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Substrate-regulated morphology of graphene

We delineate a general theoretical framework to determine the substrate-regulated graphene morphology through energy minimization. We then apply such a framework to study the graphene morphology on a substrate with periodic surface grooves. Depending on the substrate surface roughness and the graphene-substrate interfacial bonding energy, the equilibrium morphology of graphene ranges from 1) closely conforming to the substrate, to 2) remaining flat on the substrate. Interestingly, in certain cases, the graphene morphology snaps between the above two limiting states. Our quantitative results envision a promising strategy to precisely control the graphene morphology over large areas. The rich features of the substrate-regulated graphene morphology (e.g., the snap-through instability) can potentially lead to new design concepts of functional graphene device components.