Vibration analysis of original shape quartz resonator for high quality factor realization

AT-cut quartz resonators are widely used as timing devices in computers, mobile information, and communication tools, etc. Recently, quartz resonators have been applied to highly sensitive devices. To improve frequency stability, AT-cut quartz resonators must have an excellent temperature characteristic and high quality (Q) factor. Energy trapping and spurious mode coupling strongly affect the performance of resonators, and both parameters are determined by the shape of the resonator. As for achieving a higher Q, the most effective technique is to process the quartz cross-sectional shape into a plano-convex or bi-convex shape. However, it is difficult to manufacture a convex shape on the surface of a quartz wafer. For this reason, we propose an equivalent plano-convex shape, which was realized by arranging fine protrusions on the surface of quartz. In addition, the optimization of the original resonator shape has been discussed.