First-principles study on the structure and electronic properties of M₂CS_x (M = Sc, Ti, Y, Zr and Hf, x = 1, 2)

Abstract

Two-dimensional (2D) transition metal carbides/nitrides, known as MXenes, have attracted extensive attention due to their rich elemental composition and diverse surface chemistry. In this study, the crystal structure, electronic, mechanical, and electronic transport properties of M₂CS_x (M = Sc, Ti, Y, Zr, and Hf, x = 1, 2) were investigated by density functional theory (DFT). Our results showed that the studied M₂CS_x except Y₂CS₂ are thermodynamically, dynamically, thermally, and mechanically stable. The p–d hybridization between the M-d state and the C/S-p state of M₂CS is stronger than that of the corresponding M₂CS₂. However, the antibonding state would appear near the Fermi level and thus reduce the thermal stability of the material due to the introduction of sulfur vacancies in the Y-free MXenes studied. In contrast, sulfur vacancies would significantly enhance the bonding states of Y–C and Y–S bonds and improve the stability of Y₂CS_x. This provides an explanation for the experimentally observed formation of non-stoichiometric Ti₂CS_1.2. The room-temperature electron mobilities of semiconductor Sc₂CS (Y₂CS) along the x and y directions were determined to be 232.59 (818.51) and 628.22 (552.55) cm² V⁻¹ s⁻¹, and the room-temperature hole mobilities are only 88.32 (1.64) and 61.75 (17.80) cm² V⁻¹ s⁻¹. This work is expected to provide theoretical insights for the preparation and application of S-terminated MXenes.

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1. Introduction

MXenes are a large family of two-dimensional (2D) transition metal carbides, nitrides, and carbonitrides with diverse structures, compositions, and surface chemistries, and have been widely used in many fields such as energy storage,^1,2 electronic devices,^3,4 sensors,^5,6 catalysts,^7,8 the environment,^9,10 and biomedicine.¹¹ MXenes are prepared by a top-down synthesis approach, that is, selective etching of A-layer elements from MAX phase precursors. The general formula of MXenes is M_n+1X_nT_x, where M represents the transition metal element (such as Sc, Ti, V), X is the C or N element, n can vary from 1 to 4, and T_x (x is a variable) indicates the surface group. Since the first MXene (Ti₃C₂T_x) was obtained by hydrofluoric acid etching in 2011,¹² more than 30 stoichiometric MXenes have been prepared and more than 100 compositions of MXenes have been predicted.¹³ In addition, the surface termination of MXenes is dependent on the synthesis approach and MXene composition.^14–16 For example, the surface terminations of MXenes produced by wet chemical etching techniques are generally F, O, and OH.^15,17 The halogen-terminated MXenes can be synthesized by etching in Lewis acid CuCl₂/CuBr₂/CuI₂ molten salts.^18,19 These terminations can be substituted or eliminated by other functional groups such as S, Se, Te, NH groups through subsequent surface reactions, providing a new route to synthesize new MXenes that cannot be obtained by conventional Lewis acid etching.^16,20 The surface terminations of MXenes have a significant impact on the physical, chemical properties and structural stability of MXenes due to the overlapping of non-bonding valence electrons of transition metals through their low-energy electronic states.^21–23 Li et al. reported the I-terminated halogenated Ti₃C₂I₂ MXene cathode can activate and stabilize reversible I⁰/I⁺ redox couple in the I₂–Zn battery to achieve a high voltage plateau.²⁴ Superconductivity was first observed in Nb₂CT_x terminated with S, Se, or NH groups, while no superconducting transition was found for bare and O-terminated Nb₂C.¹⁶ Some M₂CT₂ (T = O, OH or S)-based multifunctional sulfur cathodes were found to effectively suppress the shuttling effect and exhibit excellent cycle performance and high specific capacity in lithium–sulfur batteries.^25–27 Zhu et al. showed the O, OH and F groups on Zr₂CT_x can be seemingly exchanged with S groups through the proposed reaction in CS₂ solution.²⁸ A number of S-functionalized MXenes have been reported as electrode materials for potential metal ion batteries due to their lower diffusion barrier and higher storage capacity.^29–37 Luo et al. investigated the nitrogen reduction reaction (NRR) of Fe adsorbed on Ti₃C₂O₂ or N/F/P/S/Cl-doped Ti₃C₂O_2−x MXene and found that F and S doping can reduce the energy barrier of the rate-determining step.³⁸ Bae et al. reported a new structural phase of Sc₂CO₂ containing C3 trimers converted from the hexagonal carbon of the typical trigonal MXene phase, with two very active anion electrons located in the voids between C3 trimers.³⁹ Additionally, Wang et al. demonstrated that the stable Sc₂CO₂ monolayer is an efficient NH₃ gas sensor with high selectivity, high sensitivity and low recovery time through analytical methods based on optical and/or electronic response.⁴⁰ In comparison, without directly considering the material stability, Hu et al. reported that Sc₂CS₂ could effectively capture the NH₃ and nicotine, while the Y₂CS₂ exhibits the extremely high sensitivity and selectivity towards NO.⁴¹ Importantly, only non-stoichiometric chalcogen-terminated MXenes were observed in the experiment, e.g. x = 1.2 and 1.1 for Ti₂CS_x, and Ti₃C₂S_x, respectively,¹⁶ despite the dynamical stability of stoichiometric M₂CS₂ (M = Sc, Ti, V, Cr, Fe, Y, Zr, Nb, Mo, Hf, Ta and W) and Ti₃C₂S₂ have been theoretically confirmed by the calculated phonon dispersions and ab initio molecular dynamics (AIMD) simulations.^{27,29,42–49} To the best of our knowledge, the non-stoichiometric structures, underlying stability mechanisms and associated physical properties of S-terminated MXenes remain unclear.

In this study, the structural stability, electronic structure, mechanical and electronic transport properties of M₂CS_x (M = Sc, Ti, Y, Zr and Hf, x = 1, 2) were investigated using density functional theory (DFT). Our results showed that the calculated cohesive energies and bond lengths of the M–C and M–S bonds of M₂CS are smaller than those of the counterpart M₂CS₂ due to the more pronounced electron transfer and stronger p–d overlaying between M-d state and C/S-p state of M₂CS. In addition, due to the introduction of sulfur vacancy in the studied MXenes except Y₂CS_x, the antibonding state would appear near the Fermi level, reducing the thermal stability of the material. Furthermore, both Sc₂CS and Y₂CS were found to be a thermodynamically stable and dynamically stable semiconductors with appropriate carrier mobility. This work is expected to provide clues for the design and preparation of novel MXenes.

2. Computational details

All the first-principles calculations were carried out by using Vienna Ab initio Simulation Package (VASP). Projector augmented wave (PAW) method⁵⁰ was employed to describe the electron–core interactions and the generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof (PBE) was used to treat the exchange–correlation potential of valence electrons.⁵¹ And the DFT-D3 method with Becke–Jonson damping were included in all calculations to account for the van der Waals (vdW) interaction.⁵² The cutoff energy of plane waves was set to 500 eV. The Monkhorst–Pack meshes with 12 × 12 × 1 and 9 × 9 × 1 k-points were used to sample the Brillouin zone for the calculations of M₂CS₂ and M₂CS cells, respectively. A large vacuum thickness of 20 Å was used to avoid the spurious interaction between adjacent monolayers. The structures studied were fully optimized using conjugate gradient algorithm, and the energy and force convergences of 10⁻⁸ eV and 10⁻⁶ eV Å⁻¹ were used for the calculations. In addition, density functional perturbation theory implemented in PHONOPY software was used to calculate phonon spectra to check the dynamical stability of the structures investigated.^53,54 And the 4 × 4 × 1 supercell of M₂CS₂, 2 × 2 × 1 supercell of M₂CS, plane wave with a cut-off energy of 650 eV and 4 × 4 × 1 k-point meshes were used for force constant calculations. AIMD simulations were performed for 4 ps in NVT ensemble with a time step of 1.0 fs to assess thermal stability of M₂CS_x. The Nosé–Hoover thermostat was applied to control the temperature. In order to predict the electronic transport properties, band gap center E_BGC was calculated by using GGA-PBE functional and calibrated against vacuum level.⁵⁵ The band edge of MXene could be accurately evaluated as follows.^56–58

E_VBM = E_BGC − ½E_g (1)

E_CBM = E_BGC + ½E_g (2)

Here E_g is the calculated band gap of MXene. Carrier mobility of 2D MXenes was studied based on the deformation potential theory according to eqn (3) because the carrier mobility of a 2D intrinsic inorganic semiconductor is mainly dominated by the phonon scattering.^59,60Here, ℏ is the reduced Planck constant, T is the temperature, k_B is the Boltzmann's constant, e is the elementary charge. m* = ℏ²/(∂²E/∂k²) is the effective mass of charge, C_2D is the elastic modulus under the strain Δa/a₀ along the transport direction, determined by C_2D = [∂²E/∂[Δa/a₀]²]/S₀, where E and S₀ is the total energy and the area of optimized supercell. And E_i represents the deformation potential constant of valence-band maximum for holes and conduction-band minimum for electrons, calculated by E_i = ∂E_edge/∂(Δa/a₀), where E_edge is the energy of ith energy band under a small compressive or tensile strain Δa/a₀ along the transport direction. All the structures were visualized by Materials Studio or VESTA3 software.⁶¹

3. Results and discussion

3.1. Crystal structure and stability of M₂CS_x

Four possible configurations for sulfur terminations of a M₂CS₂ crystal were considered in Fig. S1.† In order to assess the relative thermodynamic stabilities of the configurations studied, cohesive energy E_coh was calculated by

E_coh = [E_tot(M₂CS_x) − 2E(M) − E(C) − xE(S)]/(3 + x) (4)

where E_tot(M₂CS_x) is the total energy of M₂CS_x, E(M), E(C), and E(S) are the energies of isolated M, C, and S atoms, respectively. From the calculated total energies of M₂CS₂ configurations in Table S1,† it is found that the sulfur layers on both sides of the most stable configuration of M₂CS₂ (M = Ti, Zr and Hf) (as shown in Fig. 1 and S1B†) are directly projected to the bottom metal layer, while in the most stable configuration of Sc₂CS₂ and Y₂CS₂, the sulfur atoms on one side are projected directly to the bottom metal atoms, while the sulfur atoms on the opposite side are projected directly to the carbon atoms in the middle layer (as shown in Fig. 1 and S1C†). Apparently, stable Ti₂CS₂, Zr₂CS₂, Hf₂CS₂ are symmetric type-A structures, while energetically preferred asymmetric type-B structures do exist in Sc₂CS₂ and Y₂CS₂. Interestingly, the stable configuration of the studied M₂CS₂ resembles the counterpart M₂CO₂.^40,62 However, Zhang et al.⁴² reported that Sc₂CS₂ and Y₂CS₂ are actually stabilized in distortion variants of the asymmetric type-B phase depicted in Fig. 1 type-B. Therefore, the relative stability of the type-B phase and the distorted type-B phase of Sc₂CS₂ and Y₂CS₂ was compared, and the results are displayed in Table S2 and Fig. S2.† Noteworthily, the dipole-corrected total energies of type-B Sc₂CS₂ and Y₂CS₂ calculated in this study are larger than those reported by Zhang et al.⁴² probably due to the higher convergence criteria used in this study. And the distorted structures of type-B Sc₂CS₂ and Y₂CS₂ were optimized back to the type-B phase with the structural symmetry switched off, resulting in their almost identical total energies. This is probably due to the fact that the imaginary phonon modes around the high symmetry point K that lead to the distortion disappear in our calculated phonon spectra (Fig. S6†). This similar distorted structure was also found in transition metal dichalcogenides, but it was determined as a transient state between the 2H phase and the T_d phase.⁶³ Therefore, further exploration of this possible distorted phase of type-B Sc₂CS₂ and Y₂CS₂ is beyond the scope of this study.

Fig. 1 The optimized most stable configurations of M₂CS_x (M = Sc, Ti, Y, Zr and Hf, x = 1, 2). Type-A: the top and side views of the most stable configurations of M₂CS₂ (M = Ti, Zr and Hf), type-B: the top and side views of the most stable configurations of Sc₂CS₂ and Y₂CS₂, type-C: the top and side views of the most stable configurations of M₂CS (M = Sc, Ti, Y, Zr and Hf).

On the basis of the most stable structure of M₂CS₂, all possible configurations of M₂CS were constructed by 2 × 2 × 1 cell expansion and removal of half of the S terminations, which were done by disorder code.⁶⁴ There are six possible configures for Ti₂CS, Zr₂CS, Hf₂CS as depicted in Fig. S3,† and nine possible configures for Sc₂CS, Y₂CS as shown in Fig. S4.† Interestingly, it can be seen from Tables S3 and S4† that the S groups on both sides of all studied M₂CS are preferentially arranged in stripes, as shown in Fig. S3 DEF and S4 DEF.† That is, the strip-like S groups on both sides of M₂CS₂ are removed in turn, so that the number of S atoms removed on both sides is identical. More importantly, among all the arrangements of stripe-like S terminations, the stripe-like S terminations on both sides of M₂CS are preferentially parallel and the distance between the two stripe-like S groups is the shortest in the xy plane as displayed in Fig. 1 type-C or S3D and S4F.† This can maintain the crystalline structure of M₂CS₂ to the greatest extent. Furthermore, it is evident from Table S3† that it is most energetically unfavorable to completely remove the S atoms on one side of the symmetric type-A M₂CS₂ to expose the MXene, but this is not necessarily the case for the asymmetric type-B M₂CS₂. As with the symmetric type-A phase, it is most energetically unfavorable to remove all the S atoms projected to the bottom M atoms of the asymmetric type-B M₂CS₂ (Fig. S4A†). But it can be seen from Table S4† that removing all S atoms projected to C atoms (Fig. S4I†) is easier than removing 1 S atom projected to the bottom M atom and 3 S atoms projected to the C atoms (Fig. S4G and H†). Importantly, considering the small energy differences among the three configurations A, B, and C of the stoichiometric M₂CS₂ in Table S1,† the most stable non-stoichiometric M₂CS configurations derived from these three configurations were also investigated and presented in Fig. S5,† and their corresponding calculated energies are listed in Table S5.† It is evident from Table S5† that the total energy of the most stable configuration of M₂CS (M = Sc, Ti, Y, Zr, and Hf) with stripe-like S terminations derived from symmetric type-A M₂CS₂ (Fig. 1 and S1B†) is the smallest, indicating that regardless of the stable configuration of M₂CS₂, the stripe-like S terminations of M₂CS tend to be located on top of the underlying metal layer as shown in Fig. 1 type-C.

The calculated lattice constants, cohesive energies, space groups and bond lengths of M–S and M–C bonds of the most stable configurations of M₂CS₂ and M₂CS studied are shown in Table 1. For all M₂CS_x (x = 1 or 2) studied, the cohesive energy of M₂CS_x is negative, compared to the respective E_coh values of −6.38 and −5.06 eV per atom for Sc₂CO₂ (ref. 65) and Ti₂CO₂,⁶⁶ which indicates that they are thermodynamically stable to the isolated constituent atoms. The space group of the M₂CS₂ studied is P3m1, consistent with the experimental observations of traditional stoichiometric MXenes,¹⁶ while the space group of M₂CS (M = Sc, Ti, Y, Zr, and Hf) is P2₁/m. The lattice parameter a = 3.16 Å of Ti₂CS₂ and the lattice constant a = 6.17 Å of Ti₂CS are close to the experimentally observed a value of 3.21 Å for Ti₂CS.¹⁶ And the lattice constants of M₂CS₂ (M = Sc, Ti, Zr and Hf) are slightly larger than those of the corresponding M₂CO₂ (i.e. 3.41, 3.04, 3.31 and 3.27 Å for Sc₂CO₂, Ti₂CO₂, Zr₂CO₂ and Hf₂CO₂)⁶⁷ due to the weaker M–S bond relative to the M–O bond. Clearly, it can be seen that the lattice constant of Y₂CS_x is the largest among the studied M₂CS_x with the same formula due to the weak interatomic bonding of Y–C and Y–S, which will be explained in detail in Section 3.2. The calculated Ti–C bond length of 2.09 Å and Ti–S bond length of 2.36 Å for the Ti₂CS are in good agreement with the experimentally observed Ti–C and Ti–S bond lengths of 2.14 Å and 2.41 Å.¹⁶ Importantly, the M–C and M–S bond lengths of the M₂CS₂ studied are longer than those of the counterpart M₂CS. And the calculated E_coh of the M₂CS₂ studied are greater than those of the counterpart M₂CS. In addition, it can be found from Table 2 that the net negative charge of S and C atoms of the M₂CS₂ studied are smaller than those of the corresponding M₂CS, which indicates that more electrons are transferred from the M atom to the C and S atoms of the M₂CS than the corresponding M₂CS₂. The significant charge transfer can also be visually observed from the charge density difference in Fig. S6.† This confirms that the M–C and M–S bonds of M₂CS are stronger than the corresponding M₂CS₂.

Table 1 The calculated Lattice constant (Å), space group, cohesive energy E_coh (eV per atom) and bond lengths (Å) of M–S and M–C bonds of M₂CS_x (M = Sc, Ti, Y, Zr and Hf, x = 1, 2)

Material	Lattice constant	Bond length		Space group	Ecoh	Material	Lattice constant	Bond length		Space group	Ecoh
	a	M–S	M–C				a	M–S	M–C
Sc2CS2	3.76	2.484/2.459	2.293/2.650	P3m1	−6.03	Sc2CS	6.82	2.474	2.253	P21/m	−6.30
Ti2CS2	3.16	2.395	2.189	P3m1	−6.70	Ti2CS	6.17	2.358	2.093	P21/m	−7.00
Y2CS2	4.17	2.628/2.605	2.485/2.877	P3m1	−6.52	Y2CS	7.37	2.656	2.429	P21/m	−6.62
Zr2CS2	3.44	2.531	2.394	P3m1	−8.13	Zr2CS	6.64	2.508	2.278	P21/m	−8.15
Hf2CS2	3.40	2.508	2.366	P3m1	−7.92	Hf2CS	6.54	2.477	2.260	P21/m	−8.14

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Table 2 Loewdin atomic charge of M₂CS_x (M = Sc, Ti, Y, Zr and Hf, x = 1, 2)

Material	C	S	M	Material	C	S	M
Sc2CS2	−1.53	−0.31/−0.85	1.32/1.46	Sc2CS	−1.95	−0.94	1.45/1.48
Ti2CS2	−1.73	−0.56	1.42	Ti2CS	−1.90	−0.78	1.30/1.38
Y2CS2	−0.85	−0.43/−0.10	0.75/0.63	Y2CS	−0.91	−0.46	0.67/0.70
Zr2CS2	−1.59	−0.54	1.36	Zr2CS	−1.63	−0.69	1.28/1.30
Hf2CS2	−1.08	−0.31	0.85	Hf2CS	−1.02	−0.42	0.70/0.73

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In order to further check the dynamical stability of MXenes, the phonon dispersion curves of M₂CS_x were calculated. It is worth mentioning that small imaginary frequencies near the Γ point are often observed in the calculated phonon spectra of 2D systems, which could be caused by numerical noise owing to the vacuum region.^68–70 As shown in Fig. 2 and S6,† almost no imaginary frequency is observed in the phonon dispersions of M₂CS (M = Sc, Ti, Zr, and Y), and some small negative frequencies near the Γ point appear in the phonon dispersion curves of M₂CS₂ (M = Sc, Ti, Zr, and Hf) and Hf₂CS. This is an indication of dynamic stabilities of M₂CS_x studied except Y₂CS₂, consistent with the fact that Ti₂CS was found in experiments.¹⁶ As a comparison, the exception Y₂CS₂ shows significant imaginary frequencies in the phonon dispersion, consistent with previously reported results by Zhang et al.⁴² and Li et al.,⁶⁸ which is a sign that the formation of the Y₂CS₂ MXene probably needs more inspection from experiments. Then, AIMD simulations were performed to further evaluate the dynamical and thermal stabilities of the M₂CS_x studied as displayed in Fig. 3. There is no broken M–C and M–S bonds or obvious structural reconstruction within a simulation of 4 ps at 300 K for the M₂CS (M = Sc, Y, and Zr) and even at 900 K for the M₂CS₂ (M = Sc, Ti, Zr, and Hf) and Hf₂CS, manifesting the good thermal stability of these S-terminated MXenes. While for Ti₂CS, at 300 K, a structural reconstruction of part of the S-terminations moving from the top of bottom metal to the top of the carbon layer is observed, indicating that the strip-like S-terminations of Ti₂CS are temperature-sensitive. In contrast, Y₂CS₂ exhibits a pronounced destruction within 4 ps simulations at 300 K, which can be regarded as evidence of poor thermal stability, consistent with the observation of significant imaginary frequency. From the above analysis, it can be seen that the studied M₂CS_x except Y₂CS₂ has good dynamical and thermal stability, and it is particularly noted that the strip-shaped S functional groups of Ti₂CS are temperature sensitive and easily disturbed. Chen et al.⁷¹ demonstrated that the stabilization of a certain surface configuration of MXene was the statistical average of the adsorption and desorption of surface functional groups. Thus, the total energy of a certain surface configuration is a function of the chemical potential of the functional group. When the chemical potential of the S functional group is high, close to its upper limit (i.e., the chemical potential of elemental S₈), the stoichiometric M₂CS₂ is the thermodynamically most favorable configuration under such condition. As a comparison, when the chemical potential of the S functional group is small, the non-stoichiometric M₂CS_x may be the thermodynamically preferred configuration, and even M₂CS_x would decompose into bare M₂C and elemental sulfur or sulfide. In the experimental preparation,^16,20 sulfur-functionalized MXene was obtained by functional group substitution of halogen-functionalized MXene by Li₂S or intercalation of bare MXene by FeS or CuS. Under such preparation conditions, the chemical potential of the S functional group is generally lower, which is more conducive to the formation of non-stoichiometric S-functionalized MXenes, which may be the reason why no stoichiometric S-functionalized MXenes were observed experimentally. Zhu et al.²⁸ theoretically clarified the feasibility of interconversion of Zr₂CO₂ and excess CS₂ to Zr₂CS₂ under the release of COS. Therefore, under suitable experimental conditions with high chemical potential of the functional group S, stoichiometric S-functionalized MXenes can be prepared.

Fig. 2 The calculated phonon dispersions of the Sc₂CS and Y₂CS.

Fig. 3 Free energy fluctuations with respect to time at 300 K, 600 K and 900 K in AIMD simulations for M₂CS_x (M = Sc, Ti, Y, Zr, and Hf, x = 1, 2), and the obtained structures of M₂CS_x after AIMD simulations at specific temperature. The specified temperature in the figure is the highest temperature at which the structure can be kept stable among the three temperatures studied. Noteworthily, the reconstruction of the surface functional groups of Ti₂CS and the pronounced destruction of Y₂CS₂ were observed at the lowest temperature studied, 300 K.

3.2. Electronic structure and bonding mechanism of M₂CS_x

In order to explore the electronic structures of the S-functionalized M₂CS_x (M = Sc, Ti, Y, Zr, and Hf, x = 1, 2) studied, the calculated electronic band structures of M₂CS_x as well as the corresponding M₂CO₂ for comparison are presented in Fig. 4. It can be readily found that the studied M₂CO₂ are all indirect bandgap semiconductors, in good accordance with the previous reported results.^40,67 Interestingly, four sulfur-terminated MXenes Sc₂CS₂, Y₂CS₂, Sc₂CS, and Y₂CS were identified as indirect bandgap semiconductors with bandgaps of 1.56, 1.85, 0.68, and 0.92 eV, respectively, which are larger than the bandgaps of 1.56 and 1.37 eV for the counterparts Sc₂CO₂ and Y₂CO₂. In contrast, the energy bands of the studied M₂CS_x (M = Ti, Zr, and Hf, x = 1, 2) crossing Fermi level exhibit the metallic-like features due to the presence of nonbonding M-d states at the Fermi level in Fig. 5. Since the traditional PBE functional generally underestimates the band gap of the material, the band gap of the sulfur-terminated MXene was corrected by the HSE06 functional.⁷² After HSE06 correction, the band gaps of Sc₂CS₂, Y₂CS₂, Sc₂CS and Y₂CS were increased to 2.54, 2.75, 1.43 and 1.69 eV, respectively. Their suitable bandgap endows them with great potential as electronic devices. Cautious inspection from the calculated band gaps of M₂CS_x (M = Sc and Y, x = 1, 2) reveals that sulfur vacancy defects increase the unbonded electrons near the Fermi level of metal atoms on the MXene surface leading to the attenuation of the band gap.

Fig. 4 The band structures of M₂CS_x (M = Sc, Ti, Y, Zr, and Hf, x = 1, 2) together with the corresponding M₂CO₂. The bandgaps of semiconductor materials are shown in the figure.

Fig. 5 The projected density of states (PDOS) of the M₂CS_x (M = Sc, Ti, Y, Zr, and Hf, x = 1, 2) as well as the corresponding M₂CO₂. The green spheres in the insert indicate S vacancies. The black curves represent M-d orbitals, the red and green curves represent C-s and -p orbitals, respectively, and the blue and cyan curves represent S-s and -p orbitals, respectively.

In order to study the underlying bonding mechanism of the studied M₂CS_x, the projected density of states (PDOS) of M₂CS_x together with the corresponding M₂CO₂ for comparison were investigated as depicted in Fig. 5. For all MXenes studied, the electronic states above the Fermi level are dominated by nonbonding t_2g states and antibonding states of the M-d orbital. Noteworthily, the S-p state of M₂CS_x overlaps with the M-d state in the energy range from −4.5 eV to 0 eV, while the O-p state of M₂CO₂ hybridizes with the M-d state around −6 to −2 eV, which is an implication of the stronger M–O bond than M–S bond. Resembling the corresponding M₂CO₂, due to the splitting of the 5-fold degenerate M-d orbitals of M₂CS₂ in the octahedral crystal field of MX₆, 5 hybridization peaks of the S-p state are observed, which are more conspicuous in Y₂CS₂ and Sc₂CS₂, but this phenomenon disappears in M₂CS due to the presence of S vacancies. In particular, the p–d hybridization peaks between S and Y of Y₂CS₂ are very localized, reflecting the weak nature of the Y–S bond, which are significantly improved in Y₂CS. More importantly, the hybridization peaks between the M-d orbital and the C-p or S-p orbital of M₂CS are remarkably higher than those of the corresponding M₂CS₂, which can be regarded as evidence that the M–C and M–S bonds in M₂CS are stronger than those in M₂CS₂.

To explore bonding/antibonding states of bonds of the studied M₂CS_x (M = Sc, Ti, Y, Zr, and Hf, x = 1, 2), the projected crystal orbital Hamilton population (pCOHP) was calculated using the LOBSTER program,⁷³ as shown in Fig. 6. A positive value of −pCOHP indicates a bonding state, and a negative value indicates an antibonding state. The hybridization between M and C and between M and S of the investigated M₂CS is stronger than that of the corresponding M₂CS₂ (seen in Fig. 5) leading to greater splitting of bonding and antibonding states in Fig. 6, i.e. farther away from the Fermi energy level, consistent with the reported results of Ti₂CO₂.⁷⁴ However, the introduction of sulfur vacancies will increase the non-bonding e_g states of the metal d orbitals, thereby making the antibonding states appear near the Fermi level and significantly reducing the thermal stability of the material, consistent with the AIMD simulation results. Especially, both the bonding and antibonding states of the Y–S bond of Y₂CS₂ are very small, again manifesting a weak Y–S bond, leading to the largest lattice constant of Y₂CS₂ among all studied MXenes. On the contrary, the bonding states of the Y–C and Y–S bonds of Y₂CS are very obviously enhanced, significantly improving the stability of Y₂CS_x. Consequently, the d–p hybridization between the metal and C/S atoms of M₂CS is significantly higher than that of the corresponding M₂CS₂, resulting in stronger M–C and M–S bonds in M₂CS than in M₂CS₂. However, due to the introduction of sulfur vacancies in other studied MXenes except Y₂CS_x, the antibonding state would appear near the Fermi level, reducing the thermal stability of the material. On the contrary, sulfur vacancies would significantly enhance the bonding states of Y–C and Y–S bonds and improve the stability of Y₂CS_x.

Fig. 6 The calculated COHP curves of M₂CS_x (M = Sc, Ti, Y, Zr, and Hf, x = 1, 2). The vertical green dotted line represents the Fermi level.

3.3. Mechanical properties

The fabrication of 2D crystal-based electronics generally requires high in-plane stiffness to avoid curling and obtain free-standing membranes. Therefore, the mechanical properties of M₂CS_x (M = Sc, Ti, Y, Zr, and Hf, x = 1, 2) were investigated by examining their elastic constants. Elastic constants C_ij of 2D crystal can be obtained by the first-principles energy-strain method, which is based on the energy variant by applying a small strain ε onto the equilibrium structure. Subsequently, the in-plane Young's modulus Y_2D, in-plane shear modulus G_2D (in N m⁻¹), and Poisson's ratios v can be obtained by eqn (5)–(7)⁷⁰

Y_2D = (C₁₁² − C₁₂²/C₁₁) (5)

G_2D = 1/2(C₁₁ − C₁₂) (6)

v = C₁₂/C₁₁ (7)

The 2D crystal structure is determined to be mechanically stable when all elastic constants satisfy the well-known Born–Huang criteria:⁷⁵ For a trigonal M₂CS₂ structure: C₁₁ > 0, C₁₁ > |C₁₂|, C₆₆ > 0, and for a monoclinic M₂CS structure: C₁₁ > 0, C₁₁C₁₂ > C₁₂C₁₂, C_ij > 0. The calculated elastic constants of M₂CS_x (M = Sc, Ti, Y, Zr, and Hf, x = 1, 2) in Fig. 7 and Table 3 meet the mechanical stability criteria, indicating they are mechanically stable under ambient conditions. It is evident that all the in-plane stiffnesses of Sc₂CS_x and Y₂CS_x are much smaller than those of the M₂CS_x (M = Ti, Zr, and Hf) probably due to the smaller cohesive energies of Sc₂CS_x and Y₂CS_x relative to M₂CS_x (M = Ti, Zr, and Hf). And the maximum Y_2D and G_2D values of Sc₂CS and Y₂CS are larger than those of Sc₂CS₂ and Y₂CS₂, respectively, due to the stronger M–C and M–S bonds of M₂CS compared with M₂CS₂, while M₂CS_x (M = Ti, Zr, and Hf) show the opposite trend, which may be caused by the antibonding states of M–C bond occurring at the Fermi level of M₂CS (Fig. 6). The in-plane Young's modulus and in-plane shear modulus of 104.39 and 36.61 N m⁻¹ for Sc₂CS₂ is the smallest among all the studied M₂CS₂, which are smaller than those of Sc₂CO₂.⁶⁷ Noteworthily, the calculated in-plane Young's moduli of the semiconductors Sc₂CS and Y₂CS are 125.06–140.35 and 82.77–125.34 N m⁻¹, respectively, which are comparable to those of MoSe₂ (125 N m⁻¹) and MoS₂ (168 N m⁻¹),⁷⁶ indicating that Sc₂CS and Y₂CS monolayer have good mechanical properties. And it is further found that their Poisson's ratios v are all within 0.3. Since the low Poisson's ratio is favorable for the application of MXenes in flexible device materials,⁶⁶ Sc₂CS and Y₂CS MXenes have the potential to be used as flexible electronic devices.

Fig. 7 The elastic constants C₁₁, C₁₂, in-plane Young's moduli Y_2D, in-plane shear moduli G_2D (in N m⁻¹), and Poisson's ratios v of the M₂CS₂ MXenes studied.

Table 3 The elastic constants C₁₁, C₁₂, in-plane Young's moduli Y_2D, in-plane shear moduli G_2D (in N m⁻¹), and Poisson's ratios v of the M₂CS MXenes studied

	C11	C12	Y2D (min)	Y2D (max)	G2D (min)	G2D (max)	v (min)	v (max)
Sc2CS	138.95	42.61	125.06	140.35	50.16	50.99	0.27	0.31
Ti2CS	194.49	55.80	175.98	196.30	70.03	75.02	0.23	0.30
Y2CS	120.15	38.14	82.77	125.34	36.05	43.62	0.25	0.49
Zr2CS	196.50	56.84	176.01	194.32	69.85	74.81	0.24	0.31
Hf2CS	217.28	58.13	197.22	210.13	79.22	82.62	0.24	0.28

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3.4. Carrier mobility of nonstoichiometric Sc₂CS and Y₂CS MXenes

Carrier mobility is an important physical quantity to measure the performance of electronic devices. The orthorhombic Sc₂CS and Y₂CS supercell was adopted to calculate the carrier mobility according to deformation potential theory. As shown in Fig. 8a and e, the valence band maximum (VBM) of Sc₂CS and Y₂CS at Γ point is observed while the conduction band minimum (CBM) appears at the K point along Γ–X direction in the electronic band structure of nonstoichiometric Sc₂CS and Y₂CS. As an important band structure-derived property, effective masses of electrons at K point and holes at Γ point of Sc₂CS and Y₂CS were calculated and shown in Table 4. For both Sc₂CS and Y₂CS, it can be readily found that the effective hole mass is much larger than the effective electron mass, suggesting that electrons can have higher mobility than holes under an external electric field due to the much smaller effective mass. Interestingly, the effective electron mass and effective hole mass of Sc₂CS along x direction are larger than those along y direction, respectively, and the effective hole mass of Y₂CS material also shows the same trend, showing effective mass anisotropy. In detail, the effective mass of electrons of Sc₂CS along x direction is 0.70m_e, which is 9.4% larger than that along y direction, while the effective mass of holes along x direction (3.30m_e) is 61.8% larger than that along y direction. In comparison, for Y₂CS, the effective electron masses along the x and y directions are almost equal, but the effective hole mass along the x direction is 1.21 times larger than along the x direction. Besides the effective mass, the deformation potential constant E_l and elastic modulus C_2D of Sc₂CS and Y₂CS MXene were also calculated. The C_2D value of electrons and holes of Sc₂CS and Y₂CS along x direction is 111.98 and 91.02 J m⁻², which is 32.8% and 57.9% larger than those along the y direction, respectively. Additionally, the E_l values (7.03 eV) of holes at Γ point of Sc₂CS along x direction is 1.73 times that along y direction, while the E_l of electrons at K point along the x direction is only 0.60 times that along the y direction. And the deformation potential constants of holes at Γ point of Y₂CS along x and y directions are 4.30 and 3.76 eV, which are 0.35 and 1.75 eV larger than those of electrons at K point along x and y directions, respectively.

Fig. 8 (a) and (e) The calculated band structure of Sc₂CS and Y₂CS monolayer in the orthogonal supercell, (b) and (f) energy–strain relationship along x (Γ–X) and y (Γ–Y) directions of Sc₂CS and Y₂CS supercell, and (c), (d), (g) and (h) band edges as a function of strain along x and y directions of Sc₂CS and Y₂CS supercell, respectively.

Table 4 The calculated carrier mobilities of nonstoichiometric Sc₂CS and Y₂CS

	Carrier type	Direction	C2D (J m^−2)	E1 (eV)	m* (me)	μ (cm^2 V^−1 s^−1)	τ (fs)
Sc2CS	Electron	x	111.98	7.03	0.70	232.59	92.58
		y	84.33	4.06	0.64	628.22	228.62
	Hole	x	111.98	2.42	3.30	88.32	165.72
		y	84.33	4.06	2.04	61.75	71.72
Y2CS	Electron	x	91.02	4.30	0.55	818.51	255.98
		y	57.66	3.95	0.58	552.55	182.23
	Hole	x	91.02	3.76	14.04	1.64	13.11
		y	57.66	2.01	6.35	17.80	64.28

---

Therefore, according to eqn (3), the electron mobilities and hole mobilities of Sc₂CS and Y₂CS are predicted and summarized in Table 4. The room-temperature electron mobilities of Sc₂CS along the x and y directions were determined to be 232.59 and 628.22 cm² V⁻¹ s⁻¹, respectively, compared with the room-temperature hole mobilities of only 88.32 and 61.75 cm² V⁻¹ s⁻¹ along the x and y directions. That is, the electron mobilities along the x and y directions are about 2.63 and 10.17 times that of the holes, respectively, due to the large difference in effective mass, which exhibits pronounced anisotropy. Resembling the charge transport of Sc₂CS, the electron mobilities of Y₂CS along the x and y directions (818.51 and 552.55 cm² V⁻¹ s⁻¹, respectively) are 498 and 30 times higher than the hole mobilities along the x and y directions. Therefore, it can be said that the charge transport of Sc₂CS is predominated by electron, which is different from our recently reported Sc₂CO₂ with similar electron and hole mobilities.⁴⁰ In addition, the predicted carrier mobility of non-stoichiometric Sc₂CS is much higher than that of MoS₂ monolayer,⁷⁷ but much smaller than that of Sc₂CO₂ (ref. 40) due to defect scattering caused by sulfur vacancies. Therefore, the structurally stable Sc₂CS and Y₂CS with suitable carrier mobility and mechanical properties may serve as an excellent nanoelectronic material.

4. Conclusion

In this study, the structural stability, electronic structure, elastic and charge transport properties of M₂CS_x (M = Sc, Ti, Y, Zr, and Hf, x = 1, 2) were studied by using first-principles density functional theory. The studied M₂CS_x except Y₂CS₂ were determined to be thermodynamically, dynamically, thermally, and mechanically stable, suggesting that these S-functionalized MXenes can be successfully prepared. In contrast to all studied M₂CO₂ being indirect bandgap semiconductors, only four S-terminated MXenes (Sc₂CS₂, Y₂CS₂, Sc₂CS, and Y₂CS) were identified as indirect bandgap semiconductors. The p–d hybridization between the M-d state and the S/C-p state of M₂CS is stronger than that of M₂CS₂, indicating that the bonding strength of the M–C/S bond in M₂CS is stronger. However, due to the introduction of sulfur vacancies in the Y-free MXene, an antibonding state would occur near the Fermi level, thereby reducing the thermal stability of the material. On the contrary, the sulfur vacancies would significantly enhance the bonding state of Y–C and Y–S bonds and improve the stability of Y₂CS_x. These provides an explanation for the experimentally observed formation of non-stoichiometric M₂CS_x. And the room-temperature electron mobilities of Sc₂CS (Y₂CS) along the x and y directions were determined to be 232.59 (818.51) and 628.22 (552.55) cm² V⁻¹ s⁻¹, compared with the room-temperature hole mobilities of only 88.32 (1.64) and 61.75 (17.80) cm² V⁻¹ s⁻¹, which are much higher than that of MoS₂ monolayer, but much smaller than that of Sc₂CO₂ due to defect scattering caused by sulfur vacancies. Therefore, Sc₂CS and Y₂CS with suitable carrier mobility and mechanical properties are promising as an excellent nanoelectronic materials. This work is expected to provide theoretical insights for the preparation and application of S-terminated MXenes and the discovery of novel MXene materials.

Conflicts of interest

The authors declare no competing financial interest.

Acknowledgements

The authors acknowledge the support of the Key R & D Projects of Zhejiang Province (No. 2022C01236, 2019C01060), the National Natural Science Foundations of China (Grant No. 52250005, 21875271, U20B2021, 21707147, 51372046, 51479037, 91226202, and 91426304), the Entrepreneurship Program of Foshan National Hi-tech Industrial Development Zone, the Major Project of the Ministry of Science and Technology of China (Grant No. 2015ZX06004-001), Ningbo Natural Science Foundations (Grant No. 2014A610006, 2016A610273, and 2019A610106).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3ra03340f

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