Dimension optimization for a miniature high-frequency quartz resonatore

In this paper, optimal design of a miniature AT-cut high-frequency quartz resonator is presented. This miniature AT-cut high-frequency quartz resonator is about only 25% of the AT-cut high-frequency resonator products in current market. It can be fabricated by our newly developed manufacturing process of MEMS quartz resonator, which cannot be realized by previous mechanical process. A three-dimensional finite element model using linear cuboid-type elements was established to carry out eigen-frequency analysis. To describe quantitatively the spurious coupling strength, we carried out the linear regression analysis to recover the ideal fundamental thickness-shear vibration without spurious vibration coupling, and introduced a parameter named coupling coefficient. To describe quantitatively the energy trapping performance of the resonator, we introduced a parameter named energy trapping rate defined by ratio of vibration energy inside and outside of electrode region. Optimal dimensions of resonator providing small coupling coefficient and large energy trapping rate were determined. The optimization method can certainly be applied in the development of the miniature high-frequency quartz resonators.