Silicane as an Inert Substrate of Silicene: A Promising Candidate for

Article pubs.acs.org/JPCC

Silicane as an Inert Substrate of Silicene: A Promising Candidate for FET Run-wu Zhang,† Chang-wen Zhang,*,† Wei-xiao Ji,† Shu-jun Hu,‡ Shi-shen Yan,*,‡ Sheng-shi Li,† Ping Li,† Pei-ji Wang,† and Yu-shen Liu§ †

School of Physics and Technology, University of Jinan, Jinan, Shandong 250022, People’s Republic of China School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan, Shandong, 250100, People’s Republic of China § College of Physics and Engineering, Changshu Institute of Technology and Jiangsu Laboratory of Advanced Functional Materials, Changshu 215500, People’s Republic of China ‡

ABSTRACT: Opening up a band gap without lowering high carrier mobility and finding a suitable substrate material are a challenge for designing silicon-based nanodevices. Using density functional theory calculations incorporating vdW corrections, we find that the semiconducting silicane monolayer is free of dangling bonds, providing an ideal substrate for silicene to sit on. The nearly linear band dispersion character of silicene with a sizable band gap (44−61 meV) opening is obtained in all heterobilayers (HBLs). We also find that the effective masses of electrons and holes near the Dirac point (ranging from 0.033 to 0.045m0) are very small in HBLs, and thus high carrier mobility (105cm2 V−1 s−1) of silicene is expected. These characteristics of HBLs can be flexibly modulated by applying bias voltage or strain, suitable for the high-performance FET channel operating at room temperature.

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ilicene,1 the two-dimensional (2D) silicon counterpart of graphene, has recently attracted great attention for development of the next generation of nanoelectronic devices.2,3 The uniqueness of these 2D crystal is mainly due to its very peculiar band structure, with the π and π* bands showing linear dispersion around the Fermi level where they touch in a single point, marking the presence of massless relativistic electrons and extremely high charge carrier mobility.4 However, the lack of an intrinsic band gap implies that the current can never be turned off completely, i.e., a potential silicene-based field effect transistor (FET) is expected to show only modest on−off ratios.5 This has constituted a formidable hurdle to the use of silicene in logic and high-speed switching devices. Considerable research efforts have been performed for engineering its band structures on various metal substrates: for example, the formation of epitaxial silicene on Ag(001),6 Ag(110),7 Ag(111),8,9 ZrB2,10 Au,11 and Ir12 substrates. However, the π bands of silicene are subject to strong hybridization with metal substrate, giving rise to structures deviating from the low-buckled honeycomb configuration for the free-standing monolayer. These destroy the Dirac cone of silicene13,14 with the lower carrier mobility and hamper the applications of silicene in building electronic nanodevices. One of the effective ways to open a band gap for silicene, without heavy loss of carrier mobility, is to deposit silicene on weakly interacting semiconductor substrates. For example, Ding et al.15 reported that the GaS nanosheets could preserve the linearly dispersing bands with a gap of 0.17 eV, while the lattice © XXXX American Chemical Society

mismatch would amount to 7.5%. Although the lattice mismatch is smaller (2.3%) for ZnS(0001),16 this substrate also perturbs the band structure. Perturbations of the band structure for silicene are related to dangling bonds of the substrate. Accordingly, preservation of the Dirac cone can be achieved by H passivation of these bonds both for Si- and Cterminated SiC(0001).17 F-terminated CaF2(111) is also predicted to preserve the Dirac cone with a gap of 52 meV.18 However, there are two F layers and one Ca layer along the (111) direction, and only one of the F-terminated (111) planes has no dangling bond, which requires accurate control during preparation of the material, difficult to realize in experiments. Quite recently, Bianco et al.19 reported that the multilayer hydrogen-terminated germanene has been synthesized by using the topochemical deintercalation of CaGe2, and it can be mechanically exfoliated to a single layer onto the SiO2/Si surface. In particular, the hydrogenated silicene (silicane), which is known as layered polysilane, was experimentally realized even before silicene was synthesized.20−22 Furthermore, the silicane monolayer has been predicted to be an insulator with band gap larger than 2.93 eV as well as high carrier mobility,23,24 which has great potential for optoelectronic and sensing applications. Considering the compatibility with update silicon technology, it is very interesting to explore Received: August 15, 2014 Revised: October 5, 2014

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dx.doi.org/10.1021/jp508253x | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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Figure 1. Relaxed geometry and band structures for silicene (a, b) and silicane (c, d), respectively. In the band structures, the energies are relative to the Fermi level and indicated by a red line.

Figure 2. Optimized structures of the HBLs, AA stacking (a), aa stacking (b), AB stacking (c), ab stacking (d). The light blue and red balls represent silicon atoms and white balls represent hydrogen atoms, respectively. The corresponding band structures of four HBLs are displayed in (e)−(h), respectively.

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Table 1. Detailed Structural and Electronic Information for Silicene/Silicane HBLs with the PBE-vdW Method, Including Binding Energy of Silicene with Silicane (eV), the Interlayer Spacing d, Band Gap (meV), as Well as the Effective Masses of Electron (me) and Hole (mh) of Four Patterns at K Point along K−M and K−Γ Directionsa

a

pattern

Eb

d(Å)

Eg

mKΓ e

mKM e

mKΓ h

mKM h

AA aa AB ab

−0.26 −0.31 −0.30 −0.40

2.73 2.72 2.76 2.51

61 48 44 56

0.0445m0 0.0414m0 0.0409m0 0.0415m0

0.0371m0 0.0339m0 0.0337m0 0.0350m0

0.0453m0 0.0421m0 0.0417m0 0.0411m0

0.0375m0 0.0343m0 0.0340m0 0.0347m0

Here, m0 is the free electron mass.

Figure 3. Total density of states (DOS) of HBLs are shown in (a) AA, (b) aa, (c) AB, and (d) ab, respectively. The vertical red dot line is defined by the Fermi level.

redistribution in the HBLs. The convergence criterion of our self-consistent calculations for ionic relaxations is 10−5 eV between two consecutive steps. By using the conjugate gradient method, all atomic positions and the size of the unit cell are optimized until the atomic forces are less than 0.02 eV Å−1. For reference, we first discuss the electronic properties of isolated silicene33−35 and silicane monolayers, as shown in Figure 1. For silicene, the relaxed lattice parameter is found to be a1 = a2 = 3.86 Å, while the lattice constant of silicane is 3.89 Å, indicating that both of them have a small lattice mismatch (∼0.78%), which agrees well with the previous works,29,30 as shown in Figure 1a. Different from graphene, the larger Si−Si bond length weakens the π−π overlaps, thus resulting in a lowbuckled structure (h1 = 0.45 Å) with sp3-like hybrid orbitals. The band structure calculations demonstrate that it is a gapless semiconductor (Figure 1c) with a linear Dirac-like dispersion relationship around the Fermi energy, and the Fermi velocity is 0.6 × 106 m/s. In the case of silicane (Figure 1b), one unit cell consists of two Si and two H atoms. The lengths of Si−Si and Si−H are d2 = 2.34 Å and dSi−H = 1.50 Å, respectively, and the silicane monolayer with h2 = 0.78 Å is more bulky than the bare one. The H atoms form strong σ bonds with Si atoms, leading to an sp3 hybridization of Si atoms. In addition, it exhibits semiconducting behaviors with a direct band gap of 2.59 eV, as

silicene/silicane HBLs as a path to grow silicene on weakly interactive silicane substrate. Unfortunately, both experimental and theoretical investigations on this issue are still scarce. In the present work, we investigate stacking behaviors and electronic properties of silicene on silicane surfaces by using density functional theory (DFT) calculations. As we predicted, a band gap is opened at the Dirac point and it is tunable by controlling external bias voltage or strains. Since the effective mass (EM) of electrons and holes near Dirac point are small, we expected the carrier mobility will not loss heavily after silicene deposited on silicane. These facts suggest the potential of HBLs to fabricate as high-performance FET.25 All of the calculations are performed by means of firstprinciples calculations as implemented in the Vienna Ab initio Simulation Package (VASP).26,27 Generalized gradient approximation (GGA) with the Perdew−Burke−Ernzerhof (PBE)28 exchange correlation functional is adopted to describe the exchange-correlation interaction, which is developed for the calculations of surface systems. To properly take into account the van der Waals (vdW) interactions in the structures, the DFT-D2 method29,31 is used throughout all the calculations. In addition, the projector augmented wave method32 is used to describe the electron−ion interaction, and the dipole corrections are included considering the possible charge C



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Figure 4. Energy gaps of HBLs as a function of external E field for pattern (a) AA, (b) aa, and (c) AB, respectively. (d)−(f) givs the energy gaps of patterns AA, aa, and AB, respectively, as a function of biaxial tensile and compressive strain.

band structures. Thus, the excellent characteristics of the high carrier mobility in silicene are expected.5 However, a sizable direct band gaps (44−61 meV) at the Dirac point is opened for all systems, which are smaller than that of silicene on SiC(0001) surface18 but larger than that for graphene adsorbed on diamond (111) surface.38 Since the absence of a band gap is a significant hurdle in construction of silicene-based FET, these results make the silicene/silicane HBLs promising as an electronic material. In these cases, the source and drain electrodes should be connected directly to silicene while the silicane monolayer underneath may actually act as a back-gate to precisely control the current on−off ratio. Most importantly, the 2D silicene monolayer is free of dangling bonds and will provide an ideal substrate for silicene to sit on. Furthermore, a 61 meV band gap is significantly larger than the roomtemperature thermal energy (kBT). It is hoped that the current on/off ratio achievable for the silicene/silicane HBLs may be larger than that of a free-standing silicene monolayer, suggesting that such a proposed FET device may be realizable in the near future. Why does the silicene/silicane HBL have a larger band gap? According to π-electron tight-binding (TB) model in silicene,39 the dispersion relation near the Fermi level of silicene can be expressed as

shown in Figure 1d, which agrees well with previous theoretical results.29 Based on the symmetry of the honeycomb configuration with low-buckled geometry, we consider four stacking patterns, such as AA, aa, AB, and ab, respectively, as shown in parts a−d of Figure 2. Table 1 lists the calculated binding energy and equilibrium interlayer spacing for all patterns. It can be seen that the Bernal pattern ab is more stable than the other three ones by ∼0.20 eV, with a smallest interlayer distance of 2.61 Å. With the Tkatchenko−Scheffler method,36 the lattice parameter is found to be 3.865 Å, and the interlayer spacings are 2.77, 2.70, 2.81, and 2.68 Å, respectively. Obviously, these are in consistent with that of Grimme’s method, indicating that our results are viable. The smaller binding energy37 indicates the weakly physical interaction in HBLs interface; in other words, the interactions between two Si layers are weak van der Waals forces, different from the strong orbital hybridization in the interface of silicene/SiC HBLs.18 On the other hand, when we only considered about plain GGA method, the variational trends and equilibrium interlayer spacings given by PBE+vdW and PBE approaches are almost identical for all systems, except that PBE calculations underestimate the binding energy slightly, i.e., −0.13, −0.18, −0.14, and −0.15 eV for patterns AA, aa, AB, and ab, respectively. We note that such difference does not affect the electronic structures of HBLs at equilibrium interlayer distances. Furthermore, there is no significant change in the buckling of silicene when deposited on silicane surface. Electronic band structures of four different patterns are displayed in Figure 2. It can can be seen that the symbolic Dirac point of silicene and its intrinsic band structure with linear band dispersion are still preserved in silicene/silicane HBLs, indicating that no Si-3pz orbitals at the Fermi level are involved in the hybridization with silicane surface (see parts e−h of Figure 2). To further illustrate the origin of the band gap opening with the linear dispersion relations in HBLs, we present the corresponding total density of states (DOS) for four patterns, as shown in Figure 3. It is obvious that the electronic states near the Fermi level are fit well with energy

|E(k)| = ± Δ2 + (ℏvFk)2

Here, k is the wave vector relative to the K point, vF is the Fermi velocity, and Δ is the onsite energy difference between two sublattices (Δ = 0 for free-standing silicene). When silicene is deposited on the silicane substrate, the silicane generates inhomogeneities in the silicene electrostatic potential. This changes the potential periodicity and therefore disrupts the degeneracy of the π and π* bands at the Dirac point, leading to a nonzero band gap, Eg = 2Δ. Thus, a relatively large band gap at the Dirac point is obtained in HBLs. After establishing that a considerable energy gap can be opened in the band structure of the silicene via weak D



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gap is obtained, irrespective of stacking patterns. The smaller EM near the Dirac point suggests the charge carrier mobility in silicene will not degrade upon silicane deposition. Furthermore, the band gaps of silicene can be flexibly modulated by applying an electronic field and strain, showing a robust semiconductor behavior. All these results demonstrate the potential advantage of silicene/silicane HBLs for high-speed effective FET.

nonbonding interactions, we investigate whether the high carrier mobility of HBLs can be preserved. Table 1 lists EM of the electron (me) and hole (mh) in the valence and conduction bands for four HBLs at the K point along the K−M and the K−Γ directions. The effective mass is expressed as ⎡ d2E(k) ⎤−1 m=ℏ⎢ ⎥ ⎣ dk 2 ⎦

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2

where ℏ is the reduced Planck constant, k is the wave vector, and E(k) is the dispersion relation. On the basis of the relationship between carrier mobility (μ) and effective mass, given by μ = eτ/m, here, τ is the scattering time. Assuming that silicane has the same scattering time as graphene (∼10−13 s), the carrier mobility of HBLs is estimated to be on the order of 105 cm2 V−1 s1−, which is larger than that of experimentally observed bulk silicon. The external E-field (EEF) is an effective approach to achieve tunable electronic properties, and thus, we explored the effect of EEF on the electronic properties of silicene/silicane HBLs. Parts a−c of Figure 4 display the band gaps of HBLs as a function of EEF magnitude. For the AA pattern, we find that the band gap decrease monotonically with increase of EEF, as shown in Figure 4a. When the EEF is large enough, the system will turn metallic with energy levels crossing the Fermi level. For patterns aa and AB, the band gap increases monotonically, from 48 to 129.4 meV and from 44 to 100.1 meV, respectively (Figure 4b,c). Thus, depending on the direction and strength of EEF, the band gaps of HBLs can be efficiently tuned. The origin of band gap modulation of HBLs under EEF can be attributed to the well-known Stark effect. Explicitly, the EEF could induce an electrostatic potential difference between silicene and silicane monolayers. As a result, the energy levels of two monolayers would be separated from each other, causing a shifting of energy levels and thus decreasing the band gap. With increasing magnitude of EEF, the energy level shifting becomes more and more pronounced and finally leads to a semiconductor−metal transition. Another promising route toward the continuously tunable band gap is elastic strain engineering, which is applied to HBLs by changing the lattices as ε = (a − a0)/a0, where a (a0) is the strained (equilibrium) lattice constant of HBL. Parts d−f of Figure 4 display the band gap change trends with the external strain ε. The variation tendency of three patterns is the same as the effect of EEF, but the effect of EEF is almost linear. For the AA pattern, the band gaps decrease monotonically with the increase of strain (Figure 4d). If the tensile strain reaches ε = 4%, a smallest gap of 55.6 meV can be obtained. However, in the case of patterns aa and AB, the change trends of band gaps are different from the case of pattern AA. On the other hand, the stress trends of pattern aa and AB are identical. The variation range of pattern aa is ε = −1%−7%, while the effective strain range is from ε = −1% to ε = 5%. Under the tensile strains, we find that the curve of three patterns includes the inflection point. Pattern AA has two inflection points, ε = 0% and ε = 4%, respectively, while the tensile strain of pattern aa reaches ε = 3% and the value of the energy gap reaches 48 meV. Similarly, when the tensile strain of pattern AB reaches ε = 2%, a band gap of 44.5 meV will be achieved. In conclusion, based on DFT calculations with vdW correction, we have studied the geometric and electronic properties of silicene/silicane HBLs. It is found that the nearly linear band dispersion character of silicene with a sizable band

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Tel: 86-531-82765976. Fax: 86-531-82765976. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grant Nos. 11274143, 11434006, 61172028, and 11304121).

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REFERENCES

(1) Lebègue, S.; Eriksson, O. Electronic Structure of TwoDimensional Crystals from Ab Initio Theory. Phys. Rev. B 2009, 79, 115409−115412. (2) Cahangirov, S.; Topsakal; Akt Urk, M. E.; Şahin, H.; Ciraci, S. Two- and One-Dimensional Honeycomb Structures of Silicon and Germanium. Phys. Rev. Lett. 2009, 102, 236804−236808. (3) Ezawa, M. Topological Insulator and Helical Zero Mode in Silicene under Inhomogeneous Electric Field. New J. Phys. 2012, 14, 033003−033008. (4) Xia, C.; Watcharinyanon, S.; Zakharov, A. A.; Yakimova, R.; Hultman, L.; Johansson, L. I.; Virojanadara, C. Detailed Studies of Si Intercalation/Deintercalation of Graphene on 6H-SiC(0001). Phys. Rev. B 2012, 85, 045418−045424. (5) Son, Y. W.; Cohen, M. L.; Louie, S. G. Half-Metallic Graphene Nanoribbons. Nature 2006, 444, 347−349. (6) Kara, A.; Enriquez, H.; Seitsonen, A. P.; Lew Yan Voon, L. C.; Vizzini, S.; Aufray, B.; Oughaddou, H. A Review on Silicene - New Candidate for Electronics. Surf. Sci. Rep. 2012, 67, 1−18. (7) Le Lay, G.; Aufray, B.; Léandri, C.; Oughaddou, H.; Biberian, J. P.; De Padova, P.; Kara, A. Physics and Chemistry of Silicene NanoRibbons. Appl. Surf. Sci. 2009, 256, 524−529. (8) Feng, B. J.; Ding, Z.; Meng, S.; Yao, Y.; He, X.; Cheng, P.; Chen, L.; Wu, K. Evidence of Silicene in Honeycomb Structures of Silicon on Ag(111). Nano Lett. 2012, 12, 3507−3511. (9) De Padova, P.; Vogt, P.; Resta, A.; Avila, J.; Razado-Colambo, I.; Quaresima, C.; Ottaviani, C.; Olivieri, B.; Bruhn, T.; Hirahara, T.; et al. Evidence of Dirac Fermions in Multilayer Silicene. Appl. Phys. Lett. 2013, 102, 163106−163108. (10) Fleurence, A.; Friedlein, R.; Ozaki, T.; Kawai, H.; Wang, Y.; Yamada-Takamura, Y. Silicene: Compelling Experimental Evidence for Graphene-like Two-Dimensional Silicon. Phys. Rev. Lett. 2012, 108, 245501−245505. (11) Tchalala, M. R.; Enriquez, H.; Mayne, A. J.; Kara, A.; Roth, S.; Silly, M. G.; Bendounan, A.; Sirotti, F.; Greber, T.; Aufray, B.; et al. Formation of One-Dimensional Self-Assembled Silicon Nanoribbons on Au(110)-(2 × 1). Appl. Phys. Lett. 2013, 102, 083107−083111. (12) Meng, L.; Wang, Y.; Zhang, L.; Du, S.; Wu, R.; Li, L. F.; Zhang, Y.; Li, G.; Zhou, H. T.; Hofer, W. A.; et al. Buckled Silicene Formation on Ir(111). Nano Lett. 2013, 13, 685−690. (13) Huang, S.; Kang, W.; Yang, L. Electronic Structure and Quasiparticle Bandgap of Silicene Structures. Appl. Phys. Lett. 2013, 102, 133106−133110. (14) Lin, C. L.; Arafune, R.; Kawahara, K.; Kanno, M.; Tsukahara, N.; Minamitani, E.; Kim, Y.; Kawai, M.; Takagi, N. Substrate-Induced E



Article

Symmetry Breaking in Silicene. Phys. Rev. Lett. 2013, 110, 076801− 076805. (15) Ding, Y.; Wang, Y. Electronic Structures of Silicene Fluoride and Hydride. Appl. Phys. Lett. 2013, 100, 083102−083105. (16) Houssa, M.; van den Broek, B.; Scalise, E.; Pourtois, G.; Afanas’ev, V. V.; Stesmans, A. An Electric Field Tunable Energy Band Gap at Silicene/(0001) ZnS Interfaces. Phys. Chem. Chem. Phys. 2013, 15, 3702−3705. (17) Liu, H.; Gao, J.; Zhao, J. Silicene on Substrates: A Way To Preserve or Tune Its Electronic Properties. J. Phys. Chem. C 2013, 117, 10353−10359. (18) Kokott, S.; Pflugradt, P.; Matthes, L.; Bechstedt, F. Nonmetallic Substrates for Growth of Silicene: an Ab Initio Prediction. J. Phys.: Condens. Matter 2014, 26, 185002−185005. (19) Bianco, E.; Butler, S.; Jiang, S.; Restrepo, O. D.; Windl, W.; Goldberger, J. E. Stability and Exfoliation of Germanane: A Germanium Graphane Analogue. ACS Nano 2013, 7, 4414−4421. (20) Yamanaka, S.; Matsu-ura, H.; Ishikawa, M. New Deintercalation Reaction of Calcium from Calcium Disilicide. Synthesis of Layered Polysilane. Mater. Res. Bull. 1996, 31, 307−316. (21) Okamoto, H.; Kumai, Y.; Sugiyama, Y.; Mitsuoka, T.; Nakanishi, K.; Ohta, T.; Nozaki, H.; Yamaguchi, S.; Shirai, S.; et al. Silicon Nanosheets and Their Self-Assembled Regular Stacking Structure. J. Am. Chem. Soc. 2010, 132, 2710−2718. (22) Nakano, H.; Nakano, M.; Nakanishi, K.; Tanaka, D.; Sugiyama, Y. Preparation of Alkyl-Modified Silicon Nanosheets by Hydrosilylation of Layered Polysilane (Si6H6). J. Am. Chem. Soc. 2012, 134, 5452−5455. (23) Gao, N.; Zheng, W. T.; Jiang, Q. Density Functional Theory Calculations for Two-dimensional Silicene with Halogen Functionalization. Phys. Chem. Chem. Phys. 2012, 14, 257−262. (24) Zhang, C. W.; Yan, S. S. First-Principles Study of Ferromagnetism in Two-Dimensional Silicene with Hydrogenation. J. Phys. Chem. C 2012, 116, 4163−4166. (25) Jose, D.; Datta, A. Structures and Electronic Properties of Silicene Clusters: a Promising Material for FET and Hydrogen Storage. Phys. Chem. Chem. Phys. 2011, 13, 7304−7311. (26) Kresse, G.; Furthmuller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169−11186. (27) Kresse, G.; Hafner, J. Ab Initio Molecular-Dynamics Simulation of the Liquid-Metal-Amorphous-Semiconductor Transition in Germanium. Phys. Rev. B 1994, 49, 14251−14269. (28) Perdew, J. P.; Wang, Y. Accurate and Simple Analytic Representation of the Electron-gas Correlation-energy. Phys. Rev. B 1992, 45, 13244−13249. (29) Grimme, S. Semiempirical GGA-Type Density Functional Constructed with a Long-Range Dispersion Correction. J. Comput. Chem. 2006, 27, 1787−1799. (30) Wei, W.; Dai, Y.; Huang, B. B.; Jacob, T. Many-body Effects in Silicene, Silicane, Germanene and Germanane. Phys. Chem. Chem. Phys. 2013, 15, 8789−8794. (31) Bucko, T.; Hafner, J.; Lebègue, S.; Á ngyàn, J. G. Improved Description of the Structure of Molecular and Layered Crystals: Ab Initio DFT Calculations with van der Waals Corrections. J. Phys. Chem. A 2010, 114, 11814−11824. (32) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B 1999, 59, 1758− 1775. (33) Jose, D.; Datta, A. Structures and Chemical Properties of Silicene: Unlike Graphene. Acc. Chem. Res. 2014, 47, 593−602. (34) Jose, D.; Nijamudheen, A.; Datta, A. Tip Enhanced Raman Spectroscopy as a Probe for the Buckling Distortion in Silicene. Phys. Chem. Chem. Phys. 2013, 15, 8700−8704. (35) Jose, D.; Datta, A. Understanding of the Buckling Distortions in Silicene. J. Phys. Chem. C 2012, 116, 24639−24648. (36) Bucko, T.; Lebegue, S.; Hafer, J.; Angyan, J. G. TkatchenkoScheffler van derWaals Correction Method with and without Self-

Consistent Screening Applied to Solids. Phys. Rev. B 2013, 87, 064110−064125. (37) To check the stability of all kinds of silicene/silicane bilayers, the binding energy can be defined as Eb = Esilicene + Esilicane − Esilicene/silicane, where Esilicene, Esilicane, and Esilicene/silicane are the energies of the isolated silicene, silicane and silicene/silicane bilayers, respectively. (38) Hu, W.; Li, Z. Y.; Yang, J. R. Diamond as an Inert Substrate of Graphene. J. Chem. Phys. 2013, 138, 054701−054704. (39) Oostinga, J. B.; Heersche, H. B.; Liu, X.; Morpurgo, A. F.; Vandersypen, L. M. K. Gate-induced Insulating State in Bilayer Graphene Devices. Nat. Mater. 2007, 7, 151−157.

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Silicane as an Inert Substrate of Silicene: A Promising Candidate for

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