A Gaussian-shaped AT-cut quartz crystal resonator

This paper reports the design and fabrication of a Gaussian-shaped AT-cut quartz crystal resonator. The thickness distribution of the resonator was designed following a Gaussian-type function. The distribution was based on the analysis of thickness shearing vibration calculated using finite element analysis for a flat-shaped resonator. The vibration analysis showed improvement of the energy trapping effect, and the vibration at the wafer edge was negligible. For the experimental verification, we attempted to fabricate a Gaussian-shaped resonator using microfabrication technologies. The resonant characteristics were substantially improved by the shaping.