Theoretical basis of parametric-resonance-based atomic force microscopy

Abstract

Parametric resonance underpins the physics of swings, resonant surface waves, and particle traps. There is increasing interest in its potential applications in atomic force microscopy (AFM). In this paper, the dynamics of parametrically resonant microcantilevers for high sensitivity imaging and force spectroscopy applications is investigated theoretically. Detailed numerical parametric-resonance simulations are performed to understand how the microcantilever amplitude varies with tip-sample separation, the tip-sample interaction, and the scanning dynamics of a microcantilever probe. We find three key advantages of a parametrically resonant microcantilever for AFM applications: (a) the reduction in ringing effects near feature edges that occur for high-$Q$ microcantilevers; (b) an increase in the scanning speed while maintaining a low tip-sample interaction force while imaging; and (c) an enhanced sensitivity to long-range magnetic and electrostatic force gradients acting between the tip and the sample. Experimental results are presented with an aim to clearly identify the advantages and disadvantages that parametric resonance offers for scanning probe applications.