Tetra-silicene: A Semiconducting Allotrope of Silicene with Negative

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Tetra-Silicene: A Semiconducting Allotrope of Silicene With Negative Poisson’s Ratios Man Qiao, Yu Wang, Yafei Li, and Zhongfang Chen J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b02413 • Publication Date (Web): 08 Apr 2017 Downloaded from http://pubs.acs.org on April 15, 2017

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The Journal of Physical Chemistry

Tetra-silicene: A Semiconducting Allotrope of Silicene with Negative Poisson’s Ratios Man Qiao, † Yu Wang, † Yafei Li, †,* Zhongfang Chen‡,* †

Jiangsu Key Laboratory of New Power Batteries, Jiangsu Collaborative Innovation Centre of

Biomedical Functional Materials, School of Chemistry and Materials Science, Nanjing Normal University, Nanjing 210023, China, ‡

Department of Chemistry, Institute for Functional Nanomaterials, University of Puerto Rico, Rio Piedras Campus, San Juan, Puerto Rico 00931

* To whom correspondence should be addressed. Email: [email protected] (Y.L.) and [email protected] (Z.C.)

† ‡

Nanjing Normal University University of Puerto Rico

ACS Paragon Plus Environment


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Abstract By means of comprehensive density functional theory (DFT) computations, we designed a new two-dimensional (2D) structure of silicon, namely tetra-silicene. In tetra-silicene, each silicon atom binds with four neighboring Si atoms to form a 2D network composed of only tetragons. Our DFT computations demonstrate that tetra-silicene is of rather high experimental feasibility, as indicated by its considerable cohesive energy, all positive modes in the phonon spectrum, and the well maintained structure after 10 ps first principles molecular dynamics simulations at 500K. Tetra-silicene has rather intriguing mechanical properties featured with unusual negative

Poisson’s

ratios.

Remarkably,

different

from

hexagonal

silicene

(hexa-silicene) which is semi-metallic without a band gap, tetra-silicene is semiconducting with an appreciable indirect band gap of 0.19 eV, and it has a considerable carrier mobility of 1639.07 cm2V1s1. Encouragingly, our simulations suggest that tetra-silicene can be flexibly produced from hexa-silicene via mechanical conversion. Once synthesized, tetra-silicene would find many important applications in electronics and mechanic devices.


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Introduction The experimental realization of graphene, 1,2 an atomic monolayer of carbon atoms arranged in a honeycomb lattice by Geim and Novoselov in 2004, brought us a wonder material to the renown carbon nanomaterials family. Currently, graphene is one of the most extensively studied multifunctional material due to its many excellent properties. 3 , 4 For example, graphene is the strongest material ever measured, 5 chemically stable and inert, and conducts electricity better than any other known material at room temperature.6-8 It is expected that 2D graphene can replace the role of traditional silicon materials in field-effect transistors (FET) and logic circuits.9,10 Unfortunately, pristine graphene is semimetallic without a band gap for controllable operations. Correspondingly, a number of methods, including covalent and non-covalent functionalizations, have been proposed to open a gap in the band structure of graphene.11-17 Besides the classical graphene, researchers theoretically investigated a number of graphene allotropes composed of non-hexagons.18-21 Interestingly, some graphene allotropes can present semiconducting properties. For instance, Luo et al.20 designed a new graphene allotrope consisting of alternative parallel zigzag and armchair chains (named pza-C10), which is semiconducting with a 0.71 eV indirect band gap. Zhang et al.21 proposed a novel carbon allotrope composed entirely of carbon pentagons (named penta-graphene), which presents a considerable band gap of 3.25 eV and has a unique negative Poisson’s ratio. These studies vividly show that the properties of materials can be tuned by adjusting the topological arrangement of atoms.



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Silicon is in the same row of the periodic table as carbon, and at present it still plays a dominant role in microelectronics industry. 22 In contrast to the diverse bonding characters of carbon, silicon prefers to utilize all of its three valence p orbitals to adopt sp3 hybridization, and doesn’t have the layered structure in nature. The sp2-hybridized monolayer structure of silicon, namely silicene, remained as a hypothetical structure for some time,23,24 and was fabricated until very recently.25-29 Similar to graphene, silicene contains only hexagons (hereinafter referred to as hexa-silicene), though the structure is not purely planar but slightly buckled. Interestingly, the electronic structures of hexa-silicene and graphene are similar: both have a Dirac cone and linear electronic dispersion around the K

,23,30 the

quantum spin Hall effect (QSHE) and quantum anomalous Hall effect (QAHE) were also predicted in hexa-silicene,31 though not observed yet experimentally. Due to many important applications of nanosilicon species, hexa-silicene was expected to shine in electronics.32-35 Unfortunately, the same as graphene, hexa-silicene is also semimetallic without an appreciable band gap,23, 36 which seriously limits its applications in the field of nanoelectronics. Compared with graphene, few efforts have been given to study the allotropes of silicene. By means of density functional theory (DFT) computations, Gimbert et al. devised an allotrope of silicene, which has the same structure as that of molybdenum disulfide monolayer and is metallic. 37 Motivated by the successful design of semiconducting graphene allotropes, we quite wonder whether it is possible to design silicene allotropes that exhibit semiconducting properties. The exploration of this


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problem is expected to bring some new structures as well as excellent properties, which have both theoretical and practical significance. In this work, based on comprehensive DFT computations, we designed a new allotrope of silicon, named tetra-silicene, which is composed of entirely Si tetragons. Our computations revealed that tetra-silicene monolayer is a stable structure with considerably high thermodynamic and kinetic stabilities. Remarkably, tetra-silicene possesses an intriguing negative Poisson’s ratio. Especially, different from gapless hexa-silicene, our designed tetra-silicene is semiconducting with an indirect band gap of 0.19 eV. These fantastic properties render tetra-silicene a more promising candidate than hexa-silicene for electronics and mechanics.

Computational Methods DFT computations were performed using the plane-wave technique implemented in Vienna ab initio simulation package (VASP).38,39 Projector-augmented plane wave (PAW) approach was applied to describe the ion−electron interactions. 40 , 41 The generalized gradient approximation (GGA) expressed by the PBE functional and a 500 eV cutoff for the plane-wave basis set were adopted in all computations.42 We set the x and y directions parallel and the z direction perpendicular to the basal plane of the tetra-silicene monolayer, and adopted a supercell length of 15 Å in the z direction to avoid interaction between layers. The geometry optimizations were performed by using the conjugated gradient method, and the convergence threshold was set to be 10−5 eV in energy and 10−3 eV/Å in force. The Brillouin zone was sampled with an 8×6×1  centered k-points grid. In this work, all the band structures were computed



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using the hybrid HSE06 functional to ensure high-quality band results.43 The phonon band structure of tetra-silicene monolayer was computed using the density functional perturbation theory (DFPT) as implemented in the Phonopy program.44 To assess the thermal stability of the tetra-silicene, we performed first-principles molecular dynamics (MD) simulations. For the MD simulations, we chose a 4×4 supercell with 64 Si atoms. The initial structure of tetra-silicene monolayer was annealed in NVT ensemble for 10 ps with a time step of 1.0 fs. The temperature was controlled by using the Nose–Hoover method.45 The chemical bonding pattern of tetra-silicene was analyzed using the solid-state adaptive natural density partitioning (SSAdNDP) method,46 which is an extension of the AdNDP method47 to periodic systems and as such was derived from periodic implementation of the natural bond oribital (NBO) analysis. The SSAdNDP projection algorithm was utilized to obtain a representation of the delocalized plane wave DFT results in a localized atomic orbital (AO) basis. For 2D tetra-silicene, the aug-cc-PVTZ basis set was used to represent the projected PW density using an 8×6×1 k-points grid. The Visualization for Electronic and Structural Analysis (VESTA, series 3)48 software was used for visualization of chemical bonding.

Results and Discussions Geometric Structure and Stability of Tetra-silicene. Figure 1a presents the optimized structure of our designed tetra-silicene monolayer. Different from hexa-silicene, tetra-silicene has a rectangular unit cell with the lattice constants a and b being 3.78 and 4.62 Å, respectively. One unit cell of tetra-silicene contains four Si


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atoms, and each Si atom is bonded with four neighboring Si atoms, indicating that Si atoms are sp3 hybridized. As given in the top view, tetra-silicene is composed entirely of Si tetragons, which is rather rare in the nature. Viewed along x direction, tetra-silicene exhibits a zigzag shape, whereas it looks like a buckled bilayer structure when observed along y direction. Therefore, tetra-silicene actually has a similar puckered configuration to that of phosphorene.49-52 The buckling (measured by the spacing in the bilayer) of tetra-silicene is 1.49 Å, which is much higher than that of hexa-silicene (0.45 Å). Interestingly, though tetra-silicene is significantly buckled, four Si atoms involved in an isolated Si tetragon are exactly in the same plane. The Si-Si bond length is 2.41 Å along the x direction but shrinks slightly to 2.40 Å along the y direction, both are much longer than that in hexa-silicene (2.18 Å). The unique geometric structure of tetra-silicene also reminds us the previously reported metallic silicon tubes in which all Si atoms are also tetra-coordinate.53



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Figure 1. Top and side views of the optimized structure of tetra-silicene. The side views along the x (upper right) and y (left) directions are both shown. The red dashed lines label a unit cell, a and b represent the lattice vectors.

We then analyzed the chemical bonding pattern of tetra-silicene utilizing the newly developed SSAdNDP method,46 which can well interpret the chemical bonding patterns in terms of classical lone pairs, localized two-center-two-electron (2c-2e) bonds, as well as multi-center delocalized bonds in

bulk solids, surfaces and

nanostructures. Since each Si atom has four valence electrons, there are 16 valence electrons in one unit cell of tetra-silicene. According to our computations, there are eight 2c-2e -type SiSi bonds in one unit cell of tetra-silicene (Figure 2), accounting for 16 valence electrons. The occupation numbers (ON) are 1.92 and 1.93 for SiSi bonds along the x and y directions, respectively. Therefore, no delocalized  bond exists in tetra-silicene. In sharp contrast, in hexa-silicene, each Si atom forms three


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2c-2e -type bonds, leaving one electron involved in a delocalized 6c-2e  bond (Figure S1).

Figure 2. Schematic of SSAdNDP chemical bonding pattern for a unit cell of tetra-silicene. The iso-surface value is 0.15 e/Å3.

The unique geometry and bonding pattern may endow tetra-silicene with some distinguished properties from those of hexa-silicene. However, before revealing the properties of tetra-silicene, firstly we need to examine whether it is a stable structure for experimental realization. The stability of tetra-silicene was firstly accessed by computing its cohesive energy, which is defined as: Ecoh = (nESiEt-silicene)/n, in which ESi and Etetra-silicene are the total energies of a single Si atom and tetra-silicene monolayer, respectively, n is the number of Si atom in the supercell. According to our computations, tetra-silicene has a cohesive energy of 3.899 eV/atom, only 2 meV/atom less than that of hexa-silicene (3.901

eV/atom). Thus, thermodynamically, tetra-silicene and

hexa-silicene are equally stable.

Note that the formation of an extra Si-Si bond for



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each Si atom in tetra-silicene substantially compensates the unavailability of the relatively weak Si-Si  bonds as found in hexa-silicene, thus leading to the close cohesive energies of tetra-silicene and hexa-silicene. The favorable cohesive energy indicates that tetra-silicene has good thermodynamic stability and holds great potential to be captured experimentally. The stability of tetra-silicene was further confirmed by computing its phonon dispersion curves. There is no appreciable imaginary mode in the phonon spectrum (Figure 3), indicating the high kinetic stability of tetra-silicene monolayer. Remarkably, the highest frequency of tetra-silicene monolayer is 466 cm1, only slightly lower than that of hexa-silicene (560 cm1).23 Moreover, to examine the thermal stability of tetra-silicene, we performed first-principles molecular dynamics (FPMD) simulations using a 6×4 supercell. Tetra-silicene can maintain its structural integrity throughout a 10 ps FPMD simulation at the temperature of 500K (Figure S2), suggesting its good thermal stability.

Figure 3. Phonon spectrum of tetra-silicene.


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Mechanical and Electronic Properties of Tetra-silicene. The high stability of tetra-silicene motivated us to explore its properties and potential applications. We first assessed the mechanical properties of tetra-silicene by computing its elastic constants. Mechanically, a stable tetragonal 2D structure should meet the following criteria: C11C22  C122 > 0, C66 > 0, where Cij are the elastic constants.54 We hence computed the elastic constants of tetra-silicene to examine its mechanical stability. According to our computations, the elastic constants of tetra-silicene are C11 = 65.43 GPa, C22 = 75.74 GPa, C12 = C21 = 3.61 GPa, and C66 = 27.01 GPa, which satisfy well with the mechanical stability criteria. The in-plane Young’s modules (Y) for tetra-silicene monolayer, which can be deduced from the elastic constants by Yx = (C11C22  C12C21)/C22 and Yy = (C11C22  C12C21)/C11, are 65.26 and 75.54 N/m for x and y directions, respectively. Computed at the same levels of theory, the in-plane Young’s modules of tetra-silicene are comparable to those of hexa-silicene (Yx = Yy = 68.36 N/m) and phosphorene (Yx = 25.50 N/m, Yy = 91.61 N/m), suggesting that tetra-silicene has good mechanical properties. Remarkably, with a negative C12, tetra-silicene has negative Poisson’s ratios of 0.048 (C12/C22) and 0.055 (C12/C11) along x and y directions, respectively. Physically, the Poisson’s ratio is defined as the negative ratio of transverse to axial strain. The negative Poisson’s ratio indicates that tetra-silicene can be compressed or stretched in both two directions at the same time. In sharp contrast, hexa-silicene has a regular positive Poisson’s ratio. For a validation, we also applied a uniaxial tensile strain of 4% in the x and y directions of tetra-silicene, respectively. After full atomic



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relaxation, the equilibrium lattice parameters of the y and x directions were elongated by 0.15% and 0.2%, respectively, confirming that tetra-silicene indeed has negative Poisson’s ratios (Figure 4). Note that the negative Poisson’s ratio is rather scarce in 2D materials.21, 55 - 58 Recently, both theoretical 59 and experimental 60 studies demonstrated that phosphorene has a negative Poisson’s ratio. However, the negative Poisson’s ratio of phosphorene was observed in the out-of-plane direction, which is different from that of our tetra-silicene. Such unusual mechanical properties would confer many important applications for tetra-silicene in mechanics, such as nanoauxetic material.

Figure 4. Total energy with respect to the other side of lattice response when the tetra-silicene lattice is under 4% tensile strain along the x and y direction, respectively. The arrows indicate the equilibrium magnitude of x and y. To reveal the electronic properties of tetra-silicene, we computed the band structure of tetra-silicene using the hybrid HSE06 functional. Different from semimetallic hexa-silicene,23 tetra-silicene is semiconducting with an indirect band gap of 0.19 eV (Figure 5a). The conduction band minimum (CBM) is located at the Γ


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point, whereas the valence band maximum (VBM) lies on the Y−Γ path. Notably, the direct bang gap of tetra-silicene monolayer at the X−Γ is as high as 0.75 eV. Analyzing the band-deposed charge density distributions reveals that the VBM (Figure 5b) is mainly contributed by SiSi bonds, while the CBM (Figure 5b) is mostly contributed by the anti-bonding states between Si atoms. Note that the gapless feature of hexa-silicene and graphene is due to the existence of conjugated  states, thus the band gap opening for tetra-silicene should be attributed to the absence of  bonding. The appreciable band gap would facilitate the application of tetra-silicene in nanoelectronics.

Figure 5. (a) The HSE06 band structure of tetra-silicene. The Fermi level is set as zero. The blue double arrow denotes the direct band gap. (b) Partial charge density of the VBM and the CBM of tetra-silicene with an isosurface of 0.007 e/Å3.



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The most attractive characteristic of hexa-silicene is that it has rather high carrier mobility (2105 cm2V1s1). 61-63 We quite wonder whether the semiconducting tetra-silicene also has high carrier mobility. To this end, we computed the acoustic phonon-limited carrier (including electron and hole) mobilities of tetra-silicene on the basis of deformation potential (DP) theory, which was initially proposed by Bardeen and Shockley.64 According to the DP theory, the carrier mobility of a 2D structure can be expressed as:

2 D 

eh3Y2 D , kBTm*md (El )2

where ћ is reduced Planck constant, k is the wave vector, m* is the effective mass in the transport direction, and md  m*x m*y is the average effective mass. The term E1 represents the DP constant denoting the shift of CBM for electron or VBM for hole induced by the tiny lattice strain. Y2D is the in-plane Young’s modules as determined in our mechanical property computations. As summarized in Table 1, our designed tetra-silicene exhibits remarkable anisotropy in effective mass. The effective masses of electrons and holes along the x direction are as high as 14.89 m0 and 5.48 m0 (m0 is the mass of free electron), respectively, which are much larger than those in the y direction (0.06 m0). Such a pronounced anisotropy in effective mass for tetra-silicene should be attributed to the different atomic arrangements in x and y directions. Specifically, in the x direction the silicon chains are wrinkled into a zigzag pattern, while in the y direction the silicon atoms in each silicon chain are in the same plane. Through dilating the lattice along x


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and y directions (Figure S3), we found that the deformation potentials (E1) for electron (1.16) and hole (2.85) in the x and y directions are much higher than those in the y direction (15.60 and 5.35 for electron and hole, respectively). Table 1. Computed effective mass (m*), Young’s modulus (Y2D), DP constant (E1), and carrier mobility (μ) of tetra-silicene at 300 K along x and y directions. Carrier type

m*/m0

Y (N/m)

E1 (eV)

 (cm2V1s1)

electron (x) electron (y) hole (x) hole (y)

14.89 0.06 5.48 0.06

65.26 75.54 65.26 75.54

1.16 15.60 2.85 5.35

73.21 116.28 54.64 1639.07

The carrier mobilities of tetra-silicene were then computed on the basis of the evaluated m*, Y2D, and E1. In the x direction, the mobilities of electron and hole are 73.21 and 54.64 cm2V1s1, respectively. Remarkably, due to the much lower effective mass, the carrier mobilities of electron and hole in the y direction are 116.28 and 1639.07 cm2V1s1, respectively, which are much higher than those in the x direction. Overall, though much lower than that of hexa-silicene, the carrier mobility of tetra-silicene is much higher than those of MoS2 monolayer (200 cm2V1s1)65 and silicon bulk (1400 cm2V1s1), indicating that tetra-silicene would be a quite promising 2D material for microelectronics. Experimental Feasibility. With such unique mechanical and electronic properties, it would be desirable to realize tetra-silicene experimentally for practical applications. The comparable cohesive energy to that of hexa-silicene suggests that tetra-silicene is a rather competitive allotrope and it can be grown by chemical vapor deposition (CVD) on specific substrates with matched lattice constants and symmetry. Moreover,



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inspired by Zhu et al.’s recent simulation evidence66 that puckered black phosphorus monolayer very likely can transfer to hexagonal blue phosphorus monolayer under mechanical stretching, we propose that compressing hexa-silicene is also a promising route to produce tetra-silicene. To explore this feasibility, we investigated the phase transition pathway and energy barrier from hexa-silicene to tetra-silicene employing the nudged elastic band (NEB) as implemented in VASP. A rectangular four-atom unit cell was adopted for both hexa-silicene (initial state) and tetra-silicene (final state). A series of intermediate states (1-9) were inserted in the whole transition process. Specifically, following the convention of previous studies,66, 67 , 68 the change of lattice parameters from hexa-silicene to those of tetra-silicene have been imposed between steps 0 and 1 to ensure that the produced intermediate states can be relaxed with the same shape of unit cell. As shown in Figure 6, during the transition process, the SiB, SiC, and SiD atoms move out of the initial plane relative to the position of SiA atom. Encouragingly, the activation barrier for this transition process is only 0.25 eV/atom, much lower than that for the transition from black to blue phosphorus monolayer (0.47 eV/atom),62 which indicates the high feasibility of mechanical conversion from hexa-silicene to tetra-silicene.


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Figure 6. Total energy change during the transition from hexa-silicene to tetra-silicene. The insert is the schematic of series of structural snapshots depicting the transition from hexa-silicene to tetra-silicene. A, B, C, and D represent four Si atoms in a rectangular unit cell for both two structures.

Conclusion To summarize, by means of systematic DFT computations, we designed a new 2D allotrope of silicene, namely tetra-silicene, which is composed of entirely tetragons with all Si atoms being sp3 hybridized. Our computations demonstrate that binding energy of tetra-silicene is nearly equal to that of hexa-silicene, and tetra-silicene is kinetically stable and can withstand temperature up to 500 K. Remarkably, tetra-silicene has rather fantastic mechanic properties featured with negative Poisson’s ratios. Particularly, due to the absence of  states, tetra-silicene is semiconducting with a 0.19 eV indirect band gap, which is in sharp contrast to the gapless hexa-silicene. Moreover, tetra-silicene has a considerable carrier mobility of 1639.07 cm2V1s1. The combination of negative poisson’s ratios, appreciable band



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gap, and high carrier mobility would render tetra-silicene a promising candidate for the new generation of microelectronics. Especially, we revealed that the synthesis of tetra-silicene would be rather feasible by proposing a likely conversion pathway from hexa-silicene to tetra-silicene. With the development of experimental techniques for fabrication of 2D materials, we are optimistic that tetra-silicene can be realized experimentally in the very near future.

Supporting Information Chemical bonding patterns of hexa-silicene, the snapshot of tetra-silicene after a 10 ps FPMD simulations, band energies of CBM and VBM for tetra-silicene as a function of lattice dilation. This material is available free of charge via the Internet at http://pubs.acs.org.

Acknowledgement Support in China by Natural Science Foundation of China (No. 21522305 and 21403115) and the NSF of Jiangsu Province of China (No. BK20150045), and in USA by National Science Foundation (Grant EPS-1010094) and Department of Defense (Grant W911NF-12-1-0083) is gratefully acknowledged. The computational resources utilized in this research were provided by Shanghai Supercomputer Center.

References (1) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Gregorieva, I. V.; Firsov, A. A. Electric Field Effect in Atomically Thin Carbon Films. Science 2004, 306, 666–669. (2) Novoselov, K. S.; Jiang, D.; Schedin, F.; Booth, T. J.; Khotkevich, V. V.; Morozov, S. V.; Geim, A. K. Two-dimensional Atomic Crystals. Proc. Natl. Acad. Sci. U.S.A.


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TOC Graphic


Tetra-silicene: A Semiconducting Allotrope of Silicene with Negative

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