Radial buckle delamination around 2D material tents

Microscale tents, formed when transferring two-dimensional (2D) materials over nanoparticles or nanopillars, or when indenting a suspended 2D material drumhead with an atomic force microscope (AFM) tip, emerge to be a useful structure for the strain engineering of 2D materials. In the periphery of the tents, where the 2D materials are supported by the substrate, radial buckle delamination can often be observed, yet the formation mechanism and the profile characteristics remain unclear. Here, we suggest that the tent-induced buckles result from the 2D material-substrate interface sliding radially inward, and their profiles and extent are controlled by the interface adhesion and friction. We experimentally characterized that the crest curvature of the buckles is proportional to a characteristic length that compares the elastic bending energy of the 2D material with its adhesion energy to the substrate. We then obtain theoretical predictions for the extent of those buckles by exact closed-form solutions to Föppl–von Kármán (FvK) equations under both near-threshold and far-from-threshold conditions. Our results are highly analytical, provide a direct means to estimate the interfacial shear and adhesive properties of the 2D material-substrate system based on simple topological characterizations of buckles. Our theoretical understandings also establish a fundamental base for the rational design of 2D material tents.