First-principles study on the electrical and thermal properties of the semiconducting Sc3(CN)F2 MXene

The two-dimensional materials MXenes have recently attracted interest for their excellent performance from diverse perspectives indicated by experiments and theoretical calculations. For the application of MXenes in electronic devices, the exploration of semiconducting MXenes arouses particular interest. In this work, despite the metallic properties of Sc3C2F2 and Sc3N2F2, we find that Sc3(CN)F2 is a semiconductor with an indirect band gap of 1.18 eV, which is an expansion of the semiconducting family members of MXene. Using first-principles calculations, the electrical and thermal properties of the semiconducting Sc3(CN)F2 MXene are studied. The electron mobilities are determined to possess strong anisotropy, while the hole mobilities show isotropy, i.e. 1.348 × 103 cm2 V−1 s−1 along x, 0.319 × 103 cm2 V−1 s−1 along the y directions for electron mobilities, and 0.517 × 103 cm2 V−1 s−1 along x, 0.540 × 103 cm2 V−1 s−1 along the y directions for hole mobilities. The room-temperature thermal conductivity along the Γ → M direction is determined to be 123–283 W m−1 K−1 with a flake length of 1–100 μm. Besides, Sc3(CN)F2 presents a relatively high specific heat of 547 J kg−1 K−1 and a low thermal expansion coefficient of 8.703 × 10−6 K−1. Our findings suggest that the Sc3(CN)F2 MXene might be a candidate material in the design and application of 2D nanoelectronic devices.


Introduction
MXenes, a new class of two dimensional transition metal carbides or nitrides with the chemical formula of M n+1 X n (M ¼ Sc, Ti, V, Cr, Zr, Nb, Mo, Hf, Ta; X ¼ C, N; n ¼ 1- 3), have been synthesized from the exfoliation process for ternary layered metallic ceramics such as the MAX phases and immediately attracted extensive attention in recent years. [1][2][3][4][5] The MAX phases are a family of layered compounds with a chemical formula of M n AX n+1 (n ¼ 1-3), where A includes Al, Si, P, S, Ga, Ge, As, In, and Sn. 6,7 There are currently over 70 MAX phases known and this family is still growing due to their large number of solid solutions. 8,9 The terminations on MXenes are typically functionalized by -H, -F, ]O, and -OH groups coming from HF or H 2 O. [10][11][12] Naguib et al. 1 have denoted the functionalized MXenes as M n+1 X n T x , with T standing for the surface-terminating group. Recently, about 20 different MXenes have been reported, 13 and the family of MXenes has been expanded to double transition metals carbides M 0 2 M 00 C 2 and M 0 2 M 00 2 C 3 . 14 The large number of theoretically possible members of the MXene family, the diversity of physical properties among MXenes, and their relative convenience in synthesis merit the attraction of these compounds for novel production methods and 2D materialrelated potential applications. 15 For example, Xu et al. reported the growth of high quality crystalline MXenes achieved by a chemical vapor deposition technique. 16 Azofra et al. investigated the N 2 capture and ammonia conversion behaviour of d 2 -d 4 MXenes, 17 and the CO 2 capture and conversion may be another possible application of the MXene materials. 18 Some of the MXenes are demonstrated to be topological insulators, 19,20 exhibiting multiple Dirac cones and giant spin-orbit splitting. 21 Ashton et al. compared the thermodynamic stability of 54 MXenes, 22 nding Sc-based MXenes to be highly stable with F termination, and the low diffusion barriers for Li on uorinated MXene surfaces 23 can make Sc n+1 X n F 2 MXenes possible candidates for electrode materials in Li-ion batteries. Many of the recent studies on MXenes have been focused on the electronic, magnetic, catalytic or thermoelectric properties. 24-31 Liu et al.
systematically explored the electronic properties of Sc-based MXenes by rst-principles calculations. 32 Wang et al. investigated the band gap tuning of Sc 2 C MXene for optoelectronic devices by changing the types of surface chemical groups, 33 and heterostructures based on three different functionalized Sc 2 C MXenes were built to investigate the possible application for nanodevices. 34 The data from these works suggest that MXenes are promising as electronic devices, for which the semiconducting members are generally desired. However, most MXenes are metallic due to the inheritance of the conducting feature of the electronic band structures in transition metal carbides or nitrides. Therefore, further investigation of these materials is needed, such as the effect of compositional modi-cation on electronic properties as well as structural stability, in order to expand the MXene family, especially for intrinsically semiconducting ones. 35 In this work, the band structures of three uorinefunctionalized scandium MXenes Sc 3 C 2 F 2 , Sc 3 N 2 F 2 and Sc 3 (CN)F 2 are studied using density functional theory (DFT). Here, we demonstrate that Sc 3 (CN)F 2 is a semiconductor with an indirect band gap of 1.18 eV from the Heyd-Scuseria-Ernzerhof (HSE06) correction. This demonstrates that the design of new semiconducting MXenes is possible. The electronic, carrier mobility and thermal properties of the Sc 3 (CN)F 2 MXene are also predicted via theoretical calculations. The strong anisotropy in electron mobility has been determined. In addition, the relatively high specic heat and low thermal expansion coefficient make Sc 3 (CN)F 2 a good candidate material for nanoelectronic devices.

Computational details
The rst-principles calculations are carried out based on projector augmented-wave (PAW) potentials 36 in reciprocal space represented by a generalized gradient approximation (GGA) 37 in density functional theory with Perdew-Burke-Ernzerhof (PBE) for the exchange-correlation function as implemented in the VASP codes. 38 Plane-waves with energies up to 550 eV are employed to describe the electronic wave functions, in which the Sc 3p 6 3d 1 4 s 2 , C 2s 2 2p 2 , N 2s 2 2p 3 and F 2s 2 2p 5 electrons are considered as valence states. To avoid any articial interaction between the layers and their images, a 30Å lattice parameter in the c-axis perpendicular to the MXene surface is set. In the optimized structures, the maximum force on each atom is less than 10 À4 eVÅ À1 . The total energies are converged within 10 À6 eV. For the structural optimization, the Brillouin zone (BZ) is sampled using a set of G-centered 12 Â 12 Â 1 k-points. Due to the underestimation of energy band gaps through GGA-PBE, 39 the non-local HSE06 hybrid functional is also adopted to correct the band gap values. 32,40 The carrier mobilities of the Sc 3 (CN)F 2 MXene are calculated using the deformation potential (DP) theory 41-43 based on an orthorhombic unit cell, as the yellow rectangle highlights in Fig. 1(a). The carrier mobility has been calculated according to eqn (1) 44,45 where ħ and k B are the reduced Planck and Boltzmann constants, respectively. T denotes temperature, and m* is the carrier effective mass along the transport direction; m a is calculated by m a ¼ ffiffiffiffiffiffiffiffiffiffiffiffi m * x m * y q , where m * x and m * y are the carrier effective masses along the x and y directions, respectively, as shown in Fig. 1(c). C is the elastic modulus along the transport direction, determined by extrapolation based on the relationship of C(Da/a) 2 /2 ¼ (E À E 0 )/S 0 , where (E À E 0 ) is the change of the total energy under a small lattice variation Da from the equilibrium lattice constant a 0 along the transport direction, with a small step size (Da/a 0 $ 0.5%), and S 0 is the area of the lattice in the xy plane. Finally, E i is the deformation potential constant of the valence band maximum (VBM) for holes or the conduction band minimum (CBM) for electrons along the transport direction, calculated by E i ¼ DV i /(Da/a 0 ) with DV i as the energy change of the i th energy band. The deformation potential constant is estimated as the slope of the linear tting function between DV i and Da/a 0 .
The thermal conductivities have been calculated from the phonon dispersion of a hexagonal unit cell, as the gray rhombus marks in Fig. 1(a). The phonon thermal conductivity was calculated within the framework of Klemens' theory 46,47 where r is the mass density, calculated by M being the mass of the MXene unit cell, a is the lattice parameter in the xy plane, and d denoting the MXene layer thickness. 48 A bilayer Sc 3 (CN)F 2 MXene structure model is optimized to calculate the layer thickness. The value of d ¼ 10.284Å is measured as the distance between two middle layer Sc atom planes in the bilayer Sc 3 (CN)F 2 MXene. To accurately describe the interlayer interaction of the bilayers for Sc 3 (CN)F 2 , a zero damping van der Waals (vdW) correction (DFT-D3) of Grimme 49 has been adopted. y j , u max,j and u min,j are the group velocity and the maximum and minimum circular frequency of each j th branch, respectively. Due to the nite ake length L, the term of u min,j is redened as u min;j ¼ , where g j is the average value of the branch Grüneisen parameter, and Phonopy soware 50 combined with the VASP code is utilized for phonon dispersion calculations. The theoretical calculation is performed with density functional perturbation theory (DFPT), 51 and a 6 Â 6 Â 1 k-points mesh based on a 2 Â 2 Â 1 super-cell is adopted for calculating the dynamical matrix. The thermal expansion coefficient a is investigated based on the Grüneisen approximation, 52 c v ðj; kÞgðj; kÞ. Here, N k is the k-point number adopted in plotting the phonon spectrum, which is equal to 120 in our calculations; E s is the strain energy; c v (j,k) is the (j,k) mode contribution to the heat capacity, The computational parameters and methods applied in calculating the carrier mobility and thermal properties have been tested in our previous works on Sc 2 CF 2 , Sc 2 C(OH) 2 (ref. 54) and Hf 2 CO 2 (ref. 55) MXenes. The predicted thermal conductivity of graphene in our previous calculation (4.76 Â 10 3 W m À1 K À1 , based on a 5 mm ake length at room temperature) is consistent with the experimental results. 56

Results and discussion
The geometries and band structure properties of the F terminated MXenes Sc 3 C 2 F 2 , Sc 3 N 2 F 2 and Sc 3 (CN)F 2 are investigated using DFT calculations. As 2D hexagonal materials, the MXenes possess two high-symmetry routes, namely, the y and x directions. 57 The top view and side view of the Sc 3 (CN)F 2 MXene are shown in Fig. 1(a) and (b). The Sc 3 C 2 F 2 and Sc 3 N 2 F 2 have similar structures to Sc 3 (CN)F 2 and their side view diagrams are also shown in Fig. 2(a) and (b), respectively. According to our structure models, the x-axis coincides with the x direction, and the y-axis lies along the y direction. The G / K (G / X) and G / M (G / Y) vectors in the Brillouin zone correspond to the realspace x and y directions as shown in Fig. 1(c), respectively. The two carbon or nitrogen layers are sandwiched between three Sc layers, and two uorine layers are projected onto the central Sc layer. Table 1 lists the lattice constants, formation energies and atomic layer distances marked in Fig. 2. The optimized lattice constant of Sc 3 (CN)F 2 is similar to that of Sc 3 C 2 F 2 , and the formation energy is between that of Sc 3 C 2 F 2 and Sc 3 N 2 F 2 . As with the result of the substituted C/N atoms, the Sc-F atomic layer distances are only slightly affected, while the Sc-C and Sc- Fig. 2 Band structures of three F terminated MXenes Sc 3 C 2 F 2 (a), Sc 3 N 2 F 2 (b) and Sc 3 (CN)F 2 (c), and the vacuum energy is set as zero. Red solid and black dotted lines represent electronic energy bands from GGA-PBE and HSE06 respectively. The side view of the Sc 3 C 2 F 2 , Sc 3 N 2 F 2 and Sc 3 (CN)F 2 MXenes are shown below each band structure figure respectively. N distances show notable variations, especially for the bonds with center Sc atoms (labelled as II in Table 1). The band structures of Sc 3 C 2 F 2 , Sc 3 N 2 F 2 and Sc 3 (CN)F 2 are also provided in Fig. 2 (vacuum energy is set as zero). Both Sc 3 C 2 F 2 and Sc 3 N 2 F 2 exhibit metallic properties with the Fermi level crossed by energy bands and with band gaps above/below the Fermi levels, while Sc 3 (CN)F 2 is determined to be a semiconductor with an indirect band gap of 1.18 eV from HSE06. From the band structure plots, the three F terminated MXenes also exhibit similar shapes near the Fermi level despite the difference in band gaps. The band gap can also be observed from the partial density of states (PDOS) plot for Sc 3 (CN)F 2 in Fig. 3. From the gure, Sc and N overlap from À4.5 to À2.5 eV, while Sc and C are from À2.5 to 0 eV (forming CBM) near the Fermi level. Sc 3 C 2 F 2 and Sc 3 (CN)F 2 show similar Fermi level energy; since the Sc-C bonds are strengthened in Sc 3 (CN)F 2 as seen from the reduction of Sc-C bond lengths, the N atoms substitutions lowers the energy of Sc-C hybrid bands forming VBM bands in Sc 3 (CN)F 2 relative to that in Sc 3 C 2 F 2 around the Fermi level. Similarly, the CBM energy of Sc 3 (CN)F 2 is raised relative to the corresponding bands in Sc 3 N 2 F 2 . These result in a rise of the band gap for Sc 3 (CN)F 2 at a particular C/N ratio. This implies band engineering can be achieved in Sc-based MXenes by the structural design of the MXene, thus expanding the group of semiconducting MXenes. With the semiconducting MXene Sc 3 (CN)F 2 investigated in this work, its carrier mobilities with all the required parameters are then calculated and given in Table 2. From the table, the electron mobility of Sc 3 (CN)F 2 by CBM, the red curve in Fig. 1(d), appears to be highly anisotropic, i.e. 1.348 Â 10 3 cm 2 V À1 s À1 along the x (G / X) and 0.319 Â 10 3 cm 2 V À1 s À1 along the y (G / Y) directions, respectively. For the hole mobilities, two quasi-degenerated sub-bands are present at the VBM as Fig. 1(d) indicates, and we distinguish the two sub-bands as "h1" (orange) and "h2" (blue), respectively. Both of the subbands have been calculated, and the total hole mobilities can be estimated as the statistical average of the two sub-bands on the basis of the Boltzmann distribution. Accordingly, the hole mobilities are determined to be 0.078 Â 10 3 along the x and along the y directions for the "h1" sub-band, and are 0.956 Â 10 3 along the x and 1.003 Â 10 3 cm 2 V À1 s À1 along the y directions for the "h2" sub-band, respectively. From Table 2, one may note that, for the "h1" or "h2" sub-band, the values of the effective mass and deformation potential constant along the x and y directions are close to each other, analogous to the Sc 2 CT 2 MXenes calculated in our previous work. 54 The average hole mobilities of Sc 3 (CN)F 2 are 0.517 Â 10 3 along x and 0.540 Â 10 3 cm 2 V À1 s À1 along the y directions, respectively. Consequently, the predicted hole mobilities for Sc 3 (CN)F 2 are almost isotropic. The details of the carrier effective mass calculations are provided in the ESI. † Actually, the electron mobilities are slightly lower than that of Sc 2 CF 2 and Sc 2 C(OH) 2 , while the hole mobilities are higher than that of Sc 2 CF 2 and Sc 2 C(OH) 2 . 30 The predicted carrier mobilities are much higher than that of monolayer MoS 2 , 58 providing a hopeful application in nanoelectronics devices for the Sc 3 (CN)F 2 MXene. Moreover, in order to exclude the impact of structural disorder, i.e. the entropy effect on the semiconducting nature of Sc 3 (CN)F 2 , the possibilities of a random distribution of C and N atoms are taken into consideration as well. Three 2 Â 2 Â 1 super-cells with different C and N arrangement models are built for band structure calculations as shown in Fig. 4. Model 0 represents the ordered arrangement of C and N, and Model 1 and 2 are disordered ones. The results conrm that the Sc 3 (CN)F 2 MXene is a semiconductor and imply that the random C and N distribution can lead to a slight sub band splitting of CBM and VBM, while the slopes of the bands near the Fermi level keep similar trends, suggesting that the ordered or disordered Sc 3 (CN)F 2 MXene might have similar carrier mobilities.
The Sc 3 C 2 F 2 , Sc 3 N 2 F 2 and Sc 3 (CN)F 2 MXenes phonon dispersions along G / M / K / G are given in Fig. 5. From the gure, the absence of imaginary phonon frequencies implies the structural stabilities of those MXenes. It is well known that thermal conductivities for semiconductive materials are dominantly contributed by phonon transport. Therefore, the lattice thermal conductivities for Sc 3 (CN)F 2 are thus investigated in the  Table 2 The carrier mobilities of Sc 3 (CN)F 2 . Carrier type "e" and "h" denote "electron" and "hole", respectively. m * x and m * y are the effective masses along the x and y directions. E x and E y are the deformation potential constants, C x and C y are the elastic moduli. m x and m y are the roomtemperature carrier mobilities current work and the electronic thermal conductivity for Sc 3 (CN)F 2 is considered negligible. The values for the Sc 3 (CN)F 2 MXene are calculated according to eqn (2) based on the phonon dispersions. The required parameters, including the group velocity y j , Grüneisen parameter g j and the square of the Grüneisen parameter hg 2 j i are list in Table 3. From the table, the group velocities along the G / M (real-space y) direction for transversal acoustic (TA), longitudinal acoustic (LA) and out-ofplane acoustic (ZA) modes are larger than the G / K (real-space x) direction. In particular, the group velocity values for the ZA mode along G / M are approximately 20% higher. Moreover, the minimum values for Grüneisen parameter g j and hg 2 j i found originated from the ZA mode along the G / M direction. For the G / K direction, the minimum in g j and hg 2 j i occurs in the LA mode. The ratio of hg 2 j i between the G / K and G / M directions is the maximum by the ZA mode. These may imply that the out of plane phonon modes are responsible for anisotropy in thermal conductance. Similar phenomena can be found in the parameters for calculating the thermal conductivities of Sc 2 CF 2 , Zr 2 CO 2 and Hf 2 CO 2 MXenes. Based on the parameters obtained, the thermal conductivities of Sc 3 (CN)F 2 have been calculated.
The thermal conductivity is dependent upon the ake length d due to the existence of boundary scattering. The theoretical temperature dependence thermal conductivity of Sc 3 (CN)F 2 with ake lengths of 5 mm along the G / M and G / K directions with TA, LA and ZA contributions are plotted in Fig. 6(a) and (b), respectively. The ZA mode has the highest contribution to the theoretical thermal conductivity along the G / M direction, due to the small value for the square of the Grüneisen parameter hg 2 j i, and the same is for the LA mode along the G / M direction. At room temperature (300 K), the calculated total thermal conductivities with TA, LA and ZA contributions along the G / M and G / K directions are 179 and 75.0 W m À1 K À1 , respectively. The anisotropy in thermal conductivity is similar with that for other MXenes such as Sc 2 CF 2 , Sc 2 C(OH) 2 , 54 Ti 2 CO 2 , Zr 2 CO 2 and Hf 2 CO 2 , 55 demonstrating that anisotropic thermal conductivity may be a common feature for semiconducting MXenes including Sc 3 (CN)F 2 . The temperature dependent thermal conductivities for the Sc 3 (CN)F 2 MXene with ake lengths of 1-100 mm along the G / M and G / K directions are shown in Fig. 6(c) and (d), respectively. From the gure, the thermal conductivity increases monotonically with increasing ake length in both directions, and is more sensitive to the ake length at low temperatures. The room temperature thermal conductivity along the G / M direction increases from 123 to 283 W m À1 K À1 as the ake length increases from 1 to 100 mm, which can be understood as analogous to grain size controlled thermal conductivity for bulk materials. Comparatively, the thermal conductivity along the G / K direction increases from 55.7 to 111 W m À1 K À1 , approximately half of that in the G / M direction. Despite that the   5 The phonon dispersions of the Sc 3 C 2 F 2 (a), Sc 3 N 2 F 2 (b) and Sc 3 (CN)F 2 (c) MXenes.  60 These results indicate that the Sc 3 (CN)F 2 possesses good heat dissipation performance if used as an electronic device. The specic heat and thermal expansion coefficient are also studied from the phonon dispersion for the hexagonal BZ of Sc 3 (CN)F 2 , and the corresponding temperature dependence for Sc 3 (CN)F 2 are shown in Fig. 7(a) and (b). These results suggest that both the specic heat and thermal expansion coefficient are positively related to the temperature, and the room temperature values are 547 J kg À1 K À1 and 8.703 Â 10 À6 K À1 , respectively. By contrast, the specic heat and thermal expansion coefficient are 385 J kg À1 K À1 and 16.5 Â 10 À6 K À1 for copper, and 412 J kg À1 K À1 and 11.8 Â 10 À6 K À1 for iron. In addition, the room temperature specic heat is much higher than the value of 238 J kg À1 K À1 due to the relatively small relative atomic mass of Sc and the thermal expansion coefficient is close to the value of 6.094 Â 10 À6 K À1 for Hf 2 CO 2 MXene. 55 The relatively high specic heat and low thermal expansion coefficient make Sc 3 (CN)F 2 a good candidate material for nanoelectronic devices.

Conclusions
In this work, we report our design and theoretical calculations of the semiconducting MXene Sc 3 (CN)F 2 . Different from the mother metallic Sc 3 C 2 F 2 and Sc 3 N 2 F 2 MXenes, the Sc 3 (CN)F 2 MXene is a semiconductor with an indirect band gap of 1.18 eV from the HSE06 band structures analysis. The electrical and thermal properties of the Sc 3 (CN)F 2 MXene are subsequently predicted by the current computational study. The Sc 3 (CN)F 2 presents great anisotropy in electron mobility, and approximate isotropy in hole mobility. The electron mobilities of Sc 3 (CN)F 2 are 1.348 Â 10 3 along x and 0.319 Â 10 3 cm 2 V À1 s À1 along the y directions, and the hole mobilities are 0.517 Â 10 3 along x and 0.540 Â 10 3 cm 2 V À1 s À1 along the y directions, respectively. The thermal conductivities for the Sc 3 (CN)F 2 are studied with ake lengths of 1-100 mm. The thermal conductivity increases monotonically with increasing ake length, and the room temperature thermal conductivity along the G / M direction is 179 W m À1 K À1 with a ake length of 5 mm. In addition, the relatively high specic heat and low thermal expansion coefficient make Sc 3 (CN)F 2 a good candidate material for nanoelectronic devices. The computational data provided here is expected to be meaningful for the expansion of the MXene family towards applications in electronic devices.

Conflicts of interest
There are no conicts to declare.