Building MoSi₂N₄/ZrS₂ Heterostructure to Regulate Electron Transport for Enhancing Hydrogen Production Efficiency

Abstract

The production of hydrogen through photocatalytic water splitting has attracted considerable interest as a means of hydrogen energy. The electron–hole recombination in photocatalysts can affect the efficiency of photocatalytic hydrogen production. Therefore, the rational regulation of photogenerated electron transport has become an effective approach to enhancing hydrogen production efficiency and addressing energy challenges. Based on density functional theory (DFT) and nonadiabatic molecular dynamics (NAMD) simulations, the MoSi₂N₄/ZrS₂ (HfS₂) heterojunctions were built. The electronic properties, optical properties, interface properties, carrier transport after illumination, and photocatalytic performance of the heterojunction are investigated. The results indicate that after constructing the heterojunction, light absorption and carrier mobility significantly increased. The electron–hole pairs were effectively separated, and hydrogen production efficiency has shown a marked increase. Furthermore, the corresponding mechanistic explanation was provided. This study provides a theoretical foundation for the further development of efficient two-dimensional heterojunction photocatalysts.

1. Introduction

The increasing need for clean energy and ongoing worries about climate change and energy security make the research and use of renewable energy technologies essential. , The photocatalytic hydrogen production technology refers to the production of hydrogen gas using photocatalysts, abundant solar energy, and water. As a green and efficient hydrogen energy production technology, photocatalytic hydrogen production has attracted wide attention in both academic and industrial fields. , The photocatalyst plays a crucial role in the generation of hydrogen through water splitting. The catalyst’s light absorption capacity, , carrier transport rate, efficiency of separating photogenerated carriers, and other factors directly affect the efficiency of photocatalytic hydrogen production. Therefore, finding a low-cost and efficient photocatalyst is particularly important.

Semiconductor materials become the main focus of researchers due to possessing some properties of noble metals, such as high carrier mobility, but at a lower cost. Two-dimensional materials have more active sites available for photocatalytic hydrogen generation compared to one-dimensional and three-dimensional materials. Recently, Hong et al. successfully synthesized a novel semiconductor material, MoSi₂N₄, which possesses good environmental stability, high charge carrier mobility, and outstanding light absorption properties. Therefore, it is considered a highly promising semiconductor material for photocatalysis. Further studies by Bafekry et al. found that the monolayer MoSi₂N₄ has a significantly smaller electron effective mass than hole effective mass, a property that leads to higher electron mobility and predicts its potential application in photocatalytic water splitting. In a study by Zhong et al., it was found that the single-layer MoSi₂N₄ has excellent mechanical properties. In general, MoSi₂N₄ material is an excellent semiconductor photocatalyst due to its good light absorption capability and charge carrier mobility. The band edge of MoSi₂N₄ satisfies the oxidation–reduction potential necessary for photocatalytic hydrogen generation via water splitting. This indicates that MoSi₂N₄ has potential application value in the field of photocatalytic hydrogen production. However, MoSi₂N₄ still faces the issue of low efficiency in separating photogenerated carriers, which can impact the efficiency of photocatalytic hydrogen production. Constructing van der Waals heterojunctions can effectively promote the separation of electrons and holes, becoming a feasible strategy.

Currently, MoSi₂N₄ material has been utilized in the creation of van der Waals heterostructures with other materials, showing notable stability and enhanced performance. Zeng et al.’s study reveals that the C₂N/MoSi₂N₄ heterostructure exhibits good stability, and its band edges meet the redox potential required for photocatalytic water splitting, indicating potential application value in the field of photocatalytic water splitting. Zhao et al. have fabricated a WSi₂N₄/MoSi₂N₄ heterostructure, which exhibits enhanced light absorption and carrier mobility compared to monolayers. Zhang et al. have constructed a WSe₂/MoSi₂N₄ heterostructure that can significantly enhance the optoelectronic performance. All these results indicate that MoSi₂N₄ exhibits a high level of lattice suitability and can form heterojunctions. Their performances can be enhanced after the construction of heterojunctions. However, research on improving hydrogen production efficiency by using heterojunctions for photocatalytic water splitting is relatively scarce. Therefore, finding suitable structures to construct heterojunctions is of significant research value and is highly necessary.

In exploring potential materials to match MoSi₂N₄, transition metal–sulfur compounds , (MX₂, where M stands for transition metals and X for sulfur elements) have been considered. Previous studies have showed that ZrS₂ and HfS₂ possess exceptional electronic features, including high charge carrier mobility, good stability, etc. The lattice mismatch with MoSi₂N₄ is relatively small when constructing heterojunctions, leading to a stable geometric structure. Many studies have shown that the performances of ZrS₂ and HfS₂ are further enhanced after constructing heterojunctions. For example, Chen et al. have constructed a ZrS₂/HfSe₂ type-II heterostructure, and Patel et al. have constructed a ZrS₂/GaS heterojunction that effectively promotes the separation and transfer of charges, showing stronger light absorption than ZrS₂. Bai et al. have developed a direct Z-type heterostructure of arsenene/ZrS₂(HfS₂), which exhibits self-driven water splitting under light exposure. Zhu et al. constructed black phosphorus/HfS₂, which exhibits higher charge carrier mobility compared to monolayers, showing greater practical value. These results indicate that constructing heterojunctions using ZrS₂ and HfS₂ can enhance the performance of the single-phase materials. Although MoSi₂N₄, ZrS₂, and HfS₂ each exhibit excellent properties, whether the MoSi₂N₄/ZrS₂ (HfS₂) van der Waals heterostructures are superior to the single phase in terms of electronic and catalytic properties, in other words, whether it is possible to achieve an effect where 1 + 1 > 2 is an important research topic.

In this paper, on the basis of the density functional theory (DFT) and nonadiabatic molecular dynamics (NAMD) simulations, we systematically explored the electronic and optical properties of MoSi₂N₄, ZrS₂, HfS₂, and MoSi₂N₄/ZrS₂(HfS₂) heterostructures. This study also explored the electron transport mechanism at the interface of MoSi₂N₄/ZrS₂(HfS₂) heterostructures and the transfer of charge carriers after exposure to light. The study finds that the heterojunction exhibits higher carrier mobility and hydrogen production efficiency. Furthermore, we provided the corresponding mechanistic explanation. This research provides robust theoretical backing for the exploration of catalysts with high photocatalytic hydrogen production efficiency.

2. Computational Details

The first-principles calculations in this paper are based on DFT via VASP. , The projector-augmented wave (PAW) pseudopotential is applied in all calculations, with the cutoff energy of the plane wave set to 450 eV and generalized gradient approximation (GGA) with Perdew–Burke–Ernzerhof (PBE) to handle the exchange–correlation potential. In order to avoid interactions between neighboring heterostructures, a vacuum region of 30 Å along the z-direction is used, which is thick enough to neglect interactions between periodic layers. A 5 × 5 × 1 Γ-centered lattice in the first Brillouin zone is used for structural optimization of the lattice and calculation of electronic properties. The force convergence criterion is less than 0.01 eV/Å, and the energy convergence criterion is 10^–6 eV. Depolarization is taken into account in the calculation of the work function of the lattice cells. The Heyd–Scuseria–Ernzerhof (HSE06) mixing generalization is further used for a more accurate evaluation of the electronic and optical properties of all structural models. In order to check the thermodynamic and kinetic stability of the heterostructures, the ab initio molecular dynamics (AIMD) simulations at 300 K were performed to investigate the thermal stability of the configurations. The total simulation time was 6 ps with a step size of 1.5 fs per run. And phonon dispersion calculations were performed using the finite element displacement method implemented in the Phonopy program. The DFT-D3 method was chosen to describe the interlayer van der Waals (vdW) interactions. In order to predict more accurate optical properties, we use the GW + BSE method to obtain the absorption spectrum of the unit cells.

We have also calculated the formation energies of the two heterojunctions using eqs

$$E_{\mathrm{f}}=E_{\mathrm{H}\mathrm{e}\mathrm{t}}-E_{\mathrm{l}\mathrm{a}\mathrm{y}\mathrm{e}\mathrm{r}1}-E_{\mathrm{l}\mathrm{a}\mathrm{y}\mathrm{e}\mathrm{r}2}$$ 1

where E _Het denotes the energy of the heterojunction, and E _layer1 and E _layer2 denote the energies of the two monolayers, respectively, which were calculated using the fully relaxed geometries of the two monolayers separated from the heterojunction.

And the work function can reflect the charge transfer; the work function of the heterojunction is given by the following expression

$$\mathrm{\Phi }=E_{\mathrm{v}\mathrm{a}}-E_{\mathrm{F}}$$ 2

where E _va denotes the vacuum energy level, and E _F denotes the Fermi energy level.

The photoexcited carrier dynamics of the heterojunction is investigated by ab initio NAMD. Carrier transfer pathways and corresponding times are simulated using the Hefei-NAMD code, employing the fewest switches surface hopping (FSSH) method and time-dependent Kohn–Sham equations. Interfacial electron and hole transfer times as well as carrier recombination time simulations utilize the decoherence-induced surface hopping (DISH) method. First, the unit cell of the simulation system is constructed, and the VASP software is used to optimize the unit cell structure of the target system to obtain a stable configuration. Subsequently, based on a hybrid quantum-mechanical and classical-mechanical framework under the Born–Oppenheimer approximation, electrons are treated as a quantum subsystem, while atomic nuclei are regarded as classical particles, with nuclear quantum effects ignored (this approach is not suitable for low-temperature systems or light-atom systems such as hydrogen migration in H₂O). Molecular dynamics (MD) simulations are performed on the optimized structure to obtain a series of molecular dynamics trajectories. Finally, the structures at each time point over the last 2000 fs are intercepted, and single-electron self-consistent field (SCF) calculations are performed on each MD trajectory to obtain wave functions and energies. Relying on the completeness of the adiabatic state basis set, the fewest-switches algorithm is adopted, assuming that electronic state transitions are determined by instantaneous energy differences and coupling strengths, with the number of transitions minimized. Meanwhile, trajectory correlations are ignored, assuming that transition events are independent of each other. Additionally, it is assumed that electronic wave functions adjust instantaneously to nuclear positions while allowing interstate transitions. This simulates excited-state carrier dynamics, and further calculations of nonadiabatic coupling (NAC) matrix elements are conducted.

Here, the main factor that affects the electron hopping time is the nonadiabatic coupling, which can be expressed as

$$d_{jk}·Ṙ=⟨{\psi }_j|{\mathrm{\nabla }}_R|{\psi }_k⟩·Ṙ=⟨{\psi }_j|{\mathrm{\nabla }}_{\mathrm{R}}Ĥ|{\psi }_k⟩/{\epsilon }_k-{\epsilon }_j·Ṙ$$ 3

where $⟨{\psi }_j|{\mathrm{\nabla }}_{\mathrm{R}}Ĥ|{\psi }_k⟩$ is the vibronic coupling matrix term, ε _k – ε _j is the energy difference between the potential energy surfaces before and after electron migration, and Ṙ is the speed of the nucleus.

Using a second-order cumulant approximation in optical response theory (illustrated in the Supporting Information), we have calculated the decoherence time, which is also termed as the pure-dephasing time. The decoherence time has been obtained through the estimation of pure-dephasing function (D _ij (t)), which is calculated through the double integration of the autocorrelation function, C _ij (t). The pure-dephasing function is written as

$$D_{ij}(t)=\exp (-1/{\mathrm{\hslash }}^2{\int }_0^t\mathrm{d}{t}^{\prime }{\int }_0^{t^{\prime }}\mathrm{d}{t}^{″}{c}_{ij}(t^{″}))$$ 4

The carrier mobility was obtained according to the deformation potential theory (DP) ,

$$\mu =2e{\mathrm{\hslash }}^{3}C/(3K_{\mathrm{B}}T{|m^{*}|}^2{E}_1^2)$$ 5

where e and ℏ are the fundamental physical constants of charge and the reduced Planck’s constant. c denotes the modulus of elasticity. K _B, T, and m* are the Boltzmann constant, temperature, and effective mass, respectively, and E ₁ is the deformation potential constant.

Strong light absorption and a wide range of solar light absorption are the basic criteria for an ideal photocatalyst and even directly affect the photocatalytic efficiency. The light absorption coefficient α­(ω) is an important parameter to characterize the intensity of light absorption. The light absorption coefficient can be obtained by the following equation

$$\alpha (\omega )=\sqrt{2\omega }/c{\{{{[\epsilon }_1^2(\omega )+{\epsilon }_2^2(\omega )]}^{1/2}-{\epsilon }_1(\omega )\}}^{1/2}$$ 6

where ε₁ and ε₂ denote the real and imaginary parts of the dielectric constant, and ω denotes the frequency of electromagnetic radiation.

To further analyze the utility of the photocatalysts, we calculated the solar hydrogen production efficiency of the corrected heterojunction ,

$${\eta }_{\mathrm{S}\mathrm{T}\mathrm{H}}={\eta }_{\mathrm{a}\mathrm{b}\mathrm{s}}\times {\eta }_{\mathrm{c}\mathrm{u}}$$ 7

where the energy conversion efficiency of light absorption (η_abs) and the carrier utilization efficiency (η_cu) are defined as

$${\eta }_{\mathrm{a}\mathrm{b}\mathrm{s}}={\int }_{E_{\mathrm{g}}}^{\infty }P(\hslash \omega )\mathrm{d}(\hslash \omega )/{\int }_0^{\infty }P(\hslash \omega )\mathrm{d}(\hslash \omega )$$ 8

$${\eta }_{\mathrm{c}\mathrm{u}}=\mathrm{\Delta }G{\int }_E^{\infty }P(\hslash \omega )/\hslash \omega \mathrm{d}(\hslash \omega )/{\int }_{E_{\mathrm{g}}}^{\infty }P(\hslash \omega )\mathrm{d}(\hslash \omega )$$ 9

where ΔG is the potential difference for water decomposition (1.23 eV), E _g is the band gap of the heterojunction, is the AM1.5G solar flux at the energy of the photon, and E denotes the minimum energy of the photon at which a redox reaction can take place, denoted as

$$E=\{\begin{array}{l}{E}_{\mathrm{g}},(\chi ({\mathrm{H}}_2)\ge 0.2,\chi ({\mathrm{O}}_2)\ge 0.6)\\ E_{\mathrm{g}}+0.2-\chi ({\mathrm{H}}_2),(\chi ({\mathrm{H}}_2)<0.2,\chi ({\mathrm{O}}_2)\ge 0.6)\\ E_{\mathrm{g}}+0.6-\chi ({\mathrm{O}}_2),(\chi ({\mathrm{H}}_2)\ge 0.2,\chi ({\mathrm{O}}_2)<0.6)\\ E_{\mathrm{g}}+0.8-\chi ({\mathrm{H}}_2)-\chi ({\mathrm{O}}_2),(\chi ({\mathrm{H}}_2)<0.2,\chi ({\mathrm{O}}_2)<0.6)\end{array}$$ 10

where χ­(H₂) and χ­(O₂) are the overpotentials for the hydrogen precipitation and oxygen precipitation reactions. The intrinsic built-in electric field has a positive effect on the electron–hole separation during photocatalytic water splitting, so the modified solar-to-hydrogen (STH) efficiency η_STH is defined as

$${\eta }_{\mathrm{S}\mathrm{T}\mathrm{H}}^{\prime }={\eta }_{\mathrm{S}\mathrm{T}\mathrm{H}}\times {\int }_{{\mathrm{E}}_{\mathrm{g}}}^{\infty }P(\hslash \omega )d(\hslash \omega )/{\int }_0^{\infty }P(\hslash \omega )\mathrm{d}(\hslash \omega )$$

$$+\mathrm{\Delta }\mathrm{\Phi }{\int }_0^{\infty }P(\hslash \omega )/\hslash \omega d(\hslash \omega )$$ 11

where ΔΦ is the vacuum energy level difference between the two surfaces of the heterostructure.

The Gibbs free energy for photocatalytic water splitting was calculated, and solvation effects were taken into account using the VASPsol software package.

Details of calculations of the Gibbs free energy of HER are as follows.

The HER is demonstrated by

$$*+{\mathrm{H}}^{+}+e^{-}\to {\mathrm{H}}^{*}$$ 12

The Gibbs free energy is calculated and can be obtained by the following equation ,

$$G_{\mathrm{H}}=\mathrm{\Delta }E+\mathrm{\Delta }{E}_{\mathrm{Z}\mathrm{P}\mathrm{E}}-T\mathrm{\Delta }S+\mathrm{\Delta }{G}_{\mathrm{p}\mathrm{H}}$$ 13

Here, ΔE is the change in reaction energy. ΔE _ZPE denotes the difference in the zero-point energy. The ΔS is the entropy difference between the absorbed state and the gas state. The system temperature T is set to be 298.15 K. ΔG _pH is the Gibbs free energy correction for the concentration of H⁺ in a solution, with the calculation formula being ΔG _pH = −kT _mln­[H ⁺] = kT _mln10 × pH, where k represents the Boltzmann constant, and Tm denotes the temperature of the medium (298.15 K).

3. Results and Discussion

3.1. Geometric Structure

The geometries of the MoSi₂N₄, ZrS₂, and HfS₂ monolayers are fully optimized, as shown in Figure a,e,i. The monolayer cell of MoSi₂N₄ consists of a seven-layer atomic layer of N–Si–N–Mo–N–Si–N with a P6m1 space group, which can be regarded as a MoN₂ layer sandwiched between two Si–N bilayers. The bond length of Mo–N is 2.09 Å, and the Si–N bond length is 1.75 Å. The lattice constant of the primitive unit cell for MoSi₂N₄ is a = b = 2.91 Å, which agrees with the Bafekry’s result of 2.91 Ź⁰. The monolayer cells of ZrS₂ and HfS₂ both belong to the P3m1 space group with a hexagonal close-packed sulfide lattice, and the metal atoms are located in alternate layers of octahedral holes. The bond length of the Zr–S bond is 2.575 Å, and the Hf –S bond is 2.549 Å. The lattice constants are 3.67 Å and 3.64 Å, respectively. The result is in agreement with the experimental 3.65 Å and 3.64 Å. The AIMD simulations were performed at 300 K, the results indicate that the planar stacked network remains intact without significant structural deformation, and the total energy and temperature exhibit only minor fluctuations over time. The results demonstrate the thermodynamic stability of the three structural semiconductor monolayers. Meanwhile, the phonon spectra indicate the absence of imaginary frequencies in the Brillouin zone, further affirming the dynamical stability of the three semiconductors.

1.

Top and side view of (a) MoSi₂N₄, (e) ZrS₂, and (i) HfS₂ monolayers. Phono spectrum of (b) MoSi₂N₄, (f) ZrS₂, and (j) HfS₂ monolayers. AIMD at 300 K of (c) MoSi₂N₄, (g) ZrS₂, and (k) HfS₂ monolayers. The band structures of (d) MoSi₂N₄, (h) ZrS₂, and (l) HfS₂ monolayers are calculated by the vdW-corrected HSE06 functional.

The MoSi₂N₄/ZrS₂ (HfS₂) heterojunction was built by the supercells of √7 × √7 MoSi₂N₄ and the supercells of 2 × 2 ZrS₂ (HfS₂), as shown in Figure a,b. The lattice mismatch rates are 4.6% and 5.3%, within the lattice mismatch range for building heterojunctions. The lattice constants of the two configurations are 7.52 Å and 7.49 Å. The interlayer distances are about 3.00 Å. Due to the symmetrical structure of MoSi₂N₄, flipping the structure of ZrS₂(HfS₂) left–right does not change its structure, so different atomic alignment modes were considered. In MoSi₂N₄/ZrS₂(HfS₂), “S–N opposite” is designated as Configuration 1, “S–Si opposite” as Configuration 2, and “S positioned between N and Si atoms” as Configuration 3. The calculated formation energies for different stacking patterns of MoSi₂N₄/ZrS₂ are −1.04 eV, −1.04 eV, and −1.06 eV. It is found that Configuration 3 has the most negative formation energy and the most stable structure. And the calculated formation energies for different stacking patterns of MoSi₂N₄/HfS₂ are −1.02 eV, −1.02 eV, and −1.03 eV. Configuration 3 exhibits the most negative formation energy and the most stable structure. So we carried out research on these two most stable configurations. The results of the AIMD simulations at 300 K are shown in Figure c,d. The energies of both configurations oscillate around a fixed value within 4 ps, which confirms the thermodynamic stability of the two heterojunction structures.

2.

Top (a) and side (b) view of MoSi₂N₄/ZrS₂(HfS₂) heterostructures. AIMD at 300 K of MoSi₂N₄/ZrS₂ (c) and MoSi₂N₄/HfS₂ (d) heterostructures.

3.2. Electronic Properties

The energy band structures of MoSi₂N₄, ZrS₂, and HfS₂ monolayers were calculated by the HSE06 method, and the results are shown in Figure d,h,l. The band gaps of the monolayers are 2.28, 1.86, and 2.07 eV, respectively, and the monolayers are all indirect band gaps, which is in agreement with the results in the literature. , The energy band structures of the MoSi₂N₄/ZrS₂ (HfS₂) heterojunctions are shown in Figure a,d. Purple and blue colors represent the contributions of MoSi₂N₄ and ZrS₂ (HfS₂), respectively. In the MoSi₂N₄/ZrS₂ heterojunction, the ZrS₂ layer contributes to the conduction band minimum (CBM), while the MoSi₂N₄ layer contributes to the valence band maximum (VBM). The CBM and VBM of the MoSi₂N₄/HfS₂ heterojunction are contributed by the HfS₂ and MoSi₂N₄ layers.

3.

Band structure of MoSi₂N₄/ZrS₂ (a) and MoSi₂N₄/HfS₂ (d) heterostructures. The average electrostatic potentials along Z-direction of the MoSi₂N₄/ZrS₂ (b) and MoSi₂N₄/HfS₂ (e) vdW heterostructures. The average electron density difference of the MoSi₂N₄/ZrS₂ (c) and MoSi₂N₄/HfS₂ (f) heterostructures. The blue and pink areas represent the accumulation and consumption of electrons.

The work functions of MoSi₂N₄, ZrS₂, and HfS₂ monolayers are calculated to be 5.45 eV, 6.63 and 6.51 eV. The lower the work function, the higher the Fermi level. It is indicated that the Fermi level of MoSi₂N₄ is higher than that of ZrS₂ and HfS₂. When MoSi₂N₄ contacts with ZrS₂, electrons transfer from MoSi₂N₄ to ZrS₂ due to the difference in Fermi levels, until the Fermi levels reach equilibrium. When the Fermi level achieves balance, the work functions of the two surfaces of the MoSi₂N₄/ZrS₂ are 5.35 and 5.70 eV, respectively, as shown in Figure b. The electron transfer process led to the creation of a positively charged region on the MoSi₂N₄ side and a negatively charged region on the ZrS₂ side. An intrinsic electric field from MoSi₂N₄ to ZrS₂ is formed at the interface of the heterojunction, as shown in Figure . In other words, a Schottky barrier is formed on the interface of MoSi₂N₄ and ZrS₂. Similarly, the contact between MoSi₂N₄ and HfS₂ will also lead to the creation of a Schottky barrier on the interface of the MoSi₂N₄/HfS₂ heterojunction (shown in Figure ). Due to the difference in work functions between the two sides of the MoSi₂N₄/HfS₂ heterojunction, there are also discrepancies in the positions of the band edges.

4.

Band edge positions of the MoSi₂N₄/ZrS₂ and MoSi₂N₄/HfS₂ heterojunctions, referring to the vacuum level. Φ is the work function of the heterojunctions.

The plane-averaged differential charge density Δρ was calculated, as shown in Figure c,f. Based on the plane-averaged differential charge density, the gain and loss of electrons at heterojunction interfaces can be analyzed. Positive values indicate charge accumulation, and negative values indicate charge depletion. A built-in electric field has been established from MoSi₂N₄ to ZrS₂. In the MoSi₂N₄/ZrS₂, the ZrS₂ gains electrons, while the MoSi₂N₄ loses electrons. And electrons are gained by HfS₂ and lost by MoSi₂N₄ in the MoSi₂N₄/HfS₂. Similarly, a built-in electric field has been established from MoSi₂N₄ to HfS₂. In addition, the Bader charge can provide a quantitative description of electron gain and loss. Within the MoSi₂N₄/ZrS₂, ZrS₂ gains 0.012|e|, while MoSi₂N₄ loses 0.012|e|. In the MoSi₂N₄/HfS₂, HfS₂ gains 0.005|e|, and MoSi₂N₄ has a loss of 0.005|e|. These results are consistent with the analysis of the work function.

The Hefei-NAMD method was employed to examine the transfer of charge carriers under lighting conditions; the result of MoSi₂N₄/ZrS₂ is shown in Figure . Correspondingly, the results of NAMD for MoSi₂N₄/HfS₂ are shown in Figure S2. The population and time constants of photogenerated charge carriers can be obtained through exponential fitting (f(t) = exp­(−t/τ)). The critical orbitals involved in the charge transfer process are shown in Figure a. Process ① represents the interface electron transfer from the CBM of MoSi₂N₄ to the CBM of ZrS₂. Process ③ represents the interface hole transfer from the VBM of ZrS₂ to the VBM of MoSi₂N₄. Process ② represents the recombination of electron from the CBM of ZrS₂ and the interface hole from the VBM of MoSi₂N_4. If the time taken for Process ② is shorter than Processes ① and ③, photogenerated charge carriers will first undergo recombination, forming a Type Z heterojunction. Conversely, if the time for Process ② is longer than Processes ① and ③, electrons and holes will first migrate, forming a Type II heterojunction. The photogenerated electron (hole) transfer in MoSi₂N₄/ZrS₂ heterojunction is significantly faster than the e–h recombination process, as shown in Figure b. Obviously, the MoSi₂N₄/ZrS₂ is a type-II heterojunction. Similarly, in the MoSi₂N₄/HfS₂, the transfer speed of electrons and holes is also faster than the recombination speed of electron–hole pairs, as seen in Figure S2­(b). The MoSi₂N₄/HfS₂ is a type-II heterojunction too.

5.

(a)­Time-dependent evolution of the Kohn–Sham orbital in the MoSi₂N₄/ZrS₂ heterostructures. The red and blue lines are the components dominated by MoSi₂N₄ and ZrS₂ monolayers, respectively. (b) Averaged values of NAC between different states for the MoSi₂N₄/ZrS₂ heterostructures, respectively. The two black lines in the figure represents the band gap. The left side of the vertical black line is VBM, and the right side is CBM. The lower side of the horizontal black line is VBM, and the upper side is CBM. (c) ①Electron-transfer, ②e–h recombination, and ③hole-transfer dynamics in MoSi₂N₄/ZrS₂. (d–f) Time-dependent energy change for (d) electron transfer, (e) electron–hole recombination, and (f) hole transfer. The color bar indicates the electron or hole distribution in different energy states, and the dashed line represents the averaged electron or hole energy.

Evaluating the probability distribution of electrons or holes in selected energy states can lead to the evolution of carrier energy over time, providing a more intuitive description of carrier dynamics, as shown in Figure d,f. The transfer of electron from the CBM of MoSi₂N₄ to the CBM of ZrS₂ can occur within 1000 fs (1000 fs = 1 ps). The transfer speed of holes from the VBM of ZrS₂ to the VBM of MoSi₂N₄ is on the order of picoseconds. But the speed of hole transfer is significantly lower than that of electron transfer. However, the electron–hole recombination time significantly exceeds 1 ps, longer than the time needed for electron or hole transfer. In other words, the electron–hole recombination (e–h recombination) process is distinctly hindered, as shown in Figure e. Similarly, the transfer time of electrons and holes is longer than the recombination time of electron–hole pairs in MoSi₂N₄/HfS₂, as shown in Figure S2­(d–f). As a result, both MoSi₂N₄/ZrS₂ and MoSi₂N₄/HfS₂ heterojunctions are type II heterojunctions.

The time scale of the electron–hole recombination, electron transfer, and hole transfer in NAMD simulation is heavily influenced by the average NAC. The NAC of MoSi₂N₄/ZrS₂ is given in Figure c. The nonadiabatic coupling strength gradually increases from blue to red. With increasing coupling strength, the carrier transport speed increases. A higher level of NAC signifies an intensified electron–phonon interaction. At a constant temperature, electron transfer and hole transfer exhibit higher nuclear velocities than electron–hole recombination. The results indicate that the NAC for electron and hole transfer processes is significantly stronger than that for electron–hole recombination. In other words, the transfer speed of electrons and holes is faster than the recombination speed of electron–hole pairs, which indicates a stronger tendency to form Type II heterojunctions. And the NAC of MoSi₂N₄/HfS₂ is given in Figure S2­(c). The MoSi₂N₄/HfS₂ has a tendency to form a type-II heterojunction due to a higher NAC for electron and hole transfer in MoSi₂N₄/HfS₂ compared to electron–hole recombination.

The decoherence effect tends to slow down quantum dynamics, and if decoherence is infinitely prolonged, quantum transitions will terminatea phenomenon known as the quantum Zeno effect. The decoherence times for electron and hole transfer are longer, as shown in Figure S3. This extended pure-dephasing time indicates that electrons and holes can maintain quantum coherence for a longer duration during transfer, facilitating efficient charge separation via quantum tunneling effects. This finding is consistent with our conclusion that the heterostructure is of type-II.

The carrier mobility is obtained according to formula , and the results are shown in Table . The calculation parameters required for the calculation process are shown in Figures S4 and S5. The carrier mobility in the y-direction is significantly higher than in the x-direction for both monolayers and heterojunctions. Both in the x and y directions, the carrier mobility of electrons is noticeably higher than that of holes. The carrier mobility of MoSi₂N₄ is 111.076 cm² V^–1 s^–1, which is fairly consistent in magnitude with the value of 270 cm² V^–1 s^–1 reported by Liu et al. In the y-direction, the electron mobility of MoSi₂N₄/ZrS₂ reaches 19584.241 cm² V^–1 s^–1, significantly higher than that of MoSi₂N₄ (111.076 cm² V^–1 s^–1) and ZrS₂ (7832.84 cm² V^–1 s^–1). The electron mobility of MoSi₂N₄/HfS₂ (18902.648) is higher than that of MoSi₂N₄ (81.513 cm² V^–1 s^–1) and HfS₂ (1822.892 cm² V^–1 s^–1). The hole mobility also exhibits the same trend, showing an enhancement after building heterojunctions. These results indicate that the carrier mobility significantly increases after forming the heterojunction compared to the monolayers. Higher carrier mobility facilitates the realization of efficient optoelectronic performance.

1. Carrier Mobility of the MoSi₂N₄ Monolayer, ZrS₂ Monolayer, HfS₂ Monolayer, and MoSi₂N₄/ZrS₂(HfS₂) Heterostructures.

monolayer	direction	carrier type	C (N/m)	E d (eV)	m* (m0)	μ (cm2 V–1 s–1)
MoSi2N4	x	e	56.122	14.75	1.953	45.621
		h		6.43	5.290	45.155
	y	e	49.278	16.65	0.646	111.076
		h		6.63	1.750	82.310
ZrS2	x	e	6.780	1.93	0.964	440.418
		h		4.32	1.424	40.286
	y	e	6.737	1.37	0.321	7832.84
		h		4.94	0.474	297.636
HfS2	x	e	7.526	1.57	1.964	181.294
		h		4.68	2.095	17.604
	y	e	7.356	1.47	0.648	1822.892
		h		5.25	0.698	123.173
MoSi2N4/ZrS2	x	e	102.624	4.736	0.698	2111.634
		h		5.649	1.253	460.583
	y	e	103.033	4.668	0.233	19584.241
		h		5.74	0.418	4024.426
MoSi2N4/HfS2	x	e	105.330	4.54	0.689	2420.504
		h		5.51	1.340	434.453
	y	e	105.330	4.888	0.229	18902.648
		h		5.56	0.447	3834.347

3.3. Optical Properties

The absorption spectra based on PBE and GW + BSE of MoSi₂N₄, ZrS₂, and HfS₂ unit cell are shown in Figure S6. Compared with the absorption spectra based on PBE, the absorption spectra based on GW + BSE are blue-shifted. According to the blue-shift distances, we corrected the absorption spectra calculated by PBE, as shown in Figure . The ZrS₂ and HfS₂ monolayers have strong light absorption in the visible range. ZrS₂ shows distinct absorption peaks at 370 and 570 nm. The absorption peak of HfS₂ is mainly at 500 nm. The MoSi₂N₄ monolayer exhibits higher near-ultraviolet absorption. Absorption peaks are clearly evident at both 310 and 420 nm. After constructing the heterojunction, more absorption peaks appear. The absorption peaks of MoSi₂N₄/ZrS₂ are mainly located at about 320 and 420 nm. MoSi₂N₄/HfS₂ exhibits absorption peaks at about 390 and 500 nm. The absorption spectrum of the heterojunction exhibits a red shift in the visible light range, leading to a significant enhancement in light absorption capacity within the wavelength range of 300 to 480 nm. In the near-ultraviolet region, the absorption coefficient is also significantly enhanced. The results indicate that the heterojunction structure shows better response to visible and near-ultraviolet light compared to a single layer. The widened light absorption range and enhanced absorption coefficients of MoSi₂N₄/ZrS₂ and MoSi₂N₄/HfS₂ result in the generation of more photoexcited electrons, leading to an improved light conversion quantum efficiency.

6.

Optical absorption coefficient of the MoSi₂N₄ and ZrS₂(HfS₂) monolayers, as well as the MoSi₂N₄/ZrS₂ (a) and the MoSi₂N₄/HfS₂ (b) heterojunction.

3.4. STH Conversion Efficiency

To evaluate the STH conversion efficiency, the overpotentials of the oxidation and reduction reactions of HER and OER with respect to the CBM and VBM of the two heterojunctions were calculated, as shown in Table S1, which meets the initial conditions for photocatalytic water splitting. Based on the calculation method outlined in the computational details, the results are presented in Figure and Table S1. The hydrogen production efficiency η_STH of the MoSi₂N₄/ZrS₂ heterojunction can reach 16.09%, which is not only higher than the hydrogen production efficiency of the MoSi₂N₄ (3.88%) but also higher than many other heterojunctions, such as Zr₂CO₂/WSe₂(15.57%), SiH/GaSe(13.10%), and WSSe/WSe₂(9.10%). The enhancement of hydrogen production efficiency is closely related to the electronic properties of catalysts. As mentioned above, after the formation of heterojunctions, the speed of electron transfer increases, the absorption spectrum response range widens, and the absorption intensity strengthens. Additionally, effective separation of electron–hole pairs has been achieved in the heterojunction. These changes in electronic properties will play a positive role in improving hydrogen production efficiency.

7.

STH efficiency of other 2D materials compared with the MoSi₂N₄/ZrS₂ heterojunction.

3.5. Catalytic Performance

The hydrogen evolution reaction (HER) is correlated with the improvement in photocatalytic hydrogen production efficiency. As the transfer rate of photogenerated charge carriers accelerates and the effective separation of photogenerated electrons and holes, more photogenerated electrons will be involved in HER reaction. From the results of NAMD, it can also be observed that electrons transfer from the CBM of MoSi₂N₄ to the CBM of ZrS₂(HfS₂). The HER reaction took place on the faces of the ZrS₂ and HfS₂, indicating a higher participation of photogenerated electrons in the reaction. It could provide an evidence of improved efficiency from a catalytic perspective. The Gibbs free energy change of HER was calculated, as shown in Figure . The stable structure of H adsorption on the heterojunction surface is shown in Figure S7. Considering possible adsorption sites, it is found that the H atoms prefer to bond with the S atoms. And HER tends to occur on the ZrS₂ (HfS₂) surface. The results indicate that the free energy change of HER on the surface of MoSi₂N₄/ZrS₂ and MoSi₂N₄/HfS₂ are 0.75 and 0.98 eV, significantly lower than that on the surface of MoSi₂N₄ (2.19 eV), ZrS₂(0.80 eV), and HfS₂(0.99 eV). The outcomes of the HER align with the research findings on hydrogen production efficiency trends, and the easier progression of the HER also indirectly confirms the improvement in hydrogen production efficiency. Therefore, constructing heterojunctions can effectively regulate the hydrogen production efficiency.

8.

Differences of Gibbs free energies (ΔGs) for HER of MoSi₂N₄, ZrS₂, HfS₂, MoSi₂N₄/ZrS₂, and MoSi₂N₄/HfS₂.

In addition, the overpotentials for the OER of MoSi₂N₄/ZrS₂ and MoSi₂N₄/HfS₂ are 0.05 and 0.34 eV, which meet the conditions for the occurrence of the OER. The Gibbs free energy change of OER was calculated, as shown in Figure . The results indicate that the free energy change of the rate-determining step (RDS) of the OER on the surface of MoSi₂N₄/ZrS₂ and MoSi₂N₄/HfS₂ is 2.15 and 2.03 eV, which are significantly lower than that on the surface of MoSi₂N₄ (2.91 eV), ZrS₂(2.56 eV), and HfS₂(2.53 eV). This indicates that water splitting reactions can proceed.

9.

Differences of Gibbs free energies (ΔGs) for OER of MoSi₂N₄, ZrS₂, HfS₂, MoSi₂N₄/ZrS₂, and MoSi₂N₄/HfS₂.

4. Conclusion

This study utilized first-principles calculation methods and NAMD simulations to thoroughly examine the electronic and optical properties of monolayers and heterojunctions. Examining the interface characteristics of heterojunctions and the electron transfer following light exposure, the study also assessed hydrogen production efficiency and photocatalytic performance. The results indicate that the MoSi₂N₄/ZrS₂(HfS₂) heterojunction structure is stable under the suitable lattice mismatch. The NAMD method was used to examine the transfer of photogenerated charge carriers after illumination. The findings investigate that the speed of electron transfer and hole transfer is faster than the speed of electron–hole recombination, and the transfer mechanism of photogenerated charge carriers complements the transmission mechanism of traditional type II heterostructures. Additionally, the light absorption range becomes broader, and the intensity of light absorption also increases. The photocatalytic hydrogen production efficiency of MoSi₂N₄/ZrS₂ has been greatly improved compared to the monolayers, and it surpasses many other heterojunctions. The HER reaction proceeds more easily on the MoSi₂N₄/ZrS₂ heterojunction, providing additional evidence of the improved efficiency in photocatalytic hydrogen production. This study provides theoretical support for the search for semiconductor photocatalysts with high efficiency in hydrogen production. This study is primarily based on theoretical calculations and simulations, providing theoretical guidance for experimental research. But there may be certain deviations between the results of theoretical calculations and actual experiments. It is suggested to consider further element doping or compositing of the heterojunction to further improve the photocatalytic performance of the MoSi₂N₄/ZrS₂(HfS₂) heterojunction, so as to develop more efficient photocatalysts for the field of photocatalysis.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/prechem.5c00043.

• NAMD of MoSi₂N₄/HfS₂, data of the carrier mobility fitting process for MoSi₂N₄/ZrS₂ (HfS₂), top and side views of the H adsorption on the MoSi₂N₄/ZrS₂ (HfS₂) heterostructures, and η_STH of the MoSi₂N₄ and MoSi₂N₄/ZrS₂ (HfS₂) (PDF)

The manuscript was written through the contributions of all authors. All authors have given approval to the final version of the manuscript. M.J. contributed to investigation, methodology, and writingoriginal draft. Y.C. contributed to conceptualization and writingreview and editing. W.C. and Q.Z. contributed to investigation and methodology. Z.Y., H.R., H.Z., W.Z., and W.G. contributed to conceptualization and investigation.

The authors declare no competing financial interest.