Theoretical studies of the epitaxial growth of graphene
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Graphene, a sheet of carbon atoms organized in a honeycomb lattice, is a two dimensional crystal. Even though the material has been known for a long time, only recently has it stimulated considerable interest across different research areas. Graphene is interesting not only as a platform to study fundamental physics in two dimensions, but it also has great potential for post-silicon microelectronics owing to its exceptional electronic properties. Of the several methods known to produce graphene, epitaxial growth of graphene by sublimation of silicon carbide is probably the most promising for practical applications. This thesis is a theoretical study of the growth kinetics of epitaxial graphene on SiC(0001). We propose a step-flow growth model using coarse-grained kinetic Monte Carlo (KMC) simulations and mean-field rate equations to study graphene growth on both vicinal and nano-faceted SiC surfaces. Our models are consistent with experimental observations and provide quantitative results which will allow experimenters to interpret the growth morphology and extract energy barriers from experiments. Recently, it has been shown that graphene grown epitaxially on metal surfaces may lead to potential applications such as large area transparent electrodes. To study deposition-type epitaxial growth, we investigate a new theoretical approach to this problem called the phase field method. Compared to other methods this method could be less computationally intensive, and easier to implement at large spatial scales for complicated epitaxial growth situations.