Parametric resonance based atomic force microscopy and mass-sensing in ambient and liquid environments

Gyan Prakash, Purdue University

Abstract

Parametric resonance underpins the physics of swings, resonant surface waves, and particle traps. A parametrically excited resonator can respond in two different ways, namely, (i) Parametric Resonance and (ii) Parametric Amplification. In this work, we present theoretical studies and experimental data that characterize both regimes. There is increasing interest in the parametric excitation of a microcantilever for Atomic Force Microscopy (AFM) and Mass-Sensing applications. These applications are investigated both theoretically and experimentally. Detailed numerical simulations of parametric resonance are performed to understand how a microcantilever responds to tip-sample separation and tip-sample interaction. Simulations are performed to compare a parametrically resonant microcantilever with Q-controlled and conventionally resonated microcantilevers. We find three key advantages for AFM applications: (a) the reduction of 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. The parametric experiments were implemented using an electronic feedback circuit to self-excite a microcantilever with a signal proportional to the microcantilever’s displacement. By adjusting the gain of a feedback amplifier, both parametric resonance and parametric amplification regimes can be easily accessed. Using a laser beam bounce technique to monitor the cantilever’s displacement, a cubic non-linearity in the output of the position-sensitive photodiode has been identified. This non-linearity serves to limit the amplitude of the cantilever’s oscillation in the parametric amplification regime. The experiments were performed with an aim to clearly identify the advantages and disadvantages that parametric resonance offers for scanning probe applications. The electronic feedback technique allows an enhancement of the microcantilever’s effective quality-factor (Q-factor) by two orders of magnitude under ambient conditions. This simple observation extends the mass sensing capabilities of a conventional AFM microcantilever into the sub-picogram range. Experiments designed to parametrically oscillate a microcantilever in water using electronic feedback also show an increase in the microcantilever’s effective Q-factor by two orders of magnitude.

Degree

Ph.D.

Advisors

Reifenberger, Purdue University.

Subject Area

Mechanical engineering|Condensed matter physics|Nanotechnology

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