Surface roughness and size effects on the morphology of graphene on a substrate

We study the morphology and snap-through transitions of multilayer graphene on a corrugated elastic substrate whose surface roughness is determined by surface amplitude and wavelength. Based on the couple stress theory, we develop a theoretical model to understand the size effect on the graphene morphology. It is indicated that the surface amplitude has no effect on the corrugation of graphene, whereas increased surface wavelength results in greater corrugation of the graphene on the substrate. At high surface roughness, a snap-through transition is more likely to happen. Moreover, our results show obvious size effect on the graphene morphology for high surface roughness and compliant substrates. This work offers theoretical insights to control graphene morphology by changing the substrate surface roughness.