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
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.
Results and discussion
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.
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