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The resonance frequency of a micro-cantilever employed in atomic force microscopy (AFM) is expected to be a measure of tip-sample contact stiffness representing the elastic properties of a sample. Quantitative evaluation of the elastic properties from measurements of resonance frequency is difficult, however, because contact stiffness is influenced by adhesion energy as well as elastic properties. In this study, we propose a new method of evaluating these properties quantitatively from the nonlinear response of AFM cantilever vibrations. The nonlinear vibrations are easily excited due to the non-linearity in the tip-sample interaction. To simplify the formulas derived for evaluation of contact stiffness and adhesion, we focus on the case of perfect contact, where the tip is always in contact with the sample surface. The elastic properties and the adhesion energy are separated by finding the optimal set of values which minimizes the difference between the theoretical and experimental relationship of resonance frequency versus amplitude

A Method of Evaluating Local Elasticity and Adhesion Energy from the Nonlinear Response of AFM Cantilever Vibrations.