Frequency split reduction by directional lapping of fused quartz micro wineglass resonators

We present a study on the permanent frequency split reduction of fused quartz micro wineglass resonators by directional lapping. Using the technique, we demonstrated a near 6× reduction of frequency split (n=2 wineglass mode). The process included two steps. First, the orientations of the Principal Axes of Elasticity (PAE) were determined by measuring the mode shapes of the resonator. Then, the directional lapping was performed based on the information about PAE. Three devices were post-processed by directional lapping technique and the frequency split was reduced as predicted, demonstrating feasibility of the technique. The reduction of frequency split is directly correlated to improvements in structural isotropy and the overall performance of dynamic MEMS, such as rate and rate-integrating gyroscopes.