Investigation of quality factor variation based on tailored mode shape engineering for piezoelectric contour mode resonators

In this work, a prediction approach of quality factor (Q) variation induced by the anchor loss through mode shape engineering has been proposed by finite-element method (FEM) simulation and experimental validation. Such an effective prediction scheme as well as Q-manipulation can serve as an initial estimation of the Q enhancement in design phase before any additional anchor loss reduction approaches are applied, e.g., acoustic reflector or quarter wavelength design. Furthermore, the whole anchor loss simulation of the resonator using Perfectly Matched Layers (PMLs) is performed, which covers various designs from Length-extensional mode (LE) to Width-extensional mode (WE). Finally, the measured Q’s of 11021, 6063, and 1938 in vacuum, respectively, of the fabricated resonators featuring Length-to-Width (L/W) ratio from 1.6875 to 1.9375 are qualitatively in good agreement with the FEM simulated results.