Structures, Energetics, and Electronic Properties of Multifarious

Article pubs.acs.org/JPCC

Structures, Energetics, and Electronic Properties of Multifarious Stacking Patterns for High-Buckled and Low-Buckled Silicene on the MoS2 Substrate Linyang Li and Mingwen Zhao* School of Physics and State Key Laboratory of Crystal Materials, Shandong University, Jinan, Shandong 250100, China S Supporting Information *

ABSTRACT: The interfaces between silicene and substrate materials play important roles in the electronic properties of the systems. High-buckled (HB) silicene synthesized on bulk MoS2 surface has been reported [Adv. Mater. 2014, 26, 2096−2101]. Using first-principles calculations, we studied the interfaces between silicene and the monolayer MoS2 substrate. We found that silicene can adsorb on the MoS2 substrate via van der Waals (vdW) interactions forming silicene/MoS2 heterostructures with HB or low-buckled (LB) configuration. The lattice mismatch between LB silicene and the MoS2 substrate leads to the formation of Moiré superstructures. The heterostructures of HB silicene on the MoS2 substrate are metallic, while those of LB silicene on the MoS2 substrate are semiconductors with small band gaps due to the interface effects. The band gap is dependent on the rotation angle and stacking pattern, whereas the formation energy is not. High carrier mobility of LB silicene is preserved in these heterostructures. More interestingly, the band gap can be further tuned by applying a vertical external electric field. These features are helpful for the fabrication of nanoscaled electronic devices using silicene.

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INTRODUCTION Silicene, a silicon analogue to graphene, is attractive because it could be synthesized and processed using mature semiconductor techniques and has good compatibility with Si in the conventional semiconductor industry.1,2 This novel twodimensional (2D) material has been successfully synthesized on many kinds of metal substrates, such as Ag (111) surface,3−10 Ir substrate,11 and (0001) oriented thin films of zirconium diboride (ZrB2).12 So far, no solid evidence for the fabrication of isolated silicene has been reported,13 partially due to the strong interactions between silicene and the metal substrate. Recently, HB silicene14 with a height of about 2 Å has been synthesized on bulk MoS2 surface.15 The study of the interactions between HB silicene and the MoS2 substrate thus becomes an interesting issue, because it may pave a way to the realization of isolated silicene where the contamination from metal substrates to the electronic structure will be avoided. Additionally, the interface between silicene and the semiconducting MoS2 substrate may be useful for tuning the electronic properties of the systems. On the theoretical aspect, first-principles calculations of silicene have been performed, and many excellent mechanical and optical properties have been predicted.16−21 LB silicene has a zero band gap with π and π* bands crossing linearly at the Fermi level, and the charge carriers can be characterized by massless Dirac Fermions.14 The extremely high carrier mobility makes LB silicene an ideal material for building electronic devices, such as field effect transistor (FET).22 HB silicene, however, shows metallicity from first-principles calculations.14 © XXXX American Chemical Society

Taking spin−orbit coupling (SOC) into account, LB silicene is an intriguing 2D topological insulator,23,24 and the magnitude of the gap induced by effective SOC for the π orbital at the K point is 1.55 meV, which is much larger than that of graphene;25−27 so the quantum spin Hall effect (QSHE) is expected to be realized in LB silicene at experimental accessible low temperature.25,26 Besides graphene and its analogs, layered transition-metal dichalcogenides (TMDs) are another family of 2D materials, among which molybdenum disulfide (MoS2) has been studied intensively.28−39 The direct band gap of monolayer MoS2 and the indirect band gap of multilayer MoS2 have been confirmed by theoretical and experimental works.35−39 It has also been achieved by Novoselov et al.40 that layered materials such as MoSe2, MoTe2, WS2, TaSe2, NbSe2, NiTe2, BN, and Bi2Te3 can be efficiently exfoliated into individual layers. Interface effects play important roles in the electronic properties of heterostructures. Generally, there are two types of models in describing the heterostructure interfaces: lattice match and lattice mismatch models.41−44 In the lattice match model, the base vectors of one lattice are identical to those of another lattice. If the lattice constants of the two lattices differ slightly, one may employ a lattice match model to describe the heterostructure by fitting the lattice constants to a value between them, leading to a small-size supercell. The lattice Received: May 3, 2014 Revised: July 17, 2014

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dx.doi.org/10.1021/jp5043359 | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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match model has been employed in the studies of many interfaces, such as graphene/BN,45 HB silicene/bulk MoS2 surface,15 and LB silicene/GaS.46 For the lattice mismatch model, the base vectors of the two lattices are no longer parallel but have a rotational angle in order to compensate the lattice mismatch. This always leads to abundant forming Moiré superstructures. Recently, both theoretical and experimental works indicated that lattice mismatch at interfaces is quite crucial for their electronic properties. For example, the lattice match model of the graphene/BN interface suggests a moderate band gap at the Dirac point of graphene.41,42 However, if a small lattice mismatch (∼1.8%) is taken into account, the linear dispersion relation of graphene is preserved in the Moiré superstructures,45 which is in good agreement with experimental results.46−51The lattice mismatch model has also been used in silicene/Ag (111) surface,3−10,52,53 silicene/ BN,54−56 and graphene/MoS257−64 interfaces. In this paper, we investigated the interfaces between silicene and monolayer MoS2 (referred to as MoS2 hereafter) substrate from first-principles. In the experiment of HB silicene on bulk MoS2 surface, HB silicene is a hexagonal surface pattern with periodicity 3.2 Å, which is very close to the lattice constant of bulk MoS2 (3.16 Å),15 so we used a lattice match model to study HB silicene on the MoS2 substrate (HSMS heterostructure). For LB silicene on the MoS2 substrate (LSMS heterostructure), we adopted a lattice mismatch model to construct the heterostructure in order to keep the silicene in LB configuration. In both cases, the interactions between silicene and the MoS2 substrate are weak vdW interactions. For LSMS heterostructures, the vdW energy profile on the plane parallel to the MoS2 substrate is rather smooth. The metallic features of isolated HB silicene are preserved in the HSMS heterostructures, whereas the LSMS heterostructures are semiconductors with band gaps opened at the Dirac points of LB silicene. The LSMS heterostructures have high carrier mobility comparable to that of isolated LB silicene. Applying an external electric field along the direction perpendicular to the interface, the band gap can be further tuned in a large range. These features are helpful for the fabrication of nanoscaled electronic devices using silicene.

Table 1. Calculated Lattice Constant a, Buckling Height d, and Band Gap Eg of Silicene and Monolayer MoS2a HB silicene LB silicene monolayer MoS2 a

a (Å)

d (Å)

Eg (eV)

2.648 3.848 3.160

2.146 0.465 3.138

metallicity 0 1.75

The lattice constant of MoS2 was set to the experimental value.71,72.

positions were relaxed with a convergence of 0.02 eV/Å, while the lattice constants of supercells were fixed. The grid for BZ sampling was set to 5 × 5 × 1 for structural optimizations and 7 × 7 × 1 for energy calculations, respectively. The other computational details are the same as those for small-size supercells. For the lattice match model of the HSMS heterostructures, six stacking patterns (two AA stacking patterns and four AB stacking patterns) are taken into account,73,74 as shown in Figure 1. The structural parameters of the six patterns are

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METHODS AND COMPUTATIONAL DETAILS Our first-principles calculations were performed using the plane wave basis Vienna ab initio simulation package known as VASP65−67 code, implementing the density functional theory (DFT). The electron exchange-correlation functional was treated using a generalized gradient approximation (GGA) in the form of Perdew, Burke, and Ernzerhof (PBE).68 The vdW correction (DFT-D2) within the PBE functional proposed by Grimme69,70 was employed in all the calculations. For the HSMS heterostructures with small-size supercells, the atomic positions and lattice vectors were fully optimized using the conjugate gradient (CG) scheme without any symmetric restrictions until the maximum force on each atom was less than 0.01 eV/Å. The energy cutoff of the plane waves was set to 400 eV with the energy precision of 10−5 eV. The Brillouin zone (BZ) for relaxation is sampled by using a 15 × 15 × 1 (21 × 21 × 1 for static calculations) Gamma-centered Monkhorst− Pack grid. The structural parameters and band gap of silicene and MoS2 are summarized in Table 1, which are in good agreement with the theoretical and experimental results reported in previous literature.14,26−40,71,72 For the LSMS heterostructures with large-size supercells, only the atomic

Figure 1. Schematic representations of HB silicene on the MoS2 substrate with different stacking patterns (top view).

Table 2. Six Stacking Patterns of HSMS Heterostructuresa stacking pattern

Eform (meV)

a (Å)

strain Δ (%)

D (Å)

d (Å)

ABS-I AA-I ABM-I ABS-II AA-II ABM-II

264.7 246.5 252.8 247.0 267.6 256.0

3.084 3.071 3.073 3.072 3.084 3.084

16.5 16.0 16.0 16.0 16.5 16.5

3.479 3.102 3.152 3.089 3.514 3.201

1.907 1.973 1.970 1.975 1.905 1.913

a

Formation energy Eform (meV/Si atom), lattice constant a, strain with respect to isolated HB silicene Δ = (a − a0)/a0(a0 = 2.648 Å), interlayer distance D, and the buckling height d of HB silicene on the MoS2 substrate. B



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Table 3. Structural Parameters of LSMS Heterostructures Classified by (n, m/p, q) and Stacking Patterns in Origin (M and S)a (n m/p q)

N

Δ (%)

θ (deg)

M/S

D/d (Å)

Eform (meV)

Eg (meV)

v/vSi (%)

(3 2/3 1)

83

−0.72

9.52

(4 2/3 2)

122

−0.31

4.31

(5 1/4 1)

135

−0.22

1.95

M S M S M S

3.103/0.528 3.081/0.531 3.105/0.514 3.057/0.523 3.099/0.513 3.058/0.520

−100.0 −100.0 −102.0 −101.9 −102.2 −102.2

29.3 13.9 46.1 21.5 48.7 22.2

89.7 87.2 89.7 88.3 89.1 85.8

Rotation angle θ, strain for LB silicene Δ, number of atoms in supercell N, interlayer distance D, buckling height d, formation energy Eform (meV/Si atom), energy band gap Eg, and Fermi velocity of LSMS superstructure (v) with respected to the value of isolate LB silicene vSi.

a

Figure 2. Schematic representations of the superstructures of LB silicene on the MoS2 substrate (top view). (a) (3 2/3 1)M LSMS and (b) (3 2/3 1)S LSMS. Each supercell contains 83 atoms. The rotation angle between LB silicene and the MoS2 substrate is θ = 9.52°.

shown in Table 2. Considering the large difference between the lattice constants of LB silicene (3.848 Å) and MoS2 (3.160 Å), the LSMS heterostructures are built using a lattice mismatch model. The configurations of these superstructures start from an initial stacking pattern where a down Si atom is right above a Mo atom (M pattern) or a S atom (S pattern) in origin. The base vectors of the MoS2 substrate and LB silicene without rotation are75−78 ⇀ a1 = ( 3 /2, − 1/2)a0 ,

⇀ a 2 = ( 3 /2, 1/2)a0

⇀ b1 = ( 3 /2, − 1/2)b0 ,

⇀ b2 = ( 3 /2, 1/2)b0

Δ=

T2⃗ = −ma1⃗ + (m + n)a 2⃗

We can also construct two vectors in the LB silicene lattice as t1⃗ = pb1⃗ + qb2⃗ ,

Eform = (ESi / MS − ESi − EMS)/NSi

t 2⃗ = −qb1⃗ + (p + q)b2⃗

where ESi/MS, ESi, and EMS represent the total energies of the silicene/MoS2 heterostructure, isolated HB or LB silicene, and isolated MoS2, respectively. NSi is the number of Si atoms in the supercell of the heterostructure. Obviously, the strain energies and the interactions between silicene and MoS2 are included in the definition.

and then rotate the LB silicene lattice with respect to the MoS2 lattice to make T1⃗ and t1⃗ and T2⃗ and t 2⃗ coincide, respectively. The rotation angle θ between the two lattices is given by cos θ =

T1⃗ · t1⃗ |T1⃗ | × | t1⃗ |

=

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np + mq + (nq + mp)/2 2

m + n2 + mn ×

b0 p2 + q2 + pq

The parameters n, m, p, and q are integer numbers which are constrained by |Δ| ≤ 1% and n ≥ m, p ≥ q. These LSMS superstructures are classified by the four integer numbers and denoted as (n m/p q) hereafter. The number of atoms N in the primitive cell of the superstructures is given by N = [3 × (m2+n2+mn)+2 × (p2+q2+pq)]. The lattice constant of supercell is fixed at a0 (n2 + m2 + nm)1/2 (a0 = 3.160 Å is the experimental value of MoS2).71,72 Due to the limitation of computational resources, we only considered the superstructures with N < 150. The structural parameters of the superstructures are listed in Table 3. Figure 2 gives the two patterns (M and S) of the (3 2/3 1) LSMS superstructure with θ = 9.52° and N = 83. The formation energy (E form ) of the silicene/MoS 2 heterostructures is defined as

where a0 and b0 are the lattice constants of MoS2 and LB silicene. The base vectors of superstructure can be written as T1⃗ = na1⃗ + ma 2⃗ ,

a0 m2 + n2 + mn − b0 p2 + q2 + pq

RESULTS AND DISCUSSIONS We first considered the HSMS heterostructures built using a lattice match model. In the initial configurations, we applied the lattice constant of HB silicene to the value of the MoS2

p2 + q2 + pq

In this strategy, a low strain is inevitable, which can be represented by a parameter Δ defined as C



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Figure 3. Structure profiles of silicene on the MoS2 substrate and their corresponding ELF profiles. (a) AA-I HSMS, (b) ABS-II HSMS, (c) (3 2/3 1)M LSMS, and (d) (3 2/3 1)S LSMS. The structure profiles are on the vertical planes across dotted lines labeled as a in the corresponding structures shown in Figure 1 and 2.

buckling height d are 3.072 Å, 3.089 Å, and 1.975 Å, respectively (Figure 3 (b)). These results are also in good agreement with the experimental data for HB silicene on the bulk MoS2 surface which are D = 3 Å and d = 2 Å.15 This indicates that the interactions between HB silicene and the bulk MoS2 surface mainly come from the interactions between the top layer MoS2 and HB silicene. We then turned to LB silicene on the MoS2 substrate. It is noteworthy that there is a significant lattice mismatch up to 17.9% between LB silicene and the MoS2 substrate with respect to LB silicene. We therefore employed a lattice mismatch model to construct the LB silicene/MoS2 heterostructures. LB silicene was rotated with respect to the MoS2 lattice which leads to minimized supercells.79,80 The configuration of LB silicene is well preserved in the lattice mismatch model. We considered three rotation angles each of which corresponds to two stacking patterns (M and S), leading to six kinds of superstructures, labeled as (n m/p q)M and (n m/p q)S. The definition of the superstructures has been described in the previous part. The optimized structural parameters of these superstructures are listed in Table 3. Figure 2 (a) shows the (3 2/3 1)M superstructure and Figure 2 (b) shows the (3 2/3 1)S superstructure. Their structure profiles are shown in Figure 3 (c) and (d), respectively (left panel). Both superstructures contain 83 atoms in one supercell with a rotation angle of 9.52°. Compared with the isolated lattices, the S atoms close to the interface and the Si atoms undergo slight vertical corrugation after structure optimization due to different stacking patterns existing in the supercell. For (3 2/3 1)M superstructure, the interlayer distance D (average) between LB silicene and the MoS2 substrate is 3.103 Å, and the buckling

substrate which is 3.160 Å. This corresponds to applying 19.3% tensile strain to HB silicene, which is very close to the value (20.8%) found in HB silicene grown on bulk MoS2 surface.15 According to the relative position of the two lattices, six stacking patterns are classified as follows. (1) Half of the Si atoms (down Si atoms for ABS-I while up Si atoms for ABS-II) are placed on the top of the S atoms, while others are above the hollow sites of the MoS2 lattice, as shown in Figure 1 (a) and (b). (2) Half of the Si atoms (down Si atoms for AA-I while up Si atoms for AA-II) are placed on the top of the Mo atoms, while others are on the top of the S atoms, as shown in Figure 1 (c) and (d). (3) Half of the Si atoms (down Si atoms for ABM-I while up Si atoms for ABM-II) are placed on the top of the Mo atoms, while others are on the top of the hollow sites of the MoS2 lattice, as shown in Figure 1 (e) and (f). The relaxed lattice constant (a), interlayer distance (D), buckling height of HB silicene (d), strain for HB silicene (Δ), and the formation energy (Eform) of the six stacking patterns are listed in Table 2. The AA-I stacking pattern (Figure 1 (c)) is the energetically most favorable followed by the ABS-II (Figure 1 (b)) one which is less stable by only 0.5 meV/Si atom. This is consistent with the calculations for the experimental results.15 The structure profiles for the two patterns are shown in Figure 3 (a) and (b) (left panel). It is noteworthy that all these patterns have positive formation energies, due to the high strain energies involved in HB silicene and MoS2 with respect to the isolated one. For the AA-I pattern, the lattice constant a is 3.071 Å, which is much larger than that of isolated HB silicene (2.648 Å). The interlayer distance D is 3.102 Å, and the buckling height d is 1.973 Å (Figure 3 (a)). For the ABS-II pattern, the lattice constant a, interlayer distance D, and the D



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Figure 4. Variation of adsorption energy Ea per Si atom as a function of interlayer distance D obtained by using PBE and PBE+vdW strategies. (a) AA-I HSMS, (b) ABS-II HSMS, (c) (3 2/3 1)M LSMS, and (d) (3 2/3 1)S LSMS. The arrows indicate the positions of equilibrium states with minimal Ea.

heterostructures are in the range from −102.2 to −100.0 meV/Si atom which are nearly independent of the rotation angle and the stacking pattern.83 In recent experiments, HB silicene has been grown successfully on the bulk MoS2 surface.15 We therefore adopted four MoS2 layers to represent the substrate. Our calculations show that the AA-I and ABS-II stacking patterns are energetically most preferable with formation energy of about 273 meV/Si atom among the six patterns considered in this work. Those imply the high plausibility of the HSMS and LSMS heterostructures, and the cases of HB silicene on monolayer MoS2 and bulk MoS2 surface are very similar. The interactions between HB silicene and the bulk MoS2 surface are mainly the interactions between the top layer of bulk MoS2 and HB silicene, so we can conclude the formation energies (Eform) for LB silicene on the bulk MoS2 surface are similar to those for LSMS heterostructures. In other words, LB silicene is easier to adsorb on the bulk MoS2 surface than HB silicene. However, HB silicene on the bulk MoS2 surface was first achieved in a recent experiment.15 We deduced that the temperature in the experiments (200 °C)15 is the main reason. In the epitaxial growth of silicene on the Ag (111) surface, the final superstructures are closely related to the deposition temperature. Two types of superstructures, 4 × 4 and √13 × √13 superstructures, can coexist on the Ag (111) surface as the deposition temperature is 250 °C, whereas 2√3 × 2√3 superstructure can be observed at a higher temperature 270 °C.84 First-principles calculations show that the formation energies of 4 × 4 and √13 × √13 superstructures are lower than that of 2√3 × 2√3 superstructure.85 Therefore, lower temperature corresponds to more stable superstructures. For silicene, HB and LB configurations are separated by an energy barrier which hinders the phase transition between them once they are formed.14 The maximal formation energy difference of HSMS heterostructures is 18.2 meV/Si atom, whereas for LSMS heterostructures it is only 2.2 meV/Si atom. This indicates that the energy profile of silicene on the MoS2 substrate is smooth and cannot drive phase transition. The cases of silicene on the bulk MoS2 surface are also the same. We

height d (average) of LB silicene is 0.528 Å at the equilibrium state (Figure 3 (c)). For the (3 2/3 1)S superstructure, the interlayer distance D and the buckling height d are 3.081 and 0.531 Å, respectively (Figure 3 (d)). From Table 3, we can also see that both the interlayer distance D between LB silicene and the MoS2 substrate and the buckling height d of LB silicene are nearly independent of the rotation angle and stacking pattern. The interlayer distance of the LSMS heterostructures is shorter than the value (3.34 Å) of the heterostructures composing of LB silicene and monolayer hexagonal BN (LSBN heterostructures).55,56 The buckling height of LB silicene in LSMS heterostructures is larger than that in LSBN heterostructures.55,56 This is related to the stronger interlayer interactions in LSMS heterostructures than those in LSBN heterostructures. It is noteworthy that HSMS and LSMS heterostructures have very close interlayer distance, but the strains involved in these heterostructures are totally different. For HB silicene on the MoS2 substrate with the patterns of AA-I and ABS-II, it is stretched uniformly by about 16%, while LB silicene on the MoS2 substrate ((3 2/3 1)M and (3 2/3 1)S) is compressed slightly only by 0.72% compared with the isolated (freestanding) LB silicene. Obviously, the compressive strain (0.72%) for LB silicene can be neglected. The electron localization function (ELF)11,81,82 profiles corresponding to structure profiles are shown in Figure 3 (c) and (d) (right panel). The red regions between adjacent Si atoms (dotted line 1) indicate the covalent bonds between adjacent Si atoms. Although HB silicene undergoes significant tensile strain (∼16.0%), from the ELF profiles of AA-I (Figure 3 (a), right panel) and ABS-II (Figure 3 (b), right panel) HSMS heterostructures, there are still covalent interactions between adjacent Si atoms (dotted line 1, yellow regions). Based on the above-mentioned results, the silicene with HB and LB configurations on the MoS2 substrate both remain a continuous layer without bond breaking. The formation energies (Eform) for AA-I and ABS-II HSMS heterostructures calculated using the above-mentioned definition are 247 meV/Si atom, and those for the LSMS E



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region near the Fermi level along the highly symmetric orientations in BZ are plotted in Figure 5. The band structure

therefore deduced that lower temperature may be beneficial for growth of LB silicene on the bulk MoS2 surface in experiment, and the existing experiment conditions are beneficial for growth of HB silicene. Another promising approach obtaining LB silicene is looking for a substrate with a lattice match to LB silicene. Using the same lattice match model for HSMS heterostructures, our calculations indicate that monolayer MoTe2 substrate is suitable for epitaxial growth of LB silicene. More details can be seen in Part I of the Supporting Information. We also defined the adsorption energy Ea of silicene on the MoS2 substrate to evaluate the interactions between them (Take HSMS heterostructure for an example): Ea = [EHSMS − EHS ‐ HSMS − EMS ‐ HSMS)]/NHS

EHSMS, EHS‑HSMSS, and EMS‑HSMS represent the total energy of the HSMS heterostructure, energy of HB silicene, and energy of the MoS2 substrate with the same structures as they are in the HSMS heterostructure, respectively. NHS is the number of Si atoms in the supercell. The Ea of LSMS heterostructures can be defined analogously. Compared with the formation energy defined previously, Ea solely represents the interactions between silicene and the MoS2 substrate, and the strain energies are excluded. The adsorption energies of silicene on the MoS2 substrate at different interlayer distances are then calculated using the PBE functional with and without vdW correction (denoted as PBE +vdW and PBE), as shown in Figure 4. From this figure, we can see clearly that the PBE+vdW calculations give an obvious Ea minimum for each heterostructure, implying that silicene can stably attach on the MoS2 substrate. The PBE functional without vdW correction, however, fails to give an obvious binding state, due to the failure of PBE in describing weak interactions. The weak interactions between silicene and the MoS2 substrate can also be confirmed by the ELF profiles shown in Figure 3. In Figure 3 (a) and (b), the obvious blue regions (zero electron density) between Si atoms and their nearest S atoms (dotted line 2) suggest that no covalent bonds are formed between HB silicene and the MoS2 substrate. In Figure 3 (c) and (d), there are also obvious blue regions between most Si atoms and S atoms, but several Si atoms can have weak covalent interactions with the nearest S atoms (dotted line 2). The covalent interactions only exist in minority atoms and are very weak, so the interactions between LB silicene and the MoS2 substrate are still vdW interactions, similar to those in HSMS heterostructures. The interactions between the layers in graphite are also vdW interactions. We used a bilayer graphene of AB stacking pattern to evaluate the strength of the vdW interactions in graphite. The adsorption energy of graphene in bilayer graphene is −50 meV/C atom. This value is slightly higher than the adsorption energies of silicene on the MoS2 substrate which are −80 meV/Si atom for HSMS (AA-I and ABS-II) and −102 meV/Si atom for LSMS ((3 2/3 1)M and (3 2/3 1)S). The adsorption energy can represent the strength of the interactions between the two layers, and these indicate that the strength of the interactions between HB (LB) silicene and the MoS2 substrate is just slightly larger than that between bilayer graphene. Considering graphene has been successfully exfoliated from graphite in experiments,86 we suspect that silicene can also be exfoliated from the MoS2 substrate using similar approaches. The electronic band structures of these heterostructures are then calculated from first-principles. The band lines in the

Figure 5. Electronic band structures of isolated silicene and silicene on the MoS2 substrate. (a) HB silicene, (b) LB silicene, (c) AA-I HSMS, (d) ABS-II HSMS, (e) (3 2/3 1)M LSMS, and (f) (3 2/3 1)S LSMS. The energy at the Fermi level was set to zero. The enlarged view of the band lines at K point near the Fermi level is presented as the inset.

of isolated HB silicene exhibits clear metallic features, as shown in Figure 5 (a), in good agreement with the results reported in previous literature.14 These features are well preserved in the AA-I (Figure 5 (c)) and ABS-II (Figure 5 (d)) HSMS heterostructures. Figure 5 (b) shows the band structure of isolated LB silicene. The electronic band structure of isolated LB silicene is very similar to that of graphene where the valence and conduction bands meet at the six corners of the BZ with a linear dispersion relation (Dirac cone).14 Opening a band gap at the Dirac cones is quite crucial for the applications of LB silicene. Our first-principles calculations indicate that the interactions between LB silicene and the MoS2 substrate in the LSMS heterostructures open a small band gap at the Dirac cones. For the (3 2/3 1) M and (3 2/3 1) S LSMS heterostructures, the band structures close to the Fermi level are similar to that of isolated LB silicene. From the enlarged views at K point near the Fermi level, the band gaps of (3 2/3 1)M and (3 2/3 1)S LSMS heterostructures are 29.3 and 13.9 meV, respectively. Band gaps can also be found in other LSMS heterostructures, and the values are listed in Table 3. The F



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Figure 6. Top views and side views of the differential charge density distribution of LB silicene on BN and the MoS2 substrates with different patterns. (a) (2 1/1 1)B LSBN, (b) (3 2/3 1)M LSMS, and (c) (3 2/3 1)S LSMS. The isosurface value is ±0.004 e/Å3. Positive value is indicated in yellow and negative value is indicated in blue.

Figure 7. (a) Band structure of (5 1/4 1)M LSMS heterostructure. The energy at the Fermi level was set to zero. BZ folding moves the Dirac point from K to Γ point. Band structures of (5 1/4 1)M LSMS heterostructure in a vertical external electric field of (b) E⊥ = −0.5 V/Å and (c) E⊥ = 0.5 V/ Å. The direction of the external electric field is labeled in the figure. The enlarged view of the band lines at Γ point near the Fermi level is presented as the inset of (c).

and B atoms are no longer identical (ε ≠ 0), due to the interactions between LB silicene and the MoS2 substrate. This leads to a nonlinear energy dispersion relation, E(k) = ± (ε2 +(ℏvFk)2)1/2, so a band gap of Eg = 2ε appears at the Dirac point of LB silicene. The energy dispersion relation in the region near the Dirac point can be written approximately as E(k) ≈ ± (ε +ℏ2vF2k2/2ε). The Fermi velocities (vF) of the LSMS heterostructures can be obtained by fitting the firstprinciples data with this parabolic dispersion and are listed in Table 3. They are 85.8%−89.7% of the value of isolated LB silicene, suggesting that the high carrier mobility of isolated LB silicene is preserved in these LSMS heterostructures. It is noteworthy that only the pz atomic orbital of the Si atom is taken into account in this TB Hamiltonian. We also adopted a more accurate TB Hamiltonian involving more atomic orbitals (s, px, py, and pz) to understand the electronic structure variation of silicene. Details can be seen in Part II of the Supporting Information. The value of the band gap in LSMS heterostructures is sensitive to the rotation angle and stacking pattern, which is totally different than that in LSBN heterostructures in which the band gap is insensitive to the rotation angle and the sliding between the two lattices,55 so we compared the differential charge density (Δρ = ρLSMS − ρLS − ρMS or Δρ = ρLSBN − ρLS − ρBN) of the (2 1/1 1)B LSBN, (3 2/3 1)M, and (3 2/3 1)S LSMS heterostructures, which are shown in Figure 6. Comparing Figure 6 (a) with Figure 6 (b) and (c), we can

appearance of band gaps in the LSMS heterostructures differs significantly from the cases of graphene/BN heterostructures where the rotation-dependent Moiré pattern prevents the opening of the band gap.45 This is related to the buckled configuration of LB silicene, whereas graphene has a planar configuration. When LB silicene attaches on the MoS2 substrate, the two sublattices of LB silicene interact differently with the MoS2 substrate, which breaks the equivalency of the two sublattices. The influence for the two sublattices of LB silicene is mainly from the intrinsic electric field introduced by the MoS2 substrate. This can be further understood in terms of a simple tight-binding (TB) model. The unit cell of honeycomb LB silicene lattice consists of two atoms referred to as A and B atoms. TB Hamiltonian that describes the electronic structure of LB silicene near the Fermi level can be written as58,87 ⎛ ε ℏvF (kx − ik y)⎞ ⎟ ⎜ H= ⎟ ⎜ℏv (k + ik ) − ε F x y ⎠ ⎝

where k is the wave vector relative to the Dirac point, and vF is the Fermi velocity. For isolated LB silicene, the difference of onsite energy between the two sublattices is zero (ε = 0). A linear dispersion relation E = ± ℏvF|k| is therefore obtained. By the fitting the first-principles data using the linear relation, we got the Fermi velocity of LB silicene of about 5.33 × 105 m/s, which is comparable to that of graphene. For the LSMS heterostructures, however, the onsite energies of electrons at A G



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electric field effectively. These features of HSMS, LSMS, and LSMT heterostructures are helpful for the fabrication of nanoscaled electronic devices using silicene.

see that the charge transfer in LSMS heterostructures is more significant than that in LSBN. Comparing Figure 6 (b) with (c), the distributions of charge transfer are also different. The band gap for (2 1/1 1)B LSBN is 27 meV,55 so the charge transfer is not the main reason for the gap opened in the LSBN heterostructure. It is the intrinsic electric field of the BN substrate that makes onsite energy ε different.46,88,89 There is also an intrinsic electric field of the MoS2 substrate, but its strength is different in different superstructures. The different rotation angles and stacking patterns can make different charge transfer leading to different charge redistributions, which have a different influence on the strength of the intrinsic electric field of the MoS2 substrate, so the range of band gaps in LSMS heterostructures (34.8 meV) is larger than that in LSBN heterostructures (8 meV).55 Additionally, the obvious charge transfer between LB silicene and the MoS2 substrate may be advantageous for the light absorption of MoS2.90−92 A band gap can be opened in LB silicene by applying an external electric field along the direction perpendicular to the basal plane of LB silicene.93 The external electric field changes the onsite energy difference between the two sublattices of LB silicene and thus modifies the band gap. This mechanism still holds for the band gap modification of LSMS heterostructure.94−96 Taking the (5 1/4 1)M LSMS heterostructure as an example, we investigated the variation of the band bap in response to the external electric field. In zero electric field, the band structure of (5 1/4 1)M LSMS heterostructure is shown in Figure 7 (a) and BZ folding moves the Dirac point from K to Γ point. The band gap is 48.7 meV at Γ point. When the external electric field is increased to E⊥ = −0.5 V/Å, the band gap can be as large as 91.7 meV, which is large enough to be detected at room temperature. In the electric field of E⊥ = 0.5 V/Å, the band gap decreases to 2.9 meV. Tunable electronic band gaps of LSMS heterostructures are quite promising for applications in nanoscaled devices.

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ASSOCIATED CONTENT

S Supporting Information *

There are two parts (Part I and Part II): Part I describes the heterostructures of LB silicene on monolayer MoTe2 substrate. Part II describes the TB models for LB silicene, HB silicene, and silicene on the MoS2 substrate. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Basic Research Program of China (No. 2012CB932302), the National Natural Science Foundation of China (No. 91221101), and the National Super Computing Centre in Jinan.

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REFERENCES

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CONCLUSIONS Our first-principles calculations of silicene/MoS2 indicate that both HB and LB silicene can adsorb on the MoS2 substrate via weak vdW interactions. Energetics calculations indicate that both HSMS and LSMS heterostructures are plausible in experiments, and the latter is energetically more preferable. For LSMS heterostructures, the vdW energy profile on the plane parallel to the MoS2 substrate is rather smooth, leading to abundant Moiré patterns at the interfaces. Low temperature may facilitate the formation of LB silicene on the MoS2 substrate. Both HB and LB silicene may be easily exfoliated from the MoS2 substrate once they are formed due to the weak vdW interactions between them. The metallic electronic structure of HB silicene is preserved in the HSMS heterostructures, whereas the LSMS heterostructures are semiconductors with a small band gap opened at the Dirac point and high carrier mobility. The band gap is dependent on the rotation angle and stacking pattern. The band gap can be further tuned by applying a vertical external electric field. Using the same model with constructing HSMS heterostructures, we obtain LB silicene on monolayer MoTe2 substrate. The interactions between LB silicene and the MoTe2 substrate are stronger than those in HSMS heterostructures, and the formation energies of LSMT heterostructures are much lower than those of HSMS heterostructures. The gaps opened in Dirac points are lager enough to be detectable at room temperature, and the band gaps can be tunable by applying an H



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