Morphology Evolution of Graphene during Chemical Vapor Deposition Growth: A Phase-Field Theory Simulation

In chemical vapor depositiongrowth, depending on the growth condition, graphene islands present various shapes, such as circular, hexagonal, square, rectangular star-like, and fractal. We present a systematic phase-field model study to explore the role of three key factors, carbon flux, precursor concentration on the metal surface, and diffusion of carbon precursors, in the determination of the graphene domain shape. We find that the size of the depletion zone, that is, the area with a carbon precursor concentration gradient around the circumference of the growing graphene island, is of critical importance. In case of no depletion zone or if the size of the depletion zone is much larger than that of the graphene island, the graphene island will present the shape of a regular hexagon. However, star-like graphene islands will form if the size of the depletion zone is comparable to that of the graphene island. Further increasing the size of the graphene island will lead to a fractal-like graphene island with multiscaled branches. Although an extremely small depletion zone will lead to a graphene island with a regular shape, its edges are found to be rough. The three key parameters affect the shape of graphene by tuning the size of the depletion zone. Based on this study, a series of experimental puzzles are properly explained and the conditions for growing high-quality graphene emerge.