Microelectromechanical (MEMS) resonators are widely used in time-keeping and sensor applications due to their high quality factors and good frequency stability. In these applications, the function of MEMS resonators are often realized by driving them into self-sustained oscillations to maintain continuous tracking of changes in frequency. However, the small size and mass also make these resonators extremely sensitive to thermal fluctuations and easily become nonlinear, both of which highly degrade their performance in precision measurements. In this thesis, I explore methods of phase noise reduction on MEMS resonators driven into self-sustained oscillations.

I design a microelectromechanical trampoline resonator with its eigenfrequency obeying a non-monotonic relationship with energy. N...[ Read more ]

Microelectromechanical (MEMS) resonators are widely used in time-keeping and sensor applications due to their high quality factors and good frequency stability. In these applications, the function of MEMS resonators are often realized by driving them into self-sustained oscillations to maintain continuous tracking of changes in frequency. However, the small size and mass also make these resonators extremely sensitive to thermal fluctuations and easily become nonlinear, both of which highly degrade their performance in precision measurements. In this thesis, I explore methods of phase noise reduction on MEMS resonators driven into self-sustained oscillations.

I design a microelectromechanical trampoline resonator with its eigenfrequency obeying a non-monotonic relationship with energy. Near the extremum energy, where the eigenfrequency does not change, the resonator behaves almost like a linear resonator even if the vibration amplitude is large. The noise driven response spectra becomes narrower when the noise intensity is increased. When the resonator is driven into self-sustained oscillation by a phase locked loop, the phase noise at the extremum amplitude is ~3 times smaller than the minimum of the conventional nonlinear resonator.

I also design a two-mode microelectromechanical system. A pump at the red secondary sideband of the high frequency mode induces strong nonmonotonic positive nonlinear friction on the low frequency mode which significantly changes the dynamics of the oscillator. I study the generic features of parametric driven responses of the oscillator under such nonlinear friction. I demonstrate the electrostatic tuning of bifurcation topology of the oscillator. I present the noise squeezing from the merging of five states. In addition, I observe direct cooling on a nonzero amplitude state in the parametric oscillator in simulation. The phase noise is reduced by a factor of 1.8 compared with ordinary parametric oscillator.