Promising M₂CO₂/MoX₂ (M = Hf, Zr; X = S, Se, Te) Heterostructures for Multifunctional Solar Energy Applications

Abstract

Two-dimensional van der Waals (vdW) heterostructures are potential candidates for clean energy conversion materials to address the global energy crisis and environmental issues. In this work, we have comprehensively studied the geometrical, electronic, and optical properties of M₂CO₂/MoX₂ (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 M₂CO₂/MoX₂ heterostructures are confirmed. Interestingly, all the M₂CO₂/MoX₂ 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 M₂CO₂/MoX₂ heterostructures exhibit suitable band gaps in comparison to the M₂CO₂ and MoX₂ monolayers, which enhance the optical-harvesting abilities in the visible and ultraviolet light zones. Zr₂CO₂/MoSe₂ and Hf₂CO₂/MoSe₂ heterostructures possess suitable band edge positions to provide the competent driving force for water splitting as photocatalysts. In addition, Hf₂CO₂/MoS₂ and Zr₂CO₂/MoS₂ 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

The production of sustainable and renewable energy can effectively tackle both the increasing global energy demand and environmental pollution issues [1]. Harnessing solar energy via photocatalytic hydrogen productions and photovoltaic solar cells have been proposed as promising solutions, which optimize the utilization of solar energy in a cost-effective and efficient way [2,3,4]. The search for efficient photocatalytic and photovoltaic materials is one of the most daunting tasks in the use of solar energy nowadays. Since graphene has been successfully produced and applied [5,6,7,8], great attention has been paid to 2D materials, for instance, transition metal carbides/nitrides (MXenes) [9,10,11], carbonitrides [12] transition metal dichalcogenides (TMDCs) [13,14,15], black phosphorene [16] and silicene [17]. Herein, MXenes, first successfully divested from the MAX phase in 2011 [18,19], can be expressed by M_n+1X_nT_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].

On the other hand, the structural formula of TMDCs is generally expressed as MX₂, 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, MoS₂, MoSe_2, and MoTe₂ 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.

To further enhance the properties of 2D materials, vdW heterostructures with weak vdW interactions between vertical layers have been proposed [35,36]. Based on the interlayer coupling effect, 2D vertical vdW heterostructures exhibit distinct advantages derived from each constituent material, thereby yielding unique and promising features [37,38]. MXenes and TMDCs are potential candidates to form vdW heterostructures. For instance, MoSe₂/Ti₃C₂ [39] and MoSe₂/Ti₃C₂O₂ [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 Hf₂CO₂ and Zr₂CO₂ possess suitable band gaps for solar energy harvesting applications. The construction of heterostructures using M₂CO₂ (M = Hf, Zr) and TMDCs MoX₂ (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 MoX₂ materials but also exhibits significant potential for optoelectronic and photocatalytic applications.

In this work, we constructed the M₂CO₂/MoX₂ (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 M₂CO₂/MoX₂ heterostructures. Interestingly, the Zr₂CO₂/MoSe₂ and Hf₂CO₂/MoSe₂ 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 Hf₂CO₂/MoS₂ and Zr₂CO₂/MoS₂ 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

Our density functional theory (DFT) calculations were performed by using the VASP package [41] together with the ALKEMIE platform [42,43]. The exchange-correlation interactions between electrons were carried out using the projector-augmented wave (PAW) [44] generalized gradient approximation (GGA) of the Perdew-Burke-Ernzerhof (PBE) functional [45]. The cutoff energy for the plane-wave-basis was set to 500 eV. For both geometry optimization and electronic structure calculation, the 2D Brillouin zone was installed with a Γ-centered k point of 12 × 12 × 1 mesh. To eliminate the interactions of periodic two-layer adjacent heterostructures, a vacuum layer larger than 20 Å was added along the z-direction of the 2D models. To have the assurance that the heterogeneous structures were fully optimized, the precision energy and precision force were required to be within 10⁻⁵ 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 M₂CO₂/MoX₂ 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

To quantify the lattice constant differences between different 2D structures, the degree of lattice mismatch $K$ is defined in the theoretical calculation of heterostructures as [52]:

$$K=\frac{2\left|a_1-a_2\right|}{a_1+a_2}$$

(1)

where $a_1$ and $a_2$ are the lattice constants of the two monolayers forming the heterostructures. To examine the thermodynamic stabilities of 2D heterostructures, the formation energy $E_{\mathrm{f}}$ is obtained according to [53]:

$$E_{\mathrm{f}}=E_{{\mathrm{M}}_2{\mathrm{CO}}_2{/\mathrm{MoX}}_2}-E_{{\mathrm{M}}_2{\mathrm{CO}}_2}-E_{{\mathrm{MoX}}_2}$$

(2)

where $E_{{\mathrm{M}}_2{\mathrm{CO}}_2{/\mathrm{MoX}}_2}$ is the total energy of the M₂CO₂/MoX₂ heterostructures, $E_{{\mathrm{M}}_2{\mathrm{CO}}_2}$ and $E_{{\mathrm{MoX}}_2}$ are the total energies of pristine M₂CO₂ and MoX₂ 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:

$$E_{\mathrm{b}}=\left(E_{{\mathrm{M}}_2{\mathrm{CO}}_2{/\mathrm{MoX}}_2}-E_{{\mathrm{M}}_2{\mathrm{CO}}_2{/\mathrm{MoX}}_2}^{\mathrm{h}}\right)/S_{\mathrm{h}}$$

(3)

where $E_{{\mathrm{M}}_2{\mathrm{CO}}_2{/\mathrm{MoX}}_2}^{\mathrm{h}}$ is the sum of the total energies of M₂CO₂ and MoX₂ 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]:

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

(4)

where ${\epsilon }_1$ and ${\epsilon }_2$ are the real and imaginary parts of the optical dielectric functions, respectively. The carrier mobility of 2D materials $\mu$ was calculated by [55]:

$$\mu =\frac{2e{\hslash }^3{C}_{2\mathrm{D}}}{3K_{\mathrm{B}}T{\left|m^{\ast }\right|}^2{E}_1^2}{E}_1$$

(5)

where $e$, $\hslash$, $C_{2\mathrm{D}}$, $K_{\mathrm{B}}$, $T$, $m^{\ast }$ and $E_1$ are the electron charge, reduced Planck constant, 2D elastic modulus, Boltzmann constant, temperature, carrier effective mass, and deformation potential constant, respectively.

3. Results and Discussion

First, we analyzed the geometries and electronic structures of MoX₂ (X = S, Se, Te) and M₂CO₂ (M = Zr, Hf) monolayers. The optimized lattice constants using DFT-D3 functionals of the MoS₂, MoSe₂, MoTe₂, Zr₂CO_2, and Hf₂CO₂ 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. MoX₂ 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 MoS₂, MoSe_2, and MoTe₂ monolayers are 2.23, 2.00, and 1.63 eV. While Zr₂CO₂ and Hf₂CO₂ 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].

Furthermore, by perpendicularly combining the monolayers, M₂CO₂/MoX₂ (M = Hf, Zr; X = S, Se, Te) heterostructures were built. The lattice mismatches observed between the M₂CO₂ and MoX₂ monolayers fall within the reasonable range from 0.1% to 7.9%, which indicates the feasibility of establishing M₂CO₂/MoX₂ heterostructures. Herein, to investigate the stability of M₂CO₂/MoX₂ heterostructures, six distinct stacking configurations were examined. Taking Zr₂CO₂/MoS₂ 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 Hf₂CO₂/MoTe₂ 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/Ų [65], respectively. Moreover, the negative binding energy corresponds to the exothermic reaction, which further confirms the feasibility from the thermodynamics point of view.

In order to further confirm the dynamic and thermal stabilities of the M₂CO₂/MoX₂ heterostructures, we performed phonon dispersion calculations and AIMD simulations. For one thing, Figure 2 illustrates the phonon dispersion curves for the M₂CO₂/MoX₂ 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 M₂CO₂/MoX₂ 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, M₂CO₂/MoX₂ vdW heterostructures show good lattice dynamic and thermal dynamic stabilities.

To gain a more comprehensive comprehension of the electronic structures, the projected HSE06 band structures of the M₂CO₂/MoX₂ heterostructures are illustrated in Figure 4. It can be seen that Hf₂CO₂/MoTe₂ and Zr₂CO₂/MoTe₂ 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 M₂CO₂/MoX₂ heterostructures. As listed in Tables S1 and S4, the band gaps of Hf₂CO₂/MoS₂, Hf₂CO₂/MoSe₂, Hf₂CO₂/MoTe₂, Zr₂CO₂/MoS_2, Zr₂CO₂/MoSe₂ and Zr₂CO₂/MoTe₂ 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 Hf₂CO₂/MoS₂ and Zr₂CO₂/MoS₂ heterostructures, the VBM are primarily influenced by the contribution of the M₂CO₂ layers, while the CBM are predominantly determined by the MoX₂ layers. In contrast, the VBM and CBM are dominated by MoX₂ and M₂CO₂ monolayers in the other heterostructures, respectively. Interestingly, all the M₂CO₂/MoX₂ heterostructures are categorized as type-II heterostructures, which enables the effective separation of photo-generated charge carriers [36].

To further explore the charge transfer between M₂CO₂ and MoX₂ monolayers, the charge density difference $\Delta \rho$ can be calculated from the following [68]:

$$\Delta \rho ={\rho }_{{\mathrm{M}}_2{\mathrm{CO}}_2{/\mathrm{MoX}}_2}-{\rho }_{{\mathrm{M}}_2{\mathrm{CO}}_2}-{\rho }_{{\mathrm{MoX}}_2}$$

(6)

where the ${\rho }_{{\mathrm{M}}_2{\mathrm{CO}}_2{/\mathrm{MoX}}_2}$, ${\rho }_{{\mathrm{M}}_2{\mathrm{CO}}_2}$, and ${\rho }_{{\mathrm{MoX}}_2}$ are the charge densities of the M₂CO₂/MoX₂ heterostructures, M₂CO₂ and MoX₂ 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 Zr₂CO₂/MoS₂ heterostructure, the charges consume in the MoX₂ sides and accumulate in the M₂CO₂ 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 MoX₂ to M₂CO₂ slabs in the Hf₂CO₂/MoS₂, Hf₂CO₂/MoSe₂, Hf₂CO₂/MoTe₂, Zr₂CO₂/MoSe_2, and Zr₂CO₂/MoTe₂ heterostructures, respectively. On the contrary, for Zr₂CO₂/MoS₂, there are 0.0158 electrons from Zr₂CO₂ to the MoS₂ 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 M₂CO₂/MoX₂ 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 M₂CO₂/MoX₂ heterostructures, which confirms the vdW interaction between M₂CO₂ and MoX₂ layers.

To understand the chemical driving force for the water-splitting reaction, the band edge alignments of the M₂CO₂, MoX₂ monolayers, and M₂CO₂/MoX₂ heterostructures in conjunction with the work functions were investigated, as shown in Figure 7. The energy levels of the VBM and CBM of the MoS₂, MoSe₂, Hf₂CO₂, and Zr₂CO₂ monolayers satisfy the requirements of the redox potential of water splitting. However, the VBM of the MoTe₂ monolayer is higher than the oxidation-reduction potential. The result agrees well with the previous report [60]. Herein, the work functions for MoS₂, MoSe₂, MoTe₂, Zr₂CO_2, and Hf₂CO₂ 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, Hf₂CO₂/MoSe₂ and Zr₂CO₂/MoSe₂ heterostructures with suitable band edge alignments for water oxidations and reductions, render them effective photocatalysts for overall water splitting.

To obtain the charge carrier transport characteristics, we calculated the carrier effective masses and mobilities in M₂CO₂/MoX₂ 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 Zr₂CO₂/MoS₂ 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. The effective mass m* (m₀), deformation potentials E₁ (eV), elastic moduli C_2D (N/m), and carrier mobility μ (cm² V⁻¹s⁻¹) of MoX₂/MoX₂ heterostructures.

System	Direction	Carrier Type	E1	C2D	m*	μ
Hf2CO2/MoS2	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
Hf2CO2/MoSe2	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
Hf2CO2/MoTe2	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
Zr2CO2/MoS2	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
Zr2CO2/MoSe2	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
Zr2CO2/MoTe2	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

. On the one hand, the predicted hole mobilities of M₂CO₂/MoX₂ heterostructures are much larger than the electron mobilities. On the other hand, the carrier mobilities of M₂CO₂/MoX₂ 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 MoX₂ side, while the holes demonstrate a predilection for migration along the y-axis within the M₂CO₂ domain of the heterostructures. Interestingly, the hole mobilities of Hf₂CO₂/MoS₂ and Hf₂CO₂/MoTe₂ heterostructures in the y direction have reached 9140.34 cm² V⁻¹s⁻¹ and 7592.80 cm² V⁻¹s⁻¹, respectively, which are greater than silicon (~1400 cm² V⁻¹s⁻¹) [70]. The strong anisotropic carrier mobility in M₂CO₂/MoX₂ heterostructures can reduce the rate of electron-hole recombination, which is favorable to redox reactions and the photoelectric conversion process.

As the optical property is one of the most important indicators for considering materials in solar energy conversion applications, subsequently, we investigated the optical absorption coefficient of the M₂CO₂/MoX₂ vdW heterostructures. Figure 8 depicts the absorption coefficient curves of the M₂CO₂/MoX₂ heterostructures and the corresponding monolayers using HSE06. In general, M₂CO₂/MoX₂ 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 M₂CO₂/MoX₂ is over two-fold higher than that of M₂CO₂ and notably exceeds that of the corresponding MoX₂ monolayers. It is worth noting that Hf₂CO₂/MoS₂ and Zr₂CO₂/MoS₂ heterostructures exhibit stronger responses to infrared light than monolayers as well. Moreover, compared to M₂CO₂ and MoX₂ 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 M₂CO₂/MoX₂ heterostructures in photocatalysis and photovoltaic applications.

According to the previous analysis, Zr₂CO₂/MoSe₂ and Hf₂CO₂/MoSe₂ heterostructures are ideal materials for photocatalytic water splitting. The E_VBM of Zr₂CO₂/MoSe₂ and Hf₂CO₂/MoSe₂ are more positive than the redox potential of O₂/H₂O (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⁺/H₂O (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 Zr₂CO₂/MoSe₂ and Hf₂CO₂/MoSe₂ heterostructures as examples to further analyze the adsorption and dissociation processes of water molecules on the surface of M₂CO₂, as presented in Figure 9a. Under light irradiation, electrons in the Zr₂CO₂/MoSe₂ 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 MoSe₂ to Zr₂CO₂, and holes are from the VBM of Zr₂CO₂ to MoSe₂, 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 Zr₂CO₂ surface and the oxygen evolution reaction (OER) takes place on the MoSe₂ surface. For Hf₂CO₂/MoSe₂ heterostructure, the photocatalysis mechanism is the same. Here, we analyzed the HER processes on the Zr₂CO₂ and Hf₂CO₂ surfaces of the Zr₂CO₂/MoSe₂ and Hf₂CO₂/MoSe₂ heterostructures. Based on the crystal structure features, effective adsorption sites A~C and D~F were considered on the surfaces of Zr₂CO₂ and Hf₂CO₂, 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]:

$$E_{\mathrm{ads}}^{{\mathrm{H}}_2\mathrm{O}/\mathrm{surface}}=E_{\mathrm{tot}}^{{\mathrm{H}}_2\mathrm{O}/\mathrm{surface}}-E_{\mathrm{tot}}^{{\mathrm{H}}_2\mathrm{O}}-E_{\mathrm{tot}}^{\mathrm{surface}}$$

(7)

where $E_{\mathrm{tot}}^{{\mathrm{H}}_2\mathrm{O}/\mathrm{surface}}$, $E_{\mathrm{tot}}^{{\mathrm{H}}_2\mathrm{O}}$ and $E_{\mathrm{tot}}^{\mathrm{surface}}$ are the total energy of the absorption system, individual water molecules, and pristine surface, respectively. Herein, the location with the lowest adsorption energy is where the HER takes place. The optimized models and the corresponding adsorption energies after water adsorption at different sites are exhibited in Figure S4 and S5. Different absorbed models obtain adsorption energies from −0.061 to −0.338 eV. All the cases with negative adsorption energies indicate that the water molecule adsorption processes are thermodynamically favorable. It is observed that the adsorption energy is lower in the case of oxygen atoms as adsorption atoms, which indicates that water molecules are more stable on the surface of the heterojunction with oxygen atoms. For the Zr₂CO₂ and Hf₂CO₂ surfaces, the optimal adsorption sites are C and F, where the HER will take place most possibly.

Furthermore, the generation processes of H₂ on the Zr₂CO₂ and Hf₂CO₂ surfaces of Zr₂CO₂/MoSe₂ and Hf₂CO₂/MoSe₂ heterostructures have been illustrated in Figure 9b. For Zr₂CO₂/MoSe₂ 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 Zr₂CO₂ surface. Afterward, H atoms will form H₂ 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 Zr₂CO₂ 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 H₂ molecules on the Hf₂CO₂ surface of the Hf₂CO₂/MoSe₂ heterostructure is similar. The energies taken for the gradual approach of two distant H atoms to form an H₂ molecule and then to detach from the surface are −0.30, −6.13, and 0.08 eV, respectively.

To evaluate the application of M₂CO₂/MoX₂ heterostructures in solar cells, we conducted an estimation of the power conversion efficiency (PCE, $\eta$), which describes the ability of M₂CO₂/MoX₂ heterostructure materials to transform solar energy into electrical energy, proposed by Scharber et al. [72]:

$$\eta =\frac{0.65\left(E_{\mathrm{g}}^{\mathrm{d}}-\Delta E_{\mathrm{c}}-0.3\right){\displaystyle {\int }_{E_g}^{\infty }\frac{P\left(\hslash \varpi \right)}{h\varpi }d\left(\hslash \varpi \right)}}{{\displaystyle {\int }_0^{\infty }P\left(\hslash \varpi \right)d\left(\hslash \varpi \right)}}$$

(8)

where 0.65 is the band-fill factor, $P\left(\hslash \varpi \right)$ is the AM1.5 solar energy flux at the photon energy $\hslash \varpi$, and $E_{\mathrm{g}}^{\mathrm{d}}$ is the donor band gap. $\Delta E_{\mathrm{c}}$ is the donor and acceptor conduction band offset. To better understand the conduction band offset, Figure S6 presents the band structures of individual monolayers that have been arranged in the 2D lattice of the corresponding van der Waals heterostructure, based on the band edge data. The donor band gap $E_{\mathrm{g}}^{\mathrm{d}}$, conduction band offset $\Delta E_{\mathrm{c}}$, and calculated PCE ($\eta$) of M₂CO₂/MoX₂ heterostructures are listed in Table S6. Figure 10 shows simulated solar cell PCE as well as the charge carrier transfer route in M₂CO₂/MoX₂ heterostructures. Interestingly, the maximum PCEs of the Hf₂CO₂/MoS₂ and Zr₂CO₂/MoS₂ heterostructures are calculated to be 19.75% and 17.13% (red star highlighted in Figure 10a), respectively. Remarkably, the donor band gaps of Hf₂CO₂/MoS₂ and Zr₂CO₂/MoS₂ 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 M₂CO₂/MoX₂ heterostructures with high PCEs generate excited-free carriers to develop photocurrent more efficiently.

4. Conclusions

In conclusion, we have systematically investigated the geometrical structures, electronic structures, optical properties, photocatalytic and photovoltaic applications of M₂CO₂ (M = Hf, Zr), MoX₂ (X = S, Se, Te) monolayers and corresponding M₂CO₂/MoX₂ 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 M₂CO₂/MoX₂ 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 Hf₂CO₂/MoTe₂, and Zr₂CO₂/MoTe₂ 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 M₂CO₂ and MoX₂ monolayers, the M₂CO₂/MoX₂ heterostructures display a heightened optical absorption effect, predominantly within the ultraviolet and visible light spectra. Interestingly, the M₂CO₂/MoX₂ 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 Zr₂CO₂/MoSe₂ and Hf₂CO₂/MoSe₂ 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 Hf₂CO₂/MoS₂ and Zr₂CO₂/MoS₂ heterostructures can achieve PCE values of 19.75% and 17.13%, respectively. The present study reveals that M₂CO₂/MoX₂ vdW heterostructures are potential candidates for photocatalytic and photovoltaic device applications.