Dynamics of NEMS Resonators across Dissipation Limits

TL;DR

This paper investigates how increasing dissipation affects the oscillatory behavior of NEMS resonators, showing a transition from standing wave patterns to propagating and attenuated waves, and proposing a wave superposition model for better description.

Contribution

It experimentally maps the transition in NEMS dynamics from undamped eigenmodes to propagating waves as dissipation increases, offering a new wave superposition framework.

Findings

At low dissipation, sharp resonances match undamped eigenfunctions.

Increased dissipation leads to loss of standing wave patterns.

High dissipation results in strongly attenuated propagating waves.

Abstract

The oscillatory dynamics of nanoelectromechanical systems (NEMS) is at the heart of many emerging applications in nanotechnology. For common NEMS, such as beams and strings, the oscillatory dynamics is formulated using a dissipationless wave equation derived from elasticity. Under a harmonic ansatz, the wave equation gives an undamped free vibration equation; solving this equation with the proper boundary conditions provides the undamped eigenfunctions with the familiar standing wave patterns. Any harmonically driven solution is expressible in terms of these undamped eigenfunctions. Here, we show that this formalism becomes inconvenient as dissipation increases. To this end, we experimentally map out the position- and frequency-dependent oscillatory motion of a NEMS string resonator driven linearly by a non-symmetric force on one end at different dissipation limits. At low dissipation (high Q factor), we observe sharp resonances with standing wave patterns that closely match the eigenfunctions of an undamped string. With a slight increase in dissipation, the standing wave patterns become lost and waves begin to propagate along the nanostructure. At large dissipation (low Q factor), these propagating waves become strongly attenuated and display little, if any, resemblance to the undamped string eigenfunctions. A more efficient and intuitive description of the oscillatory dynamics of a NEMS resonator can be obtained by superposition of waves propagating along the nanostructure.