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Promising M_{2}CO_{2}/MoX_{2} (M = Hf, Zr; X = S, Se, Te) Heterostructures for Multifunctional Solar Energy Applications

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## Abstract

**:**

_{2}CO

_{2}/MoX

_{2}(M = Hf, Zr; X = S, Se, Te) vdW heterostructures, as well as their applications in the fields of photocatalytic and photovoltaic using density functional theory calculations. The lattice dynamic and thermal stabilities of designed M

_{2}CO

_{2}/MoX

_{2}heterostructures are confirmed. Interestingly, all the M

_{2}CO

_{2}/MoX

_{2}heterostructures exhibit intrinsic type-II band structure features, which effectively inhibit the electron-hole pair recombination and enhance the photocatalytic performance. Furthermore, the internal built-in electric field and high anisotropic carrier mobility can separate the photo-generated carriers efficiently. It is noted that M

_{2}CO

_{2}/MoX

_{2}heterostructures exhibit suitable band gaps in comparison to the M

_{2}CO

_{2}and MoX

_{2}monolayers, which enhance the optical-harvesting abilities in the visible and ultraviolet light zones. Zr

_{2}CO

_{2}/MoSe

_{2}and Hf

_{2}CO

_{2}/MoSe

_{2}heterostructures possess suitable band edge positions to provide the competent driving force for water splitting as photocatalysts. In addition, Hf

_{2}CO

_{2}/MoS

_{2}and Zr

_{2}CO

_{2}/MoS

_{2}heterostructures deliver a power conversion efficiency of 19.75% and 17.13% for solar cell applications, respectively. These results pave the way for exploring efficient MXenes/TMDCs vdW heterostructures as photocatalytic and photovoltaic materials.

## 1. Introduction

_{n}

_{+1}X

_{n}T

_{x}(n = 1~3), in which M is early transition metals, X refers to carbon or nitrogen, and T indicates surface terminations, such as hydroxyl groups, oxygen, or fluorine [10,20]. Usually, the functionalization of the MXenes surface makes the modulation of electronic properties more efficient [21,22], which enhances the possibility of solar energy-related applications [23,24,25,26].

_{2}, where M refers to the transition metal elements (W, Mo, Re, etc.), and X represents the elements (S, Se, and Te). TMDCs materials exhibit a similar three-layer structure, where a transition metal atom single layer is sandwiched between two hexagonal chalcogenide atom planes. TMDCs have garnered significant interest owing to their emergent properties in the realm of light-emitting and photonic devices [27,28,29]. Among the TMDCs family, MoS

_{2}, MoSe

_{2,}and MoTe

_{2}stand out with their distinguished physical and chemical properties, such as good stability, flexibility, electronic conductivity, optical, and catalytic properties [30,31,32,33]. However, the applications of transition metal dichalcogenides (TMDCs) in photocatalytic and photovoltaic applications are hindered by limitations such as inadequate spatial separation of electron-hole pairs, substantial photo-corrosion, and high light transmittance [34]. Consequently, a promising approach to enhance electron-hole separation in TMDCs is the construction of heterostructures with 2D semiconducting materials.

_{2}/Ti

_{3}C

_{2}[39] and MoSe

_{2}/Ti

_{3}C

_{2}O

_{2}[40] integrate the properties of their individual components, which show potential applications in photocatalysis, photovoltaics, and optoelectronics. The abundance and possibilities of combining MXenes and TMDCs together promote the investigation of MXene/TMDC vdW heterostructures of general interest and great importance. It is worth noting that the oxygen-functionalized MXenes materials Hf

_{2}CO

_{2}and Zr

_{2}CO

_{2}possess suitable band gaps for solar energy harvesting applications. The construction of heterostructures using M

_{2}CO

_{2}(M = Hf, Zr) and TMDCs MoX

_{2}(X = S, Se, Te) with the same hexagonal 2D lattice and restricted lattice mismatch not only serves as a remedy for the aforementioned drawbacks of MoX

_{2}materials but also exhibits significant potential for optoelectronic and photocatalytic applications.

_{2}CO

_{2}/MoX

_{2}(M = Hf, Zr; X = S, Se, Te) heterostructures to investigate their photocatalytic hydrolysis and photoelectric conversion mechanism to evaluate the potential in photocatalytic and photovoltaic applications. Using first-principles calculations, we performed a comprehensive study on the structural stability, electronic structure, photocatalytic mechanism, and optoelectronic properties of M

_{2}CO

_{2}/MoX

_{2}heterostructures. Interestingly, the Zr

_{2}CO

_{2}/MoSe

_{2}and Hf

_{2}CO

_{2}/MoSe

_{2}heterostructures have the potential for promising candidates for overall water splitting, owing to their band gaps and band edge positions that are suitable for photocatalytic water splitting. Moreover, the estimated maximum power conversion efficiencies of Hf

_{2}CO

_{2}/MoS

_{2}and Zr

_{2}CO

_{2}/MoS

_{2}heterostructures are pretty excellent and are considerably competitive with other existing heterostructures. These findings will diversify catalyst options of MXenes/TMDCs vdW heterostructures for photocatalytic hydrogen production and solar cell energy storage.

## 2. Experimental Section

#### 2.1. Computational Details

^{−5}eV and 0.01 eV/Å, respectively. The Grimme’s DFT-D3 method was used to include the long-range vdW interactions [46,47]. The HSE06 hybrid density was functional and was utilized for the precise determination of bandgap values [48]. To verify the lattice dynamic stability of heterostructures, the phono dispersion curves were calculated using Phonopy code [49] with a 3 × 3 × 1 supercell. In order to investigate the thermodynamic stability of M

_{2}CO

_{2}/MoX

_{2}heterostructures at room temperature (300 K), ab initio molecular dynamics (AIMD) simulations were performed with a supercell of size 3 × 3 × 1 [50,51].

#### 2.2. Data Analysis

_{2}CO

_{2}/MoX

_{2}heterostructures, ${E}_{{\mathrm{M}}_{2}{\mathrm{CO}}_{2}}$ and ${E}_{{\mathrm{MoX}}_{2}}$ are the total energies of pristine M

_{2}CO

_{2}and MoX

_{2}monolayers, respectively. On the other hand, we have also calculated the 2D heterostructure binding energy ${E}_{\mathrm{b}}$ to assess the strength of vdW interactions according to:

_{2}CO

_{2}and MoX

_{2}monolayers fixed in the corresponding heterostructure lattice, and ${S}_{\mathrm{h}}$ represents the 2D unit cell area. The absorption coefficients of 2D materials $\alpha \left(\omega \right)$ are derived from [54]:

## 3. Results and Discussion

_{2}(X = S, Se, Te) and M

_{2}CO

_{2}(M = Zr, Hf) monolayers. The optimized lattice constants using DFT-D3 functionals of the MoS

_{2}, MoSe

_{2}, MoTe

_{2}, Zr

_{2}CO

_{2,}and Hf

_{2}CO

_{2}monolayers are 3.16, 3.29, 3.52, 3.30, and 3.25 Å, respectively. The corresponding projected band structures are illustrated in Figure S1. MoX

_{2}monolayers are direct band gap semiconductors, where the conduction band minimum (CBM) and the valence band maximum (VBM) are located at the K point. The HSE06 band gaps of MoS

_{2}, MoSe

_{2,}and MoTe

_{2}monolayers are 2.23, 2.00, and 1.63 eV. While Zr

_{2}CO

_{2}and Hf

_{2}CO

_{2}exhibit indirect bandgap semiconductor features, whose band gap values are 1.68 and 1.69 eV, respectively. The calculated results (listed in Table S1) are consistent with the previous literature [56,57,58,59,60,61,62,63].

_{2}CO

_{2}/MoX

_{2}(M = Hf, Zr; X = S, Se, Te) heterostructures were built. The lattice mismatches observed between the M

_{2}CO

_{2}and MoX

_{2}monolayers fall within the reasonable range from 0.1% to 7.9%, which indicates the feasibility of establishing M

_{2}CO

_{2}/MoX

_{2}heterostructures. Herein, to investigate the stability of M

_{2}CO

_{2}/MoX

_{2}heterostructures, six distinct stacking configurations were examined. Taking Zr

_{2}CO

_{2}/MoS

_{2}as an example, Figure 1 displays the top and side views of the diverse stacking structures examined, and Table S2 presents the respective calculated total energies. Details of the most stable structures after structural optimization under the van der Waals correction algorithm are presented in Table S3. It is noted that stacking II is the most stable model for most systems. The only exception is that stacking IV is the most stable configuration for Hf

_{2}CO

_{2}/MoTe

_{2}heterostructure. In the following, the most stable stacking configurations were used for further electronic structure calculations. The formation energies presented in Table S3 demonstrate the energetic favorability of these heterostructures, as evidenced by their negative or minimally positive values [64]. Additionally, all heterostructures are classical van der Waals heterostructures, whose optimized interlayer distances and binding energy are around 3 Å and −20 meV/Å

^{2}[65], respectively. Moreover, the negative binding energy corresponds to the exothermic reaction, which further confirms the feasibility from the thermodynamics point of view.

_{2}CO

_{2}/MoX

_{2}heterostructures, we performed phonon dispersion calculations and AIMD simulations. For one thing, Figure 2 illustrates the phonon dispersion curves for the M

_{2}CO

_{2}/MoX

_{2}heterostructures. Owing to the existence of eight atoms within each unit cell of the heterostructure, a total of 24 spectral lines are generated in Figure 2, encompassing 21 optical modes and 3 acoustic modes. Furthermore, minimal imaginary frequencies are observed from the phonon dispersion curves, which could be eliminated by depositing the M

_{2}CO

_{2}/MoX

_{2}heterostructures onto suitable substrates or applying slight strain [66,67]. For another, it can be seen from the energy and structure evolutions in Figure 3 that total energies change in small ranges with temperature and atoms vibrate only slightly around the equilibrium position after a simulation time of 9 ps. Overall, M

_{2}CO

_{2}/MoX

_{2}vdW heterostructures show good lattice dynamic and thermal dynamic stabilities.

_{2}CO

_{2}/MoX

_{2}heterostructures are illustrated in Figure 4. It can be seen that Hf

_{2}CO

_{2}/MoTe

_{2}and Zr

_{2}CO

_{2}/MoTe

_{2}show direct band gap structures, where both VBM and CBM locate at the M point. On the other hand, the other heterostructures present indirect band gap features. Table S4 lists the calculated band gaps of the most stable configurations for M

_{2}CO

_{2}/MoX

_{2}heterostructures. As listed in Tables S1 and S4, the band gaps of Hf

_{2}CO

_{2}/MoS

_{2}, Hf

_{2}CO

_{2}/MoSe

_{2}, Hf

_{2}CO

_{2}/MoTe

_{2}, Zr

_{2}CO

_{2}/MoS

_{2,}Zr

_{2}CO

_{2}/MoSe

_{2}and Zr

_{2}CO

_{2}/MoTe

_{2}heterostructures are comparatively lower than those of their corresponding monolayers, with values of 1.35, 1.64, 0.66, 1.11, 1.69, and 1.13 eV, respectively. This observation indicates that the electron can be excited and more accessible with less light energy. In Hf

_{2}CO

_{2}/MoS

_{2}and Zr

_{2}CO

_{2}/MoS

_{2}heterostructures, the VBM are primarily influenced by the contribution of the M

_{2}CO

_{2}layers, while the CBM are predominantly determined by the MoX

_{2}layers. In contrast, the VBM and CBM are dominated by MoX

_{2}and M

_{2}CO

_{2}monolayers in the other heterostructures, respectively. Interestingly, all the M

_{2}CO

_{2}/MoX

_{2}heterostructures are categorized as type-II heterostructures, which enables the effective separation of photo-generated charge carriers [36].

_{2}CO

_{2}and MoX

_{2}monolayers, the charge density difference $\Delta \rho $ can be calculated from the following [68]:

_{2}CO

_{2}/MoX

_{2}heterostructures, M

_{2}CO

_{2}and MoX

_{2}monolayers, respectively. The 3D iso-surface and planar average of the charge difference densities along the z-direction are illustrated in Figure 5. Except for Zr

_{2}CO

_{2}/MoS

_{2}heterostructure, the charges consume in the MoX

_{2}sides and accumulate in the M

_{2}CO

_{2}regions. From the Bader charge analysis listed in Table S5, we found that 0.0066, 0.0104, 0.0157, 0.0094, and 0.0197 electrons transfer from MoX

_{2}to M

_{2}CO

_{2}slabs in the Hf

_{2}CO

_{2}/MoS

_{2}, Hf

_{2}CO

_{2}/MoSe

_{2}, Hf

_{2}CO

_{2}/MoTe

_{2}, Zr

_{2}CO

_{2}/MoSe

_{2,}and Zr

_{2}CO

_{2}/MoTe

_{2}heterostructures, respectively. On the contrary, for Zr

_{2}CO

_{2}/MoS

_{2}, there are 0.0158 electrons from Zr

_{2}CO

_{2}to the MoS

_{2}side. The charge transfer contributes to the formation of built-in electric fields between the monolayers, which drives the photo-generated electrons and holes in opposite directions and further promotes the separation of electrons from holes [69]. It has been observed that the degree of charge transfer between layers exhibits a strong correlation with photocatalytic and photovoltaic activities. The electron localization functions (ELF) further visualize the detailed chemical bonding features in M

_{2}CO

_{2}/MoX

_{2}heterostructures. Figure 6 presents the 2D contour plots of ELF in the (110) plane. It shows that the ELF bond points of the vdW bonding are about 0.040 for M

_{2}CO

_{2}/MoX

_{2}heterostructures, which confirms the vdW interaction between M

_{2}CO

_{2}and MoX

_{2}layers.

_{2}CO

_{2}, MoX

_{2}monolayers, and M

_{2}CO

_{2}/MoX

_{2}heterostructures in conjunction with the work functions were investigated, as shown in Figure 7. The energy levels of the VBM and CBM of the MoS

_{2}, MoSe

_{2}, Hf

_{2}CO

_{2}, and Zr

_{2}CO

_{2}monolayers satisfy the requirements of the redox potential of water splitting. However, the VBM of the MoTe

_{2}monolayer is higher than the oxidation-reduction potential. The result agrees well with the previous report [60]. Herein, the work functions for MoS

_{2}, MoSe

_{2}, MoTe

_{2}, Zr

_{2}CO

_{2,}and Hf

_{2}CO

_{2}monolayers are 5.68, 5.06, 4.60, 5.23, and 5.17 eV, respectively. The disparity in the work function across monolayers contributes to the electron transfer in the vdW heterostructures until the Fermi energy level reaches equilibrium, which is beneficial to form built-in electric fields. Herein, Hf

_{2}CO

_{2}/MoSe

_{2}and Zr

_{2}CO

_{2}/MoSe

_{2}heterostructures with suitable band edge alignments for water oxidations and reductions, render them effective photocatalysts for overall water splitting.

_{2}CO

_{2}/MoX

_{2}heterostructures along the x and y directions with the orthorhombic lattices. We have rebuilt the hexagonal cell to an orthorhombic cell for the carrier mobility calculations, as shown in Figure S2 by taking Zr

_{2}CO

_{2}/MoS

_{2}as an example. The effective masses (${m}^{\ast}$), deformation potentials (${E}_{1}$), 2D elastic modulus (${C}_{2\mathrm{D}}$), and carrier mobilities ($\mu $) are summarized in Table 1. On the one hand, the predicted hole mobilities of M

_{2}CO

_{2}/MoX

_{2}heterostructures are much larger than the electron mobilities. On the other hand, the carrier mobilities of M

_{2}CO

_{2}/MoX

_{2}exhibit the characteristic of high anisotropy. Generally, electron mobilities along the x direction are greater than the y direction, and vice versa, hole mobilities along the y direction are greater than the x direction. Therefore, the electrons tend to go through the x direction on the MoX

_{2}side, while the holes demonstrate a predilection for migration along the y-axis within the M

_{2}CO

_{2}domain of the heterostructures. Interestingly, the hole mobilities of Hf

_{2}CO

_{2}/MoS

_{2}and Hf

_{2}CO

_{2}/MoTe

_{2}heterostructures in the y direction have reached 9140.34 cm

^{2}V

^{−1}s

^{−1}and 7592.80 cm

^{2}V

^{−1}s

^{−1}, respectively, which are greater than silicon (~1400 cm

^{2}V

^{−1}s

^{−1}) [70]. The strong anisotropic carrier mobility in M

_{2}CO

_{2}/MoX

_{2}heterostructures can reduce the rate of electron-hole recombination, which is favorable to redox reactions and the photoelectric conversion process.

_{2}CO

_{2}/MoX

_{2}vdW heterostructures. Figure 8 depicts the absorption coefficient curves of the M

_{2}CO

_{2}/MoX

_{2}heterostructures and the corresponding monolayers using HSE06. In general, M

_{2}CO

_{2}/MoX

_{2}heterostructures exhibit significant enhancement in the optical absorption coefficient (blue curves in Figure 8), featuring multiple high absorption peaks in both the visible and ultraviolet regions. The absorption coefficient of M

_{2}CO

_{2}/MoX

_{2}is over two-fold higher than that of M

_{2}CO

_{2}and notably exceeds that of the corresponding MoX

_{2}monolayers. It is worth noting that Hf

_{2}CO

_{2}/MoS

_{2}and Zr

_{2}CO

_{2}/MoS

_{2}heterostructures exhibit stronger responses to infrared light than monolayers as well. Moreover, compared to M

_{2}CO

_{2}and MoX

_{2}monolayers, the absorption peaks of the vdW heterostructures undergo a slight redshift due to the narrowed bandgap. Therefore, the formation of heterostructures enhances optical response, showing promising potential for M

_{2}CO

_{2}/MoX

_{2}heterostructures in photocatalysis and photovoltaic applications.

_{2}CO

_{2}/MoSe

_{2}and Hf

_{2}CO

_{2}/MoSe

_{2}heterostructures are ideal materials for photocatalytic water splitting. The E

_{VBM}of Zr

_{2}CO

_{2}/MoSe

_{2}and Hf

_{2}CO

_{2}/MoSe

_{2}are more positive than the redox potential of O

_{2}/H

_{2}O (1.23 eV corresponds to the potential of −5.67 eV at pH = 0), while the E

_{CBM}is more negative than the redox potential of H

^{+}/H

_{2}O (0 eV corresponds to the potential of −4.44 eV at pH = 0). Meanwhile, they are also type-II semiconductors, which avoid the recombination of photo-generated carriers. Therefore, to further reveal the photocatalytic mechanism, we take the Zr

_{2}CO

_{2}/MoSe

_{2}and Hf

_{2}CO

_{2}/MoSe

_{2}heterostructures as examples to further analyze the adsorption and dissociation processes of water molecules on the surface of M

_{2}CO

_{2}, as presented in Figure 9a. Under light irradiation, electrons in the Zr

_{2}CO

_{2}/MoSe

_{2}heterostructure are excited from the valence bands to the conduction bands, while an equal amount of holes remain in the valence bands. Immediately afterward, electrons are transferred from the CBM of MoSe

_{2}to Zr

_{2}CO

_{2}, and holes are from the VBM of Zr

_{2}CO

_{2}to MoSe

_{2}, thus forming an internal electric field that effectively accelerates the electron-hole recombination. Combined with the projected band diagram, the hydrogen evolution reaction (HER) occurs on the Zr

_{2}CO

_{2}surface and the oxygen evolution reaction (OER) takes place on the MoSe

_{2}surface. For Hf

_{2}CO

_{2}/MoSe

_{2}heterostructure, the photocatalysis mechanism is the same. Here, we analyzed the HER processes on the Zr

_{2}CO

_{2}and Hf

_{2}CO

_{2}surfaces of the Zr

_{2}CO

_{2}/MoSe

_{2}and Hf

_{2}CO

_{2}/MoSe

_{2}heterostructures. Based on the crystal structure features, effective adsorption sites A~C and D~F were considered on the surfaces of Zr

_{2}CO

_{2}and Hf

_{2}CO

_{2}, as shown in Figure S3. The adsorption models were subjected to complete relaxation and the adsorption energies of water molecules ${E}_{\mathrm{ads}}^{{\mathrm{H}}_{2}\mathrm{O}/\mathrm{surface}}$ were calculated from [71]:

_{2}CO

_{2}and Hf

_{2}CO

_{2}surfaces, the optimal adsorption sites are C and F, where the HER will take place most possibly.

_{2}on the Zr

_{2}CO

_{2}and Hf

_{2}CO

_{2}surfaces of Zr

_{2}CO

_{2}/MoSe

_{2}and Hf

_{2}CO

_{2}/MoSe

_{2}heterostructures have been illustrated in Figure 9b. For Zr

_{2}CO

_{2}/MoSe

_{2}heterostructure, the isolated H adatoms exhibit an inclination to migrate in closer proximity to one another under a chemical driving force of −0.21 eV. This driving force is termed as the energy differential between two proximal hydrogen atoms (marked as Step-I and set to 0) and two remote hydrogen atoms (marked as Step-II) on the Zr

_{2}CO

_{2}surface. Afterward, H atoms will form H

_{2}molecules (marked as Step-III) accompanied by a chemical driving force of −4.48 eV (from −0.21 eV of Step-II to −4.69 eV of Step-III) on the Zr

_{2}CO

_{2}surface, while the system is less energetic and more thermodynamically stable. The generated hydrogen will be departed easily from the surface (marked as Step-IV), as only 0.12 eV energy is required (from −4.69 eV of Step-III to −4.57 eV of Step-IV). On the other hand, the process of producing H

_{2}molecules on the Hf

_{2}CO

_{2}surface of the Hf

_{2}CO

_{2}/MoSe

_{2}heterostructure is similar. The energies taken for the gradual approach of two distant H atoms to form an H

_{2}molecule and then to detach from the surface are −0.30, −6.13, and 0.08 eV, respectively.

_{2}CO

_{2}/MoX

_{2}heterostructures in solar cells, we conducted an estimation of the power conversion efficiency (PCE, $\eta $), which describes the ability of M

_{2}CO

_{2}/MoX

_{2}heterostructure materials to transform solar energy into electrical energy, proposed by Scharber et al. [72]:

_{2}CO

_{2}/MoX

_{2}heterostructures are listed in Table S6. Figure 10 shows simulated solar cell PCE as well as the charge carrier transfer route in M

_{2}CO

_{2}/MoX

_{2}heterostructures. Interestingly, the maximum PCEs of the Hf

_{2}CO

_{2}/MoS

_{2}and Zr

_{2}CO

_{2}/MoS

_{2}heterostructures are calculated to be 19.75% and 17.13% (red star highlighted in Figure 10a), respectively. Remarkably, the donor band gaps of Hf

_{2}CO

_{2}/MoS

_{2}and Zr

_{2}CO

_{2}/MoS

_{2}heterostructures are in the range of the ideal band gap for the best light absorption characteristics of solar cells [73,74]. As shown in Figure 10b, photon absorptions in M

_{2}CO

_{2}/MoX

_{2}heterostructures with high PCEs generate excited-free carriers to develop photocurrent more efficiently.

## 4. Conclusions

_{2}CO

_{2}(M = Hf, Zr), MoX

_{2}(X = S, Se, Te) monolayers and corresponding M

_{2}CO

_{2}/MoX

_{2}vdW heterostructures based on density functional theory calculations. Firstly, the most stable configurations of these heterostructures have been determined by the formation energy. The thermal and lattice dynamic stabilities of the M

_{2}CO

_{2}/MoX

_{2}heterostructures are demonstrated by the negligible fluctuations of total energy and atomic equilibrium positions with temperature during ab initio molecular dynamics simulations, coupled with the scarcity of imaginary frequencies present in the phonon dispersion curves. Secondly, the calculated bandgap values of these heterostructures exhibit a reduced extent in comparison to those of the associated monolayers. It is noted Hf

_{2}CO

_{2}/MoTe

_{2}, and Zr

_{2}CO

_{2}/MoTe

_{2}heterostructures display direct band gap characteristics, which are favorable for solar light absorption. Moreover, it is found that built-in polarization electric fields generated near the interfaces, as well as the high and anisotropic carrier mobility, can facilitate the photo-generated carrier separation to improve the photoelectric conversion process. In contrast to the M

_{2}CO

_{2}and MoX

_{2}monolayers, the M

_{2}CO

_{2}/MoX

_{2}heterostructures display a heightened optical absorption effect, predominantly within the ultraviolet and visible light spectra. Interestingly, the M

_{2}CO

_{2}/MoX

_{2}heterostructures all exhibit the intrinsic type-II semiconductors, the VBM and CBM primarily influenced by the contribution of different layers, which effectively hinder the recombination of electron-hole pairs. Lastly, the Zr

_{2}CO

_{2}/MoSe

_{2}and Hf

_{2}CO

_{2}/MoSe

_{2}heterostructures are considered highly prospective contenders for water splitting, given their appropriate band gaps and band edge positions that furnish ample driving force for the redox reaction of water. Furthermore, the designed Hf

_{2}CO

_{2}/MoS

_{2}and Zr

_{2}CO

_{2}/MoS

_{2}heterostructures can achieve PCE values of 19.75% and 17.13%, respectively. The present study reveals that M

_{2}CO

_{2}/MoX

_{2}vdW heterostructures are potential candidates for photocatalytic and photovoltaic device applications.

## Supplementary Materials

_{2}, (b) MoSe

_{2}, (c) MoTe

_{2}, (d) Zr

_{2}CO

_{2}, (e) Hf

_{2}CO

_{2}monolayers. (f) The first Brillouin zone and high symmetry points of the hexagonal 2D lattice; Figure S2. An orthorhombic lattice instead of the traditional hexagonal lattice was adopted to calculate the intrinsic responses to uniaxial strain in the Zr

_{2}CO

_{2}/MoS

_{2}heterostructure; Figure S3. Different adsorption sites of the water molecule on the (a) Zr

_{2}CO

_{2}and (b) Hf

_{2}CO

_{2}surfaces of the Zr

_{2}CO

_{2}/MoSe

_{2}and Hf

_{2}CO

_{2}/MoSe

_{2}heterostructures; Figure S4. Optimized structures and adsorption energies of the water molecule with H as the adsorption atom at (a) A, (b) B, (c) C adsorption site and O as the adsorption atom at (d) A, (e) B, (f) C adsorption site on the Zr

_{2}CO

_{2}surface of the Zr

_{2}CO

_{2}/MoSe

_{2}heterostructure; Figure S5. Optimized structures and adsorption energies of the water molecule with H as the adsorption atom at (a) D, (b) E, (c) F adsorption site and O as the adsorption atom at (d) D, (e) E, (f) F adsorption site on the Hf

_{2}CO

_{2}surface of the Hf

_{2}CO

_{2}/MoSe

_{2}heterostructure; Figure S6. The HSE06 band structures of mutually independent monolayers fixed in the heterostructure lattices for (a) Hf

_{2}CO

_{2}/MoS

_{2}, (b) Hf2CO

_{2}/MoSe

_{2}, (c) Hf

_{2}CO

_{2}/MoTe

_{2}, (d) Zr

_{2}CO

_{2}/MoS

_{2}, (e) Zr

_{2}CO

_{2}/MoSe

_{2}and (f) Zr

_{2}CO

_{2}/MoTe

_{2}; Table S1. The lattice constants a (Å), band gaps E

_{g}(eV) and band gap types of M

_{2}CO

_{2}(M = Zr, Hf) and MoX

_{2}(X = S, Se, Te) monolayers; Table S2. The total energy (eV) of different stacking configurations for M

_{2}CO

_{2}/MoX

_{2}heterostructures; Table S3. The lattice constants a (Å), interlayer distance d (Å), degree of lattice mismatch K, formation energy E

_{f}(meV) and binding energy E

_{b}(meV/Å

^{2}) for the most stable configurations of M

_{2}CO

_{2}/MoX

_{2}heterostructures; Table S4. The calculated band gap E

_{g}(eV) of the most stable configurations for M

_{2}CO

_{2}/MoX

_{2}heterostructures; Table S5. The total charge transfer amounts between MoX

_{2}and M

_{2}CO

_{2}in the M

_{2}CO

_{2}/MoX

_{2}heterostructures; Table S6. The conduction band offset ΔE

_{c}(eV), donor band gap ${E}_{\mathrm{g}}^{\mathrm{d}}$ (eV), and calculated power conversion efficiency (PCE) η (%) of M

_{2}CO

_{2}/MoX

_{2}heterostructures for solar cell applications. References [56,57,58,59,60,61,62,63] are cited in the supplementary materials.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Khan, K.; Tareen, A.K.; Aslam, M.; Sagar, R.U.R.; Zhang, B.; Huang, W.; Mahmood, A.; Mahmood, N.; Khan, K.; Zhang, H.; et al. Recent progress, challenges, and prospects in Two-Dimensional Photo-Catalyst materials and environmental remediation. Nano-Micro Lett.
**2020**, 12, 167. [Google Scholar] [CrossRef] - Luo, B.; Liu, G.; Wang, L. Recent advances in 2D materials for photocatalysis. Nanoscale
**2016**, 8, 6904–6920. [Google Scholar] [CrossRef] [PubMed] - Lewis, N.S.; Nocera, D.G. Powering the planet: Chemical challenges in solar energy utilization. Proc. Natl. Acad. Sci. USA
**2006**, 103, 15729–15735. [Google Scholar] [CrossRef] - Ginley, D.; Green, M.A.; Collins, R. Solar Energy Conversion Toward 1 Terawatt. MRS Bull.
**2008**, 33, 355–364. [Google Scholar] [CrossRef] - Novoselov, K.S.; Geim, A.K.; Morozov, S.V.; Jiang, D.; Katsnelson, M.I.; Grigorieva, I.V.; Dubonos, S.V.; Firsov, A.A. Two-dimensional gas of massless Dirac fermions in graphene. Nature
**2005**, 438, 197–200. [Google Scholar] [CrossRef] - Geim, A.K.; Novoselov, K.S. The rise of graphene. Nat. Mater.
**2007**, 6, 183–191. [Google Scholar] [CrossRef] - Novoselov, K.S.; Fal Ko, V.I.; Colombo, L.; Gellert, P.R.; Schwab, M.G.; Kim, K. A roadmap for graphene. Nature
**2012**, 490, 192–200. [Google Scholar] [CrossRef] - Novoselov, K.S.; Geim, A.K.; Morozov, S.V.; Jiang, D.; Zhang, Y.; Dubonos, S.V.; Grigorieva, I.V.; Firsov, A.A. Electric field effect in atomically thin carbon films. Science
**2004**, 306, 666–669. [Google Scholar] [CrossRef] [PubMed] - Shein, I.R.; Ivanovskii, A.L. Graphene-like nanocarbides and nanonitrides of d metals (MXenes): Synthesis, properties and simulation. Micro Nano Lett.
**2013**, 8, 59–62. [Google Scholar] [CrossRef] - Anasori, B.; Lukatskaya, M.R.; Gogotsi, Y. 2D metal carbides and nitrides (MXenes) for energy storage. Nat. Rev. Mater.
**2017**, 2, 16098. [Google Scholar] [CrossRef] - Fu, H.; Ramalingam, V.; Kim, H.; Lin, C.; Fang, X.; Alshareef, H.N.; He, J. MXene-Contacted Silicon Solar Cells with 11.5% Efficiency. Adv. Energy Mater.
**2019**, 9, 1900180. [Google Scholar] [CrossRef] - Li, X.; Wang, J.; Fang, Y.; Zhang, H.; Fu, X.; Wang, X. Roles of Metal-Free materials in photoelectrodes for water splitting. Acc. Mater. Res.
**2021**, 2, 933–943. [Google Scholar] [CrossRef] - Coleman, J.N.; Lotya, M.; O Neill, A.; Bergin, S.D.; King, P.J.; Khan, U.; Young, K.; Gaucher, A.; De, S.; Smith, R.J.; et al. Two-Dimensional nanosheets produced by liquid exfoliation of layered materials. Science
**2011**, 331, 568–571. [Google Scholar] [CrossRef] [PubMed] - Chhowalla, M.; Shin, H.S.; Eda, G.; Li, L.; Loh, K.P.; Zhang, H. The chemistry of two-dimensional layered transition metal dichalcogenide nanosheets. Nat. Chem.
**2013**, 5, 263–275. [Google Scholar] [CrossRef] - Sun, H.; Yan, Z.; Liu, F.; Xu, W.; Cheng, F.; Chen, J. Self-Supported Transition-Metal-Based electrocatalysts for hydrogen and oxygen evolution. Adv. Mater.
**2020**, 32, 1806326. [Google Scholar] [CrossRef] - Yang, Y.; Gao, J.; Zhang, Z.; Xiao, S.; Xie, H.; Sun, Z.; Wang, J.; Zhou, C.; Wang, Y.; Guo, X.; et al. Black phosphorus based photocathodes in wideband bifacial Dye-Sensitized solar cells. Adv. Mater.
**2016**, 28, 8937–8944. [Google Scholar] [CrossRef] [PubMed] - Zhao, J.; Liu, H.; Yu, Z.; Quhe, R.; Zhou, S.; Wang, Y.; Liu, C.C.; Zhong, H.; Han, N.; Lu, J.; et al. Rise of silicene: A competitive 2D material. Prog. Mater. Sci.
**2016**, 83, 24–151. [Google Scholar] [CrossRef] - Naguib, M.; Kurtoglu, M.; Presser, V.; Lu, J.; Niu, J.; Heon, M.; Hultman, L.; Gogotsi, Y.; Barsoum, M.W. Two-Dimensional nanocrystals produced by exfoliation of Ti
_{3}AlC_{2}. Adv. Mater.**2011**, 23, 4248–4253. [Google Scholar] [CrossRef] - Naguib, M.; Mashtalir, O.; Carle, J.; Presser, V.; Lu, J.; Hultman, L.; Gogotsi, Y.; Barsoum, M.W. Two-Dimensional transition metal carbides. ACS Nano
**2012**, 6, 1322–1331. [Google Scholar] [CrossRef] [PubMed] - Gan, J.; Li, F.; Tang, Q. Vacancies-Engineered M
_{2}CO_{2}MXene as an efficient hydrogen evolution reaction electrocatalyst. J. Phys. Chem. Lett.**2021**, 12, 4805–4813. [Google Scholar] [CrossRef] - Khazaei, M.; Arai, M.; Sasaki, T.; Chung, C.; Venkataramanan, N.S.; Estili, M.; Sakka, Y.; Kawazoe, Y. Novel electronic and magnetic properties of Two-Dimensional transition metal carbides and nitrides. Adv. Funct. Mater.
**2013**, 23, 2185–2192. [Google Scholar] [CrossRef] - Khazaei, M.; Ranjbar, A.; Arai, M.; Sasaki, T.; Yunoki, S. Electronic properties and applications of MXenes: A theoretical review. J. Mater. Chem. C
**2017**, 5, 2488–2503. [Google Scholar] [CrossRef] - Guo, Z.; Zhou, J.; Zhu, L.; Sun, Z. MXene: A promising photocatalyst for water splitting. J. Mater. Chem. A
**2016**, 4, 11446–11452. [Google Scholar] [CrossRef] - Zhang, Y.; Xiong, R.; Sa, B.; Zhou, J.; Sun, Z. MXenes: Promising donor and acceptor materials for high-efficiency heterostructure solar cells. Sustain. Energy Fuels
**2021**, 5, 135–143. [Google Scholar] [CrossRef] - Ghidiu, M.; Lukatskaya, M.R.; Zhao, M.; Gogotsi, Y.; Barsoum, M.W. Conductive two-dimensional titanium carbide ‘clay’ with high volumetric capacitance. Nature
**2014**, 516, 78–81. [Google Scholar] [CrossRef] [PubMed] - Seh, Z.W.; Fredrickson, K.D.; Anasori, B.; Kibsgaard, J.; Strickler, A.L.; Lukatskaya, M.R.; Gogotsi, Y.; Jaramillo, T.F.; Vojvodic, A. Two-Dimensional molybdenum carbide (MXene) as an efficient electrocatalyst for hydrogen evolution. ACS Energy Lett.
**2016**, 1, 589–594. [Google Scholar] [CrossRef] - Withers, F.; Del Pozo-Zamudio, O.; Schwarz, S.; Dufferwiel, S.; Walker, P.M.; Godde, T.; Rooney, A.P.; Gholinia, A.; Woods, C.R.; Blake, P.; et al. WSe
_{2}Light-Emitting tunneling transistors with enhanced brightness at room temperature. Nano Lett.**2015**, 15, 8223–8228. [Google Scholar] [CrossRef] [PubMed] - Schwarz, S.; Kozikov, A.; Withers, F.; Maguire, J.K.; Foster, A.P.; Dufferwiel, S.; Hague, L.; Makhonin, M.N.; Wilson, L.R.; Geim, A.K.; et al. Electrically pumped single-defect light emitters in WSe
_{2}. 2D Mater.**2016**, 3, 25038. [Google Scholar] [CrossRef] - Zheng, W.; Jiang, Y.; Hu, X.; Li, H.; Zeng, Z.; Wang, X.; Pan, A. Light emission properties of 2D transition metal dichalcogenides: Fundamentals and applications. Adv. Opt. Mater.
**2018**, 6, 1800420. [Google Scholar] [CrossRef] - Wang, H.; Yuan, H.; Sae Hong, S.; Li, Y.; Cui, Y. Physical and chemical tuning of two-dimensional transition metal dichalcogenides. Chem. Soc. Rev.
**2015**, 44, 2664–2680. [Google Scholar] [CrossRef] - Vante, N.A.; Jaegermann, W.; Tributsch, H.; Hoenle, W.; Yvon, K. Electrocatalysis of oxygen reduction by chalcogenides containing mixed transition metal clusters. J. Am. Chem. Soc.
**1987**, 109, 3251–3257. [Google Scholar] [CrossRef] - Bag, S.; Arachchige, I.U.; Kanatzidis, M.G. Aerogels from metal chalcogenides and their emerging unique properties. J. Mater. Chem.
**2008**, 18, 3628–3632. [Google Scholar] [CrossRef] - Pumera, M.; Sofer, Z.; Ambrosi, A. Layered transition metal dichalcogenides for electrochemical energy generation and storage. J. Mater. Chem. A
**2014**, 2, 8981–8987. [Google Scholar] [CrossRef] - Gelly, R.J.; Renaud, D.; Liao, X.; Pingault, B.; Bogdanovic, S.; Scuri, G.; Watanabe, K.; Taniguchi, T.; Urbaszek, B.; Park, H.; et al. Probing dark exciton navigation through a local strain landscape in a WSe
_{2}monolayer. Nat. Commun.**2022**, 13, 232. [Google Scholar] [CrossRef] - Jariwala, D.; Marks, T.J.; Hersam, M.C. Mixed-dimensional van der Waals heterostructures. Nat. Mater.
**2017**, 16, 170–181. [Google Scholar] [CrossRef] [PubMed] - Rivera, P.; Seyler, K.L.; Yu, H.; Schaibley, J.R.; Yan, J.; Mandrus, D.G.; Yao, W.; Xu, X. Valley-polarized exciton dynamics in a 2D semiconductor heterostructure. Science
**2016**, 351, 688–691. [Google Scholar] [CrossRef] [PubMed] - Xiong, R.; Hu, R.; Zhang, Y.; Yang, X.; Lin, P.; Wen, C.; Sa, B.; Sun, Z. Computational discovery of PtS
_{2}/GaSe van der Waals heterostructure for solar energy applications. Phys. Chem. Chem. Phys.**2021**, 23, 20163–20173. [Google Scholar] [CrossRef] [PubMed] - Xiong, R.; Shu, Y.; Yang, X.; Zhang, Y.; Wen, C.; Anpo, M.; Wu, B.; Sa, B. Direct Z-scheme WTe
_{2}/InSe van der Waals heterostructure for overall water splitting. Catal. Sci. Technol.**2022**, 12, 3272–3280. [Google Scholar] [CrossRef] - Li, N.; Zhang, Y.; Jia, M.; Lv, X.; Li, X.; Li, R.; Ding, X.; Zheng, Y.; Tao, X. 1T/2H MoSe
_{2}-on-MXene heterostructure as bifunctional electrocatalyst for efficient overall water splitting. Electrochim. Acta**2019**, 326, 134976. [Google Scholar] [CrossRef] - Xiao, W.; Yan, D.; Zhang, Y.; Yang, X.; Zhang, T. Heterostructured MoSe
_{2}/Oxygen-Terminated Ti_{3}C_{2}MXene architectures for efficient electrocatalytic hydrogen evolution. Energy Fuels**2021**, 35, 4609–4615. [Google Scholar] [CrossRef] - Furthmüller, J.; Kresse, G. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B
**1996**, 54, 11169–11186. [Google Scholar] [CrossRef] - Wang, G.; Peng, L.; Li, K.; Zhu, L.; Zhou, J.; Miao, N.; Sun, Z. ALKEMIE: An intelligent computational platform for accelerating materials discovery and design. Comput. Mater. Sci.
**2021**, 186, 110064. [Google Scholar] [CrossRef] - Wang, G.; Li, K.; Peng, L.; Zhang, Y.; Zhou, J.; Sun, Z. High-Throughput Automatic Integrated Material Calculations and Data Management Intelligent Platform and the Application in Novel Alloys. Acta Metall. Sin.
**2022**, 58, 75–88. [Google Scholar] - Joubert, D.; Kresse, G. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B
**1999**, 59, 1758–1775. [Google Scholar] [CrossRef] - Burke, K.; Ernzerhof, M.; Perdew, J.P. Generalized gradient approximation made simple. Phys. Rev. Lett.
**1996**, 77, 3865–3868. [Google Scholar] [CrossRef] - Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys.
**2010**, 132, 154104. [Google Scholar] [CrossRef] - Grimme, S.; Ehrlich, S.; Goerigk, L. Effect of the damping function in dispersion corrected density functional theory. J. Comput. Chem.
**2011**, 32, 1456–1465. [Google Scholar] [CrossRef] [PubMed] - Heyd, J.; Scuseria, G.E. Efficient hybrid density functional calculations in solids: Assessment of the Heyd–Scuseria–Ernzerhof screened Coulomb hybrid functional. J. Chem. Phys.
**2004**, 121, 1187–1192. [Google Scholar] [CrossRef] - Oba, F.; Tanaka, I.; Togo, A. First-principles calculations of the ferroelastic transition between rutile-type and CaCl
_{2}-type SiO_{2}at high pressures. Phys. Rev. B**2008**, 78, 134106. [Google Scholar] [CrossRef] - Nosé, S. A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys.
**1984**, 81, 511–519. [Google Scholar] [CrossRef] - Hoover, W.G. Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A
**1985**, 31, 1695–1697. [Google Scholar] [CrossRef] - Washburn, J.; Chen, Y. Structural transition in Large-Lattice-Mismatch heteroepitaxy. Phys. Rev. Lett.
**1996**, 77, 4046–4049. [Google Scholar] [CrossRef] - Liao, J.; Sa, B.; Zhou, J.; Ahuja, R.; Sun, Z. Design of High-Efficiency Visible-Light photocatalysts for water splitting: MoS
_{2}/AlN(GaN) heterostructures. J. Phys. Chem. C**2014**, 118, 17594–17599. [Google Scholar] [CrossRef] - Shi, G.; Kioupakis, E. Electronic and optical properties of nanoporous silicon for Solar-Cell applications. ACS Photon.
**2015**, 2, 208–215. [Google Scholar] [CrossRef] - Shockley, W.; Bardeen, J. Deformation potentials and mobilities in Non-Polar crystals. Phys. Rev.
**1950**, 80, 72–80. [Google Scholar] [CrossRef] - Gandi, A.N.; Alshareef, H.N.; Schwingenschlögl, U. Thermoelectric performance of the MXenes M
_{2}CO_{2}(M = Ti, Zr, or Hf). Chem. Mater.**2016**, 28, 1647–1652. [Google Scholar] [CrossRef] - Munawar, M.; Idrees, M.; Ahmad, I.; Din, H.U.; Amin, B. Intriguing electronic, optical and photocatalytic performance of BSe, M
_{2}CO_{2}monolayers and BSe–M_{2}CO_{2}(M = Ti, Zr, Hf) van der Waals heterostructures. RSC Adv.**2022**, 12, 42–52. [Google Scholar] [CrossRef] - Fu, C.; Li, X.; Luo, Q.; Yang, J. Two-dimensional multilayer M
_{2}CO_{2}(M = Sc, Zr, Hf) as photocatalysts for hydrogen production from water splitting: A first principles study. J. Mater. Chem. A**2017**, 5, 24972–24980. [Google Scholar] [CrossRef] - Xu, X.; Ge, X.; Liu, X.; Li, L.; Fu, K.; Dong, Y.; Meng, F.; Si, R.; Zhang, M. Two-dimensional M
_{2}CO_{2}/MoS_{2}(M = Ti, Zr and Hf) van der Waals heterostructures for overall water splitting: A density functional theory study. Ceram. Int.**2020**, 46, 13377–13384. [Google Scholar] [CrossRef] - Zhuang, H.L.; Hennig, R.G. Computational search for Single-Layer Transition-Metal dichalcogenide photocatalysts. J. Phys. Chem. C
**2013**, 117, 20440–20445. [Google Scholar] [CrossRef] - Xu, X.; Wu, X.; Tian, Z.; Zhang, M.; Li, L.; Zhang, J. Modulating the electronic structures and potential applications of Zr
_{2}CO_{2}/MSe_{2}(M = Mo, W) heterostructures by different stacking modes: A density functional theory calculation. Appl. Surf. Sci.**2022**, 599, 154014. [Google Scholar] [CrossRef] - Li, X.; Cui, X.; Xing, C.; Cui, H.; Zhang, R. Strain-tunable electronic and optical properties of Zr
_{2}CO_{2}MXene and MoSe_{2}van der Waals heterojunction: A first principles calculation. Appl. Surf. Sci.**2021**, 548, 149249. [Google Scholar] [CrossRef] - Wang, B.; Wang, X.; Wang, P.; Kuang, A.; Zhou, T.; Yuan, H.; Chen, H. Bilayer MoTe
_{2}/XS_{2}(X = Hf, Sn, Zr) heterostructures with efficient carrier separation and light absorption for photocatalytic water splitting into hydrogen. Appl. Surf. Sci.**2021**, 544, 148842. [Google Scholar] [CrossRef] - Chen, J.; He, X.; Sa, B.; Zhou, J.; Xu, C.; Wen, C.; Sun, Z. III–VI van der Waals heterostructures for sustainable energy related applications. Nanoscale
**2019**, 11, 6431–6444. [Google Scholar] [CrossRef] - Gulans, A.; Krasheninnikov, A.V.; Nieminen, R.M.; Björkman, T. Van der Waals Bonding in Layered Compounds from Advanced Density-Functional First-Principles Calculations. Phys. Rev. Lett.
**2012**, 108, 235502. [Google Scholar] [CrossRef] - Mannix, A.J.; Zhou, X.; Kiraly, B.; Wood, J.D.; Alducin, D.; Myers, B.D.; Liu, X.; Fisher, B.L.; Santiago, U.; Guest, J.R.; et al. Synthesis of borophenes: Anisotropic, two-dimensional boron polymorphs. Science
**2015**, 350, 1513–1516. [Google Scholar] [CrossRef] - Penev, E.S.; Kutana, A.; Yakobson, B.I. Can Two-Dimensional boron superconduct? Nano Lett.
**2016**, 16, 2522–2526. [Google Scholar] [CrossRef] - Guo, G.; Wang, D.; Wei, X.; Zhang, Q.; Liu, H.; Lau, W.; Liu, L. First-Principles study of phosphorene and graphene heterostructure as anode materials for rechargeable Li batteries. J. Phys. Chem. Lett.
**2015**, 6, 5002–5008. [Google Scholar] [CrossRef] - Liu, J. Origin of high photocatalytic efficiency in monolayer g-C
_{3}N_{4}/CdS heterostructure: A hybrid DFT study. J. Phys. Chem. C**2015**, 119, 28417–28423. [Google Scholar] [CrossRef] - Xie, M.; Zhang, S.; Cai, B.; Huang, Y.; Zou, Y.; Guo, B.; Gu, Y.; Zeng, H. A promising two-dimensional solar cell donor: Black arsenic–phosphorus monolayer with 1.54 eV direct bandgap and mobility exceeding 14,000 cm
^{2}V^{−1}s^{−1}. Nano Energy**2016**, 28, 433–439. [Google Scholar] [CrossRef] - Xiong, R.; Yang, H.; Peng, Q.; Sa, B.; Wen, C.; Wu, B.; Sun, Z. First-principle investigation of TcSe
_{2}monolayer as an efficient visible light photocatalyst for water splitting hydrogen production. Res. Chem. Intermed.**2017**, 43, 5271–5282. [Google Scholar] [CrossRef] - Scharber, M.C.; Mühlbacher, D.; Koppe, M.; Denk, P.; Waldauf, C.; Heeger, A.J.; Brabec, C.J. Design rules for donors in Bulk-Heterojunction solar cells—Towards 10 % Energy-Conversion efficiency. Adv. Mater.
**2006**, 18, 789–794. [Google Scholar] [CrossRef] - Loferski, J.J. Theoretical considerations governing the choice of the optimum semiconductor for photovoltaic solar energy conversion. J. Appl. Phys.
**1956**, 27, 777–784. [Google Scholar] [CrossRef] - Sa, B.; Hu, R.; Zheng, Z.; Xiong, R.; Zhang, Y.; Wen, C.; Zhou, J.; Sun, Z. High-Throughput computational screening and machine learning modeling of janus 2D III–VI van der waals heterostructures for solar energy applications. Chem. Mater.
**2022**, 34, 6687–6701. [Google Scholar] [CrossRef]

**Figure 1.**Schematic views of the Zr

_{2}CO

_{2}/MoS

_{2}heterostructures stacked by varying the position of MoS

_{2}layers. The upper layer and the lower layer represent MoS

_{2}and Zr

_{2}CO

_{2}, respectively. I to VI correspond to the six configurations.

**Figure 2.**The phonon dispersion curves of (

**a**) Hf

_{2}CO

_{2}/MoS

_{2}, (

**b**) Hf

_{2}CO

_{2}/MoSe

_{2}, (

**c**) Hf

_{2}CO

_{2}/MoTe

_{2}, (

**d**) Zr

_{2}CO

_{2}/MoS

_{2}, (

**e**) Zr

_{2}CO

_{2}/MoSe

_{2}, and (

**f**) Zr

_{2}CO

_{2}/MoTe

_{2}heterostructures.

**Figure 3.**The evolutions of total energy and structure snapshots from AIMD simulations of (

**a**) Hf

_{2}CO

_{2}/MoS

_{2}, (

**b**) Hf

_{2}CO

_{2}/MoSe

_{2}, (

**c**) Hf

_{2}CO

_{2}/MoTe

_{2}, (

**d**) Zr

_{2}CO

_{2}/MoS

_{2}, (

**e**) Zr

_{2}CO

_{2}/MoSe

_{2}, and (

**f**) Zr

_{2}CO

_{2}/MoTe

_{2}heterostructures.

**Figure 4.**The projected band structures of (

**a**) Hf

_{2}CO

_{2}/MoS

_{2}, (

**b**) Hf

_{2}CO

_{2}/MoSe

_{2}, (

**c**) Hf

_{2}CO

_{2}/MoTe

_{2}, (

**d**) Zr

_{2}CO

_{2}/MoS

_{2}, (

**e**) Zr

_{2}CO

_{2}/MoSe

_{2}and (

**f**) Zr

_{2}CO

_{2}/MoTe

_{2}heterostructures using HSE06 functional. The Fermi energy level is set to zero.

**Figure 5.**The 3D iso-surfaces and plane-averaged charge density differences along the z-direction for: (

**a**) Hf

_{2}CO

_{2}/MoS

_{2}, (

**b**) Hf

_{2}CO

_{2}/MoSe

_{2}, (

**c**) Hf

_{2}CO

_{2}/MoTe

_{2}, (

**d**) Zr

_{2}CO

_{2}/MoS

_{2}, (

**e**) Zr

_{2}CO

_{2}/MoSe

_{2}, and (

**f**) Zr

_{2}CO

_{2}/MoTe

_{2}heterostructures. The depletion and accumulation of electrons are represented by magenta and blue contours, respectively.

**Figure 6.**ELF contour plots projected on the (110) plane of (

**a**) Hf

_{2}CO

_{2}/MoS

_{2}, (

**b**) Hf

_{2}CO

_{2}/MoSe

_{2}, (

**c**) Hf

_{2}CO

_{2}/MoTe

_{2}, (

**d**) Zr

_{2}CO

_{2}/MoS

_{2}, (

**e**) Zr

_{2}CO

_{2}/MoSe

_{2}and (

**f**) Zr

_{2}CO

_{2}/MoTe

_{2}heterostructures.

**Figure 7.**Band edge alignments of the M

_{2}CO

_{2}, MoX

_{2}monolayers, and M

_{2}CO

_{2}/MoX

_{2}vdW heterostructures.

**Figure 8.**The absorption coefficient of (

**a**) Hf

_{2}CO

_{2}/MoS

_{2}, (

**b**) Hf

_{2}CO

_{2}/MoSe

_{2}, (

**c**) Hf

_{2}CO

_{2}/MoTe

_{2}, (

**d**) Zr

_{2}CO

_{2}/MoS

_{2}, (

**e**) Zr

_{2}CO

_{2}/MoSe

_{2}, and (

**f**) Zr

_{2}CO

_{2}/MoTe

_{2}heterostructures together with the pristine monolayers using HSE06 functional.

**Figure 9.**(

**a**) The schematic illustrations of the charge transfer paths and overall water splitting of Zr

_{2}CO

_{2}/MoSe

_{2}(Hf

_{2}CO

_{2}/MoSe

_{2}) heterostructure. (

**b**) The generation processes of hydrogen on the Zr

_{2}CO

_{2}(Hf

_{2}CO

_{2}) surface of Zr

_{2}CO

_{2}/MoSe

_{2}(Hf

_{2}CO

_{2}/MoSe

_{2}) heterostructure.

**Figure 10.**(

**a**) A simulated PCE map refers to the donor band gap and conduction band offset of M

_{2}CO

_{2}/MoX

_{2}heterostructures. (

**b**) Schematic illustration of free charge carrier transfer path in M

_{2}CO

_{2}/MoX

_{2}heterostructure solar cells.

**Table 1.**The effective mass m* (m

_{0}), deformation potentials E

_{1}(eV), elastic moduli C

_{2D}(N/m), and carrier mobility μ (cm

^{2}V

^{−1}s

^{−1}) of MoX

_{2}/MoX

_{2}heterostructures.

System | Direction | Carrier Type | E_{1} | C_{2D} | m* | μ |
---|---|---|---|---|---|---|

Hf_{2}CO_{2}/MoS_{2} | x | e | −10.48 | 428.34 | 1.16 | 41.00 |

h | 2.06 | 428.34 | −0.55 | 4707.47 | ||

y | e | −9.40 | 421.71 | 2.00 | 16.71 | |

h | 1.33 | 421.71 | −0.61 | 9140.34 | ||

Hf_{2}CO_{2}/MoSe_{2} | x | e | 8.44 | 419.80 | 0.51 | 323.12 |

h | 2.80 | 419.80 | −0.66 | 1743.19 | ||

y | e | 7.63 | 417.61 | 2.09 | 23.01 | |

h | 2.72 | 417.61 | −0.58 | 2393.98 | ||

Hf_{2}CO_{2}/MoTe_{2} | x | e | 7.94 | 409.12 | 0.56 | 295.46 |

h | −3.75 | 409.12 | −1.30 | 243.67 | ||

y | e | 5.87 | 404.39 | 2.22 | 33.41 | |

h | −1.78 | 404.39 | −0.49 | 7592.80 | ||

Zr_{2}CO_{2}/MoS_{2} | x | e | −11.47 | 394.34 | 0.80 | 65.10 |

h | 5.21 | 394.34 | −0.72 | 396.73 | ||

y | e | −11.49 | 335.30 | 1.37 | 19.08 | |

h | 2.88 | 335.30 | −0.61 | 1555.99 | ||

Zr_{2}CO_{2}/MoSe_{2} | x | e | 6.82 | 368.68 | 0.76 | 192.50 |

h | 1.32 | 368.68 | −0.87 | 3928.96 | ||

y | e | 4.43 | 392.74 | 2.68 | 39.24 | |

h | 2.19 | 392.74 | −0.60 | 3227.15 | ||

Zr_{2}CO_{2}/MoTe_{2} | x | e | 10.55 | 323.53 | 8.85 | 0.52 |

h | −3.29 | 323.53 | −1.64 | 155.33 | ||

y | e | 6.10 | 369.17 | 2.95 | 16.00 | |

h | −3.81 | 369.17 | −0.55 | 1192.02 |

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**MDPI and ACS Style**

Wen, J.; Cai, Q.; Xiong, R.; Cui, Z.; Zhang, Y.; He, Z.; Liu, J.; Lin, M.; Wen, C.; Wu, B.;
et al. Promising M_{2}CO_{2}/MoX_{2} (M = Hf, Zr; X = S, Se, Te) Heterostructures for Multifunctional Solar Energy Applications. *Molecules* **2023**, *28*, 3525.
https://doi.org/10.3390/molecules28083525

**AMA Style**

Wen J, Cai Q, Xiong R, Cui Z, Zhang Y, He Z, Liu J, Lin M, Wen C, Wu B,
et al. Promising M_{2}CO_{2}/MoX_{2} (M = Hf, Zr; X = S, Se, Te) Heterostructures for Multifunctional Solar Energy Applications. *Molecules*. 2023; 28(8):3525.
https://doi.org/10.3390/molecules28083525

**Chicago/Turabian Style**

Wen, Jiansen, Qi Cai, Rui Xiong, Zhou Cui, Yinggan Zhang, Zhihan He, Junchao Liu, Maohua Lin, Cuilian Wen, Bo Wu,
and et al. 2023. "Promising M_{2}CO_{2}/MoX_{2} (M = Hf, Zr; X = S, Se, Te) Heterostructures for Multifunctional Solar Energy Applications" *Molecules* 28, no. 8: 3525.
https://doi.org/10.3390/molecules28083525