- Nano Express
- Open Access
Uniaxial strain-induced mechanical and electronic property modulation of silicene
© Qin et al.; licensee Springer. 2014
- Received: 17 July 2014
- Accepted: 17 September 2014
- Published: 22 September 2014
We perform first-principles calculations of mechanical and electronic properties of silicene under uniaxial strains. Poisson's ratio and the rigidity of silicene show strong chirality dependence under large uniaxial strains. The ultimate strains of silicene with uniaxial strain are smaller than those with biaxial strain. We find that uniaxial strains induce Dirac point deviation from the high-symmetry points in the Brillouin zone and semimetal-metal transitions. Therefore, no bandgap opens under the uniaxial strain. Due to its peculiar structure and variable sp3/sp2 ratio of the chemical bond, the deviation directions of Dirac points from the high-symmetry points in the Brillouin zone and variation of Fermi velocities of silicene exhibit significant difference from those of graphene. Fermi velocities show strong anisotropy with respect to the wave vector directions and change slightly before the semimetal-metal transition. We also find that the work function of silicene increases monotonously with the increasing uniaxial strains.
61.46.-w; 62.20.D-; 73.22.Dj
- Uniaxial strain
- First-principles calculation
Silicene, the silicon analog of graphene, is a two-dimensional honeycomb lattice of silicon atoms. It has been theoretically predicted long ago  but has only been synthesized recently [2–10]. Due to a similar topology with graphene, silicene has many outstanding properties like graphene, such as the massless Dirac fermion behavior [6, 9] and a high Fermi velocity . In addition, silicene has apparent compatibility to the current silicon-based electronic industry over and above graphene. Thus, silicene also has great potential applications in nanoelectronics and spurred much attention these years.
Recent theoretical studies demonstrated that inert substrates  and point defects  could effectively tune the electronic band structures of silicene. Meanwhile, mechanical strain often brings about astonishing effects on properties of silicon materials. It can improve the mobility of bulk Si [13, 14], and strain engineering is considered to be one of the most promising strategies for developing high-performance sub-10-nm silicon devices . For one-dimensional silicon nanowires, strain can tune the size of the bandgap and turn the nature of the bandgap from indirect to direct [15, 16]. Since electrons of silicon atom tends to form sp3 hybridization rather than sp2 hybridization, the two-dimensional silicene can be easily buckled and have various configurations with different sp3/sp2 ratios. Freestanding silicene is predicted to favor a low-buckled configuration [1, 17, 18]. Silicene grown epitaxially on silver substrates in recent experiments is proposed to have several structures, such as the so-called (4 × 4)  or [8, 19] structures. Theoretical investigations also suggest several different types of silicene superstructures on the Ag(111) surface . The buckling gives silicene more flexibility over graphene and opens large opportunities for exploring interesting electromechanical properties in a buckled two-dimensional structure. Moreover, despite the great desire to obtain freestanding silicene, currently, silicene is mainly synthesized by epitaxial growth on substrates like Ag [5, 8, 9, 19], ZrB2, and Ir . The substrate could introduce strain, and understanding of strain effect is also fundamental for silicene growth. Recently, several groups have carried out theoretical investigation of the strain effect on the mechanical and electronic properties of silicene [21–28]. Silicene is found much less stiffer than graphene [21, 27] and has a lower yielding strain . Qin  and Liu  suggest that biaxial strain could induce a semimetal-metal transition. Compared with biaxial strain, uniaxial strain can further destroy the symmetry of silicene and is expected to bring new features. Zhao  and Mohan  claimed that uniaxial tensile strain can open a finite bandgap for silicene, which is important for applications in semiconductor devices. Meanwhile, Wang  declared that uniaxial strains will not open bandgaps for silicene and germanene. However, former studies of graphene [30–35] suggest that the uniaxial strain could introduce a new mechanism, and its effect needs to be studied cautiously.
In this work, we perform a careful and systematic first-principles study of the uniaxial strain effect on the mechanical and electronic properties of silicene. We find that Poisson's ratio and rigidity of silicene show strong chirality dependence, and the ultimate strain of silicene under uniaxial strain is smaller than that under biaxial strain. We show that no bandgap opens in silicene under uniaxial strain in the elastic region. Uniaxial strains shift the Dirac cones from the high-symmetry points in the Brillouin zone and induce a semimetal-metal transition for silicene. Variation of the band structures exhibits strong anisotropy. Fermi velocity under uniaxial strain is found to be a strong function of the wave vector and changes slightly before the semimetal-metal transition. The work function increases significantly under uniaxial strains.
We also calculate the strain energy to investigate the mechanical response of silicene under uniaxial strain. Here, the strain energy ES is defined as the energy difference between systems with and without strain. The strain dependencies of ES and its derivative dES/dϵ are shown in Figure 2b. Over the strain range considered, ES increases with the increasing strain, while the system keeps the similar structure and remains in the elastic region. For small strain, the ES and dES/dϵ curves coincide for both types of uniaxial strains, and dES/dϵ increases linearly with respect to the strain. The linear behavior of the dES/dϵ curve indicates that the system is in the harmonic region. When the system goes into the anharmonic region, dES/dϵ changes nonlinearly and shows anisotropy for the AC and ZZ strains. In this region, dES/dϵ increases more quickly under the AC strain than under the ZZ strain. Thus, silicene is more rigid under stretch along the AC direction than along the ZZ direction, which is analogous with graphene [40, 41]. The dES/dϵ curves have maxima at large strains for both types of strains. The strain corresponding to the maximum dES/dϵ is the ultimate strain (ϵ*). For strain larger than ϵ*, imaginary phonon frequencies are expected to appear for specific wave vectors of acoustic waves, and the system will become metastable. This phenomenon is the so-called ‘phonon instability’ [40, 42, 43]. The ultimate strains for the AC and ZZ strains are 0.17 and 0.15, respectively. Both ultimate strains are slightly smaller than that of biaxial strain of 0.18 .
We theoretically study the mechanical and electronic properties of silicene under uniaxial strain. We find significant chirality effect on the mechanical and electronic properties of silicene. Our calculation shows that silicene remains gapless with uniaxial strain due to the Dirac point deviation and semimetal-metal transition. We find that the geometric structure and variable sp3/sp2 ratio of the chemical bond of silicene give rise to peculiar electronic properties of silicene under uniaxial strain, which are much different from those of graphene. The high Fermi velocity under uniaxial strain and strain tunable work function could promote potential applications of silicene in nanoelectronic devices.
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11204281 and 11102194). The authors would like to thank the Simulation Center of CAEP for the use of their computing facilities.
- Takeda K, Shiraishi K: Theoretical possibility of stage corrugation in Si and Ge analogs of graphite. Phys Rev B 1994, 50: 14916–14922. 10.1103/PhysRevB.50.14916View ArticleGoogle Scholar
- Krishnan R, Xie Q, Kulik J, Wang XD, Lu S, Molinari M, Gao Y, Krauss TD, Fauchet PM: Effect of oxidation on charge localization and transport in a single layer of silicon nanocrystals. J Appl Phys 2004, 96: 654–660. 10.1063/1.1751632View ArticleGoogle Scholar
- Nakano H, Mitsuoka T, Harada M, Horibuchi K, Nozaki H, Takahashi N, Nonaka T, Seno Y, Nakamura H: Soft synthesis of single‒crystal silicon monolayer sheets. Angew Chem 2006, 118: 6451–6454. 10.1002/ange.200600321View ArticleGoogle Scholar
- Kara A, Léandri C, Dávila ME, Padova P, Ealet B, Oughaddou H, Aufray B, Lay G: Physics of silicene stripes. J Supercond Nov Magn 2009, 22: 259–263. 10.1007/s10948-008-0427-8View ArticleGoogle Scholar
- Aufray B, Kara A, Vizzini S, Oughaddou H, Léandri C, Ealet B, Le Lay G: Graphene-like silicon nanoribbons on Ag(110): a possible formation of silicene. Appl Phys Lett 2010, 96: 183102–183103. 10.1063/1.3419932View ArticleGoogle Scholar
- De Padova P, Quaresima C, Ottaviani C, Sheverdyaeva PM, Moras P, Carbone C, Topwal D, Olivieri B, Kara A, Oughaddou H, Aufray B, Le Lay G: Evidence of graphene-like electronic signature in silicene nanoribbons. Appl Phys Lett 2010, 96: 261905–261903. 10.1063/1.3459143View ArticleGoogle Scholar
- Fleurence A, Friedlein R, Ozaki T, Kawai H, Wang Y, Yamada-Takamura Y: Experimental evidence for epitaxial silicene on diboride thin films. Phys Rev Lett 2012, 108: 245501.View ArticleGoogle Scholar
- Jamgotchian H, Colignon Y, Hamzaoui N, Ealet B, Hoarau JY, Aufray B, Bibérian JP: Growth of silicene layers on Ag(111): unexpected effect of the substrate temperature. J Phys Condens Matter 2012, 24: 172001. 10.1088/0953-8984/24/17/172001View ArticleGoogle Scholar
- Vogt P, De Padova P, Quaresima C, Avila J, Frantzeskakis E, Asensio MC, Resta A, Ealet B, Le Lay G: Silicene: compelling experimental evidence for graphenelike two-dimensional silicon. Phys Rev Lett 2012, 108: 155501.View ArticleGoogle Scholar
- Meng L, Wang Y, Zhang L, Du S, Wu R, Li L, Zhang Y, Li G, Zhou H, Hofer WA, Gao H-J: Buckled silicene formation on Ir(111). Nano Lett 2013, 13: 685–690. 10.1021/nl304347wView ArticleGoogle Scholar
- 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. 10.1021/jp311836mView ArticleGoogle Scholar
- Gao J, Zhang J, Liu H, Zhang Q, Zhao J: Structures, mobilities, electronic and magnetic properties of point defects in silicene. Nanoscale 2013, 5: 9785–9792. 10.1039/c3nr02826gView ArticleGoogle Scholar
- Gleskova H, Wagner S, Soboyejo W, Suo Z: Electrical response of amorphous silicon thin-film transistors under mechanical strain. J Appl Phys 2002, 92: 6224–6229. 10.1063/1.1513187View ArticleGoogle Scholar
- Ieong M, Doris B, Kedzierski J, Rim K, Yang M: Silicon device scaling to the sub-10-nm regime. Science 2004, 306: 2057–2060. 10.1126/science.1100731View ArticleGoogle Scholar
- Hong K-H, Kim J, Lee S-H, Shin JK: Strain-driven electronic band structure modulation of Si nanowires. Nano Lett 2008, 8: 1335–1340. 10.1021/nl0734140View ArticleGoogle Scholar
- Shiri D, Kong Y, Buin A, Anantram MP: Strain induced change of bandgap and effective mass in silicon nanowires. Appl Phys Lett 2008, 93: 073114–073113. 10.1063/1.2973208View ArticleGoogle Scholar
- Durgun E, Tongay S, Ciraci S: Silicon and III-V compound nanotubes: structural and electronic properties. Phys Rev B 2005, 72: 075420.View ArticleGoogle Scholar
- Cahangirov S, Topsakal M, Aktürk E, Şahin H, Ciraci S: Two- and one-dimensional honeycomb structures of silicon and germanium. Phys Rev Lett 2009, 102: 236804.View ArticleGoogle Scholar
- Hanna E, Sébastien V, Abdelkader K, Boubekeur L, Hamid O: Silicene structures on silver surfaces. J Phys Condens Matter 2012, 24: 314211. 10.1088/0953-8984/24/31/314211View ArticleGoogle Scholar
- Gao J, Zhao J: Initial geometries, interaction mechanism and high stability of silicene on Ag(111) surface. Sci Rep 2012, 2: 861.Google Scholar
- Sahin H, Cahangirov S, Topsakal M, Bekaroglu E, Akturk E, Senger RT, Ciraci S: Monolayer honeycomb structures of group-IV elements and III-V binary compounds: first-principles calculations. Phys Rev B 2009, 80: 155453.View ArticleGoogle Scholar
- Liu G, Wu MS, Ouyang CY, Xu B: Strain-induced semimetal-metal transition in silicene. EPL (Europhysics Lett) 2012, 99: 17010. 10.1209/0295-5075/99/17010View ArticleGoogle Scholar
- Peng Q, Wen X, De S: Mechanical stabilities of silicene. RSC Advances 2013, 3: 13772–13781. 10.1039/c3ra41347kView ArticleGoogle Scholar
- Mohan B, Kumar A, Ahluwalia P: Electronic and optical properties of silicene under uni-axial and bi-axial mechanical strains: a first principle study. Physica E: Low-dimensional Syst Nanostructures 2014, 61: 40–47.View ArticleGoogle Scholar
- Roman RE, Cranford SW: Mechanical properties of silicene. Comput Mater Sci 2014, 82: 50–55.View ArticleGoogle Scholar
- Yang C-h, Yu Z-Y, Lu P-F, Liu Y-m, Manzoor S, Li M, Zhou S: The mechanical properties and stabilities of pristine, hydrogenated, and fluorinated silicene under tension. International Society for Optics and Photonics: SPIE MOEMS-MEMS; San Francisco; 2014:89750K-89759.Google Scholar
- Qin R, Wang C-H, Zhu W, Zhang Y: First-principles calculations of mechanical and electronic properties of silicene under strain. AIP Adv 2012, 2: 022159–022156. 10.1063/1.4732134View ArticleGoogle Scholar
- Zhao H: Strain and chirality effects on the mechanical and electronic properties of silicene and silicane under uniaxial tension. Phys Lett A 2012, 376: 3546–3550. 10.1016/j.physleta.2012.10.024View ArticleGoogle Scholar
- Wang Y, Ding Y: Strain-induced self-doping in silicene and germanene from first-principles. Solid State Commun 2013, 155: 6–11.View ArticleGoogle Scholar
- Gui G, Li J, Zhong J: Band structure engineering of graphene by strain: first-principles calculations. Phys Rev B 2008, 78: 075435.View ArticleGoogle Scholar
- Farjam M, Rafii-Tabar H: Comment on “Band structure engineering of graphene by strain: First-principles calculations”. Phys Rev B 2009, 80: 167401.View ArticleGoogle Scholar
- Pereira VM: Castro Neto AH. Peres NMR: Tight-binding approach to uniaxial strain in graphene. Phys Rev B 2009, 80: 045401.Google Scholar
- Choi S-M, Jhi S-H, Son Y-W: Controlling energy gap of bilayer graphene by strain. Nano Lett 2010, 10: 3486–3489. 10.1021/nl101617xView ArticleGoogle Scholar
- Choi S-M, Jhi S-H, Son Y-W: Effects of strain on electronic properties of graphene. Phys Rev B 2010, 81: 081407.View ArticleGoogle Scholar
- Li Y, Jiang X, Liu Z, Liu Z: Strain effects in graphene and graphene nanoribbons: the underlying mechanism. Nano Res 2010, 3: 545–556. 10.1007/s12274-010-0015-7View ArticleGoogle Scholar
- Delley B: An all-electron numerical method for solving the local density functional for polyatomic molecules. J Chem Phys 1990, 92: 508. 10.1063/1.458452View ArticleGoogle Scholar
- Delley B: From molecules to solids with the DMol[sup 3] approach. J Chem Phys 2000, 113: 7756. 10.1063/1.1316015View ArticleGoogle Scholar
- Monkhorst HJ, Pack JD: Special points for Brillouin-zone integrations. Phys Rev B 1976, 13: 5188–5192. 10.1103/PhysRevB.13.5188View ArticleGoogle Scholar
- Landau LD, Pitaevskii LP, Lifshitz EM, Kosevich AM: Theory of Elasticity, Third Edition: Volume 7. Oxford, UK: Butterworth-Heinemann; 1986.Google Scholar
- Liu F, Ming P, Li J: Ab initio calculation of ideal strength and phonon instability of graphene under tension. Phys Rev B 2007, 76: 064120.View ArticleGoogle Scholar
- Zhao H, Min K, Aluru NR: Size and chirality dependent elastic properties of graphene nanoribbons under uniaxial tension. Nano Lett 2009, 9: 3012–3015. 10.1021/nl901448zView ArticleGoogle Scholar
- Topsakal M, Cahangirov S, Ciraci S: The response of mechanical and electronic properties of graphane to the elastic strain. Appl Phys Lett 2010, 96: 091912. 10.1063/1.3353968View ArticleGoogle Scholar
- Kaloni TP, Cheng YC, Schwingenschlögl U: Hole doped Dirac states in silicene by biaxial tensile strain. J Appl Phys 2013, 113: 104305–104304. 10.1063/1.4794812View ArticleGoogle Scholar
- Goerbig MO, Fuchs J-N, Montambaux G, Piéchon F: Tilted anisotropic Dirac cones in quinoid-type graphene and α-(BEDT-TTF)2I3. Phys Rev B 2008, 78: 045415.View ArticleGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.