Probing the Mechanical Properties of 2D Materials via Atomic-Force-Microscopy-Based Modulated Nanoindentation

As the field of low-dimensional materials (1D or 2D) grows and more complex and intriguing structures are continuing to be found, there is an emerging need for techniques to characterize the nanoscale mechanical properties of all kinds of 1D/2D materials, in particular in their most practical state: sitting on an underlying substrate. While traditional nanoindentation techniques cannot accurately determine the transverse Young's modulus at the necessary scale without large indentations depths and effects to and from the substrate, herein an atomic-force-microscopy-based modulated nanomechanical measurement technique with Angstrom-level resolution (MoNI/ÅI) is presented. This technique enables non-destructive measurements of the out-of-plane elasticity of ultra-thin materials with resolution sufficient to eliminate any contributions from the substrate. This method is used to elucidate the multi-layer stiffness dependence of graphene deposited via chemical vapor deposition and discover a peak transverse modulus in two-layer graphene. While MoNI/ÅI has been used toward great findings in the recent past, here all aspects of the implementation of the technique as well as the unique challenges in performing measurements at such small resolutions are encompassed.