Corrugation-Dominated Mechanical Softening of Defect-Engineered Graphene

We measure the two-dimensional elastic modulus E^{2D} of atomically clean defect-engineered graphene with a known vacancy distribution and density in correlated ultrahigh vacuum experiments. The vacancies are introduced via low-energy (<200  eV) Ar ion irradiation, and the atomic structure is obtained via semiautonomous scanning transmission electron microscopy and image analysis. Based on atomic force microscopy nanoindentation measurements, a decrease of E^{2D} from 286 to 158  N/m is observed when measuring the same graphene membrane before and after introducing vacancies at a density of 1.0×10^{13}  cm^{-2}. This decrease is significantly greater than what is predicted by most theoretical studies and in stark contrast to some measurements presented in the literature. With the assistance of atomistic simulations, we show that this softening is mostly due to corrugations caused by local strain at vacancies with two or more missing atoms, while the influence of single vacancies is negligible. We further demonstrate that the opposite effect can be measured when surface contamination is not removed before defect engineering.