Exploring the Inter-Layer Interactions of 2D Materials with Sub-Angstrom Resolution Modulated Nanoindentation

As the field of 2D materials continues to grow, more intriguing and complex structures will be discovered, increasing the demand for techniques to properly characterize the local nanoscale mechanical properties of any and all varieties of materials. While traditional nanoindentation can measure the in-plane modulus of suspended films over holes, the technique fails to accurately determine the out-of-plane modulus, requiring such large indentation depths that substrate effects cannot be distinguished. We employ modulated nanoindentation with Angstrom resolution (MoNI/ÅI), a novel technique that enables non-destructive measurements of the out-of-plane elasticity of ultra-thin materials with sub-angstrom level indentation depths. With such high resolution, even atomically thin materials can be examined in their most practical state on any underlying substrate, without erroneous contributions from the substrate. MoNI/ÅI has been previously used to explore local pressure induced phase transformations only possible in few layer 2D materials. In our work we explored the multi-layer stiffness dependence of deposited graphene and uncovered a peak transverse stiffness in bilayer graphene that was previously unknown. We complemented these findings with MD simulations and other characterization techniques to further elucidate this phenomenon providing a deeper insight of the inter-layer forces and interactions in graphene and other 2D materials.