Design and Fabrication of a Gaussian-Shaped AT-Cut Quartz Crystal Resonator

This paper reports design and fabrication of 3D shaped AT-cut quartz crystal resonator. The thickness distribution of the resonator is designed following a Gaussian-type function. The distribution was postulated from the analysis of thickness shearing vibration calculated by a finite element analysis (FEA) for a flat-shape 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 MEMS technologies. The resonant characteristics were improved well by the shaping.