Contact stiffness modulation in contact-mode atomic force microscopy

• Effect of contact stiffness modulation on the dynamics of contact-mode AFM is investigated.
• A lumped sdof oscillator is considered for modeling the contact-mode dynamic.
• The amplitude of the contact stiffness modulation influences the frequency response.
• The stiffness modulation has an effect on the shift direction of the frequency response.

The effect of fast contact stiffness modulation on the frequency response in contact-mode atomic force microscopy is studied analytically near primary resonance. Based on the Hertzian contact theory, a lumped single degree of freedom oscillator is considered for modeling the contact-mode dynamics between the tip of the microbeam and the sample. Averaging method and perturbation analysis are performed to obtain the modulation equations of the slow dynamic. The influence of the contact stiffness modulation on the non-linear characteristic of the frequency response is examined. We find that the amplitude of the contact stiffness modulation influences significantly the amplitude of the tip oscillation as well as the shift direction of the frequency response indicating that such a modulation can be used to characterize the local elastic properties of the sample. Comparison between the analytical predictions and the numerical simulations is given and application to a real atomic force microscope example is provided.