Atomic force microscopy (AFM) methods for quantitative measurements of elastic modulus on stiff (>10 GPa) materials typically require tip-sample contact forces in the hundreds of nanonewton to few micronewton range. Such large forces can incur sample damage and preclude direct measurement of ultrathin films or nanofeatures. Here, we present a contact resonance spectroscopy AFM technique that utilizes a cantilevers higher flexural eigenmodes to enable modulus measurements on stiff materials with contact forces as low as 10 nN. Euler-Bernoulli analysis of the cantilevers fourth and fifth flexural eigenmodes in contact yielded good agreement with bulk measurements of modulus on glass samples in the 50 GPa to 75 GPa range, while analysis of the conventionally used first and second eigenmodes gave poor agreement. We used finite element analysis to understand the dynamic contact response of a cantilever with a physically realistic geometry. For tip-sample contact stiffness much greater than the cantilever spring constant, a simple analytical Euler-Bernoulli beam model yields accurate results for the higher eigenmode resonances but not for the lower eigenmodes. Compared to lower eigenmodes, the results from higher modes are found to be less affected by model parameters that are either unknown, or not considered in the analytical model. Overall, the technique enables local mechanical characterization of a class of materials whose dimensions and mechanical properties have rendered it previously inaccessible to AFM-based nanomechanics methods.
Pub Type: Journals
nanomechanics, atomic force microscopy, AFM, contact resonance, thin film, CR-FM