Optimization of tether geometry to achieve low anchor loss in Lamé-mode resonators

In this paper, we study the fundamental cause of anchor dissipation in Lamé- or wineglass-mode resonators and show that by carefully optimizing the resonator tether geometry low anchor losses can be achieved, making it possible to reach the intrinsic fxQ limit of the resonating material. Through analytical and finite element investigation, we demonstrate that the anchor loss is most significant when the flexural-mode resonance frequency of the tether is in sync with the Lamé-mode frequency of the resonating plate. This has a significant bearing on the design of Lamé-mode resonators with release holes or temperature-compensation trenches, where the modification of the resonator structure requires modification to the tether geometry to maintain a high Q. We verify the predicted results through experimental measurements and present an optimized design that exhibits a mechanical Q of 408,270 for the fundamental Lamé mode at 41.57 MHz. The fxQ for this device is 1.7×10¹³, one of the highest values reported in silicon.