  The graphene morphology regulated by nanowires patterned in parallel on a
substrate surface is quantitatively determined using energy minimization. The
regulated graphene morphology is shown to be governed by the nanowire diameter,
the nanowire spacing and the interfacial bonding energies between the graphene
and the underlying nanowires and substrate. We demonstrate two representative
regulated graphene morphologies and determine critical values of the nanowire
spacing, nanowire diameter and interfacial bonding energies at which graphene
switches between the two representative morphologies. Interestingly, we
identify a rule-of-thumb formula that correlates the critical nanowire spacing,
the critical interfacial bonding energies and the nanowire diameter in quite
well agreement with the full-scale simulation results. Results from the present
study offer guidelines in nano-structural design to achieve desired graphene
morphology via regulation with a resolution approaching the atomic feature size
of graphene.
