ERI: Improving Micromechanical Timekeeping Performance with Variable Mechanical Strain

This Engineering Research Initiation (ERI) award supports research that enables the characterization of the dynamics of micro-electro-mechanical resonators, thereby promoting public welfare and national health. These resonators consist of tiny vibrating mechanical structures that are essential elements for state-of-the-art sensing and timekeeping devices used in a wide variety of consumer, industrial, and military hardware, from satellites to cell phones. This research will study the role of variable mechanical tension at the microscale, applied in an analogous manner to the tuning peg of a guitar string, to tune the resonator vibration frequency and dramatically improve the performance of the corresponding timing reference or sensor. Theoretical and computational models will be developed to study the effects of variable tension on vibrational systems, and the models will be validated by characterizing manufactured devices. The broader impacts of this project include outreach, mentoring and training undergraduate students, inclusion of students from underrepresented groups, incorporating the research into course materials, and disseminating the results. This research aims to investigate the nonlinear dynamics of micro-electro-mechanical resonators with ultra-stable resonance frequency achieved with variable dissipation dilution (strained silicon) and internal resonance (coupling between modes). It will achieve this goal by theoretically and experimentally delineating the relationship between dissipation dilution and resonator quality factor, nonlinear vibration amplitude, noise spectrum near the resonance frequency, and oscillator frequency stability limits using micro-electro-mechanical devices which can apply large tunable strains. This project will utilize a microscale electrostatic shuttle structure to apply uniaxial strains to a silicon micromechanical beam resonator, which will enable tunability of the resonance frequency of the beam fundamental flexural mode by over ten-fold, resulting in improvements in its short-term frequency stability by more than a factor of one hundred. Varying the transduction bias voltages will adjust the oscillator from amplifier-noise-limited behavior to thermomechanical-noise-limited behavior, enabling delineation of resonator parameters in both regimes as a function of beam strain. Compared to previous fabrication-based dissipation dilution approaches, this tunable approach will enable systematic investigation of the effects of variable dissipation dilution on the resonator nonlinear dynamics and corresponding oscillator performance. The broad frequency tunability will enable concomitant studies of internal resonance with various frequency combinations, multiple-order parametric resonance in a beam resonator exhibiting non-monotonic frequency-amplitude dependence and elucidating the mechanisms underlying nonlinear dissipation by controlling the mechanical strain. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.