Employing density-functional calculations we study single and double graphene layers on Si-and C-terminated 1 × 1 -6H-SiC surfaces. We show that, in contrast to earlier assumptions, the first carbon layer is covalently bonded to the substrate, and cannot be responsible for the graphenetype electronic spectrum observed experimentally. The characteristic spectrum of free-standing graphene appears with the second carbon layer, which exhibits a weak van der Waals bonding to the underlying structure. For Si-terminated substrate, the interface is metallic, whereas on C-face it is semiconducting or semimetallic for single or double graphene coverage, respectively.PACS numbers: 68.35. Ct, 68.47.Fg, The last years have witnessed an explosion of interest in the prospect of graphene-based nanometer-scale electronics [1,2,3,4]. Graphene, a single hexagonally ordered layer of carbon atoms, has a unique electronic band structure with the conic "Dirac points" at two inequivalent corners of the two-dimensional Brillouin zone. The electron mobility may be very high and lateral patterning with standard lithography methods allows device fabrication [1]. Two ways of obtaining graphene samples have been used up to now. In the first "mechanical" method, the carbon monolayers are mechanically split off the bulk graphite crystals and deposited onto a SiO 2 /Si substrate [4]. This way an almost "freestanding" graphene is produced, since the carbon monolayer is practically not coupled to the substrate. The second method uses epitaxial growth of graphite on singlecrystal silicon carbide (SiC). The ultrathin graphite layer is formed by vacuum graphitization due to Si depletion of the SiC surface [5]. This method has apparent technological advantages over the "mechanical" method, however it does not guarantee that an ultrathin graphite (or graphene) layer is electronically isolated from the substrate. Moreover, one expects a covalent coupling between both which may strongly modify the electronic properties of the graphene overlayer. Yet, experiments show that the transport properties of the interface are dominated by a single epitaxial graphene layer [1,2]. Most surprisingly, the electronic spectrum seems not to be affected much by the substrate. As in free-standing graphene one observes the "Dirac points" with the linear dispersion relation around them. The electron dynamics is governed by a Dirac-Weyl Hamiltonian with the Fermi velocity of graphene replacing the speed of light. This leads to an unusual sequence of Landau levels in a magnetic field and hence to peculiar features in the quantum Hall effect [1,4].

The diffusion of intrinsic defects in 3C-SiC is studied using an ab initio method based on density functional theory. The vacancies are shown to migrate on their own sublattice. The carbon splitinterstitials and the two relevant silicon interstitials, namely the tetrahedrally carbon-coordinated interstitial and the 110 -oriented split-interstitial, are found to be by far more mobile than the vacancies. The metastability of the silicon vacancy, which transforms into a vacancy-antisite complex in p-type and compensated material, kinetically suppresses its contribution to diffusion processes. The role of interstitials and vacancies in the self-diffusion is analyzed. Consequences for the dopant diffusion are qualitatively discussed. Our analysis emphasizes the relevance of mechanisms based on silicon and carbon interstitials.

The annealing kinetics of mobile intrinsic defects in cubic SiC is investigated by an ab initio method based on density-functional theory. The interstitial-vacancy recombination, the diffusion of vacancies, and interstitials to defect sinks ͑e.g., surfaces or dislocations͒ as well as the formation of interstitial clusters are considered. The calculated migration and reaction barriers suggest a hierarchical ordering of competing annealing mechanisms. The higher mobility of carbon and silicon interstitials as compared to the vacancies drives the annealing mechanisms at lower temperatures including the vacancy-interstitial recombination and the formation of interstitial carbon clusters. These clusters act as a source of carbon interstials at elevated temperatures. In p-type material the transformation of the silicon vacancy into the more stable vacancy-antisite complex constitutes an annealing mechanism which is activated before the vacancy migration. Recent annealing studies of vacancyrelated centers in irradiated 3C-SiC and 4H-SiC and semi-insulating 4H-SiC are interpreted in terms of the proposed hierarchy of annealing mechanisms.

The photoluminescence center DII is a persistent intrinsic defect which is common in all SiC polytypes. Its fingerprints are the characteristic phonon replicas in luminescence spectra. We perform ab-initio calculations of vibrational spectra for various defect complexes and find that carbon antisite clusters exhibit vibrational modes in the frequency range of the DII spectrum. The clusters possess very high binding energies which guarantee their thermal stability-a known feature of the DII center. The dicarbon antisite (C2)Si (two carbon atoms sharing a silicon site) is an important building block of these clusters.

The electronic, structural and vibrational properties of small carbon interstitial and antisite clusters are investigated by ab initio methods in 3C and 4H-SiC. The defects possess sizable dissociation energies and may be formed via condensation of carbon interstitials, e.g. generated in the course of ion implantation. All considered defect complexes possess localized vibrational modes (LVM's) well above the SiC bulk phonon spectrum. In particular, the compact antisite clusters exhibit high-frequency LVM's up to 250 meV. The isotope shifts resulting from a 13 C enrichment are analyzed. In the light of these results, the photoluminescence centers DII and P−U are discussed. The dicarbon antisite is identified as a plausible key ingredient of the DII-center, whereas the carbon split-interstitial is a likely origin of the P−T centers. The comparison of the calculated and observed high-frequency modes suggests that the U-center is also a carbon-antisite based defect.