First-Principles Study on Janus-Structured Sc₂CX₂/Sc₂CY₂ (X, Y = F, Cl, Br) Heterostructures for Solar Energy Conversion

Abstract

Two-dimensional van der Waals heterostructures have good application prospects in solar energy conversion due to their excellent optoelectronic performance. In this work, the electronic structures of Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures, as well as their properties in photocatalysis and photovoltaics, have been comprehensively studied using the first-principles method. Firstly, both of the three thermodynamically and dynamically stable heterostructures are found to have type-II band alignment with band gap values of 0.58 eV, 0.78 eV, and 1.35 eV. Meanwhile, the photogenerated carriers in Sc₂CF₂/Sc₂CCl₂ and Sc₂CF₂/Sc₂CBr₂ heterostructures are predicated to follow the direct Z-scheme path, enabling their abilities for water splitting. As for the Sc₂CCl₂/Sc₂CBr₂ heterostructure, its photovoltaic conversion efficiency is estimated to be 20.78%. Significantly, the light absorption coefficients of Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures are enhanced more than those of the corresponding monolayers. Moreover, biaxial strains have been observed to considerably tune the aforementioned properties of heterostructures. All the theoretical results presented in this work demonstrate the application potential of Sc₂CX₂/Sc₂CY₂ (X, Y = F, Cl, Br) heterostructures in photocatalysis and photovoltaics.

1. Introduction

With the depletion of traditional fossil fuels and the escalating global energy crisis, it is imperative and urgent to explore green and renewable energy sources. The use of semiconductor materials in applications such as photocatalysis or solar cells to convert abundant solar energy into clean power holds significant promise [1]. For instance, Fujishima and Honda were pioneers in demonstrating that TiO₂ could serve as a photocatalyst for water splitting [2]. Nevertheless, the efficiency of TiO₂ in converting solar energy to hydrogen is hindered by its wide band gap and high rate of carrier recombination. Chapin et al. were the first to create a solar cell using single-crystal silicon as the primary material. However, the photoelectric conversion efficiency (PCE) was disappointingly low, measuring only 6% [3]. As a result, the quest for suitable materials for photocatalysis and photovoltaics has been a prominent research area for a considerable period of time.

The discovery of graphene has sparked researchers’ interest in two-dimensional (2D) materials [4,5]. The 2D materials demonstrate amazing properties, including high carrier mobility, a semiconducting band gap, prominent catalytic activities, and abundant active sites. Therefore, they can be utilized in the fields of photocatalytic water splitting and photovoltaics. At present, many 2D materials have been synthesized experimentally or theoretically, such as transition metal carbides/nitrides (MXenes) [6], transition metal dichalcogenides (TMDCs) [7], hexagonal boron nitride (h-BN) [8], black phosphorus (BP) [9], and silicene [10]. However, 2D materials have a large band gap, poor light absorption capacity, and a high carrier recombination rate, thereby leading to low efficiency. Therefore, various strategic techniques such as doping [11], metal loading [12], and constructing heterostructures have been proposed. Among these strategies, constructing van der Waals (vdW) heterostructures with type-II band alignment has promising applications in the fields of photocatalytic water splitting and solar cells due to the lower exciton binding energy and enhanced optical absorbance compared to monolayers [13]. In type-II heterostructures, the photogenerated electron–hole pairs are separated onto different monolayers, which significantly reduces the carrier recombination rate. With the deepening of research, direct Z-scheme heterostructures can be designed by selecting two appropriate monolayer materials. In the Z-scheme heterostructure, photogenerated electrons and holes accumulate on the surfaces of distinct monolayers. The Z-scheme heterostructure not only possesses a strong redox ability to drive photocatalytic reactions but also provides active sites for spatially separated oxidation and reduction processes [14]. This mechanism significantly enhances the efficiency of water splitting in the heterostructure. According to previous research, the narrow band gap of the direct Z-scheme heterostructures can achieve a broader range of solar energy harvesting [15]. The Z-scheme heterostructures show great promise in photocatalytic water splitting, photocatalytic reduction of carbon dioxide, and environmental remediation [16,17]. In recent years, more and more Z-scheme heterostructures have been discovered and studied. Indeed, examples such as the WO₃/Bi₂MoO₆ heterostructure [18], β-SnSe/HfS₂ heterostructure [19], GaSe/ZrS₂ heterostructure [20], MoSTe/g-GeC heterostructure [21], GeC/BSe heterostructure [22], and SnC/PtS₂ heterostructure [23] all represent direct Z-scheme heterostructures.

On the other hand, MXenes have been widely explored in applications such as photocatalysts, solar cells, heavy-metal removal, battery anodes, and electromagnetic interference shielding. MXenes are produced from their corresponding MAX phases, where M represents an early transition metal, A represents a group of IIIA or IVA elements, and X represents a C or N atom [24]. MXenes have attracted increasing attention due to their excellent stability and large specific surface area. In the field of photocatalysis, heterostructures based on MXenes, such as Cs₂AgBiBr₆/Ti₃C₂T_x [25], Hf₂CO₂/WS₂ [26], AsP/Sc₂CO₂ [27], and Sc₂CF₂/MoSSe [28], exhibit superior electronic properties. For the application of solar cells, Wen et al. demonstrated that the PCE of Hf₂CO₂/MoS₂ and Zr₂CO₂/MoS₂ heterostructures in solar cell applications was 19.75% and 17.13%, respectively [29]. The PCE of Ti₂CO₂/Zr₂CO₂ and Ti₂CO₂/Hf₂CO₂ heterostructures reaches 22.74% and 19.56%, respectively [30]. This indicates that MXenes have promising potential for applications as photovoltaic materials. Pure Sc₂C exhibits metallic properties; however, after functionalization by F, Cl, and Br atoms, Sc₂CF₂, Sc₂CCl₂, and Sc₂CBr₂ exhibit semiconductor characteristics with band gaps of 1.85 eV, 1.70 eV, and 1.54 eV, respectively [31]. As a member of MXenes, Sc₂CX₂ (X = F, Cl, Br) exhibits kinetic and thermal stabilities, which have potential applications in photocatalytic water splitting and solar cells [32]. However, the Sc₂CF₂ monolayer cannot facilitate the oxygen evolution reaction (OER) because its valence band maximum (VBM) is higher than that of E_O2/H2O. For Sc₂CCl₂ and Sc₂CBr₂ monolayers, the conduction band minimum (CBM) is lower than E_H+/H2, which renders them unable to meet the requirements for the HER. The construction of heterostructures using Sc₂CF₂, Sc₂CCl₂, and Sc₂CBr₂ not only addresses the mentioned deficiency of materials but also shows significant potential for photocatalytic and optoelectronic applications. Zhang et al. investigated the electrical and optical properties of Sc₂CF₂/WSSe heterostructures and found that they have the potential for water splitting [33]. In addition, Sun et al. revealed that the PCE of the Sc₂CCl₂/SiS₂ heterostructure can reach 23.20%, indicating promising prospects for application in the field of solar cells [34]. It is noteworthy that the VBM and CBM of the Sc₂CF₂ monolayer are higher than those of the Sc₂CCl₂ (or Sc₂CBr₂) monolayer, and the VBM and CBM of the Sc₂CBr₂ monolayer are higher than those of the Sc₂CCl₂ monolayer. This indicates that the Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures may have a type-II band alignment. In addition, the CBM in Sc₂CCl₂ (or Sc₂CBr₂) and the VBM in Sc₂CF₂ are very close. This suggests that photogenerated carrier transfer in the Sc₂CF₂/Sc₂CCl₂ and Sc₂CF₂/Sc₂CBr₂ heterostructures may follow the Z-scheme pathway. Therefore, it is worthwhile to study the Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures. Their potential applications in photocatalytic water splitting and solar cells show great promise.

In this paper, three types of monolayers, namely Sc₂CF₂, Sc₂CCl₂, and Sc₂CBr₂, were successfully vertically stacked to create Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures. The stacking geometries, electronic, and optical properties of the heterostructures have been systematically studied based on first-principles calculations. According to band edge alignment and charge carrier transfer processes, the Sc₂CF₂/Sc₂CCl₂ and Sc₂CF₂/Sc₂CBr₂ heterostructures were found to have a direct Z-scheme band alignment, making them promising for photocatalytic water splitting applications. On the other hand, the Sc₂CCl₂/Sc₂CBr₂ heterostructure showed potential for use in solar cells, with a notable PCE of 20.78%. The present findings indicate that Sc₂CX₂/Sc₂CY₂ (X, Y = F, Cl, Br) heterostructures have the potential for application in solar energy conversion.

2. Computation Details

In this paper, all calculations are carried out using the projection enhanced wave method based on density functional theory (DFT) [35], as implemented in the Vienna Ab initio Simulation Package (VASP5.4.4) [36]. Electron–ion interactions were explained using the projected augmented wave pseudopotential (PAW), while the exchange potential and the correlation potential were described using the generalized gradient approximation (GGA) with Perdew–Burke–Ernzerhof (PBE) functional [37]. The valence electron configurations of Sc, C, F, Cl, and Br atoms are 3p⁶3d¹4s², 2s²2p², 2s²2p⁵, 3s²3p⁵, and 4s²4p⁵, respectively. The energy cutoff for obtaining the relaxed lattice vector and atomic positions was set to 500 eV. All geometrical structures were relaxed until the forces and energy on each atom converged to 0.01 eV Å⁻¹ and 10⁻⁵ eV, respectively. For the calculation of heterostructures, we utilized the DFT-D3 method to treat the interlayer vdW interaction [38]. The K-point grid for energy convergence was set to 15 × 15 × 1 for structural optimization. A vacuum layer of 20 Å was arranged along the z-axis to eliminate interactions between adjacent layers. The Heyd–Scuseria–Ernzerh (HSE06) hybrid functional was used to calculate accurate electronic and optical properties [39]. The thermal stability of the Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures was further evaluated through ab initio molecular dynamics (AIMD) simulations with the NVT ensemble [40,41]. AIMD simulations were performed using a 4 × 4 × 1 supercell at 300 K. In our AIMD simulation, a total simulation time of 6 ps with a time step of 1 fs was set.

3. Results and Discussion

The structural parameters and electronic properties of Sc₂CX₂ (X = F, Cl, Br) were initially studied. The atomic structures of optimized Sc₂CX₂ (X = F, Cl, Br) monolayers are displayed in Figure 1a. The lattice constant of the Sc₂CF₂ monolayer was determined to be 3.235 Å, which closely matches the theoretical value of 3.26 Å, as reported by Khang et al. [42]. The corresponding result of 3.422/3.499 Å for the Sc₂CCl₂/Sc₂CBr₂ monolayer is close to the previous theoretical value of 3.42/3.507 Å [31,43]. When the surface groups change from F to Br, the lattice parameters increase slightly due to the increase in the halogen atomic radius [31]. In addition, the band structures of the Sc₂CX₂ (X = F, Cl, Br) monolayers were calculated using the HSE06 method, as displayed in Figure 1b–d. It can be distinctly observed that the band shapes are fundamentally the same, despite the differences in band gap values. Moreover, we can observe that Sc₂CX₂ (X = F, Cl, Br) monolayers are all indirect band gap semiconductors. The CBM and VBM of the Sc₂CX₂ (X = F, Cl, Br) monolayers are located at the M point and Γ point, with corresponding band gaps of 1.80 eV, 1.70 eV, and 1.55 eV, respectively. All band gap values are in good agreement with the earlier reports, with percentage differences of less than 2% [32,44,45]. The results verify the rationality of our approach and parameterization.

Then, the structural properties of Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures were researched in pursuit of the most stable configuration. There are three typical stacking configurations for all three heterostructures, i.e., A, B, and C, as illustrated in Figure 2. The structure coordinate information (POSCAR) is provided in Table S1.

Table 1. The lattice constants, layer spacing (d), and binding energy (E_b) of three possible stackings in Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures.

System	Configuration	Lattice Constants a (Å)	d (Å)	Eb (meV*Å−2)
Sc2CF2	-	3.235	-	-
Sc2CCl2	-	3.422	-	-
Sc2CBr2	-	3.499	-	-
Sc2CF2/Sc2CCl2	A	3.321	2.74	−35.06
	B	3.320	3.13	−35.67
	C	3.321	2.69	−34.77
Sc2CF2/Sc2CBr2	A	3.356	2.84	−27.74
	B	3.356	3.24	−28.53
	C	3.357	2.81	−27.35
Sc2CCl2/Sc2CBr2	A	3.458	3.23	−19.36
	B	3.458	3.62	−19.96
	C	3.459	3.20	−18.90

presents various parameters associated with different stackings. For each heterostructure, the lattice constants of the three configurations closely match the lattice constants of the corresponding monolayer. In order to assess the stability of the heterostructures and determine the most stable configurations, the binding energy (E_b) values of all configurations are computed as follows:

$$E_{\mathrm{b}}=\frac{E_{\mathrm{H}}-E_{{\mathrm{S}\mathrm{c}}_2\mathrm{C}{\mathrm{X}}_2}-E_{{\mathrm{S}\mathrm{c}}_2\mathrm{C}{\mathrm{Y}}_2}}{S_0}$$

where $E_{\mathrm{H}}$ represents the energy of the Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures, respectively. Here, $S_0$ represents the interface area, while $E_{{\mathrm{S}\mathrm{c}}_2\mathrm{C}{\mathrm{X}}_2}$ and $E_{{\mathrm{S}\mathrm{c}}_2\mathrm{C}{\mathrm{Y}}_2}$ represent the energy of the Sc₂CF₂, Sc₂CCl₂, and Sc₂CBr₂ monolayers, respectively. From Table 1, we can see that the minus E_b values for all stacking configurations manifest that the interface formation is exothermic, which is favorable for their preparation [46]. Clearly, for Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures, stacking-B exhibits the smallest E_b of −35.67 meV∙Å⁻², −28.53 meV∙Å⁻², and −19.96 meV∙Å⁻², indicating that stacking-B is the most stable among the three stacking configurations. In addition, this value is smaller than the previously reported C₂N/ZnSe heterostructure (−12.1 meV∙Å⁻²) [47] and BiTeCl/GeSe heterostructure (−11.07 meV∙Å⁻²) [48], revealing that Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ are vdW heterostructures. Thus, only the stacking-B heterostructure was taken into consideration in all the following calculations. Indispensably, AIMD simulations are performed to validate the thermodynamic stability of the heterostructure. As depicted in Figure S1, the geometrical structures of the Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures remained stable during the 6 ps simulation at a temperature of 300 K. No bonds were broken, and the energy fluctuation was minimal, indicating that each heterostructure is sufficiently stable at room temperature. Furthermore, to verify the dynamical stability of the Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures, we calculated their phonon spectrum with a 3 × 3 × 1 supercell and implemented them in the PHONOPY code with the density functional perturbation theory (DFPT), as shown in Figure S2. It can be seen that there are some insignificant imaginary frequencies near the G-point. This phenomenon also exists in the phonon spectra of some experimentally prepared 2D materials, but the imaginary frequency near the G-point can be ignored [49,50,51]. This phenomenon may be attributed to inadequate computational accuracy, which can be eliminated by creating a larger supercell or setting a higher parameter accuracy. Thus, the Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures are dynamically stable.

The projected band structures of Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures were calculated based on the HSE06 hybrid functional, as depicted in Figure 3a–c. It can be found that the Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures all show the characteristics of semiconductors with indirect band structures. The VBM and CBM are located at the M point and Γ point, with band gaps of 0.58 eV, 0.78 eV, and 1.35 eV, respectively. Compared with the band gaps of monolayers, the significantly reduced band gaps of heterostructures are due to the interaction of vdW forces, which lead to a change in the band structure upon contact [21]. It should be noted that the smaller band gap of Sc₂CF₂/Sc₂CCl₂ and Sc₂CF₂/Sc₂CBr₂ heterostructures can lead to improved optical absorption performance during the photocatalytic reaction process. In addition, we can clearly see that the VBM and CBM of the three heterostructures are each occupied by two monolayers, demonstrating an inherent type-II heterostructure. Among them, the VBM of Sc₂CF₂/Sc₂CCl₂ and Sc₂CF₂/Sc₂CBr₂ heterostructures is mainly attributed to the Sc₂CF₂ monolayer, while the CBM mainly comes from the Sc₂CCl₂ (or Sc₂CBr₂) monolayer. Hence, electrons mainly occupy Sc₂CCl₂ (or Sc₂CBr₂), while holes mainly occupy Sc₂CF₂. Similarly, the VBM of the Sc₂CCl₂/Sc₂CBr₂ heterostructure is mainly contributed by the Sc₂CBr₂ layer, whereas the CBM is entirely dominated by the Sc₂CCl₂ layer. It is certain that the type-II band structures can separate the photoexcited electrons and holes into different monolayers, which is conducive to reducing the carrier recombination rate. This separation can improve the utilization of photogenerated carriers and extend their lifetime [44].

In addition, Figure 3d–f shows the projected density of states (PDOS) of the Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures, respectively. From Figure 3d, it can be seen that in the Sc₂CF₂/Sc₂CCl₂ heterostructure, the peak with the highest energy below the Fermi level mainly originates from the Sc and C atoms in Sc₂CF₂, while the peak with the lowest energy above the Fermi level is mainly contributed by the Sc atom in Sc₂CCl₂. This shows that the VBM of the Sc₂CF₂/Sc₂CCl₂ heterostructure is contributed by the Sc₂CF₂, while the CBM is contributed by the Sc₂CCl₂. As shown in Figure 3e, the VBM of the Sc₂CF₂/Sc₂CBr₂ heterostructure is mainly contributed by the Sc and C atoms of Sc₂CF₂, while the CBM mainly comes from the Sc atom of Sc₂CBr₂. This indicates that the VBM of the Sc₂CF₂/Sc₂CBr₂ heterostructure comes from the electronic states of Sc₂CF₂, while the CBM comes from the electronic states of Sc₂CBr₂. In Figure 3f, we can clearly observe that the CBM of the Sc₂CCl₂/Sc₂CBr₂ configuration is contributed by the Sc atom of Sc₂CCl₂. However, the VBM is not only contributed by the Sc and C atoms but also by the Br atom. This shows that the VBM of the Sc₂CCl₂/Sc₂CBr₂ heterostructure originates from the Sc₂CBr₂ monolayer, while the CBM comes from the Sc₂CCl₂ monolayer. In addition, the orbitals of the C atom and Sc atom are completely hybridized. This PDOS result further confirms that the CBM and VBM of Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures are located on different monolayers.

In Figure 3g–i, we displayed the band decomposed charge densities of the VBM and CBM in Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures, respectively. In Sc₂CF₂/Sc₂CCl₂ and Sc₂CF₂/Sc₂CBr₂ heterostructures, it can be observed that the VBM is located in Sc₂CF₂, while the CBM is located in Sc₂CCl₂ (or Sc₂CBr₂). Consistent with the above analysis, the VBM and CBM of the Sc₂CCl₂/Sc₂CBr₂ heterostructure are located on the lower layer (Sc₂CBr₂) and upper layer (Sc₂CCl₂), respectively. There is no charge density overlap between the VBM and CBM, indicating that heterostructures like Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ can effectively separate electrons and holes [52].

The above analysis shows that the Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures exhibit staggered type-II band alignment. This structure can promote the effective separation of holes and electrons, reduce the carrier recombination rate, and play an important role in photocatalytic water splitting and optoelectronic devices.

The difference in work functions between two semiconductors can lead to charge redistribution and the formation of an electric field at the interface. This electric field will determine the transfer process of photogenerated charges. Thus, the work functions of the Sc₂CF₂, Sc₂CCl₂, and Sc₂CBr₂ monolayers, as well as the Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures, are calculated using the following formula:

$$\Phi =E_{vac}-E_F$$

in which $E_{vac}$ and $E_F$ represent the vacuum level and Fermi level, respectively. As shown in Figure S3a–c, Sc₂CF₂, Sc₂CCl₂, and Sc₂CBr₂ monolayers exhibit a fixed work function of 5.02 eV, 5.86 eV, and 5.48 eV, respectively, due to their highly symmetrical crystal structure [28]. Compared to Sc₂CCl₂ and Sc₂CBr₂ monolayers, the Sc₂CF₂ monolayer exhibits a smaller work function and a higher Fermi level. Thus, in the Sc₂CF₂/Sc₂CCl₂ and Sc₂CF₂/Sc₂CBr₂ heterostructures, free electrons can migrate from Sc₂CF₂ to Sc₂CCl₂ (or Sc₂CBr₂) until their Fermi levels reach equilibrium. As shown in Figure 4a,b, the work functions of the Sc₂CF₂/Sc₂CCl₂ and Sc₂CF₂/Sc₂CBr₂ heterostructures are 5.19 eV and 4.99 eV, respectively. At the same time, there are potential drops of 5.43 eV and 3.25 eV at the Sc₂CF₂/Sc₂CCl₂ and Sc₂CF₂/Sc₂CBr₂ heterostructures, indicating the presence of a built-in electric field at the interface of the heterostructures [52]. It also indicates that electrons are inclined to flow to Sc₂CCl₂ (or Sc₂CBr₂) monolayers. The built-in electric field will create a driving force to promote the combination of photogenerated electron–hole pairs between the electrons in the CBM of Sc₂CCl₂ (or Sc₂CBr₂) and the holes in the VBM of Sc₂CF₂. As displayed in Figure 4c, the difference in monolayer work function leads to the transfer of electrons from Sc₂CBr₂ to Sc₂CCl₂, causing a decline in the Fermi level in Sc₂CCl₂ and Sc₂CBr₂. The work function of the heterostructure in the final equilibrium state is 5.34 eV. Moreover, a potential drop of 2.12 eV is found across the interface. This is proof of a built-in electric field at the interface of the Sc₂CCl₂/Sc₂CBr₂ heterostructure.

During the formation of a heterostructure, the charge near the interface will be redistributed due to the presence of interlayer interactions. In order to explore the charge transfer mechanism of Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures, the planar averaged charge density difference and 3D differential charge density difference were calculated using the following equation:

$$∆\rho ={\rho }_{het}-{\rho }_{SCX}-{\rho }_{SCY},$$

where the ${\rho }_{het}$ stand for the density of Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures, and the ${\rho }_{SCX}$ and ${\rho }_{SCY}$ represent the corresponding densities of Sc₂CF₂, Sc₂CCl₂, and Sc₂CBr₂ monolayers. As shown in Figure 4d,e, for Sc₂CF₂/Sc₂CCl₂ and Sc₂CF₂/Sc₂CBr₂, it can be clearly seen that a large number of negative charges are assembled in the side of Sc₂CCl₂ (or Sc₂CBr₂) monolayers, while positive charges cluster on the side of Sc₂CF₂. This leads to the formation of a built-in electric field from Sc₂CF₂ to Sc₂CCl₂ (or Sc₂CBr₂). As shown in Figure 4f, the electrons at the interface are depleted near the Sc₂CBr₂ monolayer and accumulate at the Sc₂CCl₂ monolayers, forming a built-in electric field from Sc₂CBr₂ to Sc₂CCl₂. In addition, the Bader charges obtained indicate that about 0.0072 |e| (0.0052 |e|) are transferred from the Sc₂CF₂ monolayer to the Sc₂CCl₂ (or Sc₂CBr₂) monolayers in the case of the Sc₂CF₂/Sc₂CCl₂ (Sc₂CF₂/Sc₂CBr₂) heterostructure. Furthermore, around 0.0018 |e| is transferred from Sc₂CBr₂ to Sc₂CCl₂ within the Sc₂CCl₂/Sc₂CBr₂ heterostructure.

In addition to the band gap value, the band edge alignment is also a crucial parameter for evaluating the application of the heterostructure. Therefore, we computed the band alignments of Sc₂CF₂, Sc₂CCl₂, and Sc₂CBr₂ monolayers, as well as the Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures, using the method suggested by Toroker et al. [53]. Figure 5a reveals that the VBM of the Sc₂CF₂ monolayer exceeds that of E_O2/H2O. The Sc₂CCl₂ and Sc₂CBr₂ monolayers exhibit very similar characteristics in their band edge alignments, with both CBM being lower than the energy level of E_H+/H2. Based on the aforementioned analysis, the band positions of the Sc₂CF₂, Sc₂CCl₂, and Sc₂CBr₂ monolayers are unsuitable for photocatalysis. For the Sc₂CF₂/Sc₂CCl₂ and Sc₂CF₂/Sc₂CBr₂ heterostructures, the VBM and CBM of the Sc₂CF₂ layer are higher than those of the Sc₂CCl₂ (or Sc₂CBr₂) layer, further affirming that the heterostructure exhibits a type-II band alignment. For the Sc₂CCl₂/Sc₂CBr₂ heterostructure, both the VBM and CBM of Sc₂CBr₂ exceed those of the Sc₂CCl₂ layer, indicating a type-II band alignment. The CBM of Sc₂CCl₂ is lower than that of E_H+/H2, making the Sc₂CCl₂/Sc₂CBr₂ heterostructure unsuitable for photocatalytic water splitting reactions.

The photocatalytic water splitting reaction mechanism of Sc₂CF₂/Sc₂CX₂ (X = Cl, Br) is shown in Figure 5b. In general, three possible processes are considered here: ① The photoexcited holes at the VBM of Sc₂CF₂ recombine with electrons at the CBM of Sc₂CCl₂ (or Sc₂CBr₂), which represents a direct Z-scheme transfer path (indicated by the green line with double-headed arrows). ②–③ Photogenerated electrons at the CBM of Sc₂CF₂ migrate to the CBM of Sc₂CCl₂ (or Sc₂CBr₂), while photogenerated holes at the VBM of Sc₂CCl₂ (or Sc₂CBr₂) migrate to the VBM of Sc₂CF₂. This migration follows a traditional type-II path (indicated by gray lines with arrows). Electronic property analysis shows that the band alignments of the Sc₂CF₂/Sc₂CX₂ (X = Cl, Br) heterostructure are made up of the CBM of the Sc₂CCl₂ (or Sc₂CBr₂) layer and the VBM of the Sc₂CF₂ layer. Compared to the band gap of two monolayers, the heterostructure has a smaller band gap (Figure 5a), indicating a higher rate of photogenerated electron–hole pair recombination at the interface compared to the rate of intralayer recombination. Meanwhile, due to the built-in electric field from Sc₂CF₂ to Sc₂CCl₂ (or Sc₂CBr₂), the recombination of photogenerated electrons in the CBM of Sc₂CCl₂ (or Sc₂CBr₂) and photogenerated holes in the VBM of Sc₂CF₂ is accelerated, promoting the recombination of path ① carriers. In addition, electrons have varying additional potential energies at different points in the space charge region, a phenomenon known as energy band bending [54]. The positive charge on the Sc₂CCl₂ (or Sc₂CBr₂) is repelled by the holes on the Sc₂CF₂, causing the energy band to bend downward. Correspondingly, as the electrons move, the energy bands of the Sc₂CF₂ bend upward, forming a potential barrier at the interface. Due to the presence of built-in electric fields and potential barriers, the transfer of electrons from the CBM of Sc₂CF₂ to the CBM of Sc₂CCl₂ (or Sc₂CBr₂), as well as the transfer of holes from the VBM of Sc₂CCl₂ (or Sc₂CBr₂) to the VBM of Sc₂CF₂, are suppressed. Therefore, electron transfer in paths ② and ③ is repressed. After absorbing photon energy, the electrons are excited to the CBM, while the holes remain in the VBM. Due to the obstruction of path ② and path ③, photogenerated electrons gather in the CBM of Sc₂CF₂, while photogenerated holes gather in the VBM of Sc₂CCl₂ (or Sc₂CBr₂), which facilitates the efficient separation of photogenerated carriers and prolongs their lifetime [23]. Therefore, it is difficult for electrons and holes to transfer following the type-II pathway, and the Sc₂CF₂/Sc₂CX₂ heterostructure should be used as the photocatalyst for the Z-scheme. According to the above analysis, the Sc₂CF₂ layer exhibits a higher reduction ability. Photogenerated electrons and hydrogen ions undergo a reduction reaction on the CBM of the Sc₂CF₂ layer to produce hydrogen. Meanwhile, in the highly oxidizing Sc₂CCl₂ (or Sc₂CBr₂) layer, the photogenerated holes on the VBM react with hydroxyl groups to produce oxygen, thereby improving the photocatalytic performance.

Differently, the Sc₂CCl₂/Sc₂CBr₂ heterostructure is not suitable as a photocatalyst due to the fact that the CBM is lower than the energy level of E_H+/H2 (Figure 5a). However, they can function as absorption layers for solar cells. As shown in Figure 5c, the conduction band offset and valence band offset between the Sc₂CCl₂ and Sc₂CBr₂ layers are 0.11 eV and 0.40 eV, respectively. Therefore, under the influence of valence band offset, the photogenerated holes in the Sc₂CCl₂ layer tend to jump to the VBM of the Sc₂CBr₂ layer. Simultaneously, due to the lower CBM energy of Sc₂CCl₂ in the Sc₂CCl₂/Sc₂CBr₂ heterostructure, photogenerated electrons tend to move to the CBM of Sc₂CCl₂, resulting in a type-II band alignment. The very small conduction band offset can improve the energy conversion efficiency of the solar cell, while the large valence band offset limits the electrons in the Sc₂CCl₂ monolayer and the holes in the Sc₂CBr₂ monolayer [55]. Therefore, the rate of electron hole recombination will decrease, and the lifetime of photogenerated carriers will be extended. This will promote the formation of indirect excitons, which can be utilized in optoelectronic devices.

Considering that the construction of vdW heterostructures is an effective approach to enhance optical absorption and achieve excellent photovoltaic performance, therefore, to analyze the optical properties of the Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures, we calculated the optical absorption of the Sc₂CF₂ monolayer, Sc₂CCl₂ monolayer, Sc₂CBr₂ monolayer, and the Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures, as shown in Figure 6a–c. Among them, the optical absorption coefficient is determined by the following equation [56]:

$$\mathsf{\alpha }\left(\mathsf{\omega }\right)=\sqrt{2}\mathsf{\omega }\sqrt{\sqrt{{\mathsf{\epsilon }}_1^2\left(\mathsf{\omega }\right)+{\mathsf{\epsilon }}_2^2\left(\mathsf{\omega }\right)}-{\mathsf{\epsilon }}_1(\mathsf{\omega })}$$

where ${\mathsf{\epsilon }}_1(\mathsf{\omega })$ and ${\mathsf{\epsilon }}_2(\mathsf{\omega })$ represent the real and imaginary parts of the complex dielectric function $\mathsf{\epsilon }(\mathsf{\omega })$, respectively. As illustrated in Figure 6a, we found that, compared to monolayers Sc₂CF₂ and Sc₂CCl₂, the Sc₂CF₂/Sc₂CCl₂ heterostructure has a wide absorption range from UV light to visible light due to its reduced band gap. It can be seen that the optical absorption coefficient of the Sc₂CF₂/Sc₂CCl₂ heterostructure is much larger than that of Sc₂CF₂ and Sc₂CCl₂ in both the UV and visible light ranges. More importantly, the Sc₂CF₂/Sc₂CCl₂ heterostructure shows a high absorption coefficient in the visible light region, reaching up to 2.53 × 10⁵ cm⁻¹ at a wavelength of 410 nm. The enhancement of the optical absorption coefficient is mainly due to the interlayer coupling between two monolayers of the Sc₂CF₂/Sc₂CCl₂ heterostructure [57]. Therefore, it is expected that the Sc₂CF₂/Sc₂CCl₂ heterostructure can act as an efficient visible light-harvesting photocatalyst. As can be seen from Figure 6b, compared with the Sc₂CF₂ monolayer and Sc₂CBr₂ monolayer, the significantly increased optical absorption in the UV and visible light regions of the Sc₂CF₂/Sc₂CBr₂ heterostructure is due to the interlayer coupling [58]. At the same time, compared with the Sc₂CF₂ monolayer and Sc₂CBr₂ monolayer, the increase in the optical absorption range of the Sc₂CF₂/Sc₂CBr₂ heterostructure is on account of the decrease in the band gap. Therefore, compared to the Sc₂CF₂ and Sc₂CBr₂ monolayers, the Sc₂CF₂/Sc₂CBr₂ heterostructure exhibits superior optical absorption performance, enabling efficient solar energy harvesting.

Light-absorbing materials not only need to have a suitable electronic structure but also need to have the ability to harvest solar light. Therefore, it is of great significance to study the optical properties of the Sc₂CCl₂/Sc₂CBr₂ heterostructure. The calculated absorption spectra of Sc₂CCl₂ and Sc₂CBr₂ monolayers, as well as the Sc₂CCl₂/Sc₂CBr₂ heterostructure, are shown in Figure 6c. In the UV and visible regions, the absorption intensity of Sc₂CCl₂ and Sc₂CBr₂ monolayers is weak. However, the absorption peak of the Sc₂CCl₂/Sc₂CBr₂ heterostructure in the visible region is nearly 2.33 × 10⁵ cm⁻¹, which is 1.71 times that of the Sc₂CCl₂ monolayer. The enhancement of the optical absorption coefficient is mainly due to the interlayer coupling between two monolayers of the Sc₂CCl₂/Sc₂CBr₂ heterostructure [58]. Compared to both monolayers, the absorption range of the Sc₂CCl₂/Sc₂CBr₂ heterostructure increases due to its reduced band gap. Therefore, it can be concluded that the Sc₂CCl₂/Sc₂CBr₂ heterostructure would be a promising material for solar cells.

For device applications, in addition to the electronic and optical properties of the Sc₂CCl₂/Sc₂CBr₂ heterostructure analyzed above, such as limited band gaps, strong solar light-harvesting capabilities, and easy separation of electrons and holes with type-II band alignment, the ability to convert photon energy into electricity is also critical for solar cell applications. We use the method developed by Scharber et al. to calculate the PCE of solar cells, and its formula is as follows [59]:

$$\mathsf{\eta }=\frac{{\mathrm{J}}_{\mathrm{s}\mathrm{c}}{\mathrm{V}}_{\mathrm{o}\mathrm{c}}{\mathsf{\beta }}_{\mathrm{F}\mathrm{F}}}{{\mathrm{P}}_{\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}}}=\frac{0.65({\mathrm{E}}_{\mathrm{g}}^{\mathrm{d}}-\mathsf{\Delta }{\mathrm{E}}_{\mathrm{c}}-0.3){\int }_{{\mathrm{E}}_{\mathrm{g}}^{\mathrm{d}}}^{\mathrm{\infty }}\frac{{\mathrm{J}}_{\mathrm{P}\mathrm{h}\left(\mathrm{\hslash }\mathsf{\omega }\right)}}{\mathrm{\hslash }\mathsf{\omega }}\mathrm{d}(\mathrm{\hslash }\mathsf{\omega })}{{\int }_0^{\mathrm{\infty }}{\mathrm{J}}_{\mathrm{P}\mathrm{h}}\left(\mathrm{\hslash }\mathsf{\omega }\right)\mathrm{d}\left(\mathrm{\hslash }\mathsf{\omega }\right)}$$

where 0.65 represents the band fill factor, ${\mathrm{E}}_{\mathrm{g}}^{\mathrm{d}}$ stands for the optical band gap of the donor, and $\mathsf{\Delta }{\mathrm{E}}_{\mathrm{c}}$ represents the conduction band offset (CBO). The open circuit voltage is ${\mathrm{E}}_{\mathrm{g}}^{\mathrm{d}}-\mathsf{\Delta }{\mathrm{E}}_{\mathrm{c}}-0.3$, and ${\mathrm{J}}_{\mathrm{P}\mathrm{h}}\left(\mathrm{\hslash }\mathsf{\omega }\right)$ is the 1.5 AM solar energy flux at the photon energy $\left(\mathrm{\hslash }\mathsf{\omega }\right)$. As shown in Figure 6d, the calculated PCE of the Sc₂CCl₂/Sc₂CBr₂ heterostructure is about 20.78% (highlighted by the red star), which surpasses that of many other heterostructures, such as GeSe/AsP (16%) [13], InS/InSe (13.17%) [60], Hf₂CO₂/MoS₂ (19.75%) [29], and MoS₂/BP (20.42%) [61] heterostructures (highlighted by the green circle). Thus, we conclude that the Sc₂CCl₂/Sc₂CBr₂ heterostructure is more promising and competitive for 2D vdW heterostructure solar cells.

Strain engineering is an effective method to change the structural, electronic, and magnetic properties of 2D materials [62]. In addition, strain is unavoidable in industrial production, which comes from bending, external loads, and lattice mismatch [46]. Applying a biaxial strain will alter the band structure of the heterostructure and affect its photocatalytic and photovoltaic performance [42,45]. Then, the effects of in-plane biaxial strain on the electronic properties of Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures are systematically studied. Here, the inner-layer biaxial strain (ε_in) is defined by ε_in = [(L − L₀)/L₀] × 100%, where L and L₀ are the lattice constants before and after the strain application, respectively. The applied strains η are −8%, −6%, −4%, −2%, 2%, 4%, 6%, and 8%, respectively. A negative value of η means that compressive strain is applied to the heterostructure. When η is positive, it indicates that tensile strain is applied to the heterostructure.

As shown in Figure S4, the electronic properties of the Sc₂CF₂/Sc₂CCl₂ heterostructure are significantly changed by applying biaxial strain. Compared with the Sc₂CF₂/Sc₂CCl₂ heterostructure without strain (Figure 3a), the applied strain changes the band gap of the heterostructure. From Figure 7a, it can be seen that when the compressive strain is −8%, −6%, −4%, and −2%, the band gap of the heterostructure decreases to 0.36, 0.39 eV, 0.46 eV, and 0.52 eV, respectively. Among them, the positions of the CBM and VBM have not changed and are still located at the high symmetry points M and Γ, as shown in Figure S4a–d. When the tensile strains are +2%, +4%, +6%, and +8%, respectively, the band gaps of the heterostructure increase to 0.62 eV, 0.66 eV, 0.72 eV, and 0.75 eV, respectively. The positions of the CBM and VBM are still located at the high symmetry points M and Γ, respectively (Figure S4e–h). With the increase in strain, the CBM of the Sc₂CCl₂ monolayer gradually moves away from the Fermi level, causing an increase in the band gaps. It can be seen from Figure 7b that the Sc₂CF₂/Sc₂CCl₂ heterostructure maintains a type-II band alignment throughout the strain. As for the band edge, all the heterostructures maintained photocatalytic activity under strain.

The electronic properties of the Sc₂CF₂/Sc₂CBr₂ heterostructure changed significantly when biaxial strain was applied, as shown in Figure S5. In contrast to the strain-free Sc₂CF₂/Sc₂CBr₂ heterostructure (Figure 3b), applying strain not only alters the band gaps of the heterostructure but also changes the band alignment of the heterostructure. As can be seen from Figure 7a, the band gaps of the Sc₂CF₂/Sc₂CBr₂ heterostructure decrease to 0.31 eV, 0.66 eV, and 0.77 eV when the compression strain is −6%, −4%, and −2%, with the CBM and VBM located at highly symmetric points M and Γ (Figure S5b–d). However, when the compressive strain increases to −8%, the band gap of the Sc₂CF₂/Sc₂CBr₂ heterostructure decreases to 0 eV. This indicates that the heterostructure transitions from an indirect band gap semiconductor to a metal under −8% compressive strain because the CBM (VBM) moves below (above) the Fermi level, as shown in Figure S5a. When the tensile strain was +2%, +4%, +6%, and +8%, the CBM and VBM were located at highly symmetric points M and Γ, with band gaps increasing to 0.79 eV, 0.80 eV, 0.81 eV, and 0.82 eV, respectively, as shown in Figure S5e–h. From Figure 7c, when the compressive strain is between −6% and −4%, the VBM of the Sc₂CBr₂ layer is positioned at a higher energy level than that of the VBM of the Sc₂CF₂ layer. Consequently, the VBM of the Sc₂CF₂/Sc₂CBr₂ heterostructure shifts from the Sc₂CF₂ layer to the Sc₂CBr₂ layer, leading to a transition from type-II to type-I. In addition, when the compression strain is −2%, the VBM of Sc₂CBr₂ is higher than that of E_O2/H2O, which is unfavorable for the photocatalytic reaction. By analyzing the band structure of the Sc₂CF₂/Sc₂CBr₂ heterostructure under strain, it is considered that the strain affects the relative position of atoms as well as the bonding properties and strength of the atoms, leading to a change in the band structure. The band alignment of the Sc₂CF₂/Sc₂CBr₂ heterostructure can be changed from type-I to type-II under different strain conditions.

For the Sc₂CCl₂/Sc₂CBr₂ heterostructure, the applied biaxial strain range is still −8%~8%. As shown in Figure S6, it is noteworthy that under −8%~6% biaxial strains, the heterostructures consistently maintain type-II banding and retain indirect band gap characteristics. As displayed in Figure 7a, the band gaps of the Sc₂CCl₂/Sc₂CBr₂ heterostructure decrease to 0.17 eV, 0.55 eV, 0.88 eV, and 1.14 eV when compressive strain is applied. As the tensile strain increases, the band gap also increases, reaching 1.53 eV, 1.67 eV, 1.79 eV, and 1.88 eV, respectively. Under −8%~6% biaxial strains, the CBM and VBM are still contributed by Sc₂CCl₂ and Sc₂CBr₂, located at the M and Γ points, respectively, as depicted in Figure 7d. Unlike these changes, under the tensile strain of 8%, the CBM of the Sc₂CCl₂ layer becomes higher than the CBM of the Sc₂CBr₂ layer. Thus, the CBM of the Sc₂CCl₂/Sc₂CBr₂ heterostructure shifts from the Sc₂CCl₂ layer to the Sc₂CBr₂ layer, leading to a type-II to type-I transformation. In addition, we calculated the PCE values of the Sc₂CCl₂/Sc₂CBr₂ heterostructure under various biaxial strains, as illustrated in Figure 6d (highlighted by the black star). From Figure S7, we can see that a maximum PCE of 20.07% can be achieved under 2% tensile strain.

4. Conclusions

In summary, based on density functional theory calculations, we have systematically explored the electronic structure and optical properties towards photocatalytic water splitting as well as the photovoltaic applications for Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ vdW heterostructures. AIMD simulation and phonon spectrum results show that the Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures are thermally and dynamically stable. Sc₂CF₂/Sc₂CCl₂, Sc₂CF₂/Sc₂CBr₂, and Sc₂CCl₂/Sc₂CBr₂ heterostructures exhibit type-II band alignments with the CBM and VBM located in different monolayers. By further analyzing the band alignment and charge carrier transfer processes, the Sc₂CF₂/Sc₂CCl₂ and Sc₂CF₂/Sc₂CBr₂ heterostructures exhibit a direct Z-scheme photocatalyst. These properties can effectively separate the photogenerated carriers, making them suitable for photocatalytic water splitting. Remarkably, a PCE of 20.78% can be achieved for the Sc₂CCl₂/Sc₂CBr₂ heterostructure, which is higher than that of many other reported heterostructures. In addition, all the heterostructures exhibit excellent optical absorption coefficients in both the visible and UV regions, reaching the order of 10⁵ cm⁻¹. This theoretical work demonstrates that the Sc₂CX₂/Sc₂CY₂ (X, Y = F, Cl, Br) heterostructures are promising candidates for applications in photocatalytic and photovoltaic devices.