Dynamics of NEMS resonators across dissipation limits

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 at 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.

Imaging Nanomechanical Vibrations and Manipulating Parametric Mode Coupling via Scanning Microwave Microscopy

“…To date, various sensitive transduction schemes have been achieved for detecting and manipulating nanomechanical resonators. These mainly include methods based on electrical detection or optical interferometry. − The former technology is widely used for testing electrically integrated nanomechanical systems, which requires the design and nanofabrication of on-chip circuits to detect and control vibrating elements. However, this technique does not have the spatial resolution required to study localized mechanical vibrations.…”

Atmospheric-Pressure Mass Spectrometry by Single-Mode Nanoelectromechanical Systems

“…Apart from requiring two measurement channels running in parallel, the applicability of multimode techniques requires the knowledge of mode shapes that deviate from their ideal values due to non-idealities in nanofabrication, the local stress on the device, and the random accumulation of adsorbates on the surface. In addition to these factors, a recent study uncovered that the displacement profiles of the NEMS devices are altered to some degree when the NEMS are operated under atmospheric conditions due to the higher dissipation − (i.e., lower quality factor) caused by viscous damping of air compared to the vacuum, when the devices are driven from one extremity of the device. − This difference is evident in flexural resonance modes, which are needed for accurate reverse calculation of the mass and the landing position of an analyte particle. Therefore, the governing equations for multimodal detection now introduce uncertainties for obtaining the mass spectrum of the particles.…”