Photonic crystals in biology

Poster Session, Tuesday, June 15
Theme A1 - B702
Ab-initio Investigation of Structural Properties of 6H-SiC {0001} Surfaces
Ahmet Cicek 1 *, Oguz Gulseren 2 and Bulent Ulug 1
1 Department of Physics, Faculty of Arts and Sciences, Akdeniz University, Antalya 07058, Turkey
2 Department of Physics, Bilkent University, Ankara 06800, Turkey
Abstract-Structural properties of unreconstructed 6H-SiC surfaces are studied by using pseudopotential plane-wave calculations based on
density functional theory. Surface truncation is observed to lead to relaxation of outermost atoms such that the Si or C atoms at the surface move
inwards in the growth direction, while the adjacent atoms of the other species move outwards. Intra- and inter-layer separations are observed to
vary more significantly for the topmost bilayer. It is seen that at least 12-bilayer slab structures must be considered for an adequate description
of 6H-SiC {0001} surfaces.
The {0001} surfaces of hexagonal SiC polytypes, especially
6H, are recently under intense investigation due to ease of
epitaxial graphene growth [1-4]. Growth mechanisms and
geometry of the reconstructions on 6H SiC surfaces are not
easy to treat in theoretical studies, where simple cases such as
3 3R30
reconstruction for the Si-terminated [5-7] and
2x2 reconstruction for the C-terminated face [8] are in itially
treated. Surface is defined by a finite number of bilayers (BL)
permitting computationally-affordable investigations. Since
the introduced stress propagates through the surface and
charge separation occurs at the two faces terminated by Si and
C atoms, a thorough study must investigate the minimum slab
thickness to describe the surface [10].
In this work, structural properties of unreconstructed
6H-SiC {0001} surfaces are investigated by ab-initio
calculations under Generalized Gradient Approximation
(GGA) and Local Density Approximation (LDA). First,
structural properties of the bulk are investigated by geometry
optimization [9]. The optimized bulk geometry is utilized as
the starting configuration for geometry optimization of the
surfaces. The investigated 6H-SiC (0001) and (000 1 ) surfaces
are demonstrated in Figure-1. Important entities in the
investigations are intra- and inter-layer separations of BLs,
denoted by d i and z i in Figure-1(a)., respectively.
Figure 1. Unreconstructed 6H-SiC {0001} 1x1 surfaces for geometry
optimization computations employing (a) and (c) 6 bilayers, (b) and
(d) 12 bilayers.
Computations are carried out by employing slabs of 6 and 12
BLs. Vacuum distance between adjacent supercells is 20A 0
and cut-off energy is 50Ry, where 12x12x2 and 12x12x1
Monkhorst-Pack meshes are employed for 6-BL and 12-BL
slabs, respectively. For geometry optimization, Broyden-
Fletcher-Goldfarb-Shanno (BFGS) algorithm is employed
where 1, 2, 3, 4 or 6 topmost BLs are relaxed for 6-BL and 1,
2, 3, 6, 7, 8 or 9 topmost BLs are relaxed for 12-BL slabs.
Ideal bulk 6H-SiC is composed of ABCACB… stacking of
atoms where neighboring atoms around any atom form a
regular tetrahedron with d i=z i /3. However, both LDA and
GGA computations reveal that small displacements take place
so that d 1 =62.6p m and z 1 =187.1p m for LDA, wh ile
d 1 =63.5p m and z 1 =189.8pm for GGA.
Relaxed slab geometries show that the outermost surface
atom moves towards the surface and the next atom of the other
species moves outwards. Displacement of the top Si atoms is
around 5pm inwards and the neighboring C atoms move
approximately 2.5 p m outwards for the (0001) surface for
LDA computations. For GGA, considerably smaller
displacements are observed. On the other hand, C atoms of the
(000 1 ) surface are displaced more significantly, where LDA
results reveal around 17pm shifts inwards. The outward
displacement of the Si atoms of the (000 1 ) surface is around
8pm. Again, smaller displacements are observed for GGA.
Comparisons of results for 6 and 12 BL slabs show that
atomic displacements do not converge as the number of
relaxed BLs is increased for the case of 6-BL slabs, whereas
convergence is achieved for 12-BL slabs.
In summary unreconstructed {0001} surfaces of 6H-SiC,
the surface must be described by at least 12 bilayers, where
relaxation of 3 or 6 BLs is sufficient for obtaining optimized
surface geometry.
This study is supported by Akdeniz University Scientific
Research Projects Coordination Unit (Project No:
2008.01.0105.010) and by TUBITAK (Grant No: 107T720).
*Corresponding author: acicek@akdeniz.edu.tr
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