Layer dependent out-of-plane elastic modulus of graphene

Abstract

Contact resonance atomic force microscopy (CR-AFM) was used to spatially map variations in the out-of-plane elastic modulus of graphene covered surfaces of a silicon wafer having a native oxide. A modulus of 0.973 ± 0.001 TPa was measured for one layer of graphene covering the silicon substrate, consistent with many experimental and theoretical studies. A monotonic decrease in the measured contact resonance frequency with increasing layers of graphene covering the silicon substrate was observed, resulting in a decrease in the measured modulus by 4.95% with four layers of graphene covering the substrate. The interplay between the hydrophobic graphene layers covering the hydrophilic silicon substrate, the interlayer spacing of graphene, and the range of adhesion from the substrate are proposed to influence the stiffness of the graphene–graphene interaction, which was probed with the sub-Ångström displacements with CR-AFM measurements.