  Spatially nonuniform strain is important for engineering the pseudomagnetic
field and band structure of graphene. Despite the wide interest in strain
engineering, there is still a lack of control on device-compatible strain
patterns due to the limited understanding of the structure-strain relationship.
Here, we study the effect of substrate corrugation and curvature on the strain
profiles of graphene via combined experimental and theoretical studies of a
model system: graphene on closely packed SiO2 nanospheres with different
diameters (20-200 nm). Experimentally, via quantitative Raman analysis, we
observe partial adhesion and wrinkle features and find that smaller nanospheres
induce larger tensile strain in graphene, theoretically, molecular dynamics
simulations confirm the same microscopic structure and size dependence of
strain and reveal that a larger strain is caused by a stronger, inhomogeneous
interaction force between smaller nanospheres and graphene. This
molecular-level understanding of the strain mechanism is important for strain
engineering of graphene and other two-dimensional materials.
