Fluctuations and nonlinearities in micromechanical thermal-piezoresistive resonators
Keywords: Mechanical Engineering.

Micro- and nanoelectromechanical (MEM/NEM) resonators underlie many of the sensors and oscillators that are used in scientific research and technology. A wide range of techniques have been demonstrated for tuning the effective damping in MEM/NEM resonators. This dissertation explores two emerging effective damping tuning techniques, parametric pumping and thermal-piezoresistive pumping. This work studies the fluctuations and nonlinear dynamics of micromechanical resonators subjected to these effective damping tuning mechanisms, and demonstrates their utility for novel sensor and oscillator topologies. The first chapter introduces quality factor, related to inverse damping, in MEM/NEM resonators. Quality factor is then compared to "effective" quality factor, which arises when an external source or sink of energy is introduced to modify the resonator dynamics without modifying the thermal noise force. The various techniques for tuning the effective quality factor, such as external feedback control, optical pumping, mechanical pumping, thermal-piezoresistive pumping, and degenerate parametric pumping, are summarized. The second chapter presents a capacitive and piezoresistive sensing scheme for detecting the vibrations of encapsulated silicon micromechanical resonators. The low-noise capacitive sensing scheme enables radio-frequency displacement measurements across 1 μm capacitive gaps with 99.8% thermomechanical-noise-limited resolution, which is optimal for studying fluctuations. The piezoresistive transduction scheme provides a linear displacement readout at large vibration amplitudes while avoiding capacitive feedthrough, which is optimal for studying nonlinear dynamics. The third chapter investigates a recently discovered feedback mechanism in silicon MEM/NEM resonators known as thermal-piezoresistive pumping (TPP). A coupled finite-element model is developed and experimentally validated to predict the dependence of effective quality factor on direct current for arbitrary geometries, orientations, and doping. The thermomechanical noise spectrum in the presence of TPP reveals that TPP modifies the resonator transfer function without substantially influencing the thermal noise force. Beyond the self-oscillation threshold, the nonlinearities stabilize the vibrations. Two mechanisms for stabilizing the vibrations are identified and characterized: repulsive contact and geometric nonlinear damping. Piecewise viscous dissipation and piecewise nonlinear dissipation is observed during contact with the sidewalls, which is responsible for the amplitude stabilization during repulsive contact. The fourth chapter theoretically and experimentally investigates degenerate parametric pumping in MEM/NEM resonators. An improved model is derived to describe the thermomechanical noise spectrum of a parametrically pumped resonator below the parametric oscillation threshold, and is corroborated with experiments on a micromechanical cantilever. A model is derived and experimentally validated to describe the nonlinear dynamics of parametric oscillations in the presence of a Duffing/Kerr nonlinearity and nonlinear damping. For special values of nonlinear damping, a novel parametric-oscillator-based frequency reference scheme is demonstrated