  Strain engineering of graphene through interaction with a patterned substrate
offers the possibility of tailoring its electronic properties, but will require
detailed understanding of how graphene's morphology is determined by the
underlying substrate. However, previous experimental reports have drawn
conflicting conclusions about the structure of graphene on SiO2. Here we show
that high-resolution non-contact atomic force microscopy of SiO2 reveals
roughness at the few-nm length scale unresolved in previous measurements, and
scanning tunneling microscopy of graphene on SiO2 shows it to be slightly
smoother than the supporting SiO2 substrate. Quantitative analysis of the
competition between bending rigidity of the graphene and adhesion to the
substrate explains the observed roughness of monolayer graphene on SiO2 as
extrinsic, and provides a natural, intuitive description in terms of highly
conformal adhesion. The analysis indicates that graphene adopts the
conformation of the underlying substrate down to the smallest features with
nearly 99% fidelity.
