Home
Search
Collections
Journals
About
Contact us
My IOPscience
Nonmetallic substrates for growth of silicene: an ab initio prediction
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 185002 (http://iopscience.iop.org/0953-8984/26/18/185002) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 128.103.149.52 This content was downloaded on 22/06/2014 at 16:12
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 185002 (4pp)
doi:10.1088/0953-8984/26/18/185002
Nonmetallic substrates for growth of silicene: an ab initio prediction S Kokott1, P Pflugradt, L Matthes and F Bechstedt Institut für Festkörpertheorie und -optik, Friedrich-Schiller-Universität and European Theoretical Spectroscopy Facility (ETSF), Max-Wien-Platz 1, 07743 Jena, Germany E-mail: [email protected] and [email protected] Received 20 January 2014, revised 17 February 2014 Accepted for publication 19 February 2014 Published 14 April 2014 Abstract
By means of first-principles calculations we predict the stability of silicene layers as buckled honeycomb lattices on Cl-passivated Si(1 1 1) and clean CaF2(1 1 1) surfaces. The van der Waals interaction between silicene and the inert substrate stabilizes the adsorbate system while not destroying the Si pz-derived linear bands forming Dirac cones at the Brillouin zone corners. Only small gaps of about 3 and 52 meV are opened. Keywords: silicene, first principles calculations, Cl-passivated Si(1 1 1) surface, CaF2(1 1 1) surface, Dirac cones (Some figures may appear in colour only in the online journal)
1. Introduction
adsorbate system. The origin of these conical linear bands is traced back to the interaction of silicene with the silver substrate [14–16]. Si-based Dirac cones are the subject of an ongoing controversial discussion [8], [14–19]. In this paper, we investigate, by means of parameter-free DFT calculations, silicene deposited on two novel substrates, Cl-passivated Si(1 1 1)1 × 1 and clean CaF2(1 1 1)1 × 1 surfaces, as indicated in figure 1: (i) The substrates possess a fundamental gap. (ii) The silicene and their surface lattices are nearly commensurable. (iii) The chemical interaction between silicene and the substrates should be weak because of the absence of dangling bonds. We especially study the bonding, energetic, structural, and resulting electronic properties of the Si overlayers.
The graphene-like allotrope of silicon, silicene, represents a buckled two-dimensional (2D) honeycomb lattice [1]. Despite the partly sp3 bonding, the theory predicts Dirac cones at the corner points K and K′ of the 2D hexagonal Brillouin zone (BZ) for freestanding silicene sheets. The accompanying massless Dirac fermions in the low-energy regime provide unique electronic, IR-optical, and transport properties [2–5]. In contrast to other novel 2D materials, silicene can be ideally used in current Si-based device technologies. The major problem of the application of silicene is its preparation. Recently, the epitaxial growth of silicene on metallic and halfmetallic substrates such as Ag(1 1 1) [6–9], ZrB2 [10], and Ir(1 1 1) [11] has been reported. Theory predicts the use of hydrogen-passivated Si(1 1 1) and Ge(1 1 1) substrates because of their lattice match [12]. For deposition of silicene on Ag(1 1 1), two ARPES experiments [6, 9] but also the mapping of differential conductance [8] have been claimed to confirm Si pz-based conical linear bands. Recently, Dirac cones have been reported for bilayer silicene on Ag(1 1 1) [13]. However, theoretical studies based on the density functional theory (DFT) showed the absence of Si-derived conical linear bands for the mostly studied 3 × 3 silicene on Ag(1 1 1)4 × 4
2. Methods The structural optimization and total-energy calculations are performed within the DFT as implemented in the Vienna Ab-initio Simulation Package (VASP) [20]. The van der Waals (vdW) interaction is included according to Dion et al [21]. The correlation taken in local density approximation (LDA) is corrected by a nonlocal correction that accounts for dispersion forces. The exchange functional in generalized gradient approximation (GGA) is used in the version
1
Author to whom any correspondence should be addressed.
0953-8984/14/185002+4$33.00
1
© 2014 IOP Publishing Ltd Printed in the UK
S Kokott et al
J. Phys.: Condens. Matter 26 (2014) 185002
Figure 1. Silicene adsorbed on (a) Cl-passivated Si(1 1 1)1 × 1 and (b) clean CaF2(1 1 1)1 × 1 surface. Si atoms: blue, Cl: green, Ca:
yellow, F: red.
5
Parameter
Freestanding Cl/Si(1 1 1)1 × 1 CaF2(1 1 1)1 × 1
a (Å) Δ (Å) D (Å) vF (106 m s−1) Eg (meV) EDirac (eV)
3.857 0.480 — 0.53 0 0
3.861 0.490 3.12 0.48 3 0.21
Total energy (eV/1×1 cell)
Table 1. Lattice constant a and buckling amplitude Δ of freestanding and adsorbed silicene from total-energy DFT calculations including vdW. The distance D between the bottom silicene atom and the Cl− or F− ion layer characterizes the adsorbate substrate interaction. Parameters of the resulting 2D band structure of silicene near a K or K′ point, the Fermi velocity vF and the energy gap Eg are also listed. In addition, the energy shift of the Dirac point with respect to the Fermi level EDirac is given.
3.878 0.431 2.70 0.49 52 0
4
Bulklike
Silicene
3
4.1eV
2 1 0
1.3eV
-1 -2
0
Configuration coordinate
1
Figure 2. Total energy along the path from configuration 0 (silicene on Cl/Si(1 1 1)1 × 1) to configuration 1 (bulk-like Cl/Si(1 1 1)1 × 1 with two more Si layers) including vdW interaction. Configuration 0 defines the energy zero.
optB86b. Details of the implementation of the vdW functional are described by Klimeš et al [22]. The pseudopotentials are generated using the projector-augmented-wave (PAW) method [23]. The plane-wave expansion is limited by a cutoff energy of 280 and 400 eV for the Cl/Si(1 1 1) and CaF2 system, respectively. Despite the well-known DFT underestimation of the gap of Si and CaF2 bulk and of the Fermi velocity vF of the massless Dirac particles in silicene [2, 4, 24], the resulting electronic structures are sufficient to demonstrate the appearance of characteristic features such as Dirac cones. The Cl-passivated Si(1 1 1)1 × 1 and the CaF2(1 1 1)1 × 1 surfaces are simulated by repeated symmetric slabs of 18 and 24 atomic layers respectively. In the Si case both sides are covered by chlorine. In the CaF2(1 1 1) slabs, fluorine layers form the surface. Additionally, on each slab surface one silicene sheet is adsorbed. The vacuum between two slabs is chosen to be 20 Å. The slightly biaxially strained silicene, the chlorine layer, and the uppermost atomic layers in the slab are allowed to relax using a conjugate-gradient algorithm until the Hellmann–Feynman forces are below 0.01 meV Å−1. The BZ of the resulting superlattice structure is sampled with a 16 × 16 × 1 k-point grid. Many different starting
geometries with different displacements of the strained silicene overlayer relative to positions of the Cl− or F− surface atoms are investigated. 3. The substrates Upon reaction of Cl atoms with the cleavage Si(1 1 1)7 × 7 surface and subsequent repeated annealing, the favorable bulk like 1 × 1 surface [25] appears. A stable monolayer of Cl− ions covers the Si(1 1 1)1 × 1 surface with almost Si+ ions in the topmost atomic layer, even when the sample is held at 550°C. The projected fundamental gap with a minimum value of 1.1 eV is free of surface states. The Cl/Si(1 1 1)1 × 1 surface is indeed passivated, while the 2D hexagonal symmetry of the uppermost Si layer is conserved. The Si(1 1 1)1 × 1 surface is perfectly lattice-matched to the Bravais lattice of the 1 × 1 silicene sheet with a deviation of only 0.1% (see theoretical lattice constants in table 1). 2
S Kokott et al
J. Phys.: Condens. Matter 26 (2014) 185002
Figure 3. Band structure of silicene adsorbed on (a) Cl/Si(1 1 1)1 × 1 and (b) CaF2(1 1 1)1 × 1, respectively. The silicene character obtained by projection onto corresponding Si atoms is indicated by black dots with varying intensity of the color. The red-dashed horizontal line represents the Fermi level.
The results for a F−-terminated CaF2(1 1 1)1 × 1 substrate are rather similar. However, as a consequence of the slightly increased biaxial strain, the buckling amplitude of silicene is reduced (see table 1). The distance D = 2.70 Å between overlayer and substrate is somewhat smaller than in the Cl/Si(1 1 1)1 × 1 case but still indicates a influence of the vdW bonding. To investigate the influence of the 1 × 1 unit-cell constraint, we have also studied 3 × 3 lateral unit cells for both substrates, Cl/Si(1 1 1) and CaF2(1 1 1). Despite significant initial displacements, the silicon overlayers relax back into the silicene geometry optimized within 1 × 1 cells. This result supports the statement of a stable configuration. The band structures of the silicene-covered (a) Cl-passivated Si(1 1 1)1 × 1 surface and (b) CaF2(1 1 1) substrate are displayed in figure 3. The regions of the dense slab bands mainly indicate the projected bulk (a) Si or (b) CaF2 band structures. The striking differences in the chemical bonding of the substrates are indicated by the completely different band width and energy gaps. The gaps are free of surface states. Only in the pockets of the projected valence bands do such states associated with Cl–Si bonds appear near K and M. The electronic-structure modifications, due to the silicene overlayer, are indicated by additional bands whose chemical nature has been determined by projections onto the silicene atoms. As a consequence of the weak vdW bonding one observes the almost unchanged band structure of freestanding silicene. This is especially true for the Dirac cones around K within the fundamental gaps. The corresponding band states are still derived mainly from Si pz orbitals. The weak vdW bonding only slightly modifies the bands near the Fermi energy and a K point. The Fermi velocities of the Dirac cones are conserved (see table 1). In the case of the Cl/Si(1 1 1) substrate, practically no gap is opened. Only the Fermi level is shifted by 0.2 eV toward lower energies, i.e., holes are created in the π-state-derived cone. The projected bulk conduction band minima near M indicate a small electron transfer into the substrate. On CaF2(1 1 1) the silicene overlayer opens a small gap between the π* and π cones. The Fermi energy remains in the gap center.
The natural cleavage CaF2(1 1 1)1 × 1 surface is terminated by a complete triple layer of F−–Ca2+–F− monoatomic layers with a topmost F− layer for electrostatic reasons [26]. The latter one consists of a trigonal arrangement of F− ions spaced by 3.878 Å (see table 1), that leads to a lattice mismatch to silicene of 0.5%. Calculations show that such a small tensile strain does not destroy the Dirac cones. Because of the inertness of the CaF2(1 1 1) surface, it is suggested as a convenient substrate for a van der Waals epitaxy of almost strain-free overlayers [27]. The completely filled outermost electron shell of the F− ions makes the uppermost surface triple layer inert. The silicene atoms should not chemically react with an intact triplelayer surface, similar to the behavior of oxygen atoms [28].
4. Results In the resulting minimum-energy structure of silicene on Cl/Si(1 1 1)1 × 1 the two silicene atoms in the unit cell occupy high-symmetric positions at the long diagonal of the rhombus representing the primitive 1 × 1 surface cell. The buckling amplitude Δ of the silicene sheet is little influenced. The stable position of the sheet in a distance of D = 3.12 Å (see table 1) is mainly caused by the vdW dispersion forces. Despite the large distance, the binding energy EB = 215 meV/cell is larger than for silicene on H/Si(1 1 1)1 × 1 [12] because of the increased dipole moment of the Cl−-Si+ bonds. This value is large compared to the thermal energy kBT = 25 meV at room temperature. There is an energy barrier between the silicene adsorbate system (configuration 0) compared to the Cl-passivated Si(1 1 1)1 × 1 substrate with two more Si layers (configuration 1) of about 4.1 eV/1 × 1 cell (see figure 2). To approximate this barrier we displace the two Si atoms of silicene and the Cl atom in 18 steps toward configuration 1 on condition that the distance of two atoms never comes below the sum of the covalent radii. Of course, the calculated energy barrier is very high due to the constraint of a 1 × 1 cell, but it clearly shows that the silicene configuration on an intact Cl-passivated Si(1 1 1) surface represents a true local minimum on the total-energy surface, and that this configuration should be stable against thermal fluctuations. 3
S Kokott et al
J. Phys.: Condens. Matter 26 (2014) 185002
[10] Fleurence A, Friedlein R, Ozaki T, Kawai H, Wang Y and Yamada-Takamura Y 2012 Experimental evidence for epitaxial silicene on diboride thin films Phys. Rev. Lett. 108 245501 [11] Meng L et al 2013 Buckled silicene formation on Ir(1 1 1) Nano Lett. 13 685–90 [12] Kokott S, Matthes L and Bechstedt F 2013 Silicene on hydrogen-passivated Si(1 1 1) and Ge(1 1 1) substrates Physica Status Solidi: Rapid Res. Lett. 7 538–41 [13] Avila J, De Padova P, Cho S, Colambo I, Lorcy S, Quaresima C, Vogt P, Resta A, Le Lay G and Asensio C M 2013 Presence of gapped silicene-derived band in the prototypical (33) silicene phase on silver (1 1 1) surfaces J. Phys.: Condens. Matter 25 262001 [14] Lin C-L, Arafune R, Kawahara K, Kanno M, Tsukahara N, Minamitani E, Kim Y, Kawai M and Takagi N 2013 Substrate-induced symmetry breaking in silicene Phys. Rev. Lett. 110 076801 [15] Gori P, Pulci O, Ronci F, Colonna S and Bechstedt F 2013 Origin of Dirac-cone-like features in silicon structures on Ag(1 1 1) and Ag(1 1 0) J. Appl. Phys. 114 113710 [16] Pflugradt P, Matthes L and Bechstedt F 2014 Silicene-derived phases on Ag(1 1 1) substrate versus coverage: ab initio studies Phys. Rev. B 89 035403 [17] Arafune R, Lin C-L, Nagao R, Kawai M and Takagi N 2013 Comment on ‘Evidence for Dirac fermions in a honeycomb lattice based on silicon’ Phys. Rev. Lett. 110 229701 [18] Chen L, Liu C-C, Feng B, He X, Cheng P, Ding Z, Meng S, Yao Y and Wu K 2013 Chen et al reply: Phys. Rev. Lett. 110 229702 [19] Tsoutsou D, Xenogiannopoulou E, Golias E, Tsipas P and Dimoulas A 2013 Evidence for hybrid surface metallic band in (4 × 4) silicene on Ag(1 1 1) Appl. Phys. Lett. 103 231604 [20] Kresse G and Furthmüller J 1996 Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set Phys. Rev. B 54 11169–86 [21] Dion M, Rydberg H, Schr E, Langreth D C and Lundqvist B I 2004 Van der Waals density functional for general geometries Phys. Rev. Lett. 92 246401 [22] Klimeš J, Bowler D R and Michaelides A 2011 Van der Waals density functionals applied to solids Phys. Rev. B 83 195131 [23] Kresse G and Joubert D 1999 From ultrasoft pseudopotentials to the projector augmented-wave method Phys. Rev. B 59 1758 75 [24] Huang S, Kang W and Yang Li 2013 Electronic structure and quasiparticle bandgap of silicene structures Appl. Phys. Lett. 102 133106 [25] Boland J J and Villarrubia J S 1990 Formation of Si(1 1 1)–(1 × 1)Cl Phys. Rev. B 41 9865–70 [26] Tasker W P 1979 The stability of ionic crystal surfaces J. Phys. C: Solid State Phys. 12 4977 [27] Koma A 1992 Van der Waals epitaxy—a new epitaxial growth method for a highly lattice-mismatched system Thin Solid Films 216 72–6 [28] Saiki K, Sato Y and Koma A 1989 Adsorption of oxygen on electron-bombarded CaF2 (1 1 1) surfaces Japan. J. Appl. Phys. 28 L134–7
5. Conclusions Summarizing, by means of first-principles calculations we have shown that the Cl-passivation of Si(1 1 1) and the cleavage of CaF2 lead to inert surfaces formed by halogen ions Cl− or F− with completely filled valence shells on top. The silicene with a buckling similar to the freestanding 2D system forms a vdW-bonded adsorbate. The outstanding properties known for freestanding silicene are preserved for the slab system, because of the weak bonding. We suggest intensive experimental studies of the deposition of silicene on the two investigated substrates. In contrast to the silicene/Ag(1 1 1) adsorbate system with strong chemical bonds, the electronic structure of silicene should be detectable within the fundamental gaps of the studied substrates. Acknowledgments LM acknowledges financial support of the Carl-Zeiss Foundation. References [1] Durgun E, Tongay S and Ciraci S 2005 Silicon and III–V compound nanotubes: structural and electronic properties Phys. Rev. B 72 075420 [2] Guzmán-Verri G G and Lew Yan Voon L C 2007 Electronic structure of silicon-based nanostructures Phys. Rev. B 76 075131 [3] Cahangirov S, Topsakal M, Aktürk E, Şahin H and Ciraci S 2009 Two- and one-dimensional honeycomb structures of silicon and germanium Phys. Rev. Lett. 102 236804 [4] Bechstedt F, Matthes L, Gori P and Pulci O 2012 Infrared absorbance of silicene and germanene Appl. Phys. Lett. 100 261906 [5] Matthes L, Gori P, Pulci O and Bechstedt F 2013 Universal infrared absorbance of two-dimensional honeycomb group-IV crystals Phys. Rev. B 87 035438 [6] Vogt P, De Padova P, Quaresima C, Avila J, Frantzeskakis E, Asensio M C, Resta A, Ealet B and Le Lay G 2012 Silicene: compelling experimental evidence for graphenelike two-dimensional silicon Phys. Rev. Lett. 108 155501 [7] Lin C-L, Arafune R, Kawahara K, Tsukahara N, Minamitani E, Kim Y, Takagi N and Kawai M 2012 Structure of silicene grown on Ag(1 1 1) Appl. Phys. Express 5 045802 [8] Chen L, Liu C-C, Feng B, He X, Cheng P, Ding Z, Meng S, Yao Y and Wu K 2012 Evidence for Dirac fermions in a honeycomb lattice based on silicon Phys. Rev. Lett. 109 056804 [9] De Padova P et al 2013 Evidence of Dirac fermions in multilayer silicene Appl. Phys. Lett. 102 163106
4
Search
Collections
Journals
About
Contact us
My IOPscience
Nonmetallic substrates for growth of silicene: an ab initio prediction
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 185002 (http://iopscience.iop.org/0953-8984/26/18/185002) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 128.103.149.52 This content was downloaded on 22/06/2014 at 16:12
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 185002 (4pp)
doi:10.1088/0953-8984/26/18/185002
Nonmetallic substrates for growth of silicene: an ab initio prediction S Kokott1, P Pflugradt, L Matthes and F Bechstedt Institut für Festkörpertheorie und -optik, Friedrich-Schiller-Universität and European Theoretical Spectroscopy Facility (ETSF), Max-Wien-Platz 1, 07743 Jena, Germany E-mail: [email protected] and [email protected] Received 20 January 2014, revised 17 February 2014 Accepted for publication 19 February 2014 Published 14 April 2014 Abstract
By means of first-principles calculations we predict the stability of silicene layers as buckled honeycomb lattices on Cl-passivated Si(1 1 1) and clean CaF2(1 1 1) surfaces. The van der Waals interaction between silicene and the inert substrate stabilizes the adsorbate system while not destroying the Si pz-derived linear bands forming Dirac cones at the Brillouin zone corners. Only small gaps of about 3 and 52 meV are opened. Keywords: silicene, first principles calculations, Cl-passivated Si(1 1 1) surface, CaF2(1 1 1) surface, Dirac cones (Some figures may appear in colour only in the online journal)
1. Introduction
adsorbate system. The origin of these conical linear bands is traced back to the interaction of silicene with the silver substrate [14–16]. Si-based Dirac cones are the subject of an ongoing controversial discussion [8], [14–19]. In this paper, we investigate, by means of parameter-free DFT calculations, silicene deposited on two novel substrates, Cl-passivated Si(1 1 1)1 × 1 and clean CaF2(1 1 1)1 × 1 surfaces, as indicated in figure 1: (i) The substrates possess a fundamental gap. (ii) The silicene and their surface lattices are nearly commensurable. (iii) The chemical interaction between silicene and the substrates should be weak because of the absence of dangling bonds. We especially study the bonding, energetic, structural, and resulting electronic properties of the Si overlayers.
The graphene-like allotrope of silicon, silicene, represents a buckled two-dimensional (2D) honeycomb lattice [1]. Despite the partly sp3 bonding, the theory predicts Dirac cones at the corner points K and K′ of the 2D hexagonal Brillouin zone (BZ) for freestanding silicene sheets. The accompanying massless Dirac fermions in the low-energy regime provide unique electronic, IR-optical, and transport properties [2–5]. In contrast to other novel 2D materials, silicene can be ideally used in current Si-based device technologies. The major problem of the application of silicene is its preparation. Recently, the epitaxial growth of silicene on metallic and halfmetallic substrates such as Ag(1 1 1) [6–9], ZrB2 [10], and Ir(1 1 1) [11] has been reported. Theory predicts the use of hydrogen-passivated Si(1 1 1) and Ge(1 1 1) substrates because of their lattice match [12]. For deposition of silicene on Ag(1 1 1), two ARPES experiments [6, 9] but also the mapping of differential conductance [8] have been claimed to confirm Si pz-based conical linear bands. Recently, Dirac cones have been reported for bilayer silicene on Ag(1 1 1) [13]. However, theoretical studies based on the density functional theory (DFT) showed the absence of Si-derived conical linear bands for the mostly studied 3 × 3 silicene on Ag(1 1 1)4 × 4
2. Methods The structural optimization and total-energy calculations are performed within the DFT as implemented in the Vienna Ab-initio Simulation Package (VASP) [20]. The van der Waals (vdW) interaction is included according to Dion et al [21]. The correlation taken in local density approximation (LDA) is corrected by a nonlocal correction that accounts for dispersion forces. The exchange functional in generalized gradient approximation (GGA) is used in the version
1
Author to whom any correspondence should be addressed.
0953-8984/14/185002+4$33.00
1
© 2014 IOP Publishing Ltd Printed in the UK
S Kokott et al
J. Phys.: Condens. Matter 26 (2014) 185002
Figure 1. Silicene adsorbed on (a) Cl-passivated Si(1 1 1)1 × 1 and (b) clean CaF2(1 1 1)1 × 1 surface. Si atoms: blue, Cl: green, Ca:
yellow, F: red.
5
Parameter
Freestanding Cl/Si(1 1 1)1 × 1 CaF2(1 1 1)1 × 1
a (Å) Δ (Å) D (Å) vF (106 m s−1) Eg (meV) EDirac (eV)
3.857 0.480 — 0.53 0 0
3.861 0.490 3.12 0.48 3 0.21
Total energy (eV/1×1 cell)
Table 1. Lattice constant a and buckling amplitude Δ of freestanding and adsorbed silicene from total-energy DFT calculations including vdW. The distance D between the bottom silicene atom and the Cl− or F− ion layer characterizes the adsorbate substrate interaction. Parameters of the resulting 2D band structure of silicene near a K or K′ point, the Fermi velocity vF and the energy gap Eg are also listed. In addition, the energy shift of the Dirac point with respect to the Fermi level EDirac is given.
3.878 0.431 2.70 0.49 52 0
4
Bulklike
Silicene
3
4.1eV
2 1 0
1.3eV
-1 -2
0
Configuration coordinate
1
Figure 2. Total energy along the path from configuration 0 (silicene on Cl/Si(1 1 1)1 × 1) to configuration 1 (bulk-like Cl/Si(1 1 1)1 × 1 with two more Si layers) including vdW interaction. Configuration 0 defines the energy zero.
optB86b. Details of the implementation of the vdW functional are described by Klimeš et al [22]. The pseudopotentials are generated using the projector-augmented-wave (PAW) method [23]. The plane-wave expansion is limited by a cutoff energy of 280 and 400 eV for the Cl/Si(1 1 1) and CaF2 system, respectively. Despite the well-known DFT underestimation of the gap of Si and CaF2 bulk and of the Fermi velocity vF of the massless Dirac particles in silicene [2, 4, 24], the resulting electronic structures are sufficient to demonstrate the appearance of characteristic features such as Dirac cones. The Cl-passivated Si(1 1 1)1 × 1 and the CaF2(1 1 1)1 × 1 surfaces are simulated by repeated symmetric slabs of 18 and 24 atomic layers respectively. In the Si case both sides are covered by chlorine. In the CaF2(1 1 1) slabs, fluorine layers form the surface. Additionally, on each slab surface one silicene sheet is adsorbed. The vacuum between two slabs is chosen to be 20 Å. The slightly biaxially strained silicene, the chlorine layer, and the uppermost atomic layers in the slab are allowed to relax using a conjugate-gradient algorithm until the Hellmann–Feynman forces are below 0.01 meV Å−1. The BZ of the resulting superlattice structure is sampled with a 16 × 16 × 1 k-point grid. Many different starting
geometries with different displacements of the strained silicene overlayer relative to positions of the Cl− or F− surface atoms are investigated. 3. The substrates Upon reaction of Cl atoms with the cleavage Si(1 1 1)7 × 7 surface and subsequent repeated annealing, the favorable bulk like 1 × 1 surface [25] appears. A stable monolayer of Cl− ions covers the Si(1 1 1)1 × 1 surface with almost Si+ ions in the topmost atomic layer, even when the sample is held at 550°C. The projected fundamental gap with a minimum value of 1.1 eV is free of surface states. The Cl/Si(1 1 1)1 × 1 surface is indeed passivated, while the 2D hexagonal symmetry of the uppermost Si layer is conserved. The Si(1 1 1)1 × 1 surface is perfectly lattice-matched to the Bravais lattice of the 1 × 1 silicene sheet with a deviation of only 0.1% (see theoretical lattice constants in table 1). 2
S Kokott et al
J. Phys.: Condens. Matter 26 (2014) 185002
Figure 3. Band structure of silicene adsorbed on (a) Cl/Si(1 1 1)1 × 1 and (b) CaF2(1 1 1)1 × 1, respectively. The silicene character obtained by projection onto corresponding Si atoms is indicated by black dots with varying intensity of the color. The red-dashed horizontal line represents the Fermi level.
The results for a F−-terminated CaF2(1 1 1)1 × 1 substrate are rather similar. However, as a consequence of the slightly increased biaxial strain, the buckling amplitude of silicene is reduced (see table 1). The distance D = 2.70 Å between overlayer and substrate is somewhat smaller than in the Cl/Si(1 1 1)1 × 1 case but still indicates a influence of the vdW bonding. To investigate the influence of the 1 × 1 unit-cell constraint, we have also studied 3 × 3 lateral unit cells for both substrates, Cl/Si(1 1 1) and CaF2(1 1 1). Despite significant initial displacements, the silicon overlayers relax back into the silicene geometry optimized within 1 × 1 cells. This result supports the statement of a stable configuration. The band structures of the silicene-covered (a) Cl-passivated Si(1 1 1)1 × 1 surface and (b) CaF2(1 1 1) substrate are displayed in figure 3. The regions of the dense slab bands mainly indicate the projected bulk (a) Si or (b) CaF2 band structures. The striking differences in the chemical bonding of the substrates are indicated by the completely different band width and energy gaps. The gaps are free of surface states. Only in the pockets of the projected valence bands do such states associated with Cl–Si bonds appear near K and M. The electronic-structure modifications, due to the silicene overlayer, are indicated by additional bands whose chemical nature has been determined by projections onto the silicene atoms. As a consequence of the weak vdW bonding one observes the almost unchanged band structure of freestanding silicene. This is especially true for the Dirac cones around K within the fundamental gaps. The corresponding band states are still derived mainly from Si pz orbitals. The weak vdW bonding only slightly modifies the bands near the Fermi energy and a K point. The Fermi velocities of the Dirac cones are conserved (see table 1). In the case of the Cl/Si(1 1 1) substrate, practically no gap is opened. Only the Fermi level is shifted by 0.2 eV toward lower energies, i.e., holes are created in the π-state-derived cone. The projected bulk conduction band minima near M indicate a small electron transfer into the substrate. On CaF2(1 1 1) the silicene overlayer opens a small gap between the π* and π cones. The Fermi energy remains in the gap center.
The natural cleavage CaF2(1 1 1)1 × 1 surface is terminated by a complete triple layer of F−–Ca2+–F− monoatomic layers with a topmost F− layer for electrostatic reasons [26]. The latter one consists of a trigonal arrangement of F− ions spaced by 3.878 Å (see table 1), that leads to a lattice mismatch to silicene of 0.5%. Calculations show that such a small tensile strain does not destroy the Dirac cones. Because of the inertness of the CaF2(1 1 1) surface, it is suggested as a convenient substrate for a van der Waals epitaxy of almost strain-free overlayers [27]. The completely filled outermost electron shell of the F− ions makes the uppermost surface triple layer inert. The silicene atoms should not chemically react with an intact triplelayer surface, similar to the behavior of oxygen atoms [28].
4. Results In the resulting minimum-energy structure of silicene on Cl/Si(1 1 1)1 × 1 the two silicene atoms in the unit cell occupy high-symmetric positions at the long diagonal of the rhombus representing the primitive 1 × 1 surface cell. The buckling amplitude Δ of the silicene sheet is little influenced. The stable position of the sheet in a distance of D = 3.12 Å (see table 1) is mainly caused by the vdW dispersion forces. Despite the large distance, the binding energy EB = 215 meV/cell is larger than for silicene on H/Si(1 1 1)1 × 1 [12] because of the increased dipole moment of the Cl−-Si+ bonds. This value is large compared to the thermal energy kBT = 25 meV at room temperature. There is an energy barrier between the silicene adsorbate system (configuration 0) compared to the Cl-passivated Si(1 1 1)1 × 1 substrate with two more Si layers (configuration 1) of about 4.1 eV/1 × 1 cell (see figure 2). To approximate this barrier we displace the two Si atoms of silicene and the Cl atom in 18 steps toward configuration 1 on condition that the distance of two atoms never comes below the sum of the covalent radii. Of course, the calculated energy barrier is very high due to the constraint of a 1 × 1 cell, but it clearly shows that the silicene configuration on an intact Cl-passivated Si(1 1 1) surface represents a true local minimum on the total-energy surface, and that this configuration should be stable against thermal fluctuations. 3
S Kokott et al
J. Phys.: Condens. Matter 26 (2014) 185002
[10] Fleurence A, Friedlein R, Ozaki T, Kawai H, Wang Y and Yamada-Takamura Y 2012 Experimental evidence for epitaxial silicene on diboride thin films Phys. Rev. Lett. 108 245501 [11] Meng L et al 2013 Buckled silicene formation on Ir(1 1 1) Nano Lett. 13 685–90 [12] Kokott S, Matthes L and Bechstedt F 2013 Silicene on hydrogen-passivated Si(1 1 1) and Ge(1 1 1) substrates Physica Status Solidi: Rapid Res. Lett. 7 538–41 [13] Avila J, De Padova P, Cho S, Colambo I, Lorcy S, Quaresima C, Vogt P, Resta A, Le Lay G and Asensio C M 2013 Presence of gapped silicene-derived band in the prototypical (33) silicene phase on silver (1 1 1) surfaces J. Phys.: Condens. Matter 25 262001 [14] Lin C-L, Arafune R, Kawahara K, Kanno M, Tsukahara N, Minamitani E, Kim Y, Kawai M and Takagi N 2013 Substrate-induced symmetry breaking in silicene Phys. Rev. Lett. 110 076801 [15] Gori P, Pulci O, Ronci F, Colonna S and Bechstedt F 2013 Origin of Dirac-cone-like features in silicon structures on Ag(1 1 1) and Ag(1 1 0) J. Appl. Phys. 114 113710 [16] Pflugradt P, Matthes L and Bechstedt F 2014 Silicene-derived phases on Ag(1 1 1) substrate versus coverage: ab initio studies Phys. Rev. B 89 035403 [17] Arafune R, Lin C-L, Nagao R, Kawai M and Takagi N 2013 Comment on ‘Evidence for Dirac fermions in a honeycomb lattice based on silicon’ Phys. Rev. Lett. 110 229701 [18] Chen L, Liu C-C, Feng B, He X, Cheng P, Ding Z, Meng S, Yao Y and Wu K 2013 Chen et al reply: Phys. Rev. Lett. 110 229702 [19] Tsoutsou D, Xenogiannopoulou E, Golias E, Tsipas P and Dimoulas A 2013 Evidence for hybrid surface metallic band in (4 × 4) silicene on Ag(1 1 1) Appl. Phys. Lett. 103 231604 [20] Kresse G and Furthmüller J 1996 Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set Phys. Rev. B 54 11169–86 [21] Dion M, Rydberg H, Schr E, Langreth D C and Lundqvist B I 2004 Van der Waals density functional for general geometries Phys. Rev. Lett. 92 246401 [22] Klimeš J, Bowler D R and Michaelides A 2011 Van der Waals density functionals applied to solids Phys. Rev. B 83 195131 [23] Kresse G and Joubert D 1999 From ultrasoft pseudopotentials to the projector augmented-wave method Phys. Rev. B 59 1758 75 [24] Huang S, Kang W and Yang Li 2013 Electronic structure and quasiparticle bandgap of silicene structures Appl. Phys. Lett. 102 133106 [25] Boland J J and Villarrubia J S 1990 Formation of Si(1 1 1)–(1 × 1)Cl Phys. Rev. B 41 9865–70 [26] Tasker W P 1979 The stability of ionic crystal surfaces J. Phys. C: Solid State Phys. 12 4977 [27] Koma A 1992 Van der Waals epitaxy—a new epitaxial growth method for a highly lattice-mismatched system Thin Solid Films 216 72–6 [28] Saiki K, Sato Y and Koma A 1989 Adsorption of oxygen on electron-bombarded CaF2 (1 1 1) surfaces Japan. J. Appl. Phys. 28 L134–7
5. Conclusions Summarizing, by means of first-principles calculations we have shown that the Cl-passivation of Si(1 1 1) and the cleavage of CaF2 lead to inert surfaces formed by halogen ions Cl− or F− with completely filled valence shells on top. The silicene with a buckling similar to the freestanding 2D system forms a vdW-bonded adsorbate. The outstanding properties known for freestanding silicene are preserved for the slab system, because of the weak bonding. We suggest intensive experimental studies of the deposition of silicene on the two investigated substrates. In contrast to the silicene/Ag(1 1 1) adsorbate system with strong chemical bonds, the electronic structure of silicene should be detectable within the fundamental gaps of the studied substrates. Acknowledgments LM acknowledges financial support of the Carl-Zeiss Foundation. References [1] Durgun E, Tongay S and Ciraci S 2005 Silicon and III–V compound nanotubes: structural and electronic properties Phys. Rev. B 72 075420 [2] Guzmán-Verri G G and Lew Yan Voon L C 2007 Electronic structure of silicon-based nanostructures Phys. Rev. B 76 075131 [3] Cahangirov S, Topsakal M, Aktürk E, Şahin H and Ciraci S 2009 Two- and one-dimensional honeycomb structures of silicon and germanium Phys. Rev. Lett. 102 236804 [4] Bechstedt F, Matthes L, Gori P and Pulci O 2012 Infrared absorbance of silicene and germanene Appl. Phys. Lett. 100 261906 [5] Matthes L, Gori P, Pulci O and Bechstedt F 2013 Universal infrared absorbance of two-dimensional honeycomb group-IV crystals Phys. Rev. B 87 035438 [6] Vogt P, De Padova P, Quaresima C, Avila J, Frantzeskakis E, Asensio M C, Resta A, Ealet B and Le Lay G 2012 Silicene: compelling experimental evidence for graphenelike two-dimensional silicon Phys. Rev. Lett. 108 155501 [7] Lin C-L, Arafune R, Kawahara K, Tsukahara N, Minamitani E, Kim Y, Takagi N and Kawai M 2012 Structure of silicene grown on Ag(1 1 1) Appl. Phys. Express 5 045802 [8] Chen L, Liu C-C, Feng B, He X, Cheng P, Ding Z, Meng S, Yao Y and Wu K 2012 Evidence for Dirac fermions in a honeycomb lattice based on silicon Phys. Rev. Lett. 109 056804 [9] De Padova P et al 2013 Evidence of Dirac fermions in multilayer silicene Appl. Phys. Lett. 102 163106
4
