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Realization and analysis of parametric resonances in a nanowire mechanical system with nanomanipulation inside a scanning electron microscope

Min-Feng Yu
University of Illinois at Urbana-Champaign, US

Keywords: parametric resonance, nanostructure, nanomanipulation

We realize parametric resonances in a nanowire mechanical system using an oscillating electric field. The realization of high order parametric mechanical resonance in macroscopic systems is generally difficult due to mechanical energy losses and strict conditions applied at higher n determined by the system parameters; high order (for n up to 4) parametric mechanical resonance was only recently observed in MEMS resonators. A nanomanipulation stage was developed for use inside a field emission scanning electron microscope. We report the discovery of up to four parametric resonances for cantilevered nanowires. Resonances at drive frequencies near 2f0/n, where f0 is the nanowire’s fundamental resonance, for n from 1 to 4 were observed inside a scanning electron microscope, and analyzed. A theory for a forced vibration system that includes a forcing term proportional to the amplitude of the resonance was used for the analysis, regions of instability were mapped, and hysteresis in the parametric resonance response curve was observed. Excellent agreement between the theory and experiment was found. The resonances were found to originate from the amplitude dependent electric field force acting on the nanowire and can be described by the Mathieu equation, which has known regions of instability in the parameter space.

NSTI Nanotech 2003 Conference Technical Program Abstract

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