Frequency shift and hysteresis suppression in contact-mode AFM using contact stiffness modulation

Abstract

Abstract. In this paper the frequency response shift and hysteresis suppression of contact-mode atomic force microscopy is investigated using parametric modulation of the contact stiffness. Based on the Hertzian contact theory, a lumped single degree of freedom oscillator is considered for modeling the cantilever dynamics contactmode atomic force microscopy. We use the technique of direct partition of motion and the method of multiple scales to obtain, respectively, the slow dynamic and the corresponding slow flow of the system. As results, this study shows that the amplitude of the contact stiffness modulation has a significant effect on the frequency response. Specifically, increasing the amplitude of the stiffness modulation suppresses hysteresis, decreases the peak amplitude and produces shifts towards higher and lower frequencies.

A Proportional Derivative (PD) Controller for Suppression the Vibrations of a Contact-Mode AFM Model

“…From equations (10) the secular terms are removed by (equate the secular terms to zero), result in solvability conditions for the first order approach, like:…”

“…The hysteresis suppression and frequency response shift of contact mode AFM is illustrated by [10] applying parametric modification of the contact hardness. They used multiple perturbation technique and direct partition of motion to get the corresponding slow flow and the slow dynamic of the model, respectively.…”