Article pubs.acs.org/cm
Semimetallic Two-Dimensional TiB12: Improved Stability and Electronic Properties Tunable by Biaxial Strain Junjie Wang,*,†,‡ Mohammad Khazaei,‡ Masao Arai,‡ Naoto Umezawa,‡ Tomofumi Tada,† and Hideo Hosono*,† †
Materials Research Center for Element Strategy, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama, Kanagawa 226-8503, Japan ‡ International Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan S Supporting Information *
ABSTRACT: Recently, the successful synthesis of two-dimensional (2D) boron on metallic surfaces has motivated great interest in improving the stability of 2D boron to allow the realization of promising materials. Through the use of an ab initio evolutionary search algorithm, we have discovered a series of TiBx (2 ≤ x ≤ 16) structures that consist of earth-abundant titanium and boron atoms in 2D arrangements. These structures are greatly stabilized by electron transfer from Ti to B, therefore, leading to much better stability than the 2D boron sheets proposed so far. In particular, TiB12 has a low enough energy to make it competitive to a mixture of the well-known TiB2 compound and a 2D α-boron sheet and exhibits a quasi-Dirac point with a 0.02 eV gap. Interestingly, the work function and conductivity of this 2D TiB12 material are calculated to be tunable through the application of biaxial strain. The possibility of synthesis and novel electronic properties expected for 2D TiB12 render it a promising new 2D material for nanoelectronic applications. behavior,17,18 whereas a semiconducting 2D boron with a band gap of 2.07 eV was obtained on copper surfaces.16 However, the synthesis of free-standing 2D boron remains a challenge, but perhaps the unique properties expected for it can be achieved with more stable derivatives. In a previous study, researchers found that metals bound to graphene can transfer electrons to graphene without ruining graphene’s Dirac dispersion.23 Inspired by this finding, researchers theoretically studied 2D metal boride structures MB2 or MB4 (M = Ti, Mo) and demonstrated that the Dirac cone of 2D boron can survive the introduction of metals.8,9 However, in the previous investigations, the 2D structures of MB2 or MB4 were simply peeled from the corresponding bulk compounds without considering other structures with the same M:B ratio or alternative 2D structures with different compositions. There-
1. INTRODUCTION As a nearest neighbor of carbon in the periodic table, boron has three valence electrons and shows unique bonding because of its inability to achieve filled octets through classical 2c-2e B−B bonds.1,2 Stable clusters derived from electron-deficient bonding, for example, three-center two electron bonds, are characteristic of boron-rich compounds, with a diverse range of structure patterns resulting. The idea of two-dimensional (2D) materials based on boron has attracted enormous attention in recent years.3−22 Several configurations of 2D boron have been theoretically identified4−6,10,13,14 and some characteristic electronic and mechanical features, such as Dirac cones7,14 and extremely high flexibility,22 have been observed, stimulating further research efforts on these unusual materials. Very recently, following the theoretical prediction that the use of a “sticky” metal substrate can lower the barrier to 2D nucleation,11 three different groups have successfully synthesized 2D boron on different metal supports.16−18 Interestingly, the 2D boron deposited on silver surfaces shows metallic © 2017 American Chemical Society
Received: April 7, 2017 Revised: July 3, 2017 Published: July 3, 2017 5922
DOI: 10.1021/acs.chemmater.7b01433 Chem. Mater. 2017, 29, 5922−5930
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Figure 1. Results of an evolutionary search of 2D TiBx materials. (a) Formation energies per atom for 2D TiBx-multilayers (closed circles). The stability of reported 2D-FeB6 with respect to the bulk phases of Fe, FeB, and α-boron sheet is presented (red stars) for comparison. (b) The optimized configuration of 2D TiB12, along with its (c) phonon dispersion, and (d) equilibrium structure at 2000 K after a 10 ps FPMD simulation. Blue-gray and green balls indicate Ti and B atoms, respectively. Also shown in panel c is the ΓYMNΓ path tracing the boundaries of the irreducible wedge of the 2D Brillouin zone of TiB12.
fore, the global thermodynamic stability of the proposed MB2 or MB4 2D configurations remains uncertain. To address this drawback, we have carried out a systematic ab initio evolutionary search24−26 for stable structures of 2D boron sheets containing transition metals. In this communication, we choose Ti as a representative transition metal due to its earth abundance, well-studied boride chemistry, and important role in 2D materials.27 A series of 2D structures of TiBx, which include a graphene-like monolayer and “sandwich”-shaped multilayered configurations, have been predicted. After the stability of all predicted structures was carefully examined, we found that the stability of 2D boron sheets can be remarkably improved by the introduction of Ti atoms. Furthermore, “sandwich”-shaped 2D configurations are found to be much more favorable than their graphene-like TiBx counterparts. Among these predicted structures, the “sandwich”-shaped structure TiB12 (Cm2m) is presented in detail. Our calculations show that such a configuration of TiB12 possesses the lowest energy (Figure 1a) with respect to bulk TiB2 and the 2D αboron sheet proposed previously5 and exhibits semimetallic characteristics with a quasi-Dirac point near the Fermi level. Moreover, the obtained structures in present systematic search have much better thermodynamic stability than those reported previously.9,15
Recently, strain engineering has been considered as one of the best possible strategies to tune the electronic properties of 2D materials.28−35 Our predicted 2D TiB12 material shows a sandwich-shaped zigzag-structure similar to those of the transition-metal dichalcogenies (TMDs), a family of 2D materials in which strain engineering has been proposed as a strategy for the tuning of electronic properties32,33 because of their ability to bear larger strains than graphene (for which uniaxial and biaxial strains larger than 10% have been achieved experimentally).34,35 We will thus explore in this work how the electronic properties of 2D TiB12 may be tuned by imposing biaxial strains. Through an extensive structure search followed by detailed electronic structure study, we will illustrate how the stability of boron sheets can be improved by introducing transition metals, while maintaining the superior properties desired of these sheets.
2. COMPUTATIONAL METHODS The structure searches for stable 2D TiBx (2 ≤ x ≤ 16) sheets were performed through the combined use of the Universal Structure Predictor: Evolutionary Xtallography (USPEX)24−26 and the Vienna ab initio simulation package (VASP).36,37 Details regarding the general search procedure can be found in the USPEX literature24−26 and our previous work.38,39 Structure searches were performed for different compositions of TiBx (2 ≤ x ≤ 16) using unit cells containing less than 5923
DOI: 10.1021/acs.chemmater.7b01433 Chem. Mater. 2017, 29, 5922−5930
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Chemistry of Materials 40 atoms. In the slab models, the predicted 2D TiBx configurations were arranged in the XY plane and separated from adjacent layers by a vacuum thickness of 20 Å along the Z direction. In the VASP calculations, we adopted the projector-augmented wave (PAW)40 approach to describe the ion-electron interaction. The generalized gradient approximation (GGA) in the Perdew−Burke−Ernzerhof (PBE)41 formulation was used to treat the electron exchangecorrelation interaction. The energy cutoff was set to 520 eV with the energy precision being 10−6 eV. The atomic positions were fully relaxed until the maximum force on each atom was less than 10−3 eV/ Å. The Monkhorst−Pack k-point mesh resolution for the high throughput structure searches and molecular dynamics simulations was 2π × 0.04 Å−1, whereas a finer k-mesh of 2π × 0.02 Å−1 was used for the structure optimizations. To examine the dynamical stability of the structures, phonon dispersion calculations were carried out using the linear response method42 implemented in the CASTEP code.43 The first-principles molecular dynamics (FPMD) simulations over a canonical ensemble (NVT) were performed using VASP to check the thermal stability of the predicted TiB12 2D structure. In the FPMD simulations, the TiB12 2D structure with a 3 × 3 supercell (9 Ti atoms and 108 B atoms) was annealed at different temperatures for 10 ps. To study the effect of strain on the electronic properties of the predicted TiB12 structure, we modeled the strained cell by compressing/stretching the lattice in the XY-plane in increments of 1%, with the strain being defined as ε = (a − a0)/a0, where a and a0 are the strained and the equilibrium lattice constants, respectively.
that the position of 2D-FeB6 is 0.17 eV higher than the convex hull between FeB and α-boron sheet. Therefore, we can see that the 2D TiB12 configuration predicted through an extensive structure search shows superior thermodynamic stability over the previously reported structures.9,15 To compare the thermodynamic stability of 2D TiB12 with the most stable 2D boron sheets that have been described so far (those with Pmmm7 and C2/m14 symmetries), the formation energies of the 2D TiB12 were calculated relative to Ti bulk and these reported boron sheets. The calculated formation energies are −0.211 and −0.228 eV/atom, respectively, proving that the 2D TiB12 structure presented here achieves higher stability than the combination of Ti bulk and the most stable 2D boron sheets proposed to date. The details of the structural parameters of the 2D TiB12 model and its stability relative to 2D boron sheet structures are presented in the Table S2. The crystal structure and 2D Brillouin zone of 2D TiB12 are shown in Figure 1b. The crystal structure of 2D TiB12 possesses two layers of B atoms and one layer of Ti atoms in the center, with a mirror plane running through the Ti atoms. Each layer of B atoms shows a structural pattern similar to that of the previously reported B12 configuration of 2D boron.2 In order to examine whether the predicted structure is in an energy minimum, the phonon dispersion of 2D TiB12 was computed along the high-symmetry path ΓYMNΓ in the 2D Brillouin zone. No imaginary frequencies were observed, indicating that the 2D TiB12 structure is dynamically stable (Figure 1c). The recently synthesized 2D boron sheets were all prepared on metal surfaces at high temperatures in the range of 500− 1000 K.16−18 Therefore, to evaluate the thermal stability of the 2D TiB12 structure at elevated temperatures, we carried out a series of FPMD simulations at 500, 1000, 1500, and 2000 K for 10 ps. As is shown in Figure 1d, there is no sign of disruption even in the 2000 K simulation. As can be seen in Figure S3, the simulation results at 500, 1000, and 1500 K also do not show any structural decomposition. Therefore, it is expected that 2D TiB12 will be stable at temperatures as high as 2000 K in vacuum. Consequently, we can conclude that not only is 2D TiB12 the most stable TiBx configuration but that it also shows potential for being realized synthetically. To study the role of Ti atom in the stabilization and electronic structure of TiB12 sheet, we removed Ti atom from TiB12 and fully relaxed the geometry of remaining B12 sheet. The electronic structure results for this B12 sheet can be found in Figure S4. The computed phonon dispersion of the B12 sheet (Figure S4b) shows imaginary frequencies emerge following the removal of the Ti atoms, revealing the critical importance of Ti in stabilizing this boron sheet structure. The total charge density analysis of 2D TiB12 (Figure 2a) shows that electrons are distributed around the B atoms, with no appreciable concentration of electron density along the Ti− B contacts, a typical characteristic of ionic compounds. A calculation of Bader Charges44 for the compound verifies that there is charge transfer from the Ti to the B atoms, with 1.33 electrons being transferred per Ti atom (see Figure S5 for further details of the Bader charge analysis of the 2D TiB12 and B12 sheets). As shown in Figure S6, because of the charge transfer from Ti to B atoms, the accumulation of electrons on the B atoms encompassing the Ti atoms (in out-of-plane π orbitals) is significant and can help the formation of stable B−B bonds, which is consistent with the results of a previous study.6 Moreover, the Coulombic attraction between Ti and B atoms could also stabilize the boron sheet.
3. RESULTS AND DISCUSSION During the ab initio evolutionary searches, 2D TiBx structures with monolayer and multilayer geometries were obtained by constraining the initial slab thickness to 0.1 and 3 Å, respectively. For each composition, the most stable configuration is presented in Figures S1 and S2. The calculated formation energies Ef = (ETiBx − ETi − xEB)/(x + 1) and cohesive energies Ecoh = (ETi‑a + xEB‑a − ETiBx)/(x + 1) are shown in Table S1. ETi, EB, and ETiBx are the calculated total energies of bulk titanium, the α-boron sheet5,7 and one formula unit of 2D TiBx, respectively. ETi‑a and EB‑a stand for the total energies of isolated Ti and B atoms. Here, it is evident that most TiBx 2D structures (except both structures of TiB3 and the monolayer structure of TiB15) have better stability than the physical mixture of the reported α-boron sheet5,7 and Ti bulk. It is also seen that the multilayer structures are much more stable than monolayer of the same composition. Moreover, the search results show that the 2D structures with even number of B atoms can have a better chance to form the sandwich-shaped 2D configurations (Figure S2) and have lower formation energies than those structures with odd number of B atoms (Table S1). Therefore, only the formation energies of the 2DTiBx configurations with an even number of B atoms are shown in the convex hull of Figure 1a. The distance of the energy points for different structures to the convex hull along the energy axis indicates their global stability. In this regard, the 2D TiB12 with a formation energy of −0.281 eV/atom is located on the convex hull line between TiB2 bulk and α-boron sheet (the computed formation energy with respect to the bulk TiB2 and α-boron sheet is slightly negative, at −0.00085 eV/atom), which means the stability of this structure is thermodynamically competitive against TiB2 and an α-boron sheet. The point for 2D TiB2, however, which adopts the same structure as previously reported in the literature,9 is about 0.9 eV above the convex hull. To compare the thermodynamic stability of TiB12 with the recently predicted FeB6 monolayer,15 the convex hull of Fe−B system is also presented in Figure 1a. One can see 5924
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and d. The calculated band structure reveals that 2D-TiB12 exhibits semimetallic character, with features similar to those recently reported for NbP.48 By comparing the band structures of pristine 2D B12 and the TiB12 sheet (Figure S4c and S4d), it is seen that the former shows metallic characteristics, while the latter is semimetallic. As is illustrated in Figure 2c and 2d, the Ti and B atoms, respectively, provide dominant contributions to the bottom of the conduction band and the top of the valence band. A quasi-Dirac point, which is 0.09 eV below the Fermi level, appears with a very small gap of 0.02 eV along the N−Γ line where the valence and conduction bands nearly meet. From the projected band structures, it is seen that both the B(p) and Ti(d) orbitals contribute significantly to the quasiDirac cone. The three-dimensional (3D) Dirac cone and constant-energy contour for the valence band near one cone with an energy interval of 0.02 eV are plotted in Figure 2e, which reveal the anisotropy of the Dirac cone. Although there is a small gap, the bands at the quasi-Dirac point are linearly dispersed (Figure 2e). Therefore, the Fermi velocity (vf) can be estimated by computing the slopes of the bands near the quasiDirac cone, yielding 0.60 × 106 and 0.50 × 106 m/s along the kx and ky directions, respectively. The computed vf values are almost the same as that recently calculated for a 2D boron sheet (0.56 × 106 m/s)7 and is comparable with that of graphene (0.82 × 106).49 Therefore, this quasi-Dirac point is still very interesting as it will behave as a true Dirac-cone for phenomena with energy scales larger than the small gap. Consequently, the semimetallic 2D TiB12 is anticipated to exhibit excellent electronic properties. The electronic properties of the predicted 2D TiB12 can also be engineered by applying biaxial strain (Figure 3a). The effect of biaxial strain on the work function is illustrated in Figure 3b, where a range in the work function (WF) from 5.00 to 5.75 eV is achieved through varying the biaxial strain. We also found that tensile strain (positive strain) increases the work function slightly, whereas compressive strain (negative strain) decreases the work function dramatically. Since the WF is calculated as WF = Evac − EF, where Evac is the vacuum potential and EF is the Fermi energy,50 the key to this dependence is how strain affects both the EF and the Evac. In the present study, we have used a thick enough vacuum layer (20 Å) in the slab model to assume the Evac is independent of the strain. Generally, the EF is affected by the number of bands that cross it and the shape of their dispersion.51,52 As is seen in Figure 2c and 2d, the energy states around the EF are mainly composed of Ti(d) and B(p) orbitals, which means B(p)-B(p) and B(p)-Ti(d) interactions control the EF. The plane-averaged charge density differences along the Z direction for strained TiB12 sheets relative to the unstrained structure are shown in Figure 4a. A decrease/increase in charge density is seen for the TiB12 sheet upon applying tensile/ compressive strain. Furthermore, Figures 4b and 4c respectively show the partial charge densities around the EF of TiB12 sheets when tensile and compressive strains are applied. The electron density at the EF decreases with increasing in tensile strain, which can be understood in terms of changes in the overlap between the valence and conduction bands. As shown in Figures 4d and 4e, TiB12’s valence bandwidth decreases under tensile strain (14.62 vs 15.46 eV for the unstrained 2D sheet) because of the reduced orbital overlap between neighboring atoms. This shrinking of the valence bandwidth not only causes decreased overlap between the valence and conduction bands but also leads to a downward shift of the EF. This explains the
Figure 2. Overview of the electronic structure of 2D TiB12, including top and side views of (a) the charge density, (b) the electron localization function, (c) the band structure, (d) the projected DOS distributions, and (e) 3D Dirac cone in the vicinity of the quasi Dirac point. The values of isosurfaces for panels a and b are 0.50 e/Å3 and 0.80, respectively. The sizes of the dots in panel c represent the contributions from the Ti and B atoms. The inset of panel e presents constant-energy contours for the valence band side of the quasi-Dirac cone with an energy spacing of 0.02 eV.
To further analyze the Ti−B and B−B bonding in our 2D TiB12 structure, we calculated its electron localization function (ELF).45−47 The results are presented in Figure 2b with an isosurface at ELF = 0.80. The values of the ELF, which can range from 0 to 1, indicate the degree of localization of electrons. The isosurface of ELF at 0.80 highlights the localization of electrons not only along individual B−B bonds, but also at the centers of triangles and rhombuses. This picture is consistent with the coexistence of covalent 2c− 2e and multicenter−2e bonds among the B atoms, with the nature of the Ti−B bonds being primarily ionic. In addition, the decomposed band structure and projected density of states (DOS) of 2D TiB12 are shown in Figure 2c 5925
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Figure 3. Influence of biaxial strain on the work function (WF) of 2D TiB12. (a) Illustration of the biaxial strains imposed. (b) The calculated relative work functions (WF−WF0) as functions of biaxial strain.
Figure 4. Influence of strain on the charge density and band character of 2D TiB12. (a) Plane-averaged charge density difference profiles of 6% (blue line) and −6% (red line) biaxial strained TiB12 structures relative to the unstrained sheet. Partial charge densities around the Fermi level (Ef − 0.05 eV10%) in Graphene. Nano Lett. 2014, 14, 4107− 4113. (35) Shioya, H.; Craciun, M. F.; Russo, S.; Yamamoto, M.; Tarucha, S. Straining Graphene Using Thin Film Shrinkage Methods. Nano Lett. 2014, 14, 1158−1163. (36) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for ab initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 11169. (37) Kresse, G.; Furthmüller, J. Efficiency of ab-initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50. (38) Wang, J.; Umezawa, N.; Hosono, H. Mixed Valence Tin Oxides as Novel van der Waals Materials: Theoretical Predictions and Potential Applications. Adv. Energy Mater. 2016, 6, 1501190. (39) Wang, J.; Hao, D.; Ye, J.; Umezawa, N. Determination of Crystal Structure of Graphitic Carbon Nitride: Ab Initio Evolutionary Search and Experimental Validation. Chem. Mater. 2017, 29, 2694−2707. (40) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 1758−1775. (41) Perdew, J. P.; Ernzerhof, M.; Burke, K. Rationale for Mixing Exact Exchange with Density Functional Approximations. J. Chem. Phys. 1996, 105, 9982. (42) Baroni, S.; de Gironcoli, S.; dal Corso, A.; Giannozzi, P. Phonons and related crystal properties from density-functional perturbation theory. Rev. Mod. Phys. 2001, 73, 515−562. (43) Clark, S. J.; Segall, M. D.; Pickard, C. J.; Hasnip, P. J.; Probert, M. I. J.; Refson, K.; Payne, M. C. First Principles Methods using CASTEP. Z. Kristallogr. - Cryst. Mater. 2005, 220, 567−570. (44) Henkelman, G.; Arnaldsson, A.; Jónsson, H. A Fast and Robust Algorithm for Bader Decomposition of Charge Density. Comput. Mater. Sci. 2006, 36, 354−360. (45) Savin, A.; Jepsen, O.; Flad, J.; Andersen, O. K.; Preuss, H.; von Schnering, H. G. Electron Localization in Solid-State Structures of the Elements: the Diamond Structure. Angew. Chem., Int. Ed. Engl. 1992, 31, 187−188. (46) Silvi, B.; Savin, A. Classification of Chemical Bonds based on Topological Analysis of Electron Localization Functions. Nature 1994, 371, 683−686. (47) Becke, A. D.; Edgecombe, K. E. A Simple Measure of Electron Localization in Atomic and Molecular Systems. J. Chem. Phys. 1990, 92, 5397−5403. (48) Shekhar, C.; Nayak, A. K.; Sun, Y.; Schmidt, M.; Nicklas, M.; Leermakers, I.; Zeitler, U.; Skourski, Y.; Wosnitza, J.; Liu, Z.; Chen, Y.; Schnelle, W.; Borrmann, H.; Grin, Y.; Felser, C.; Yan, B. Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal candidate NbP. Nat. Phys. 2015, 11, 645−649. (49) Malko, D.; Neiss, C.; Viñes, F.; Görling, A. Competition for Graphene: Graphynes with Direction-Dependent Dirac Cones. Phys. Rev. Lett. 2012, 108, 086804. (50) Khazaei, M.; Arai, M.; Sasaki, T.; Ranjbar, A.; Liang, Y. Y.; Yunoki, S. OH-terminated Two-Dimensional Transition Metal Carbides and Nitrides as Ultralow Work Function Materials. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 92, 075411. (51) Ciraci, S.; Batra, I. P. Theory of the Quantum Size Effect in Simple Metals. Phys. Rev. B: Condens. Matter Mater. Phys. 1986, 33, 4294−4297. (52) Batra, I. P.; Ciraci, S.; Srivastava, G. P.; Nelson, J. S.; Fong, C. Y. Dimensionality and Size Effects in Simple Metals. Phys. Rev. B: Condens. Matter Mater. Phys. 1986, 34, 8246−8257. 5929
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