Determining local modulus and strength of heterogeneous films by force–deflection mapping of microcantilevers

Abstract

Estimating the elastic modulus and strength of heterogeneous films requires local measurement techniques. For local mechanical film testing, microcantilevers were cut into suspended many-layer graphene using a focused ion beam. An optical transmittance technique was used to map thickness near the cantilevers, and multipoint force–deflection mapping with an atomic force microscope was used to record the compliance of the cantilevers. These data were used to estimate the elastic modulus of the film by fitting the compliance at multiple locations along the cantilever to a fixed-free Euler–Bernoulli beam model. This method resulted in a lower uncertainty than is possible from analyzing only a single force–deflection. The breaking strength of the film was also found by deflecting cantilevers until fracture. The average modulus and strength of the many-layer graphene films are 300 and 12 GPa, respectively. The multipoint force–deflection method is well suited to analyze films that are heterogeneous in thickness or wrinkled.