Performance optimization of high order RF microresonators in the presence of squeezed film damping

• Design of a bulk microresonator that can be operated under different resonant modes.
• Characterization of the resonator to evaluate the effect of squeezed film damping on its performance.
• Development of a numerical model to evaluate squeezed film damping for various operating modes.
• Devising device and process design methods to minimize squeezed film damping on device performance.
• Devising metrics to choose a resonant mode for improved performance and reduced sensitivity to ambient pressure.

Silicon microresonators are gradually penetrating the low- to mid-range markets for traditional timing and frequency references while generating many new opportunities along the way. A key characteristic requirement for resonators in such applications is attaining a high quality factor, which leads to lower insertion losses and improved oscillator stability. In this work, we demonstrate that it is possible to take advantage of the higher order resonant modes to push the performance limits of bulk resonators and achieve high quality factors while relaxing the packaging requirements. In particular, we study the effect of squeezed-film damping on the behaviour of high frequency, higher order resonant modes of bulk resonators. A micromachined bulk resonator was designed and fabricated such that its fundamental extensional mode as well as its first two Lamé modes could be excited and monitored. The resonator exhibited a high quality factor of 1.2 × 106 for its first Lamé mode at 8 MHz. When the second Lamé mode of the device at 16 MHz was excited, the measured f·Q product was 1.37 × 1013 Hz. Experimental results from this device were used to verify a numerical model which was developed to study squeezed-film damping and its relation with device design and operating parameters. The model demonstrates that there are optimum operating parameters when a high frequency resonator is needed. The model can be used as a design tool to study the effects of electrode separation and structural thickness on squeezed-film damping for different modes.