Corrugations in Free-Standing Graphene

Although both the tendency of 2D materials to bend out of plane as well as its effect on materials' properties are well known, the factors influencing this phenomenon have not been extensively studied. Graphene, the one-atom-thick membrane of carbon atoms, is both arguably the best known 2D material, as well as the most prone to spontaneous corrugations. Here, we use electron diffraction to systematically study the factors influencing corrugations in graphene, including the size of the free-standing area, the preparation method, the amount of surface contamination, and electron-beam-induced structural disorder. We find that mechanically exfoliated graphene is less corrugated than graphene grown via chemical vapor deposition (corrugation amplitude of (0.83±0.10) Å compared to (1.33±0.20) Å for a free-standing area with a diameter of 1.7μm). Similarly, corrugation amplitude grows by more than a factor of two when the diameter of the free- standing area is increased from 1.7μm to ca. 3.0μm. Electron beam irradiation affects the corrugation in two ways, firstly by removing the hydrocarbon contamination, which decreases corrugation, and secondly by creating increasing amounts of disorder into the material, which again increases corrugation. Overall, our results show that control over the sample during both initial preparation and post-preparation treatment allows for a change in the amount of corrugation in free-standing 2D materials, which may lead to new advances in their use in applications.