Proceedings of nanoGe Fall Meeting19 (NFM19)
Publication date: 18th July 2019
Epitaxial growth methods are on one hand a powerful technology used in producing thin films on substrates. On the other hand, the rational optimization of growth conditions is rather difficult as a result of various factors controlling growth processes. We develop mathematical modeling for epitaxial growth motivated by a recently found scaling relation between the domain radius and time for chemical vapor deposition of graphene. Mathematically, we need to solve the self-consistent equation; when the boundary moves, its position should be determined to match the spatial profile of diffusing absorbents. We derive a closed equation for the growth rate constant. We obtain approximate analytical expressions for the growth rate in terms of the two-dimensional diffusion constant and the rate constant for the attachment of absorbents to the solid domain. In experiments, the area is decreased by stopping the source gas flow. The rate of decrease of the area is also obtained. The theoretical results presented provide a foundation to study controlling factors for domain growth.
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