Anisotropic electronic conduction in stacked two-dimensional titanium carbide

Stacked two-dimensional titanium carbide is an emerging conductive material for electrochemical energy storage which requires an understanding of the intrinsic electronic conduction. Here we report the electronic conduction properties of stacked Ti3C2T2 (T = OH, O, F) with two distinct stacking sequences (Bernal and simple hexagonal). On the basis of first-principles calculations and energy band theory analysis, both stacking sequences give rise to metallic conduction with Ti 3d electrons contributing most to the conduction. The conduction is also significantly anisotropic due to the fact that the effective masses of carriers including electrons and holes are remarkably direction-dependent. Such an anisotropic electronic conduction is evidenced by the I−V curves of an individual Ti3C2T2 particulate, which demonstrates that the in-plane electrical conduction is at least one order of magnitude higher than that vertical to the basal plane.


Results
Crystal structure. The performance of Ti 3 C 2 T 2 in practical applications is believed to be dominated by its stacking manner. Nevertheless, most theoretical works focused on monolayer MXene 18-20 instead of their stacked forms. In this study, the stacked Ti 3 C 2 T 2 was systematically investigated by DFT-D in which the long-range interactions are taken into accounts. Since the termination is primarily OH functional group 13,21 , Ti 3 C 2 T 2 in this work is simplified to Ti 3 C 2 (OH) 2 (see Supplementary Table S2 for detailed structure information). According to the relative position of adjacent layers, there are two distinct stacking types [21][22][23][24] for Ti 3 C 2 (OH) 2 , i.e., AA (simple hexagonal, SH) and AB (Bernal). Figure 1 presents the projection of the two stacking configurations.
The formation energies of the two distinct stacking configurations were calculated with two schemes of PW91-OBS (refs 25,26) and PBE- Grimme (refs 27,28). The results are summarized in Table 1. From an energetic point of view, the formation energies of Bernal and SH Ti 3 C 2 (OH) 2 are all positive, implying that both of them are thermodynamically stable. The Bernal stacking is somewhat more energetically favorable than the SH one. It is noted that the energy difference between the two stackings is quite small (< 65 meV/atom), which is consistent with the previous calculation results 21 . Valence charge density distribution. Valence electrons contribute to chemical bonding and most electronic conduction 29 . The electronic structure of stacked Ti 3 C 2 (OH) 2 in real space was investigated by valence electron density based on the optimized crystal structures. Figure 2a-d show the distribution of the valence electron density on specific planes of the stacked Ti 3 C 2 (OH) 2 . For both stacked structures, they share a common feature that the intralayer bonding is strong, while the interlayer is weak since there are electron density dilution zones between neighboring Ti 3 C 2 (OH) 2 layers. The strong intralayer bonding is inherited from the Ti 3 C 2 blocking sheet of Ti 3 AlC 2 in which pd hybridization or pd bonding 8 of Ti 3d− C 2p predominates. The covalently bonded chain Ti2-C-Ti1-C-Ti2 (Fig. 2) is reserved by the OH group, which forms bonds with surface Ti and C atoms. The weak interlayer bonding is derived from the long-range electrostatic interaction between the adjacent Ti 3 C 2 (OH) 2 layers. The interaction is  Band structure. Band structure describes the relation between electronic energy and electron wavevector in momentum space. The microscopic behavior of electrons in a solid is most conveniently specified in terms of the electronic band structure 30 . Figure 3a,b depict the band structures and density  There are three main features for the band structures: First, they are both dominated by 2D in-plane covalent bonds, with the modification of weak interlayer interactions. As a result, the band structure shows a strongly anisotropic feature with less energy dispersion along c-axis. As presented in Fig. 3a,b, the dispersion of the bands perpendicular to the basal planes (M− L) is almost negligible, demonstrating essentially a 2D character of the electronic structures. The anisotropy of the band structures near and below the Fermi energy (E F ) indicates that the conductivity is also anisotropic. Specifically, the electrical conductivity along the c-axis should be much lower than that in the basal plane. This feature can be also found in the free-standing monolayer and bilayer Ti 3 C 2 (OH) 2 ( Fig. S2). Second, resembling that of monolayer 16,18 and bilayer Ti 3 C 2 (OH) 2 , the band structure exhibits typical metallic conduction with bands crossing E F along various directions, which results in a finite DOS (3.19 states/eV cell and 4.51 states/eV cell for Bernal and SH, respectively) at E F . Third, at E F , the DOS mainly originates from the nearly free electron states 31 of Ti2 3d and Ti1 3d (88% of the total DOS at E F for Bernal and 68% for SH Ti 3 C 2 (OH) 2 , see Supplementary Fig. S3). Since the electronic transport properties are governed by the electrons near E F , the 3d electrons of Ti contribute predominantly to the electronic conduction.
Fermi surface. The band occupation around E F accounts for the metallic nature of matters, and the electrons at the Fermi surface (FS) determine the transport properties like conductivity of materials 32 . It is thus important to establish the shape of FS. Figure 3c,d illustrate the shape of the whole FS.
Corresponding to the fact that four double-degenerate half-filled bands across E F in the band structure (denoted as FS 1, 2, 3 and 4 in Fig. 3a,b), there are four envelopes consisting of the whole FS. Red regions correspond to pockets of holes and blue regions to pockets of electrons. Both FSs show a hexagonal electron pocket around the c * axis in reciprocal space and surrounding six cylindrical hole pockets. Around c * there is a region of electrons, and a relatively flat band across E F along Γ -K and H-A. The FS of Bernal is disconnected while that of SH is connected by electron pockets. Interestingly, the hole-like pockets in the FSs of the two configurations are similar: cylindrical hole pockets are around H and K. In consistent with the band structure analysis, the FSs of stacked Ti 3 C 2 (OH) 2 , as well as those of monolayer and bilayer Ti 3 C 2 (OH) 2 ( Supplementary Fig. S4), all show obvious 2D features.
Effective mass. The effective masses of carriers including electrons and holes represent their response to the applied external fields. Generally speaking, an electron in a periodic potential is accelerated relative to the lattice in an applied electric or magnetic field, as if the mass of the electron is equal to its effective mass 32 . To understand the dynamics of electrons and holes, the effective masses for electron ⁎ m e and hole ⁎ m h were evaluated along the parabola at several points indicated in Supplementary Figs S5 and S6. Fitting these parabolas can give the minimums for the effective mass since the dispersion is strong in these directions (Fig. 3a,b). The effective masses of carriers at high-symmetry points in Ti 3 C 2 (OH) 2 are listed in Table 2. The fitted parabolas are shown in Supplementary Figs S7 and S8. It is found that the effective mass in the basal plane are quite small (< 0.5 m 0 , Table 2), in stark contrast, the effective electron and hole masses perpendicular to the layers are extremely large (they are estimated to be infinite by fitting nearly flat parabolas along Γ -A). Therefore, the carriers respond much more quickly in the basal plane than those along the c-axis, which agrees with the afore-discussed features of electron density distribution, band structure and FS shape. In the basal plane, the holes' effective masses are generally one order of magnitude less than those of electrons, indicating that holes response to applied electric field much more easily.

Discussion
The present results obtained by ab initio calculation indicate that the formation energies of both Bernal and SH Ti 3 C 2 (OH) 2 are all negative, suggesting that both stacking sequences are thermodynamically stable. Besides, the Bernal Ti 3 C 2 (OH) 2 is somewhat more energetically favorable than the SH one, and its XRD pattern matches the experimental pattern better than that of SH one (Fig. 4, see Supplementary  Table S3 for simulated XRD data). However, this does not necessarily rule out the SH structure because most of its calculated peaks match the experimental XRD pattern well too (Fig. 4). In fact, the selected area electron diffraction shows a feature of non-periodic combination of different stacking along [0001] (see Supplementary Fig. S9). It is believed that both stacking structures likely coexist in the prepared sample. Anyway, as shown in the band structures, no matter which specific structure the stacked Ti 3 C 2 (OH) 2 has, the electron conduction is highly anisotropic. The anisotropy is more straightforwardly shown in the FS than the band structures. FS is the boundary between ground states and excited states. The volume inside of the FS corresponds to occupied states while the outside represents unoccupied states at zero temperature. The volume inside the surface determines the low-energy free carrier plasmon frequencies and the electrical conductivity 10 . Since the electron velocities are orthogonal to the FS, the flat part at the top and bottom of the Brillouin zone (Fig. 3d) gives rise to the most important contributions to the conduction along the c direction, whereas the transversal part of the FS is mainly responsible for the in-plane conduction. For the two structures, the Fermi cylinder of hole shows obvious features of 2D materials 33 , indicating that the carrier in two structures is transferred preferentially in the basal plane.
To experimentally testify the predicted conductivity anisotropy, I-V curves were measured on individual Ti 3 C 2 T 2 particulates with two distinct morphologies, i.e., laminated-structure-free and accordion-like. Ti 3 C 2 T 2 particulates with the two morphologies are both conductivity anisotropic (Fig. 5 and Fig. S10). The estimated in-plane electrical conductivity is one order of magnitude higher than that vertical to the basal plane (see Supplementary Fig. S11 for the discussions on contract resistance). Interestingly, by in situ I-V measurement on accordion-like Ti 3 C 2 T 2 particulates (Supplementary Fig. S10), it is found that  The estimated in-plane electrical conductivity is one order of magnitude higher than the vertical electrical conductivity.
the electronic conductivity vertical to the basal plane is highly mode-dependent (stretching or shrinking). The value measured in shrinking mode is at least 10 times higher than that measured in stretching mode. This mode-sensitive feature can be used to manufacture micro-displacement-sensitive devices.
In summary, ab initio calculations have demonstrated that the electronic conduction of both Bernal and SH Ti 3 C 2 (OH) 2 is highly anisotropic, which was experimentally evidenced by the in situ I−V measurements of an individual Ti 3 C 2 T 2 particulate. Quantitatively, the in-plane electrical conductivity is at least one order of magnitude higher than that vertical to the basal plane. The excellent consistency between first-principles prediction and experimental results demonstrated in this work may lead to a comprehensive understanding on the structural and electronic properties of the emerging MXenes in stacked form. Moreover, it offers fundamental information for exploring the electron-involved applications of MXenes.

Methods
First-principles calculations. The DFT and DFT-D calculations were performed using the Cambridge Sequential Total Energy Package (CASTEP) 34,35 . The electron-ion interaction was represented by using plane-wave pseudo potential. Vanderbilt-type ultrasoft potentials 36 were utilized for the calculations. Configurations of H− 1s 1 , C− 2s 2 2p 2 , O− 2s 2 2p 4 , Ti− 3s 2 3p 6 3d 2 4s 2 were treated as valence electrons. The electronic exchange correlation energy was treated as GGA-PBE and GGA-PW91. The long-range interaction was considered by dispersion correction 37 within the OBS and Grimme methods. The Monkhorst-Pack scheme 38 with 9 × 9 × 2 k points meshes were used for the integration in the irreducible Brillouin zone so that the individual spacing was less than 0.05 Å −1 (9 × 9 × 1 k points meshes for monolayer and bilayer). We performed cutoff energy evaluation on the calculations results. It was found that increasing the energy from 380 to 500 eV within the identical calculation scheme gives rise to negligible changes in total energy, lattice parameter and atomic position. Thereby, the cutoff energy was set as 380 eV. The Broyden-Fletcher-Goldfarb-Shanno minimization scheme 39 was used to minimize the total energy and interatomic forces. Fermi level was smeared by 0.1 eV. The convergence for energy was chosen as 1.0 × 10 −9 eV/atom, and the structures were relaxed until the maximum force exerted on the atoms became less than 0.001 eV/Å. Electronic structure calculations were carried out with GGA-PW91-OBS scheme.
Preparation of Ti 3 C 2 T 2 . Individual Ti 3 C 2 T 2 particulates with two distinct morphologies, i.e., laminated-structure-free and accordion-like were prepared in a mild etching condition and a harsh condition, respectively. For the laminated-structure-free Ti 3 C 2 T 2 particulates, the etching process was carried out by immersing the porous Ti 3 AlC 2 monolith in a diluted hydrofluoric acid solution (HF, 10 wt.%) for 72 h at room temperature. The porous Ti 3 AlC 2 was prepared by the method reported previously 40 . After that, the resulting sediment was washed several times with deionized water and immersed therein for one day, followed by vacuum filtration. The filtered sample was subsequently dried overnight at 70 °C in an oven. The accordion-like lamellas for the investigation were synthesized by exfoliating porous Ti 3 AlC 2 in HF (40 wt.%) for 24 h. After that, the resulting sediment was washed several times with deionized water and immersed therein for one day, followed by vacuum filtration. The filtered sample was subsequently dried by supercritical carbon dioxide drying under a condition above the critical point of CO 2 (T C = 31.1 °C, P C = 7.39 MPa). The filtered sample was transferred into an autoclave in which ethanol was filled to minimize the evaporation of water from the wet sample during the following processes of heating and pressurizing. As soon as the autoclave was heated up to 40 °C, CO 2 pre-heated to that temperature was pumped into the autoclave at a flow rate of 0.54 kg h −1 to a pressure of 100 bar. After the solvent was completely replaced at that pressure by CO 2 for 5 h, the CO 2 was vented by slowly reducing the pressure to ambient ( / ∆ ∆ P t = − 3 bar min −1 ) while keeping the temperature. I−V curve measurement. The measurements were conducted in a field-emission scanning electron microscope (FEI, NanoSEM 430) equipped with a four-probe micromanipulator (Kleindiek MM3A-EM) in its vacuum chamber at room temperature. The silicon wafer was used as a substrate to support the well distributed MXene particulates, which were ultrasonically dispersed in an ethanol solution prior to dropping them onto the substrate. For picking up the particulate and measuring its I−V curves, two probes were used to connect to a Keithley 4200-SCS semiconductor characterization system. We employed a commercial tungsten probe due to its sufficient hardness and sharpness to reach the experimental goal. Prior to loading the particulate, two tungsten probes were manipulated to achieve tip-to-tip contact (Fig. 5) and then subjected to Joule heating by applying a scanned voltage from 0 to 10 V several times in order to fully remove the surface tungsten oxide layer on the probes. The final electrical resistance of the treated tungsten probes was measured to be around 7 Ω (Supplementary Fig. S12). The targeted single particulate on the substrate was picked up by manipulating the two probes. Before recording the I−V signals, two important steps are necessary: (i) the separation of the picked up particulate from the substrate so that the possible influence of the substrate on the measurements can be ruled out; (ii) the blocking of the electron beam to exclude a possible influence of electron bombardment and charging effects.