The Combined Effects of an External Field and Novel Functional Groups on the Structural and Electronic Properties of TMDs/Ti3C2 Heterostructures: A First-Principles Study

Abstract

The stacking of Ti₃C₂ with transition metal dihalide (TMDs) materials is an effective strategy to improve the physical properties of a single material, and the tuning of the related properties of these TMDs/Ti₃C₂ heterostructures is also an important scientific problem. In this work, we systematically investigated the effects of an external field and novel functional groups (S, Se, Cl, Br) on the structural and electronic properties of TMDs/Ti₃C₂X₂ heterostructures. The results revealed that the lattice parameters and interlayer distance of TMDs/Ti₃C₂ increased with the addition of functional groups. Both tensile and compressive strain obviously increased the interlayer distance of MoS₂/Ti₃C₂X₂ (X = S, Se, Cl, Br) and MoSe₂/Ti₃C₂X₂ (X = Se, Br). In contrast, the interlayer distance of MoSe₂/Ti₃C₂X₂ (X = S, Cl) decreased with increasing compressive strain. Furthermore, the conductivity of TMDs/Ti₃C₂ increased due to the addition of functional groups (Cl, Br). Strain caused the bandgap of TMDs to narrow, and effectively adjusted the electronic properties of TMDs/Ti₃C₂X₂. At 9% compressive strain, the conductivity of MoSe₂/Ti₃C₂Cl₂ increased significantly. Meanwhile, for TMDs/Ti₃C₂X₂, the conduction band edge (CBE) and valence band edge (VBE) at the M and K points changed linearly under an electric field. This study provides valuable insight into the combined effects of an external field and novel functional groups on the related properties of TMDs/Ti₃C₂X₂.

1. Introduction

Due to the inter-layer coupling effect, heterostructures formed by vertically stacking different two-dimensional (2D) materials can achieve ultra-high-performance improvements and possess unprecedentedly excellent physical properties [1,2,3]. The transition metal dihalides (TMDs) have excellent band gap widths in the range of 1.0 eV to 2.0 eV [4]. The monolayer MoS₂, as a typical representative member of the most studied TMD family, is a semiconductor material with a direct band gap of 1.8 eV, and it is widely used in logic transistors and photodetector devices [5,6]. Similarly, the monolayer MoSe₂, as another important member of TMDs, has many promising applications in electronics and optoelectronics due to its unique electronic, optical, mechanical, chemical, and thermal properties [7,8]. However, TMDs also have some negative properties that affect their application. For example, their carrier effective mass is relatively high, while the carrier mobility is very low [9,10], which hinders their application in high-performance nanodevices. Several studies have shown that the heterogeneous structures formed by stacking TMDs with other 2D materials can significantly modulate the structural, electronic, and mechanical properties of TMDs. For example, the studies of Biroju et al. [11] showed that MoS₂ stacked with a bilayer graphene heterostructure can improve electronic conductivity, electrochemical properties, and photochemical properties. Li et al. [12] systematically investigated electron density differences and band gaps of Cu₃N/MoS₂ heterostructures, and the results showed that the charge was mainly accumulated and consumed near the atoms, with only a small amount of charge accumulating between the layers, and the bandgap of Cu₃N/MoS₂ heterostructures can be efficiently tuned with the variation of the interlayer distance. Moreover, Cu₃N/MoS₂ heterostructures have a stable structure and excellent photoelectric properties. Celal et al. [13] investigated the structural and electronic properties of GaN/MoSe₂ heterostructures with van der Waals (vdW) correction. An indirect band gap of 1.371 eV was obtained when the GaN monolayers were adsorbed on MoSe₂ monolayers, while when GaN was stacked on MoSe₂ monolayers, the indirect band gap in GaN monolayers was maintained at 0.341 eV. Based on these studies, we can conclude that combining TMDs with other two-dimensional layered materials to form heterogeneous structures may be an effective way to tune and improve the relevant properties of TMDs.

MXenes are a new and important member of the family of 2D materials discovered in recent years and are complex layered 2D material systems representing a large class of transition metal nitriles, carbides, and carbonitrides [14,15,16]. Ti₃C₂ is a typical transition metal carbide with multilayer metal ion adsorption behavior, with ultra-high electrical conductivity and extraordinary mechanical and electronic properties [17,18]. Ti₃C₂ is expected to be the most competitive material candidate in some fields, such as high-performance ultra-thin electronics and storage [19,20]. Mathis et al. [21] investigated the MXene nanosheets (Al-Ti₃C₂), and found they have higher quality, increased oxidation resistance, and electronic conductivity increased to 20,000 S/cm. Al-Ti₃C₂ is a promising electric nanodevice. Li et al. [22] systematically investigated the interfacial properties of monolayer WS₂ in contact with a series of MXenes using first-principles calculations. The results showed that Ti₃C₂ couples strongly with WS₂, leading to the metallization of monolayer WS₂ and the formation of ideal Ohmic contacts in the vertical direction. Moreover, during the electrode fabrication process, the face-to-face stacking of 1 nm thickness MXene limits the accessibility to electrolyte ions [23,24], which hinders the electronic properties utilization of its surface. For Ti₃C₂, heterostructure stacking is also a valuable tool for improving the electronic properties since it can not only add the excellent properties of a single 2D material but also provide a stable gallery space [25,26,27], which could prevent face-to-face stacking of MXene. For example, Wu et al. [28] systematically investigated the energy storage and electronic properties of N-Ti₃C₂/NiCo₂S₄ heterostructures. Owing to the unique heterostructure and friendly interfacial interaction, the N-Ti₃C₂/NiCo₂S₄ heterostructure had a stable structure, low internal resistance, and excellent rate performance. Debow et al. [29] found that the strong electronic coupling between Ti₃C₂O_x and TiO₂ is due to their proximity; the Ti₃C₂O_x-generated electrons are transferred into the conduction band of the TiO₂ semiconductor over the Schottky barrier with a fast time constant of 180 fs, leading to an increase in conductivity.

Currently, there are a large number of studies on TMD and MXene heterostructures. Jing et al. [30] systematically investigated the structural and electronic properties of MoS₂/Ti₃C₂T_x (T = OH, F and O) heterostructures, and the results showed that the MoS₂/Ti₃C₂F₂ heterostructure is an n-type Schottky contact and the Schottky barrier height (SBH) is 0.73 eV, while the MoS₂/Ti₃C₂O₂ heterostructure is a p-type Schottky contact with an SBH of 0.33 eV. Moreover, the tensile strain can effectively adjust the position of the conduction band edge (CBE) of MoS₂, which leads to an effective reduction of the Fermi energy level pinning and SBH, thus allowing for Ohmic contact. Guan et al. [31] studied heterostructures composed of Ti₃C₂T₂ (T = O and F atoms) and metallic MoS₂ (1T phase) for lithium-ion battery (LIB) applications. The different surface functional groups in MXenes were found to significantly alter the redox reaction of Li atoms in the Ti₃C₂T₂ and 1T-MoS₂ interfaces. The diffusion curve became significantly flattened from the bared to O and F terminated Ti₃C₂, with the Schottky barrier height reducing dramatically from 0.80 eV to 0.22 eV and 0.29 eV, respectively. The surface functional group O or F can remove the spatial site resistance of Li embedding by disrupting the strong interaction between the two layers while providing additional adsorption sites for Li diffusion. Li et al. [32] found that MoS₂/Ti₂C heterostructures have good thermoelectric and transport properties, and the applied electric field or strain can significantly improve their thermoelectric and transport properties. Xu et al. [33] found that MoSe₂/Ti₃C₂T_x (T = OH, O, and F) heterostructures exhibit excellent electrochemical properties at very high currents and have a large potential for sodium ion storage, which can be applied to high-performance sodium–ion batteries. Ling et al. [34] demonstrated by a first-principles method that MoS₂/Ti₃C₂–OH heterostructures can enhance the catalytic activity of MoS₂ at low sulfur vacancy concentrations. Combining the MoS₂/Ti₃C₂-OH heterostructure with strain engineering can realize the potential of efficient hydrogen production. Based on these previous studies, TMDs/MXenes heterostructures can improve the related properties of single TMDs or MXenes, and the surface functional groups of the monolayer MXenes are an effective way to tune the properties of the TMDs/MXenes heterostructures. However, these studies have mainly focused on the surface functional groups O, F, and OH.

Recently, Kamysbayev et al. [35] successfully synthesized MXenes with novel functional groups (S, Se, Cl, Br, Te) capped with Ti₃C₂, all of which showed in-plane tensile strain, especially Ti₃C₂Te₂, which had the maximum in-plane tension, showing in-plane lattice expansion of more than 18%. Lattice expansion promoted the appearance of Ti₃C₂ electron mobility over 10⁴ cm²/V·s at room temperature, as well as superconductivity. Based on the studies of Kamysbayev et al. [35], it can be concluded that these novel functional groups (S, Se, Cl, Br) obviously induce a change in the related properties of Ti₃C₂. Moreover, as we know, the external field can induce fancy changes in the properties of 2D materials. However, it is still unclear about the effects of these novel functional groups (S, Se, Cl, Br) and external fields on the structural and electronic properties of the TMDs/Ti₃C₂ heterostructures. In this paper, we first systematically investigated the structural and electronic properties of these TMDs/Ti₃C₂X₂ (X = S, Se, Cl, Br) heterostructures using the density functional theory (DFT), and discussed in detail the effects of these novel surface functional groups on the related properties of these TMDs/Ti₃C₂ heterostructures. In addition, we then further explored the effect of external biaxial strain and electric field on the structural and electronic properties of these TMDs/Ti₃C₂X₂ heterostructures.

2. Calculation Method

All calculations were performed within the framework of density functional theory using the CASTEP code [36]. The Perdew–Burke–Ernzerhof (PBE), based on the generalized gradient approximation (GGA), was used as the exchange–correlation function [37]. In order to accurately represent the van der Waals interactions between monolayer TMDs and 2D Ti₃C₂, a semi-empirical dispersion correction in Grimme format (DFT–D) was used [38]. The Ultrasoft pseudopotential [39] was used to describe the ion–electron interaction. The valence electrons performed as the [Ar]3p3d4s configuration for the Ti atom, the [Ne]3s3p configuration for the S and Cl atoms, the [Kr]4d5s configuration for the Mo atom, the [He]2s2p configuration for the C atom, and the [Ar]4p4s configuration for Br and Se atoms. The energy cutoff was set to 450 eV [40]. Structural optimization was performed using a 9 × 9 × 1 Monkhorst–Pack grid K-point sampling in the Brillouin zone in the unit cell, with the optimization energy convergence parameter set to 10⁻⁵ eV/atom and the force convergence parameter on the atoms set to 0.03 eV/Å [41]. The K-point grid was increased to 11 × 11 × 1 for the calculation of energy bands and density of states [42]. A vertical vacuum layer thickness of more than 15 Å was set to prevent periodic boundary interactions between adjacent layers [43]. The binding energy of the TMDs/Ti₃C₂ heterostructure was defined as:

$E_{\mathrm{b}}=\left(E_{TMDs/T{i}_3{C}_2}-E_{T{i}_3{C}_2}-E_{TMDs}\right)/A$

where $E_{TMDs/T{i}_3{C}_2}$, $E_{T{i}_3{C}_2}$, and $E_{TMDs}$ are the total energies of the heterostructure, bare Ti₃C₂, and the TMD monolayer, respectively, and A is the interface area [44]. We not only investigated the structural and electronic properties of pristine TMDs/Ti₃C₂ and TMDs/Ti₃C₂X₂ (X = S, Se, Cl, Br) but also explored the effect of biaxial strain on the structural and electronic properties of TMDs/Ti₃C₂ and TMDs/Ti₃C₂X₂ (X = S, Se, Cl, Br) heterostructures. The biaxial strain was defined as:

ε_x = (a − a₀)/a₀ × 100%

ε_y = (b − b₀)/b₀ × 100%

where and a₀ are the x-axis lattice constants in the presence and absence of strain, respectively; and b and b₀ are the y-axis lattice constants in the presence and absence of strain, respectively [45]. In addition, positive (negative) values indicate tensile (compressive) strain. All heterostructure structures were relaxed.

3. Results and Discussions

3.1. Structural Properties of the TMDs/Ti₃C₂ Heterostructures

The lattice constants of our optimized MoS₂, MoSe₂, and Ti₃C₂ monolayers were 3.15 Å, 3.24 Å and 3.12 Å, respectively, which were in good agreement with the previous studies [46,47]. They all have a hexagonal crystal structure with a space group of P63/mmc, and they possess a lattice mismatch rate within a reasonable range of less than 4%, allowing the construction of heterostructures [48]. According to the high-symmetry stacking mode, there are six possible TMDs/Ti₃C₂ configurations, taking MoS₂/Ti₃C₂ heterostructures as an example, see Figure 1 (six high-symmetry MoSe₂/Ti₃C₂ heterostructures, see Figure S1): (a) the ZM_SA Configuration: S and Mo atoms of MoS₂ are on top of Ti and C atoms of Ti₃C₂, respectively; (b) the ZM_AA Configuration: S and Mo atoms of MoS₂ are on top of C and Ti atoms of Ti₃C₂, respectively; (c) the ZM_AS Configuration: S and Mo atoms of MoS₂ are on top of Ti atoms and hollow sites of Ti₃C₂, respectively; (d) the MZ_SA Configuration: S and Mo atoms of MoS₂ are on top of C atoms and hollow sites of Ti₃C₂, respectively; (e) the MZ_AA Configuration: Mo and S atoms of MoS₂ are on top of C atoms and hollow sites of Ti₃C₂, respectively; (f) the MZ_AS Configuration: Mo and S atoms of MoS₂ are on top of Ti atoms and hollow sites of Ti₃C₂, respectively.

Table 1 lists our calculated binding energies, interlayer distance, and bond lengths for the six possible stacking configurations of MoS₂/Ti₃C₂ heterostructures. It can be seen that the binding energies of these MoS₂/Ti₃C₂ heterostructures were all negative, indicating that the formation of all the heterostructures was exothermic. A lower binding energy represents a more stable heterostructure structure. The ZM_SA configuration of MoS₂/Ti₃C₂ had the lowest binding energy of −1.79 meV/Å, so it was energetically the most stable configuration among the six configurations. It is noted that the interlayer distance d of the MoS₂/Ti₃C₂ heterostructure was very small (in the range of 1.68 Å to 2.47 Å), which indirectly indicated a strong interaction between the layers [49,50]. Table 2 presents the binding energy of −1.03 meV/Å for the most stable configuration SA_ZM of the MoSe₂/Ti₃C₂ heterostructure, while the AS_ZM configuration had the maximum binding energy of −0.39 meV/Å. The binding energies of all six configurations were negative, indicating the stability of the MoSe₂/Ti₃C₂ heterostructure. The interlayer distance d of the six configurations of MoSe₂/Ti₃C₂ heterostructures ranged from 1.89 Å to 2.56 Å, which was similar to that of MoS₂/Ti₃C₂ heterostructures.

A comparison of the data in Table 1 and Table 2 showed that the binding energies of all these MoS₂/Ti₃C₂ heterostructures were smaller than those of the corresponding MoSe₂/Ti₃C₂ heterostructures; meanwhile, MoS₂/Ti₃C₂ had a smaller interlayer distance than the MoSe₂/Ti₃C₂ heterostructures. These findings showed that the MoS₂/Ti₃C₂ heterostructures are more stable. We calculated the Ti–C bond length in the original monolayer Ti₃C₂ as 2.057 Å. As shown in Table 1 and Table 2, the Ti(3)–C(2) bond length d_Ti(3)–C(2) showed almost no change, but the Ti(1)–C(1) bond lengths of the upper layer of Ti₃C₂ were stretched in the TMDs/Ti₃C₂ heterostructures. The reason for this may be that the charge transfer from Ti₃C₂ to TMDs leads to the stretching of the Ti(1)–C(1) bond. The Mo–S(1) minus Mo–S(2) value (d₁₂) and Mo–Se(1) minus Mo–Se(2) value (d₃₄) are also presented in Table 1 and Table 2. d₁₂ ranged from 0.021 Å to 0.134 Å, and d₃₄ ranged from 0.013 Å to 0.107 Å, indicating that the TMDs/Ti₃C₂ heterostructure slightly destabilizes the TMDs monolayer. Moreover, the d₁₂ values in the MoS₂/Ti₃C₂ heterostructure were all greater than the d₃₄ in the MoSe₂/Ti₃C₂ heterostructure, suggesting that the interlayer electron coupling effect of MoS₂/Ti₃C₂ is greater than that of MoSe₂/Ti₃C₂. This conclusion was consistent with the results of our calculated interlayer distance and binding energy. We also noted that the binding energy and interlayer distance of the ZM_SA configurations were the smallest, so the ZM_SA configuration is the most stable configuration among the 12 configurations of MoS₂/Ti₃C₂ heterostructures and MoSe₂/Ti₃C₂ heterostructures considered here.

We also further investigated the effects of novel functional groups (S, Se, Cl, Br) on the structural properties of TMDs/Ti₃C₂ heterostructures. Previous experimental studies [51] have shown that the Ti₃C₂X₂ (X = S, Se, Cl, Br) are the most stable when the surface functional groups of Ti₃C₂ are located in the cavity centers of Ti atoms and aligned perpendicularly to the Ti atoms in the middle layer because of the site-blocked repulsion reaction between the C atoms and the surface functional groups. Therefore, in this work, when the surface of Ti₃C₂ was terminated by functional groups (S, Se, Cl, Br) in MoS₂/Ti₃C₂X₂ and MoSe₂/Ti₃C₂X₂ heterostructures, we focused on the case that the functional groups are located above the hole center of the Ti atom and perpendicular to the middle Ti atom, as shown in Figure 2a,b, respectively.

It can be clearly observed from Figure 2c that the lattice parameters of TMDs/Ti₃C₂X₂ heterostructures changed significantly due to the addition of surface functional groups. The lattice parameter of the MoS₂/Ti₃C₂ heterostructure was 3.124 Å. With the addition of each functional group, the lattice parameter obviously increased, and MoS₂/Ti₃C₂Br₂ had the maximum lattice parameter of 3.224 Å. The lattice parameter of MoS₂/Ti₃C₂S₂, MoS₂/Ti₃C₂Se₂ and MoS₂/Ti₃C₂Cl₂ increased to 3.163 Å, 3.179 Å and 3.186 Å, respectively. Similarly, the lattice parameters of the MoSe₂/Ti₃C₂ heterostructure increased with the addition of functional groups. The lattice parameters of the MoSe₂/Ti₃C₂ heterostructure were 3.148 Å, while MoSe₂/Ti₃C₂S₂, MoSe₂/Ti₃C₂Se₂, MoSe₂/Ti₃C₂Cl₂, and MoSe₂/Ti₃C₂Br₂ were 3.189 Å, 3.213 Å, 3.221 Å, and 3.262 Å, respectively. Therefore, the surface functional groups had a significant effect on the structural properties of MoS₂/Ti₃C₂X₂ and MoSe₂/Ti₃C₂X₂.

To further understand the stability of these TMDs/Ti₃C₂X₂ heterostructures, we calculated the binding energy, interlayer distance, and structural parameters of TMDs/Ti₃C₂X₂ (X = S, Se, Cl, Br) as shown in Table 3. We provide the coordinates of the TMDs/Ti₃C₂X₂ (X = S, Se, Cl, Br) optimized structure in the Supplementary Materials, see Table S1. The binding energies of MoS₂/Ti₃C₂X₂ and MoSe₂/Ti₃C₂X₂ were negative. The MoSe₂/Ti₃C₂Cl₂ heterostructure possessed the highest binding energy (−3.12 meV/Å), while the MoS₂/Ti₃C₂S₂ heterostructure had the lowest binding energy (−8.44 meV/Å), indicating that the MoS₂/Ti₃C₂S₂ heterostructure was more stable. The interlayer distance of these heterostructures varied from 2.78 Å to 3.14 Å, which was significantly larger than that of the TMDs/Ti₃C₂ heterostructure, and a larger interlayer distance indicated a weaker electronic coupling between the monolayer TMDs and T₃C₂X₂. It can be concluded that MoS₂/Ti₃C₂X₂ and MoSe₂/Ti₃C₂X₂ are typical van der Waals heterostructures.

It can also be seen from Table 3 that in MoS₂/Ti₃C₂X₂ and MoSe₂/Ti₃C₂X₂, the surface functional group of monolayer Ti₃C₂ caused an increase in the Ti–C bond length (d_Ti–C). Among them, the d_Ti–C of the MoSe₂/Ti₃C₂S₂ heterostructure reached 2.193 Å, an increase of 0.136 Å from the original 2.057 Å. The Ti–C bond length d_Ti–C of the MoS₂/Ti₃C₂Cl₂ heterostructure increased by 0.047 Å. The bond lengths between Ti(1) and X in the top layer of Ti₃C₂X₂ were almost the same as those between Ti(2) and X in the bottom layer of Ti₃C₂X₂, which means that the stacking of MoS₂ and MoSe₂ in these heterostructures hardly changes the spatial structure of Ti₃C₂X₂. The strong coupling between the Ti₃C₂ and TMD interface was weakened by the functional group (S, Se, Cl, Br). The value of d₅₆ was defined as Mo–Se(1) minus Mo–Se(2) or Mo–S(1) minus Mo–S(2) in TMDs/Ti₃C₂X₂ (X = S, Se, Cl, Br). The MoS₂/Ti₃C₂S₂ heterostructure possessed the maximum d₅₆ (0.009 Å), while d₅₆ was zero in the MoSe₂/Ti₃C₂Se₂ heterostructure, indicating that the spatial structure and two-dimensional properties of the original MoSe₂ were well preserved. The above results show that the addition of surface functional groups can seriously weaken the electronic coupling between the monolayer TMDs and Ti₃C₂.

3.2. Electronic Properties of the TMDs/Ti₃C₂X₂ Heterostructures

To investigate the electronic properties of the TMDs/Ti₃C₂ heterostructures, we choose the most stable configurations of ZM_SA and SA_ZM to further study the electronic properties of MoS₂/Ti₃C₂X₂ and MoSe₂/Ti₃C₂X₂, respectively. The energy band structures and density of states of the MoS₂/Ti₃C₂ heterostructure are presented in Figure 3. The Fermi energy level is set at zero energy. From Figure 3a, it can be seen that some energy bands cross the Fermi energy level, indicating the metallic nature of the MoS₂/Ti₃C₂ heterostructure. Because of a strongly coupled interaction between the MoS₂ and Ti₃C₂ monolayer, the energy bands have been hybridized severely. The total and partial density of states of the MoS₂/Ti₃C₂ heterostructure is shown in Figure 3b; it can be seen that the energy band near the Fermi level is mainly dominated by the 3d orbit of the Ti atom and the 4d orbit of the Mo atom. Remarkably, the electrons of the S 3p orbit in the conduction band are unusually more than that of the Ti 3p orbit. Therefore, the conduction band is mainly contributed by the Mo 4d, S 3p, and Ti 3d orbitals. The energy band structures and density of states of the MoSe₂/Ti₃C₂ heterostructure are presented in Figure 4. We note that the energy band of the MoSe₂/Ti₃C₂ heterostructure (see Figure 4a) has no obvious hybridization around the Fermi level, which is different from the MoS₂/Ti₃C₂ heterostructure. Compared with MoS₂/Ti₃C₂, MoSe₂/Ti₃C₂ has more concentrated energy bands, leading to a decrease in conductivity. The total and partial density of states of the MoSe₂/Ti₃C₂ heterostructure is shown in Figure 4b; we know that the energy bands near the Fermi energy level are dominated by Ti 3d and Mo 4d orbitals. The Ti 3p orbital and C 2p orbital make a slight contribution near the Fermi energy level. The conduction band is mainly formed by Ti 3d and Mo 4d orbitals, while the valence band is formed by C 2p, Ti 3d, and Mo 4d orbitals, and the C 2p orbital plays a dominant role in the MoSe₂/Ti₃C₂ heterostructure. Finally, by comparing the density of states of MoS₂/Ti₃C₂ with that of the MoSe₂/Ti₃C₂ heterostructure, we find that the peak of Ti 3d and Mo 4d in the MoS₂/Ti₃C₂ heterostructure moves towards a higher energy level.

It is well known that both MoS₂ and MoSe₂ are semiconductors in nature and exhibit a direct band gap at the K point in the Brillouin zone [52]. However, our calculations show that the S 3p orbitals, the Se 4p orbitals, and the Mo 4d orbitals in the TMDs/Ti₃C₂ heterostructure have a large number of electrons crossing the Fermi energy level, which is sufficient to indicate that Ti₃C₂ induces a significant change in the electronic properties of the TMDs monolayer.

To further understand the electronic properties, the Mulliken charge and bond populations of TMDs/Ti₃C₂ were calculated; see Tables S2 and S3. The interlayer electron coupling of the MoS₂/Ti₃C₂ heterostructure is strong due to the overlap of electron clouds between MoS₂ and Ti₃C₂ (the bond population of the S–Ti bond is 0.48 Å). The Ti₃C₂ in the MoS₂/Ti₃C₂ heterostructure obtains 0.06 e from the upper MoS₂ layer, and the Ti atom in Ti₃C₂ loses 1.55 e, and 1.50 e of Ti is transferred to the C atom. The bonding behavior of the MoS₂/Ti₃C₂ heterostructure is covalent in nature, as indicated by the bond populations. For MoSe₂/Ti₃C₂, the bond population of the Se–Ti bond has a large negative value (−0.83 Å), suggesting a weak van der Waals interaction between MoSe₂ and Ti₃C₂. According to the positive and negative values of the bond population, we can conclude that the bonding behavior in the MoSe₂/Ti₃C₂ heterostructure is a combination of covalent and ionic bonds.

The Mulliken charge analysis shows that more electrons are transferring from Ti₃C₂ to MoS₂ in the MoS₂/Ti₃C₂ heterostructure. We also noted that the Mo atom in MoSe₂/Ti₃C₂ and MoS₂/Ti₃C₂ obtains 0.35e and 0.01e, respectively. Moreover, the partial density of states in Figure 3b and Figure 4b shows that the density of the electrons of the Mo 4d orbital in the MoSe₂/Ti₃C₂ heterostructure at the Fermi energy level is much higher than that in the MoS₂/Ti₃C₂ heterostructure. As a result, the Mo 4d orbital in MoSe₂/Ti₃C₂ obtains more electrons from other atoms than that in MoS₂/Ti₃C₂.

The electronic properties of these heterostructures were affected by the surface termination atoms of Ti₃C₂, as illustrated in Figure 5 and Figure 6. Compared with MoS₂/Ti₃C₂ and MoSe₂/Ti₃C₂, the electronic properties of MoS₂/Ti₃C₂X₂ and MoSe₂/Ti₃C₂X₂ were obviously different. Although TMDs/Ti₃C₂X₂ heterostructures still exhibited metallic behavior, the peak values of density of states (DOS) at the Fermi level were lower than those of TMDs/Ti₃C₂ heterostructures. Based on our calculated DOS, it is worth noting that MoS₂ and MoSe₂ retained the semiconductor nature in the TMDs/Ti₃C₂X₂ heterostructures. This means that the presence of surface functional groups (Cl, Br, S, Se) weakened the interaction strength between TMDs and Ti₃C₂. Compared with the DOS of the original monolayer MoS₂ and MoSe₂, see Figures S2 and S3, that of MoS₂ and MoSe₂ in MoS₂/Ti₃C₂Br₂ and MoS₂/Ti₃C₂Cl₂ showed an upward shift of the Fermi energy level. From the partial density of states (PDOS) of MoS₂/Ti₃C₂Br₂ and MoS₂/Ti₃C₂Cl₂, it can be seen that the energy band near the Fermi level was mainly contributed to by the Ti 3d orbit. The Mo atom 4d orbital in MoS₂/Ti₃C₂Br₂ made a small charge contribution, while the Mo atom 4d orbital in MoS₂/Ti₃C₂Cl₂ made almost no charge contribution to the Fermi level. In addition, the atoms of the functional groups Cl and Br made almost no contribution near the Fermi level, as shown in Figure 5a,b. When the Ti₃C₂ surface was terminated by S and Se functional groups, the DOS of MoS₂ and MoSe₂ showed a downward shift of the Fermi level, while the S 3p and Se 4p orbitals made an obvious charge contribution near the Fermi level. The energy band near the Fermi level became flatter, and the effective mass of the electron was larger, so the conductivity decreased. It can be seen from the density of states of Ti₃C₂X₂ (X = S, Se) that the S 3p and Se 4p orbital charges and Ti 3d orbital generated strong hybridization, respectively, as shown in Figure 5c,d. The metal behavior of the MoS₂/Ti₃C₂X₂ (X = Br, Cl, S, Se) heterostructure was mainly dominated by the Ti 3d orbital charge.

Figure 6a shows the energy band and density of states of the MoSe₂/Ti₃C₂Br₂ heterostructure. The bottom of the conduction band of MoSe₂ moved downward and coincides with the Fermi level. At the Fermi energy level, only the Ti 3d orbital charge contributed. For MoSe₂/Ti₃C₂Cl₂ and MoSe₂/Ti₃C₂S₂, as shown in Figure 6b,c, the Fermi energy level was located between the top of the valence band and the bottom of the conduction band. The Ti 3d orbital dominated the metal properties of MoSe₂/Ti₃C₂Cl₂ and MoSe₂/Ti₃C₂S₂. For MoSe₂/Ti₃C₂Se₂, as shown in Figure 6d, the energy band structure of MoSe₂ remained unchanged, and the Fermi level was located at the top of the valence band. The Se 4p and Ti 3d orbitals in Ti₃C₂Se₂ generate strong hybridization, which dominated the conductivity of MoSe₂/Ti₃C₂Se₂. Moreover, the PDOS of MoSe₂ and MoS₂ showed that both S 3p orbitals in MoS₂ and Se 4p orbitals in MoSe₂ made no charge contribution at the Fermi energy level. When S and Se were used as the functional group terminal in Ti₃C₂, the S 3p and Se 4p orbital charges played a leading role in the Fermi energy level.

3.3. Effect of Biaxial Strain on the Structural and Electronic Properties of the TMDs/Ti₃C₂ Heterostructures

Strain can be used to tune the electronic properties of two-dimensional materials [53,54]. Here, we systematically investigated the effect of biaxial strain on the structural and electronic properties of TMDs/Ti₃C₂ and TMDs/Ti₃C₂X₂. Considering a series of biaxial tensile or compressive strains ε in 0.01 steps from −9% to +9%, ε > 0 and ε < 0 represented the tensile and compressive strains, respectively. Figure 7a shows the variation curve of the MoS₂/Ti₃C₂ interlayer distance with biaxial tensile (compressive) strain. It can be seen that the interlayer distance d of the MoS₂/Ti₃C₂ heterostructure varies linearly with an increasing biaxial tensile or compressive strain. The interlayer distance of MoS₂/Ti₃C₂ decreases to 1.56 Å when the biaxial tensile strain reaches 9%. Therefore, the biaxial tensile strain can enhance the electronic coupling strength between the monolayer MoS₂ and Ti₃C₂. However, its interlayer distance gradually increases when subjected to biaxial compressive strain, and the interlayer distance increased to 1.89 Å at 9% compressive strain, indicating that the electron coupling strength between the monolayer MoS₂ and Ti₃C₂ is severely weakened by the biaxial compressive strain. Figure 7b presents the variation curve of the MoSe₂/Ti₃C₂ interlayer distance with the biaxial tensile (compressive) strain. The result is completely different to that of the MoS₂/Ti₃C₂ heterostructure. The interlayer distance of the MoSe₂/Ti₃C₂ heterostructure shows a fluctuating change with an increasing biaxial tensile or compressive strain. Based on the above Mulliken charge and bond populations analysis of MoS₂/Ti₃C₂ and MoSe₂/Ti₃C₂, it can be seen that the bond population of S–Ti in MoS₂/Ti₃C₂ is positive, while that of Se–Ti in MoSe₂/Ti₃C₂ is negative. Therefore, the reason may be that the MoSe₂/Ti₃C₂ heterostructure has van der Waals interactions rather than strong electron coupling interactions.

We further investigated the effect of the biaxial tensile and compressive strain on the interlayer distance d of TMDs/Ti₃C₂X₂ heterostructures; see Figure 8. It can be seen that under the condition of the applied strain, the interlayer distance of TMDs/Ti₃C₂X₂ heterostructures presents a completely different behavior to that of MoS₂/Ti₃C₂. The reason is the different electronic coupling strength between the monolayer TMDs and Ti₃C₂X₂ due to the surface functional groups. The interlayer distance between MoS₂ and Ti₃C₂Cl₂ remains almost unchanged under the compressive strain, while it increases slightly with the increase in the tensile strain, as shown in Figure 8a. The interlayer distance of MoS₂/Ti₃C₂S₂ heterostructures presents a steady increase under tensile strain. When the compressive strain is in the range from 0 to 5%, its interlayer distance rapidly increases; when the compressive strain is above 5%, its interlayer distance is almost unchanged. For the MoS₂/Ti₃C₂Br₂ heterostructure, under the condition of compressive or tensile strain, the coupling strength between valence electrons of Br atoms and the 4d orbital of Mo atoms is weakened. As a result, the interlayer distance between MoS₂ and Ti₃C₂Br₂ increases slightly with the increase in the applied strain. Compared with MoS₂/Ti₃C₂X₂ (X = S, Br, Cl), the interlayer distance of MoS₂/Ti₃C₂Se₂ presents a significantly fluctuating change in the case of compressive strain. The reason may be that the Se atom induces the aberration of a crystal lattice due to its larger atomic radii [35]. When the compressive strain is applied, the lattice distortion becomes more pronounced, resulting in the fluctuation of the interlayer distance. For MoSe₂/Ti₃C₂X₂ (X = S, Se, Cl, Br), we also observed a similar trend under the condition of compressive strain; see Figure 8b. Therefore, we concluded that the fluctuation in the interlayer distance in MoS₂/Ti₃C₂X₂ (X = Se) and MoSe₂/Ti₃C₂X₂ is mainly attributed to the existence of the Se atom, and the displacement of the Se atom affects the structural stability of these heterostructures.

Figure 8b shows that the interlayer distance of MoSe₂/Ti₃C₂X₂ dramatically increases with the increase in the tensile strain, and the interlayer distances of MoSe₂/Ti₃C₂Se₂ and MoSe₂/Ti₃C₂Br₂ at 9% tensile strain increase to 3.23 Å and 3.26 Å, respectively. Under the compressive strain, their interlayer distance increases nonlinearly. Therefore, the applied strain weakened the interlayer interaction between MoSe₂ and Ti₃C₂X₂ (X = Se, Br). For MoSe₂/Ti₃C₂S₂ and MoSe₂/Ti₃C₂Cl₂, their interlayer distance presents the same trend under the applied strain. Under the tensile strain, the interlayer distance increases, while under the compressive strain, the interlayer distance becomes increasingly smaller. Moreover, the interlayer distance of MoSe₂/Ti₃C₂S₂ is more sensitive to the applied strain than that of MoSe₂/Ti₃C₂Cl₂. It is noted that the interlayer distance of MoSe₂/Ti₃C₂S₂ increased to 3.52 Å at 9% tensile strain, in contrast; its interlayer distance decreased to 2.91 Å at 9% compressive strain.

To explore the effect of biaxial strain on the electronic properties of TMDs/Ti₃C₂ heterostructures, we first investigated the Mulliken charge of TMD/Ti₃C₂ heterostructure under tensile and compressive strain. Table 4 shows the Mulliken charge population of MoS₂/Ti₃C₂ heterostructures, at free strain, Ti₃C₂ loses 0.07e, which is transferred to the monolayer MoS₂. At a tensile strain of 9%, Ti₃C₂ loses more electrons (0.11e). Moreover, Mo atoms also lose 0.05 electrons when subjected to tensile strain. At a compressive strain of 9%, Ti₃C₂ loses fewer electrons (0.03e). Table 5 shows the Mulliken charge population of MoSe₂/Ti₃C₂ heterostructures. At a compressive strain of 9%, MoSe₂ loses more electrons (0.08e), which are transferred to Ti₃C₂. These results showed that the interlayer electron transfer in both MoS₂/Ti₃C₂ and MoSe₂/Ti₃C₂ can be well regulated by biaxial strain. The difference is that in the MoS₂/Ti₃C₂ heterostructure the electrons are transferred from Ti₃C₂ to MoS₂, while in the MoSe₂/Ti₃C₂ heterostructure, the electrons are transferred from MoSe₂ to Ti₃C₂. Moreover, in the MoS₂/Ti₃C₂ heterostructure the transferring electrons increase with increasing tensile strain, while in the MoSe₂/Ti₃C₂ heterostructure, they increase with increasing compressive strain.

To further investigate the effect of biaxial strain on the electronic properties of TMDs/Ti₃C₂ heterostructures, we calculated their energy band structures and density of states under different strains. Figure 9a presents the energy band structures of MoS₂/Ti₃C₂ heterostructures under compressive strain. As the compressive strain increased, the valence band I moved down and away from the Fermi energy level, and it became flatter and flatter. The energy bands II and III at the Γ point were split, and the energy band II became more dispersed. Moreover, the energy bands III and IV were combined, and then they moved away from the Fermi energy level with increasing compressive strain. Figure 9b shows the energy band structures of MoS₂/Ti₃C₂ heterostructures under tensile strain. It can be seen that the increase in the tensile strain caused the valence bands I, II, and III to move away from the Fermi energy level and become flatter. Moreover, the conduction bands IV and V moved toward the Fermi energy level, and they showed more hybridization, resulting in an increase in the conductivity of the MoS₂/Ti₃C₂ heterostructure [55].

Figure 10 shows the DOS of the MoS₂/Ti₃C₂ heterostructure under different biaxial strains. It was obvious that the Fermi energy level was dominated by Mo 4d and Ti 3d orbitals. Moreover, the contribution of the Mo 4d orbital to the conduction band lessened with increasing compressive strain, while the contribution of Mo 4d and Ti 3d orbitals to the valence band increased with the increasing tensile strain. It can also be seen that the peak value of Ti atoms in the range of the conduction band increased with increasing tensile strain, while the peak value of Mo atoms remained almost unchanged with increasing tensile strain. The peak value of Mo atoms in the range of the valence band increased with the tensile strain and moved toward the Fermi energy level. Based on our calculated DOS of the MoS₂/Ti₃C₂ heterostructure, the interlayer interaction between the monolayer MoS₂ and Ti₃C₂ presented different behavior under tensile and compressive strain, and the interaction strength was strengthened under tensile strain, but weakened under compressive strain.

Figure 11a gives the energy band structures of the MoSe₂/Ti₃C₂ heterostructure under different compressive strains. With increasing compressive strain, the conduction bands III and IV gradually merged at the Γ point and moved away from the Fermi level. The valence band I become flatter, while the valence band II crossing the Fermi level became more tortuous, indicating a decrease in conductivity. Figure 11b displays the energy band structures of the MoSe₂/Ti₃C₂ heterostructure under different tensile strains. As the tensile strain increased, the energy bands II and III were split at the Γ point, and the energy bands IV and V showed more hybridization. Moreover, the energy bands crossing the Fermi energy level became more dispersed under tensile strain, inducing an increase in conductivity. We also noted that the pseudogap of the MoSe₂/Ti₃C₂ heterostructure disappeared with increasing compressive or tensile strain. Therefore, the applied strain can effectively tune the electronic properties of the TMDs/Ti₃C₂ heterostructures.

Figure 12 illustrates the DOS of the MoSe₂/Ti₃C₂ heterostructure with different biaxial strains. The peak value of Mo 4d orbitals at −1.8 eV gradually decreased under compressive strain, while the peak value of Ti 3d orbitals at 0.9 eV increased with increasing compressive strain. Under tensile strain, the peak value of both the Ti 3d orbital at 0.9 eV and the Mo 4d orbital at 1.2 eV increased with increasing tensile strain. Moreover, the peak value of Ti 3d orbitals moved away from the Fermi level, while in contrast, the peak value of the Mo 4d orbitals moved toward the Fermi energy level. It can be inferred from the variation of the DOS of MoSe₂/Ti₃C₂ heterostructure with the strain that tensile strain increases the interlayer interaction, while compressive strain weakens the interlayer interaction. This result was consistent with the MoS₂/Ti₃C₂ heterostructure.

We also investigated the DOS of MoS₂/Ti₃C₂X₂ under different biaxial strains, as shown in Figure 13, Figure 14, Figures S5 and S6. Compared with MoS₂/Ti₃C₂Se₂ and MoS₂/Ti₃C₂Br₂, the external strain had a slight effect on the DOS of MoS₂/Ti₃C₂Cl₂ and MoS₂/Ti₃C₂S₂, see Figures S5 and S6. The monolayer MoS₂ remained in its band gap when a compressive strain was applied, while its band gap gradually disappeared with increasing tensile strain. This indicated that the tensile strain can improve the interaction strength between the monolayer MoS₂ and Ti₃C₂Cl₂ (or Ti₃C₂S₂). For MoS₂/Ti₃C₂Se₂ and MoS₂/Ti₃C₂Br₂, the tensile strain induced the Mo 4d orbital to cross the Fermi level, indicating that the semiconductor nature of the monolayer MoS₂ was completely destroyed. This means more electrons were transferred from the monolayer Ti₃C₂Br₂ (or Ti₃C₂Se₂) to MoS₂. We also noted that the S 3p orbital in MoS₂/Ti₃C₂Br₂ obviously crossed the Fermi level when the compressive strain reached 9%. In contrast, compressive strain cannot result in the S 3p and Mo 4d orbitals crossing the Fermi level in MoS₂/Ti₃C₂Se₂, suggesting that MoS₂ can preserve its band gap under compressive strain, while the position of its conduction band minimum (CBM) and valence band maximum (VBM) will be obviously shifted.

For comparison, the DOS of MoSe₂/Ti₃C₂X₂ under different biaxial strains was also investigated, see Figure 15, Figure 16, Figures S7 and S8. For these four kinds of MoSe₂/Ti₃C₂X₂ heterostructures, the band gap of monolayer MoSe₂ disappeared with increasing compressive or tensile strain, and the Mo 4d orbitals and Se 4p orbitals passed through the Fermi energy levels. Therefore, the MoSe₂/Ti₃C₂X₂ heterostructure is more sensitive to external strain than the MoS₂/Ti₃C₂X₂ heterostructure. Moreover, these MoSe₂/Ti₃C₂X₂ heterostructures had a similar response to external strain. When there was no strain, the single-layer MoSe₂ maintained its original semiconductor properties (see Figure 6), and the Fermi energy level was at the VBM of the MoSe₂. When the tensile or compressive strain was above 6%, MoSe₂ was transformed into a conductor. The tensile and compressive strain can obviously increase the charge contribution of Mo 4d orbitals and Se 4p orbitals at the Fermi energy level. Moreover, under compressive strain, the PDOS peak value of these MoSe₂/Ti₃C₂X₂ heterostructures becomes sharper, indicating that the electron localization is strong.

3.4. Effect of Electric Field on the Electronic Properties of the TMDs/Ti₃C₂X₂ Heterostructures

Some studies [56,57] have shown that the electric field is a useful way to tune the electronic properties of heterostructures. In this section, we focus on the effects of the vertical electric field on the electronic properties of TMDs/Ti₃C₂X₂ heterostructures. To determine the effect of different directions of the applied electric field on the electronic properties of these heterostructures, we defined that the direction of the TMDs pointing to Ti₃C₂X₂ was the positive direction of the applied vertical electric field, and the reverse direction was negative. The gradient from −0.9 V/Å to +0.9 V/Å for the applied electric field was taken in steps of 0.3 V/Å.

Figure 17 shows the DOS of MoS₂/Ti₃C₂X₂ and PDOS of MoS₂ in MoS₂/Ti₃C₂X₂ (X = S, Se, Cl, Br) under different electric fields. The monolayer MoS₂ maintained its band gap under the positive and negative electric fields. The position of the valence band maximum (VBM) and conduction band minimum (CBM) of MoS₂ in MoS₂/Ti₃C₂Br₂ and MoS₂/Ti₃C₂Cl₂ remained almost unchanged under the negative electric field. In contrast, the VBM and CBM of MoS₂ in MoS₂/Ti₃C₂Br₂ and MoS₂/Ti₃C₂Cl₂ underwent a significant shift under the positive electric field, and the peak of the Mo 4d orbital moved toward a higher energy level, as shown in Figure 17a,b. Compared with MoS₂/Ti₃C₂Br₂ and MoS₂/Ti₃C₂Cl₂, the effect of the electric field on the VBM and CBM of MoS₂ in MoS₂/Ti₃C₂Se₂ and MoS₂/Ti₃C₂S₂ presented a completely reverse case. The position of VBM and CBM of MoS₂ in MoS₂/Ti₃C₂Se₂ and MoS₂/Ti₃C₂S₂ remained almost unchanged under the positive electric field, while obviously moving under the negative electric field. Moreover, the peak position of the Mo 4d orbital remained almost constant, see Figure 17c,d. The DOS values of MoSe₂ in MoSe₂/Ti₃C₂X₂ (X = S, Se, Cl, Br) under different electric fields were investigated, and the results were very similar to the MoS₂/Ti₃C₂X₂, see Figure S4. Compared with MoS₂/Ti₃C₂Br₂ and MoS₂/Ti₃C₂Se₂, the total DOS of MoS₂/Ti₃C₂S₂ and MoS₂/Ti₃C₂Cl₂ obviously moved near the Fermi Level, suggesting the shift of VBE and CBE of MoS₂. Moreover, under the condition of a positive electric field, the total DOS of MoS₂/Ti₃C₂Cl₂ presented a sharp peak around 1 eV.

We further analyzed the energy band structure of TMDs/Ti₃C₂X₂ (X = S, Se, Cl, Br) heterostructures near the Fermi energy level in the electric field range from −0.9 V/Å to 0.9 V/Å, as shown in Figure 18. Figure 18a gives the variation patterns of the energy band edges at the M and K points near the Fermi energy level for MoS₂/Ti₃C₂X₂ (X = Se, Br) heterostructures under different electric fields. For MoS₂/Ti₃C₂Br₂, the conduction band edge (CBE) and valence band edge (VBE) at both the M the K points moved towards a higher energy level with increasing electric field strength in the positive direction, while they were almost pinned under the negative electric field. In contrast, both the CBE and the VBE of MoS₂/Ti₃C₂Se₂ at the K point moved towards a higher energy level with increasing negative electric field strength, while the CBE at the K point under the positive electric field moved towards a lower energy level. Under the positive electric field, both the CBE and VBE of MoS₂/Ti₃C₂Se₂ at the M point remained unchanged. For MoS₂/Ti₃C₂X₂ (X = S, Cl), see Figure 18b, the VBE and CBE of MoS₂/Ti₃C₂Cl₂ at the M point and K point near the Fermi level were similar to those of the MoS₂/Ti₃C₂Br₂ heterostructure. The energy level of both the CBE and VBE of MoS₂/Ti₃C₂S₂ at the M point increased linearly with increasing positive electric field strength, while it decreased slightly with the negative electric field. It is worth noting that the CBE and VBE of MoS₂/Ti₃C₂S₂ at the K point were almost pinned under the positive and negative electric fields. For MoSe₂/Ti₃C₂Br₂, the energy level of the CBE and VBE at the M and K points decreased linearly with an increasing positive electric field, while it increased with an increasing negative electric field, see Figure 18c. The energy band edge of MoSe₂/Ti₃C₂Se₂ was almost independent of the positive and negative electric fields. From Figure 18d, we know that for MoSe₂/Ti₃C₂S₂ the energy level of the CBE and VBE at the K point and M point were insensitive to the external electric field. For MoSe₂/Ti₃C₂Cl₂, the energy level of the CBE at the K point and M point showed a slight change under the condition of the positive electric field, while it could be pinned when the negative electric field was applied. The energy level of the VBE at the K point and M point remained unchanged when the electric field strength was increased to 0.3 V/Å. The energy band edges of TMDs/Ti₃C₂X₂ (X = S, Se, Cl, Br) heterostructures showed a significant change near the Fermi energy level under different directional electric fields, indicating that the combined functional group with the electric field can effectively tune the related properties of TMDs/Ti₃C₂X₂ (X = S, Se, Cl, Br) heterostructures.

4. Conclusions

The effects of biaxial strain and functional groups as well as electric fields on the structural and electronic properties of TMDs/Ti₃C₂ heterostructures were systematically investigated based on the density functional theory method. The six possible configurations of MoS₂/Ti₃C₂ and MoSe₂/Ti₃C₂ heterostructure stacks were first designed, and then geometrically optimized. ZM_SA were identified as the most energetically stable structural types of MoS₂/Ti₃C₂ heterostructures with a binding energy of −1.79 meV/Ų. The most energetically stable structure type of MoSe₂/Ti₃C₂ heterostructures was SA_ZM, its binding energy of −1.03 meV/Ų. The surface functional groups (S, Se, Cl, Br) of the monolayer Ti₃C₂ resulted in the lattice expansion of TMDs/Ti₃C₂X₂ heterostructures, and the MoSe₂/Ti₃C₂Br₂ heterostructure possessed the maximum lattice parameters (3.262 Å). The conductivity of MoS₂/Ti₃C₂ and MoSe₂/Ti₃C₂ can be enhanced by increasing the biaxial tensile strain. When the surface of the monolayer Ti₃C₂ was occupied by S, Se, Cl, or Br, the coupling strength between the monolayer TMDs and Ti₃C₂ was obviously weakened, while the biaxial strain effectively improved their interaction strength. The different surface functional groups induced a different response of the electronic properties of TMDs/Ti₃C₂X₂ heterostructures to the external electric field. The energy bands around the Fermi energy level of TMDs/Ti₃C₂X₂ heterostructures obviously changed under the combined effect of surface functional groups with an electric field. These results demonstrated that TMDs/Ti₃C₂X₂ (X = S, Se, Cl, Br) heterostructures possess rich electronic properties. Moreover, both MoS₂/Ti₃C₂X₂ (X = Se, Br) and MoSe₂/Ti₃C₂X₂ (X = S, Se, Cl, Br) are rather sensitive to an external strain field, while only TMDs/Ti₃C₂X₂ (X = Cl, Br) strongly depends on an external positive electric field. We hope that these studies can provide a theoretical foundation for the application of TMDs/MXenes heterostructures in the field of high-performance nanoelectronic devices.

Author Contributions

S.Z.: Data curation, Formal analysis, Investigation, Methodology, Resources, Software, Validation, Visualization, Roles/Writing—original draft, Writing-review & editing. C.L.: Conceptualization, Investigation, Methodology, Funding acquisition, Project administration, Supervision, Validation, Writing—review & editing. C.W.: Investigation, Visualization. D.M.: Investigation, Visualization. B.W.: Investigation, Visualization. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Data are available on request from the corresponding author.

Conflicts of Interest

The authors declare that there is no conflict of interest regarding publication of this manuscript.

Footnotes

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Figures and Tables

Figure 1. A schematic diagram of top and side views of MoS2/Ti3C2 heterostructures for different stackings. (a) the ZM_SA Configuration; (b) the ZM_AA Configuration; (c) the ZM_AS Configuration; (d) the MZ_SA Configuration; (e) the MZ_AA Configuration; (f) the MZ_AS Configuration.

Figure 2. Structural properties of TMDs/Ti3C2X2 heterostructures. (a) Diagram of top and side views of MoSe2/Ti3C2X2 heterostructures; (b) Diagram of top and side views of MoS2/Ti3C2X2 heterostructures; (c) The lattice parameters of TMDs/Ti3C2X2 heterostructures.

Figure 3. (a) the band structure, and (b) the total and partial density of states of MoS2/Ti3C2. The Fermi level is set to 0 eV.

Figure 4. (a) the band structure, and (b) the total and partial density of states of MoSe2/Ti3C2. The Fermi level is set to 0 eV.

Figure 5. Band structures and densities of states of the MoS2/Ti3C2 heterostructure with different terminated groups: (a) -Br, (b) -Cl, (c) -S and (d) -Se. The Fermi level is set to 0 eV. The vertical dashed line gives the location of the Fermi level. The red line represents the Fermi level. The green line represents the high symmetry point of the Brillouin zone.

Figure 6. Band structures and densities of states of the MoSe2/Ti3C2 heterostructure with different terminated groups: (a) -Br, (b) -Cl, (c) -S and (d) -Se. The Fermi level is set to 0 eV. The vertical dashed line gives the location of the Fermi level.

Figure 6. Band structures and densities of states of the MoSe2/Ti3C2 heterostructure with different terminated groups: (a) -Br, (b) -Cl, (c) -S and (d) -Se. The Fermi level is set to 0 eV. The vertical dashed line gives the location of the Fermi level.

Figure 7. (a) Relationship curve between MoS2/Ti3C2 interlayer distance and biaxial strain, (b) Relationship curve between MoSe2/Ti3C2 interlayer distance and biaxial strain.

Figure 8. (a) Relationship curve between MoS2/Ti3C2X2 (X = Se, Br, S, Cl) interlayer distance and biaxial strain, (b) Relationship curve between MoSe2/Ti3C2X2 (X = Se, Br, S, Cl) interlayer distance and biaxial strain.

Figure 9. (a) Energy band structures of MoS2/Ti3C2 heterostructure under different compress strains. (b) Energy band structures of MoS2/Ti3C2 heterostructure under different tensile strains. The Fermi level is set to 0 eV. The red line represents the Fermi level. The green line represents the high symmetry point of the Brillouin zone. I/II/III/IV/V represents different energy bands.

Figure 10. The partial density of states (PDOS) of MoS2 and Ti3C2 for the MoS2/Ti3C2 heterostructure with different biaxial strains. The Fermi level is set to 0 eV.

Figure 11. (a) Energy band structures of MoSe2/Ti3C2 heterostructure under different compress strains. (b) Energy band structures of MoSe2/Ti3C2 heterostructure under different tensile strains. The Fermi level is set to 0 eV. The red line represents the Fermi level. The green line represents the high symmetry point of the Brillouin zone. I/II/III/IV/V represents different energy bands.

Figure 12. The partial density of states (PDOS) of MoSe2 and Ti3C2 for the MoSe2/Ti3C2 heterostructure with different biaxial strains. The Fermi level is set to 0 eV. The red line represents the Fermi level.

Figure 13. Density of states of the MoS2/Ti3C2Br2 heterostructure with different biaxial strains. The Fermi level is set to 0 eV.

Figure 14. Density of states of the MoS2/Ti3C2Se2 heterostructure with different biaxial strains. The Fermi level is set to 0 eV.

Figure 14. Density of states of the MoS2/Ti3C2Se2 heterostructure with different biaxial strains. The Fermi level is set to 0 eV.

Figure 15. Density of states of the MoSe2/Ti3C2Br2 heterostructure with different biaxial strains. The Fermi level is set to 0 eV.

Figure 15. Density of states of the MoSe2/Ti3C2Br2 heterostructure with different biaxial strains. The Fermi level is set to 0 eV.

Figure 16. Density of states of the MoSe2/Ti3C2Se2 heterostructure with different biaxial strains. The Fermi level is set to 0 eV.

Figure 17. The DOS of MoS2/Ti3C2X2 and PDOS of MoS2 in MoS2/Ti3C2X2 heterostructures under different electric fields. (a) X-Br, (b) X-Cl, (c) X-Se and (d) X-S.

Figure 17. The DOS of MoS2/Ti3C2X2 and PDOS of MoS2 in MoS2/Ti3C2X2 heterostructures under different electric fields. (a) X-Br, (b) X-Cl, (c) X-Se and (d) X-S.

Figure 18. (a) The VBE and CBE at M and K points of MoS2/Ti3C2Br2 and MoS2/Ti3C2Se2 under different electric fields. (b) The VBE and CBE at M and K points of MoS2/Ti3C2S2 and MoS2/Ti3C2Cl2 under different electric fields. (c) The VBE and CBE at M and K points of MoSe2/Ti3C2Se2 and MoSe2/Ti3C2Br2 under different electric fields. (d) The VBE and CBE at M and K points of MoSe2/Ti3C2S2 and MoSe2/Ti3C2Cl2 under different electric fields.

Table 1

Binding energy (E_b), interlayer distance (d), Mo–S(1) minus Mo–S(2) constant (d₁₂), and bond lengths Ti–C (d_Ti–C) for MoS₂/Ti₃C₂ heterostructures, respectively.

Configurations	Eb (meV/Å2)	d (Å)	d12 (Å)	dTi(3)–C(2) (Å)	dTi(1)–C(1) (Å)
(a) ZM_SA	−1.79	1.68	0.069	2.059	2.125
(b) ZM_AA	−1.21	1.69	0.078	2.057	2.152
(c) ZM_AS	−1.42	2.47	0.031	2.058	2.069
(d) MZ_SA	−1.27	2.03	0.109	2.055	2.094
(e) MZ_AA	−1.48	1.92	0.134	2.057	2.081
(f) MZ_AS	−1.55	2.46	0.021	2.063	2.067

Table 2

Binding energy (E_b), interlayer distance (d), Mo–Se(1) minus Mo–Se(2) constant (d₃₄), and bond lengths Ti–C (d_Ti–C) for MoSe₂/Ti₃C₂ heterostructures, respectively.

Configurations	Eb (meVÅ2)	d (Å)	d34 (Å)	dTi(3)–C(2) (Å)	dTi(1)–C(1) (Å)
(g) SA_ZM	−1.03	1.89	0.051	2.064	2.119
(h) AA_ZM	−1.01	2.56	0.013	2.071	2.073
(i) AS_ZM	−0.39	2.51	0.021	2.067	2.074
(j) SA_MZ	−0.76	2.12	0.101	2.061	2.096
(k) AA_MZ	−0.96	2.09	0.107	2.068	2.083
(m) AS_MZ	−0.59	2.01	0.063	2.069	2.122

Table 3

Binding energy (E_b), interlayer distance (d), Mo–S(1) minus Mo–S(2) or Mo–Se(1) minus Mo–Se(2) constant (d₅₆), and bond lengths Ti–X d_Ti–X and Ti–C d_Ti–C for TMDs/Ti₃C₂X₂ (X = S, Se, Br, Cl) heterostructures, respectively.

Configurations	Eb (meVÅ2)	d (Å)	d56 (Å)	dTi(1)–C (Å)	dTi(2)–X (Å)	dTi(1)–X (Å)
MoS2/Ti3C2S2	−8.44	2.83	0.009	2.182	2.397	2.389
MoS2/Ti3C2Se2	−3.95	2.78	0.007	2.146	2.520	2.496
MoS2/Ti3C2Cl2	−3.17	3.02	0.003	2.104	2.503	2.492
MoS2/Ti3C2Br2	−8.42	3.07	0.004	2.117	2.626	2.621
MoSe2/Ti3C2S2	−3.55	3.03	0.003	2.193	2.501	2.403
MoSe2/Ti3C2Se2	−4.82	3.00	0.000	2.170	2.628	2.542
MoSe2/Ti3C2Cl2	−3.12	3.14	0.003	2.120	2.509	2.506
MoSe2/Ti3C2Br2	−8.41	2.99	0.001	2.127	2.638	2.617

Table 4

Mulliken charge (electron) of MoS₂/Ti₃C₂.

Species	Ion	Total	Charge	Total	Charge	Total	Charge
		Compressive 9%		Strain Free		Tensile 9%
C	1	4.70	−0.70	4.75	−0.75	4.78	−0.78
C	2	4.69	−0.69	4.71	−0.71	4.71	−0.71
S	1	5.94	0.06	5.98	0.02	6.05	−0.05
S	2	6.01	−0.01	6.06	−0.06	6.11	−0.11
Ti	1	11.24	0.76	11.25	0.75	11.34	0.66
Ti	2	11.62	0.38	11.59	0.41	11.57	0.43
Ti	3	11.72	0.28	11.63	0.37	11.49	0.51
Mo	1	14.08	−0.08	14.03	−0.03	13.95	0.05

Table 5

Mulliken charge (electron) of MoSe₂/Ti₃C₂.

Species	Ion	Total	Charge	Total	Charge	Total	Charge
		Compressive 9%		Strain Free		Tensile 9%
C	1	4.69	−0.69	4.71	−0.71	4.71	−0.71
C	2	4.70	−0.70	4.75	−0.75	4.78	−0.78
Se	1	5.87	0.13	5.86	0.14	5.90	0.10
Se	2	5.68	0.32	5.77	0.23	5.74	0.26
Ti	1	11.27	0.73	11.27	0.73	11.36	0.64
Ti	2	11.71	0.29	11.62	0.38	11.49	0.51
Ti	3	11.71	0.29	11.67	0.33	11.69	0.31
Mo	1	14.37	−0.37	14.35	−0.35	14.33	−0.33

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/nano13071218/s1, Figure S1: A schematic diagram of top and side views of MoSe₂/Ti₃C₂ heterostructures for different stackings; Figure S2: Band structures and densities of states of the MoS₂; Figure S3: Band structures and densities of states of the MoSe₂; Figure S4: The DOS of MoSe₂/Ti₃C₂X₂ and PDOS of MoSe₂ in MoSe₂/Ti₃C₂X₂ heterostructures under different electric fields. (a) X-Br, (b) X-Cl, (c) X-Se and (d) X-S; Figure S5: Density of states of the MoS₂/Ti₃C₂Cl₂ heterostructure with different biaxial strains; Figure S6: Density of states of the MoS₂/Ti₃C₂S₂ heterostructure with different biaxial strains; Figure S7: Density of states of the MoSe₂/Ti₃C₂Cl₂ heterostructure with different biaxial strains; Figure S8: Density of states of the MoSe₂/Ti₃C₂S₂ heterostructure with different biaxial strains; Table S1: Optimized structural parameters for the TMDs/Ti₃C₂X₂ (X = S, Se, Br, Cl) heterostructure; Table S2: Mulliken charge (electron), bond length (Å) and bond populations of MoS₂/Ti₃C₂; Table S3: Mulliken charge (electron), bond length (Å) and bond populations of MoSe₂/Ti₃C₂.

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