Wrinkles are ubiquitous for graphene
films grown on various substrates by chemical vapor deposition at
high temperature due to the strain induced by thermal mismatch between
the graphene and substrates, which greatly degrades the extraordinary
properties of graphene. Here we show that the wrinkle formation of
graphene grown on Cu substrates is strongly dependent on the crystallographic
orientations. Wrinkle-free single-crystal graphene was grown on a
wafer-scale twin-boundary-free single-crystal Cu(111) thin film fabricated
on sapphire substrate through strain engineering. The wrinkle-free
feature of graphene originated from the relatively small thermal expansion
of the Cu(111) thin film substrate and the relatively strong interfacial
coupling between Cu(111) and graphene, based on the strain analyses
as well as molecular dynamics simulations. Moreover, we demonstrated
the transfer of an ultraflat graphene film onto target substrates
from the reusable single-crystal Cu(111)/sapphire growth substrate.
The wrinkle-free graphene shows enhanced electrical mobility compared
to graphene with wrinkles.