeTe/ZrSe₂/HfSeTe-III, the HfSeTe/ZrSe₂/HfSeTe-II had different vacuum energy levels on the two surfaces. Thus, we evaluated E^Abs_CBM and E^Abs_VBM with different V_vac's according to eqn (1) and (2). Results demonstrated that only one of the two CBMs relative to the two HfSeTe monolayers can straddle the hydrogen reduction potential, although all VBMs of the three configurations can drive the OER. Consequently, these heterostructures were not considered in the following discussion because they were similar to the bilayer heterostructures discussed in the above sections.

The trilayer sandwich configuration ZrSe₂/HfSeTe/ZrSe₂ had a staggered arrow-up type band alignment, and the directions of E_in were also from the HfSeTe into the ZrSe₂ monolayer, as shown in Fig. 2q and S1h.† The photocatalytic dual Z-scheme with the HER on CBM@HfSeTe and the OER on both ZrSe₂ monolayers is shown in Fig. 2r. However, CBMs@HfSeTe in Table S1,† regardless of any one of the two V_vac's, failed to match the HER condition of −4.44 eV. Therefore, these sandwich configurations cannot drive the HER. The sandwich configurations, which were relatively more easily prepared than the trilayer heterostructures with three different monolayers, conferred difficulty in achieving an efficient photocatalytic overall water-splitting performance, although the dual Z-scheme can be constructed for some of them.

3.3 Dual Z-scheme heterostructures comprising Bi/InAs₃, HfSeTe, and ZrSe₂ monolayers

Trilayer Bi/HfSeTe/ZrSe₂ and InAs₃/HfSeTe/ZrSe₂ heterostructures were constructed by adding the InAs₃ or Bi monolayer onto the bilayer HfSeTe/ZrSe₂ heterostructure, respectively. The synthesis procedure similar to the bilayer heterostructures can also be used to prepare trilayer heterostructures, as demonstrated by the preparations of the BiFeO₃/g-C₃N₄/WO₃,²⁴ Ag₃PO₄/AgBr/g-C₃N₄,²⁸ and V₂O₅/CdS/CoS₂ heterostructures.³⁰ Thus, the present Bi/HfSeTe/ZrSe₂ and InAs₃/HfSeTe/ZrSe₂ heterostructures may be fabricated in a similar way. The InAs₃ and Bi monolayers optimized and calculated by HSE06 are shown in Fig. S4e–h.† The lattice constant and bandgap of 4.22 Å and 1.02 eV for the Bi monolayer approached the theoretical 4.24 Å and 1.16 eV obtained by Singh et al.,⁶¹ whereas those for the InAs₃ monolayer were 7.85 Å and 1.19 eV, respectively. The CBMs of the two monolayers can match the HER condition, but the VBMs cannot satisfy the OER one, as demonstrated in Table S2.† Considering that the primary cells of the two monolayers substantially differed from the bilayer HfSeTe/ZrSe₂ heterostructures, we constructed trilayer heterostructures by using the 2 × 2 supercell of the HfSeTe/ZrSe₂ heterostructures and the √3 × √3 supercell of Bi or the primary cell of the InAs₃ monolayer. As a result, the lattice mismatch ratios of the Bi/HfSeTe/ZrSe₂ and InAs₃/HfSeTe/ZrSe₂ heterostructures were <1.5%.

Eight different configurations were considered and represented by Bi/HfSeTe/ZrSe₂-I, Bi/HfSeTe/ZrSe₂-II, HfSeTe/ZrSe₂/Bi-I, HfSeTe/ZrSe₂/Bi-II, InAs₃/HfSeTe/ZrSe₂-I, InAs₃/HfSeTe/ZrSe₂-II, HfSeTe/ZrSe₂/InAs₃-I, and HfSeTe/ZrSe₂/InAs₃-II. Their geometric structures, band structures, and carrier migration pathways are shown in Fig. S7 and S3.† The negative E_f's in Table S1† demonstrated that the heterostructures are stable in energy. The band alignments of HfSeTe/ZrSe₂/Bi-I, HfSeTe/ZrSe₂/Bi-II, and HfSeTe/ZrSe₂/InAs₃-I were arrow-down, whereas those of HfSeTe/ZrSe₂/InAs₃-II were arrow-up (Fig. S7b, e, k, n†). The InAs₃/HfSeTe/ZrSe₂-II band alignment was the type-I and type-II on the two interfaces, respectively (Fig. S7h†), thereby losing the conditions necessary to form a dual Z-scheme. The E_in directions were from the bottom and top layers to the middle layer in the above five configurations, as shown in Fig. S1k, l, n, o and p.† The photocatalytic dual Z-schemes for HfSeTe/ZrSe₂/Bi-I, HfSeTe/ZrSe₂/Bi-II, and HfSeTe/ZrSe₂/InAs₃-I are shown in Fig. S7c, f and l.† Unfortunately, CBMs@HfSeTe cannot match the HER condition for the three trilayer heterostructures, although the VBMs in the middle layer satisfied the OER requirement. As shown in Fig. S7i,† CBM@ZrSe₂ in InAs₃/HfSeTe/ZrSe₂-II cannot meet the HER condition. As for the photocatalytic scheme of HfSeTe/ZrSe₂/InAs₃-II, the electrons in CBM@ZrSe₂ transferred into the CBMs of the InAs₃ and HfSeTe monolayers, and the holes in the VBM of the InAs₃ and HfSeTe transferred into VBMs@ZrSe₂, as presented in Fig. S7o.† Thus, the carrier migration in HfSeTe/ZrSe₂/InAs₃-II was a dual conventional type-II scheme rather than a dual Z-scheme. However, CBM@HfSeTe and VBM@ZrSe₂ cannot straddle the H⁺/H₂ and H₂O/O₂ potentials, respectively. As a result, HfSeTe/ZrSe₂/Bi-I, HfSeTe/ZrSe₂/Bi-II, InAs₃/HfSeTe/ZrSe₂-II, HfSeTe/ZrSe₂/InAs₃-I, and HfSeTe/ZrSe₂/InAs₃-II cannot drive overall photocatalytic water splitting.

Notably, cascade band alignments were observed for Bi/HfSeTe/ZrSe₂-I, Bi/HfSeTe/ZrSe₂-II, and InAs₃/HfSeTe/ZrSe₂-I, as shown in Fig. 3b, e and h. Results of Bader charge analysis and Δρ in Fig. S1i, j and m† demonstrated that the E_in directions at the two interfaces of the heterostructures were arranged as bottom → middle → top monolayers. Accordingly, the electrons in CBM@ZrSe₂ recombined with the holes in VBM@HfSeTe, and the electrons in CBM@HfSeTe recombined with the holes in VBM@Bi or VBM@InAs₃. The outcome was the formation of a cascade dual Z-scheme, as shown in Fig. 3c, f and i. Therefore, the HER and OER were driven by CBM@Bi or CBM@InAs₃ and VBM@ZrSe₂, and all band edges of Bi/HfSeTe/ZrSe₂-I, Bi/HfSeTe/ZrSe₂-II, and InAs₃/HfSeTe/ZrSe₂-I can meet the conditions of the HER and OER, respectively. The working CBMs for HERs on Bi/HfSeTe/ZrSe₂-I and Bi/HfSeTe/ZrSe₂-II had larger overpotentials than those of InAs₃/HfSeTe/ZrSe₂-I, whereas their overpotentials for the OER were smaller than those of InAs₃/HfSeTe/ZrSe₂-II. As shown in Fig. S5c–e,† AIMD simulations at 300 K demonstrated that the three trilayer heterostructures were thermodynamically stable. Moreover, the stability of the considered heterostructures in the solution was explored by optimizing the geometric structures of the Bi/HfSeTe/ZrSe₂-I, Bi/HfSeTe/ZrSe₂-II, and InAs₃/HfSeTe/ZrSe₂-II trilayer heterostructures in the solution environments of water, formic acid, and acetone solvents using VASPsol,⁶² respectively. As shown in Fig. S6,† the structures of the three configurations were obviously unchanged in the three neutral, acidic, and alkaline solutions, respectively. The solvation energy (ΔE_sol) of the three trilayer heterostructures, summarized in Table S3,† was defined by ΔE_sol = E_sol − E_vac. In this equation, E_sol and E_vac represent the total energy of the heterostructures with and without solution, respectively. The negative ΔE_sol's of the three trilayer heterostructures indicated that they were also stable in the solutions. Accordingly, we further explored the photocatalyst performance of Bi/HfSeTe/ZrSe₂-I, Bi/HfSeTe/ZrSe₂-II, and InAs₃/HfSeTe/ZrSe₂-I.

Fig. 3 The geometric structures, band alignments, project density of states, and the schemes for HERs and OERs. (a)–(c) Bi/HfSeTe/ZrSe₂-I, (d)–(f) Bi/HfSeTe/ZrSe₂-II, and (g)–(i) InAs₃/HfSeTe/ZrSe₂-I.

3.4 STH conversion efficiencies and effects of strain engineering

The STH conversion efficiencies η′_STH's of the three trilayer heterostructures can be calculated by⁶³where P (ℏω) is the AM1.5 G solar-energy flux at the photoenergy hω, E_g is the larger one of the bandgaps projected on the monolayers, and ΔG is the potential difference of 1.23 eV for water splitting. Δφ is the electrostatic potential difference between the two outer surfaces, and E is the energy of photos that can actually be utilized for water splitting and evaluated by

The η′_STH's for the three trilayer heterostructures Bi/HfSeTe/ZrSe₂-II, Bi/HfSeTe/ZrSe₂-II, and InAs₃/HfSeTe/ZrSe₂-I were 40.52%, 39.47%, and 41.04%, respectively. They were much higher than the 22.08% of the corresponding bilayer HfSeTe/ZrSe₂-I. According to eqn (S4)–(S7),† the smaller value of the maximum one of the bandgaps of monolayers and the larger overpotentials for the HER and OER were responsible for the high η′_STH. For the present trilayer heterostructures, the narrower bandgaps were the dominant factor causing the higher η′_STH than that of the bilayer one because the overpotentials of the working CBMs and VBMs of the trilayer heterostructures did not substantially increase. Notably, the η′_STH's of Bi/HfSeTe/ZrSe₂-I, Bi/HfSeTe/ZrSe₂-II, and InAs₃/HfSeTe/ZrSe₂-II were much larger than those of ZrS₂/MoSSe (6.4%),⁶⁴ HfSe₂/InSe (25.24%),¹⁵ and AlP₃/GaP₃ (16.89%).⁶⁵ Moreover, the η′_STH can also be compared with the experimental data if the AQE and experimental STH conversion efficiency (STH_exp) are available in the literature,⁶⁶ although the ideal quantum efficiency was used in eqn (3). For example, the GaN:Mg/InGaN:Mg nanowires⁶⁷ and Rh/Cr₂O₃/Co₃O₄-loaded InGaN/GaN nanowires⁶⁸ had STH_exp's of 3.3% and 9% corresponding to the η′_STH's of 7.5% and 17.7%, respectively. They were apparently lower than those of the present trilayer heterostructures.

As shown in Fig. 4a, the Bi/HfSeTe/ZrSe₂-II and InAs₃/HfSeTe/ZrSe₂-I heterostructures can maintain stability within the range of −3% to +4% biaxial strain because their strain energy E_s showed a quadratic character. The deformations of Bi/HfSeTe/ZrSe₂-I cannot maintain elasticity under −3% compressed strain, and only the range of −2% to +4% strains was considered for this heterostructure. As shown in Fig. 4b–d and listed in Tables S4–S6,† the bandgaps and overpotentials changed under the strains. As a result, the η′_STH increased to 41.53% and 41.12% for Bi/HfSeTe/ZrSe₂-I and Bi/HfSeTe/ZrSe₂-II under 1% biaxial strain, respectively, whereas the other strains reduced the η′_STH's because of the increased bandgap of the monolayers and the decreased overpotentials of HERs and OERs. For the same reasons, the η′_STH of InAs₃/HfSeTe/ZrSe-I was boosted under −3% to −1% compressed strains but decreased under the tensile strains. The maximum η′_STH of 43.57% for InAs₃/HfSeTe/ZrSe-I can be achieved under −2% compressed strains. Overall, most of the considered strains resulted in obviously decreased η′_STH, although smaller lifts were also observed for the light strains. Therefore, heavy strains, regardless of being compressive or tensile, should be avoided to maintain the high η′_STH's of the present trilayer heterostructures.

Fig. 4 The strain engineering for heterostructures. (a) The strain energies for Bi/HfSeTe/ZrSe₂-I, Bi/HfSeTe/ZrSe₂-II, and InAs₃/HfSeTe/ZrSe₂-I. (b)–(d) The potentials of band edges and STH conversion efficiency η′_STH of Bi/HfSeTe/ZrSe₂-I, Bi/HfSeTe/ZrSe₂-II, and InAs₃/HfSeTe/ZrSe₂-I under biaxial strains. The blue balls represent η′_STH.

3.5 Dynamics of photogenerated carriers for cascade dual Z-scheme heterostructures

To confirm the photocatalyst performance of Bi/HfSeTe/ZrSe₂-I, Bi/HfSeTe/ZrSe₂-II, and InAs₃/HfSeTe/ZrSe₂-I, we performed NAMD simulations by using the Hefei-NAMD⁴⁰ code (the details in ESI†) which has been used to analyze the carrier dynamics theoretically for the experimental observations of MoS₂/MoSe₂,^69,70 ReSe₂/MoS₂,^71,72 and MoS₂/WS₂.^73,74 As shown in Fig. 5a–c, nine different processes occurred in the trilayer heterostructure, including the electron transfer (①②), hole transfer (③④), interlayer e–h recombination (⑤⑥), and intralayer e–h recombination (⑦⑧⑨). Fig. 6 demonstrates that carriers tended to transfer into the adjacent states according to the evolution of the spatial distributions and the average energies of the carriers in each CBM and VBM of the three monolayers at 300 K for 10 ps based on the DISH.⁴⁹ Moreover, the carrier energy relaxation processes in the three trilayer heterostructures had different time scales, which can be understood through the nonadiabatic coupling (NAC) elements between different states.^75,76 In general, a large NAC corresponds to a higher hopping probability. According to eqn (S9),† a larger electron–phonon (e–p) coupling, a smaller energy gap, and a faster velocity of nuclei lead to a larger NAC matrix element. As shown in Fig. 5d–f, the Fourier transforms of the normalized autocorrelation function (ACF) for the fluctuations of the energy difference between the initial and final states were calculated and used to estimate the contribution of e–p coupling and nuclear velocity.⁷⁰ The low frequency and weak intensity peaks in the Fourier energy spectrum dominated the slow dephasing process,^77,78 and the long pure-dephasing time was also beneficial for ultrafast carrier transfer. As shown in Fig. S8 and S9,† the low-frequency modes were similar among the six processes in Bi/HfSeTe/ZrSe₂-I and Bi/HfSeTe/ZrSe₂-II. The peaks at 66 and 103 cm⁻¹ correspond to the out-of-plane vibrations of the Hf–Se and Hf–Te bonds; the peaks at 140 and 202 cm⁻¹ correspond to the out-of-plane vibration of Se, Te, Hf, and Zr atoms; and the side peaks near 262 cm⁻¹ correspond to the vibration of Se and Zr atoms in the ZrSe₂ monolayer. This finding demonstrated their approximately equal nuclear velocities. As shown in Fig. S10,† all low-frequency vibration modes observed for the six processes in InAs₃/HfSeTe/ZrSe₂-I were contributed by the out-of-plane vibrations of all bonds, which increased the e–p coupling, causing fast carrier transfer.

Fig. 5 The time-dependent evolution of the Kohn–Sham orbital, Fourier transforms of normalized ACF of the energy difference fluctuation between the initial and final states, and averaged values of NAC between different states for (a), (d) and (f) Bi/HfSeTe/ZrSe₂-I, (b), (e) and (g) Bi/HfSeTe/ZrSe₂-II, and (c), (f) and (h) InAs₃/HfSeTe/ZrSe₂-I. The purplish red, orange, and green lines in (a), (b), and (c) represent the states dominated by Bi, HfSeTe, and ZrSe₂ monolayers, respectively. The inset diagram shows nine photogenerated carrier dynamics pathways: the electron transfer (➀➁), the hole transfer (➂➃), the interlayer electron–hole recombination (➄➅), and the intralayer electron–hole recombination (➆➇➈).

Fig. 6 The time-dependent evolution of the electron/hole spatial localization and distribution in each state in Bi/HfSeTe/ZrSe₂-I, Bi/HfSeTe/ZrSe₂-II, and InAs₃/HfSeTe/ZrSe₂-I. The purplish red, blue, orange, and green lines represent the energy states dominated by Bi, InAs₃, HfSeTe, and ZrSe₂ monolayers, respectively. The descent or ascent lines represent the evolution of the averaged energy of the carriers in the considered states. (a), (g) and (m) CBM@Bi/InAs₃, (b), (h) and (n) CBM@HfSeTe, (c), (i) and (o) CBM@ZrSe₂, (d), (j) and (p) VBM@ZrSe₂, (e), (k) and (q) VBM@HfSeTe, and (f), (l) and (r) VBM@Bi/InAs₃.

As presented in Fig. 5f–h and listed in Tables S7–S9,† the strong NAC originating from the narrow bandgaps between the adjacent states accelerated the carrier transfer into the involved states. A few peaks existed in the spectral density of the six states of Bi/HfSeTe/ZrSe₂-I due to the gentle fluctuations of Kohn–Sham orbitals, demonstrating that the slight vibration of atoms contributed minimally to the NAC, as shown in Fig. 5f. Therefore, all energy relaxation processes in Bi/HfSeTe/ZrSe₂-I were slow, and the time scale difference in the six energy relaxation processes was nearly 10 times, which was averse to the transfer of carriers in the heterostructure and promoted the photocatalytic process, as shown in Fig. 6a–f. The numerous strong peaks, as well as the small bandgaps between CBM@Bi and the adjacent state in the Bi/HfSeTe/ZrSe₂-II, further led to the strongest NAC (47.17 meV) in the six energy states, as shown in Fig. 5g. Hence, the electron relaxation in the highest CBM was the quickest one among the six processes of Bi/HfSeTe/ZrSe₂-II, as shown in Fig. 6g–l. Similarly, the NAC between VBM@ZrSe₂ and the adjacent states was the strongest one (48.63 meV), as shown in Fig. 5h, so entire hole relaxation on this energy level was the quickest one among the six processes of InAs₃/HfSeTe/ZrSe₂-I, as shown in Fig. 6m–r. Moreover, all energy relaxation processes in Bi/HfSeTe/ZrSe₂-II were in the same time scale, which benefited the carrier cycling and were utilized in the photocatalysis.

The carrier population evolution relative to time in Fig. 7 demonstrated a characteristic of exponential function among the six transfer processes of the interlayer carriers. As in a previous analysis method,^69,79 we fit the time population evolutions with the function f(t) = exp(−t/τ) to understand the evolution tendency. The τ corresponding to the carrier population of 1/e was defined as the carrier lifetime because the transfer process corresponding to this carrier population of an electronic state was considered irreversible and over. Generally, the slow carrier transfer in CBM@Bi/CBM@InAs₃ and VBM@ZrSe₂ was beneficial for the carriers to participate in the redox reaction of the Z-schemes. As shown in Fig. 7, the longest carrier lifetimes of 14.64 and 126.77 ps were attributed to Bi/HfSeTe/ZrSe₂-I among the three heterostructures, indicating that the redox abilities of the two energy levels can be effectively protected. The Z-schemes with Bi/HfSeTe/ZrSe₂-II and InAs₃/HfSeTe/ZrSe₂-I were more efficient than that with Bi/HfSeTe/ZrSe₂-I owing to the quick carrier transfer migrations during the interlayer e–h recombination processes in CBM@HfSeTe, VBM@HfSeTe, CBM@ZrSe₂, and VBM@Bi/InAs₃ in the former two heterostructures. When the carrier migrations and recombination were involved, InAs₃/HfSeTe/ZrSe₂-I was superior to the others.

Fig. 7 The carrier transfer dynamics in Bi/HfSeTe/ZrSe₂-I, Bi/HfSeTe/ZrSe₂-II, and InAs₃/HfSeTe/ZrSe₂-I. (a), (d) and (g) CBM@Bi/InAs₃ and CBM@HfSeTe, (b), (e) and (h) VBM@ZrSe₂ and VBM@HfSeTe, and (c), (f) and (i) CBM@ZrSe₂ and VBM@Bi/InAs₃.

3.6 Gibbs free energies of the HER and OER

According to the Sabatier principle,⁸⁰ the closer the Gibbs free energy ΔG is to zero, the easier the reaction proceeds. As shown in Table S10,† the absorbed energy of the H atom on every unequal position demonstrated that the H atom preferred to adsorb onto the Bi₁ atom in Bi/HfSeTe/ZrSe₂-I and Bi/HfSeTe/ZrSe₂-II and on the In atom in InAs₃/HfSeTe/ZrSe₂-I. The adsorption sites with the lowest energy were selected to calculate the ΔGs for the HER and OER. The results are presented in Fig. S11.† The potential of the photogenerated electrons (U_e) for the HER was measured from the CBM to the H⁺/H₂ potential, whereas that of the photogenerated holes (U_h) for the OER was determined by the difference between the VBM and the potential of H⁺/H₂.^81,82 When the ΔG_H*'s were less than eU_es, the HER proceeded spontaneously. Similarly, the OER spontaneously proceeded when all ΔG's of the intermediates in the OER (ΔG_OER's) were less than the eU_h's. Considering that pH can impact the redox potentials of overall water splitting,⁸³ we calculated the ΔG's for the HER and OER with pH 0–14 according to the method described in the ESI.†

As shown in Fig. 8, the eU_e's with Bi/HfSeTe/ZrSe₂-I, Bi/HfSeTe/ZrSe₂-II, and InAs₃/HfSeTe/ZrSe₂-I were 0.81, 0.88, and 0.32 eV, respectively. The HERs at pH 0 on Bi/HfSeTe/ZrSe₂-I and Bi/HfSeTe/ZrSe₂-II can spontaneously proceed because the ΔG_*H's of 0.68 and 0.41 eV were smaller than the corresponding eU_e's. However, the ΔG_*H of 0.34 eV with InAs₃/HfSeTe/ZrSe₂-I was 0.02 eV larger than the eU_e, indicating that the HER cannot spontaneously proceed. pH can affect the redox potentials for the HER and OER. As shown in Fig. S12,† the HERs on Bi/HfSeTe/ZrSe₂-I and Bi/HfSeTe/ZrSe₂-II spontaneously proceeded within the pH ranges of 0.0–2.37 and 0.0–7.97, respectively, although the HER on InAs₃/HfSeTe/ZrSe₂-I failed in all pH values. However, the ΔG_*H's with Bi/HfSeTe/ZrSe₂-I were smaller than the reported values that have been experimentally determined on some materials (e.g., 1.5 eV for Mo₂CO₂ ⁸⁴) for HERs, indicating that all of them were feasible if additional energy was provided. During the calculations of the Gibbs free energies of (ΔG_max's), the reactions with the *OH intermediates were the rate-limiting steps for all considered OERs. The OERs with the three heterostructures had 2.13, 2.14, and 2.13 eV of ΔG_max's, and spontaneously proceed within the pH ranges of 6.44–14, 6.78–14, and 3.22–14, as shown in Fig. S12.† If the HER and OER were involved, only Bi/HfSeTe/ZrSe₂-II can drive them to proceed spontaneously within pH 6.78–7.97.

Fig. 8 The Gibbs free energy changes for (a) HERs and (b) OERs at pH = 0 of Bi/HfSeTe/ZrSe₂-I, Bi/HfSeTe/ZrSe₂-II, and InAs₃/HfSeTe/ZrSe₂-I, respectively.

4. Conclusions

We constructed cascade dual Z-schemes with very high STH efficiency by using the trilayer Bi/HfSeTe/ZrSe₂-I, Bi/HfSeTe/ZrSe₂-II, and InAs₃/HfSeTe/ZrSe₂-I heterostructures after examining eight trilayer heterostructures. We found that the bilayer or trilayer heterostructures comprising HfSe₂ and ZrSe₂ monolayers were type-I or dual type-I band alignments and cannot drive the HERs. Meanwhile, the HfSeTe/ZrSe₂-I heterostructure met the overall water splitting requirements but had low overpotentials for the HER. For the four sandwich configurations formed with the HfSeTe and ZrSe₂ monolayers, the CBMs and VBMs cannot simultaneously match the potential conditions of the HER and OER. The cascade dual Z-schemes with η′_STH's of 40.52%, 39.47%, and 41.04% were constructed for Bi/HfSeTe/ZrSe₂-I, Bi/HfSeTe/ZrSe₂-II, and InAs₃/HfSeTe/ZrSe₂-I after examining eight configurations obtained by adding the Bi or InAs₃ monolayer into the bilayer HfSeTe/ZrSe₂ heterostructures. Results of NAMD simulations demonstrated that the redox abilities of the three cascade dual Z-scheme heterostructures, especially for Bi/HfSeTe/ZrSe₂-I, were protected because of the slow carrier migrations in CBM@Bi(InAs₃) and VBM@ZrSe₂. The ΔG_*H's and ΔG_OER's demonstrated the thermodynamic feasibility of the HERs and OERs driven by the three trilayer heterostructures. Remarkably, Bi/HfSeTe/ZrSe₂-II can drive the HER and OER to proceed spontaneously at pH 6.78–7.97. Therefore, Bi/HfSeTe/ZrSe₂-II was a candidate for developing an efficient photocatalyst for hydrogen production from overall water splitting. The cascade dual Z-scheme was a promising mechanism to achieve high STH efficiency and worth extending to develop more photocatalysts.

Author contributions

X. Q. Wan: data curation, investigation, writing-original draft preparation. C. L. Yang: conceptualization, methodology, supervision, writing – reviewing and editing. X. H. Li: methodology. Y. L. Liu: visualization. W. K. Zhao: software.

Conflicts of interest

The authors declare no competing financial interest.

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 12374232). C. L. Yang acknowledges the Xinjiang Tianchi Talent Program (2023).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3ta06755f

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