Strain-Induced Semimetal-Metal Transition in Silicene

OFFPRINT Strain-induced semimetal-metal transition in silicene

G. Liu, M. S. Wu, C. Y. Ouyang and B. Xu EPL, 99 (2012) 17010

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Strain-induced semimetal-metal transition in silicene

G. Liu, M. S. Wu, C. Y. Ouyang and B. Xu(a)

College of Physics and Communication Electronics, Jiangxi Normal University - Nanchang, Jiangxi, 330022, PRC

received 16 April 2012; accepted in ﬁnal form 19 June 2012 published online 11 July 2012

PACS 73.22.-f – Electronic structure of nanoscale materials and related systems PACS 71.15.Mb – Density functional theory, local density approximation, gradient and other corrections

Abstract – The eﬀect of the tensile strain on the electronic structure of the silicene is studied by using ﬁrst-principles density functional theory. It is found that a semimetal-metal transition occurs when an in-plane strain larger than 7.5% is applied in silicene. The downward movement of the lowest conduction band at Γ-point, which originates from the weakened interaction between neighboring Si atoms, leads to the transition. The proposed mechanical control of the electronic properties will widen the application of the silicene in Si-based nanotechnology.

Silicene, a two-dimensional (2D) monolayer honeycomb field [21]. If the semimetal-metal transition can be real- structure of silicon atoms, has recently attracted intensive ized, the potential applications of silicene will be wider in attention from the scientific community [1–12]. Compared the future nanotechnology. with graphene, the hottest 2D materials in the past several In this letter, we study the response of silicene under years, silicene could have more potential application in the the biaxial tensile strain. The transition from semimetal future Si-based nanotechnology, because they could enable to metal is predicted in silicene when the strain is beyond the electronics industry to produce fast nanoscale elec- 7.5%. Energy band structures reveal that the transition tronics without retooling to use carbon instead of silicon. results from the downward shift of the lowest conduction Experimentally, Nakano et al. reported the synthesis of band at Γ-point as increasing the strain. Further analysis silicene via the chemical exfoliation of CaSi2 [13]. Recently, of partial charge density shows that the downward shift of the possible growth of silicene nanoribbon on Ag (100) the lowest conduction band is related to the weakening of or Ag (110) substrates has been reported [14–17]. Since the π∗ bond due to the increase of the Si-Si bond length. silicon prefers sp3 hybridization instead of sp2, silicene All calculations were performed using the Vienna ab is energetically favorable as a low-buckled (LB) struc- initio simulation package (VASP) code, and adopting ture [18,19]. More interestingly, theoretical calculations the projector augmented-wave (PAW) potentials [22] on silicene show that the π and π∗ bands linearly cross and Perdew-Burke-Ernzerhof (PBE) generalized gradient at the Fermi level, reflecting the semimetallic or zero- approximation (GGA) exchange correlation functional gap semiconducting character of silicene [18,19]. Similar [23]. The energy cutoff for expansion of wave functions to graphene, therefore, it is important to modify a silicene and potentials is 550 eV. Monkhorst-Pack special k-point sheet in order to tailor its properties. For example, hydro- method [24] was used with a grid of 40 × 40 × 1. The genation of silicene can open a gap [3,7]. By using ab initio entire systems were relaxed by conjugate gradient method calculations, Ni et al. predicted that a vertical electric until the force on each atom is less than 0.001 eV/A.˚ The field is able to open a band gap in semimetallic single- 1 × 1 unit cell was employed in our calculations. We set layer buckled silicene [20]. They also found that the size up a vacuum region of 11.76 A˚ along the direction vertical of the band gap can be linearly tuned by the intensity of to the silicene layer to avoid the interaction between two the electric field. Though many efforts have been focused adjacent images. on the transition from semimetal to semiconductor for The relaxed structure of silicene is shown in fig. 1. The silicene, the study related to its change from semimetal optimized lattice parameter a is 3.86 A,˚ in agreement with to metal is not available in the literature except for the previous results (a =3.86 A)˚ [25]. The Si-Si bond length case subjected to a sufficiently high transverse electric is calculated to be 2.27 A,˚ showing a contraction of the bond compared with bulk Si. The buckling parameter Δ (a)E-mail: [email protected] (as shown in fig. 1(a)) is 0.46 A,˚ also consistent with other

17010-p1 G. Liu et al.

without strain present the semimetallic character, with π and π∗ bands both crossing the Fermi level at the K-point, as shown in fig. 2(a). When the strain increases to be 2.5%, it is found that the energy band structure preserves the semimetallic property except for a somewhat downward shift of the conduction band minimum at Γ-point (CBM-Γ). Further increasing the strain, CBM- Γ decreases more. When the strain reaches 7.5%, CBM-Γ Fig. 1: (Color online) Schematic views of geometric structure touches the Fermi level. In this case, the silicene is also for silicene. (a) Top view; (b) side view. Δ is the buckling regarded as a semimetal. However, the semimetallic char- parameter. acter is changed when the strain exceeds 7.5%. As shown in fig. 2(e), the lowest conduction band crosses the Fermi level near the Γ-point, leading to a metallic behavior with a low density of states near the Fermi level. Simultane- ously, the highest valence band is pushed upward near the K-point, also crossing the Fermi level. As increasing the strain, more parts of the lowest conduction band near the Γ-point drop and become filled. In order to study the relationship between the strain and the decrease of CBM-Γ, we plotted the energy difference of CBM-Γ with respect to the Fermi level as a function of the tensile strain, as shown in the insert of fig. 2(f). It is found that the energy difference of CBM-Γ with respect to the Fermi level decreases almost linearly as increasing the tensile strain. The value changes from about 2.0 eV to −0.72 eV, with the strain ranging from 0.0% to 12.5%. Obviously, the energy of CBM-Γ is significantly affected by the external strain. The situation is somewhat different from that of graphene. Graphene without strain has a direct zero band gap between π and π∗ bands crossing at the K-point of the 2D hexagonal Brillouin zone, which is similar to that of silicene. However, graphene with a symmetrical tensile strain distribution shows no significant changes in the electronic structure, and is always a zero–band-gap semiconductor even if the large strain (ε = 30%) is applied [27,28]. Therefore, the transition from semimetal to metal is diffi- cult to be observed in graphene under the tensile strain. In order to explain the reason why the energy of Fig. 2: (Color online) (a)–(f) Energy band structures of silicene CBM-Γ is essentially affected by the strain in silicene, with strain ε =0.0%, 2.5%, 5.0%, 7.5%, 10.0%, and 12.5%, we calculated the band decomposed charge density of the respectively. Fermi levels are all set to 0 eV. The insert in (f) Γ-point for the lowest conduction band, which can be shows the energy difference of CBM-Γ with respect to the Fermi seen in fig. 3. Two extreme cases are considered in our level as a function of strain. calculations. Figures 3(a) and (b) correspond to the case without strain, while figs. 3(c) and (d) to the case with ε =12.5%. Basically, it could be found that in the case report [20]. To study the elastic property of silicene, we ∗ defined the modified Young’s modulus without strain, the charge density of CBM-Γ shows π bonds character. The charge densities primarily locate 2 1 ∂ E around Si atoms. The composed orbitals possess the Ys = , (1) 2 hybridized character of the s and pz orbitals [18]. When S0 ∂ε ε=0 the strain reaches the value of 12.5%, however, the charge where S0, E,andε are the equilibrium area, total energy, densities move to one side (top or bottom of the Si atoms), and strain, respectively. The calculated Young’s modulus suggesting the delocalization. Therefore, the interaction ∗ for the silicene is 0.178TPa nm, which is significantly lower between the hybridized s-pz orbitals, as well as the π than that of graphene (0.420 TPa nm) [26]. bond, is weakened, which thus results in the decrease of The energy bands of the silicene when the applied tensile the energy level of CBM-Γ. strain (ε =Δa/a) ranging from 0.0% to 12.5% are shown Considering that the strain could affect the structure in figs. 2(a)–(f). Obviously, the energy bands of the silicene of the silicene, we carefully examined the structures of

17010-p2 Semimetal-metal transition in silicene

Fig. 4: (Color online) (a) Energy band structures of buckled silicene (solid line) and graphene-like silicene (dashed line) with strain ε =0.0%; (b) energy band structure of graphene- like silicene with strain ε =0.0% (solid line), and ε =12.5% (dashed line).

7.5%. Therefore, tensile and compressive strain could be both used to tune the conductive of the silicene. From the application point of view, however, the tensile strain Fig. 3: (Color online) Band decomposed charge density of the is more convenient to realize for 2D materials. Another conduction band minimum at Γ-point with different strain. (a), (b): top view and side view for ε =0.0%; (c), (d): top view reason why we mainly considered the tensile strain is that and side view for ε =12.5%. the silicene is unstable from the lattice dynamics point of view when the small compressive strain (5%) is applied, because the imaginary frequencies can be found in this the silicene with ε =0.0% and ε =12.5%. Compared with case. the case without strain, two features could be found for In conclusion, we studied the electronic structure of the structure with ε =12.5%: one is that the buckling of silicene in the presence of tensile strain using density silicene is lowered from 0.46 Ato0.34˚ A,˚ the other is that functional theory. Silicene keeps its semimetal character the Si-Si bond length is enlarged from 2.27 Ato2.53˚ A.˚ To until the strain is 7.5%. When the strain is larger than study the effect of the buckling on the electronic structure, 7.5%, silicene transforms into a metal. According to the we compared the band structure of buckled silicene with energy band, we found that this transition results from that of planar graphene-like silicene for the case without the downward shift of the lowest conduction band at the strain, which can be seen in fig. 4(a). The solid line Γ-point. Band decomposed charge density reveals that the ∗ corresponds to the case with buckling, and the dashed weakening of the π bond is the underlying reason. line to that without buckling. Clearly, except for the slight downward shift of the bands for the planar configuration, ∗∗∗ no other essential difference could be found between the planar silicene and the buckled one. Therefore, the change This work is supported by the National Natural Science of the energy of CBM-Γ is insignificant even if the buckling Foundation of China (Grant No. 10904054), the Natural is lowered to zero, which is the extreme case. According Science Foundation of Jiangxi (Grant No. 2009GQW008 to the results mentioned above, obviously, the change of and 2010GZW0028), the Foundation of Jiangxi Normal the electronic structure is dominated by the latter factor, University (Grant No. 2261). namely the elongation of the bond lengths. In order to prove this, we also considered the graphene-like silicene REFERENCES without buckling. The energy bands are calculated for the silicene with strain ε =0.0%, and ε =12.5%, as shown in [1] Buzman-Verri´ G. G. and Lew Yan Voon L. C., Phys. fig. 4(b). The solid line corresponds to the case without Rev. B, 76 (2007) 075131. strain, and the dashed line to that with strain ε =12.5%. [2] Lalmi B., Oughaddou H., Enriquez H., Kara A., It is found that the energy of CBM-Γ is also lower than the Vizzini S., Ealet B. and Aufray B., Appl. Phys. Lett., Fermi level for this graphene-like silicene when the applied 97 (2010) 223109. strain reaches 12.5%. In the graphene-like silicene the [3] Lew Yan Voon L. C., Sandberg E., Aga R. S. and 97 strain merely affects the Si-Si bond length. This suggests Farajian A. A., Appl. Phys. Lett., (2010) 163114. Wang S. Q. Phys. Chem. Chem. Phys. 13 that the weakening of the Si-Si bond is the most important [4] , , (2011) 11929. [5] Liu C. C., Feng W. X. and Yao Y. G., Phys. Rev. Lett., drive force for the semimetal-metal transition in silicene 107 (2011) 076802. when the biaxial tensile strain is applied. [6] Buzman-Verri´ G. G. and Lew Yan Voon L. C., Actually, the electronic properties of silicene in the J. Phys.: Condens. Matter, 23 (2011) 145502. presence of compressive strain are also studied (not shown [7] Houssa M., Sanlise E., Sankaran K., Pourtois G., here). Our results reveal that the silicene would behave as Afanas’ev V. V. and Stesmans A., Appl. Phys. Lett., a metal when the applied compressive strain is beyond 98 (2011) 223107.

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