Reconstructions of 6H-SiC(0001) Surfaces Studied by Scanning Tunneling Microscopy and Reflection High-Energy Electron Diffraction

Abstract

We study the level spacing distribution p(s) in the spectrum of random networks. According to our numerical results, the shape of p(s) in the Erdős-Rényi (E-R) random graph is determined by the average degree k and p(s) undergoes a dramatic change when k is varied around the critical point of the percolation transition, k = 1. When k 1, the p(s) is described by the statistics of the Gaussian orthogonal ensemble (GOE), one of the major statistical ensembles in Random Matrix Theory, whereas at k = 1 it follows the Poisson level spacing distribution. Closely above the critical point, p(s) can be described in terms of an intermediate distribution between Poisson and the GOE, the Brodydistribution. Furthermore, below the critical point p(s) can be given with the help of the regularized Gamma-function. Motivated by these results, we analyse the behaviour of p(s) in real networks such as the internet, a word association network and a protein-protein interaction network as well. When the giant component of these networks is destroyed in a node deletion process simulating the networks subjected to intentional attack, their level spacing distribution undergoes a similar transition to that of the E-R graph.

<i>In Situ </i>Study on Oxygen Etching of Surface Buffer Layer on SiC(0001) Terraces

“…Figure 4(a) shows a RHEED pattern from the SiC with graphene in the azimuth direction of [1010] before oxygen etching, showing diffraction spots of SiC (1×1), SiC (6 √ 3×6 √ 3) and graphene, as has been observed previously [25,26]. The SiC (6 √ 3×6 √ 3), which indicates the presence of the buffer layer are still observed in the RHEED pattern for the oxygen etched surface (Fig.…”

Observations of Graphitized SiC Surfaces by STM

“…• with respect to the SiC lattice [3]. Diffraction spots from the graphite lattice remain even after annealed at 1800…”

“…It has also been found that, on 6H-SiC(0001) Siterminated surfaces, graphite layers or carbon nanotubes with shorter length than that on the C-terminated surfaces are produced depending on sample preparation procedures [10]. Previously, we have found that string-shaped structures consisting of graphite structure are produced along step edges on 6H-SiC(0001) Si-terminated surfaces by annealing in UHV [3]. Recently, Derycke, et al have determined string-shaped structures on 6H-SiC(0001) Siterminated surfaces to be carbon nanotubes produced in the direction parallel to the surfaces [11].…”

“…SiC is also an attractive material in the characterization of atomic structure on the surface. SiC surfaces are graphitized or carbonized by annealing at high temperatures under decreased pressures [2,3] or under oxygen molecules [4]. This is due to evaporation of Si from SiC surfaces caused by annealing in the decreased pressures.…”

“…On the other hand, periodic structures are formed by annealing SiC surfaces in ultra high vacuum (UHV), especially by annealing in a Si-rich environment to prevent the surface graphitization. Depending on polytypes, polarity and sample preparation procedures, various surface structures have been reported [3,[5][6][7][8].…”