Abstract
Micromechanical oscillators provide periodic output signals for clocks and sensors by vibrating in a single mechanical mode. The mode is conventionally excited into self-sustained oscillations and stabilized with an external electronic feedback loop. A paradigm is emerging for sustaining vibrations by coupling the mechanical mode with internal degrees of freedom, such as photons, electrons, or auxiliary mechanical modes. An open question in these hybrid vibrational systems is the corresponding internal sources of nonlinearity that can stabilize the oscillations, and their impact on oscillator performance. Here, we delineate two kinds of amplitude-stabilization mechanisms in micromechanical oscillators, geometric nonlinear damping and repulsive contact, and show that these mechanisms can coexist in the same device and their interplay and resonance frequency stability can be tuned in situ by adjusting the feedback strength. An auxiliary source of viscous dissipation and nonlinear dissipation accompanies the repulsive contact, which stabilizes the amplitude during sidewall collisions. The onset of self-sustained oscillations yields distinct spectral-temporal signatures that can be used to identify the amplitude stabilization nonlinearities.
Highlights
Micro- and nanoelectromechanical (MEM/NEM) resonators often serve as the frequency-determining elements within oscillators for resonant sensors and timing references
Positive nonlinear damping provides another route for stabilizing the oscillation amplitude, and geometric nonlinear dissipation has been observed in MEM/NEM resonators constructed from doubly clamped beams [35,48,49,50] and membranes [51,52]
We delineate two kinds of amplitude stabilization mechanisms in hybrid vibrational systems sustained via the coupling between electrons and mechanical vibrations: geometric nonlinear damping and repulsive contact
Summary
Micro- and nanoelectromechanical (MEM/NEM) resonators often serve as the frequency-determining elements within oscillators for resonant sensors and timing references. Positive nonlinear damping provides another route for stabilizing the oscillation amplitude, and geometric nonlinear dissipation has been observed in MEM/NEM resonators constructed from doubly clamped beams [35,48,49,50] and membranes [51,52]. We investigate the geometric nonlinear dissipation and repulsive contact mechanisms as a resource for amplitude stabilization in MEM/NEM oscillators. For amplitude stabilization via repulsive contact, we demonstrate stable operation for over 1 billion cycles, and show that significant improvements in oscillator frequency stability can be attained by utilizing a feedback strength close to threshold. We show that repulsive contact is a robust mechanism for stable operation of oscillators within hybrid vibrational systems based on electron coupling, and can be readily implemented for other domains of coupling and for a wide variety of other flexural and bulk mode resonator geometries
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