  We determine the graphene morphology regulated by substrates with herringbone
and checkerboard surface corrugations. As the graphene/substrate interfacial
bonding energy and the substrate surface roughness vary, the graphene
morphology snaps between two distinct states: 1) closely conforming to the
substrate and 2) remaining nearly flat on the substrate. Such a snapthrough
instability of graphene can potentially lead to desirable electronic properties
to enable graphene-based devices.
