Tailored Etch Profiles for Wafer-Level Frequency Tuning of Axisymmetric Resonators

This paper reports a wafer-level technique for the systematic elimination of the modal frequency difference between a nominally degenerate pair of modes in an axisymmetric resonator design. A targeted etch process is developed in which masking resist and a conformal layer are ablated at specific sites on the resonator thereby exposing the underlying silicon and enabling site-specific mass removal by SiDRIE. A model of the perturbed resonator dynamics guides the selection of the ablation sites so that the subsequent timed etch reduces the modal frequency differences by a prescribed amount. This wafer-level process is demonstrated on seven resonators whose modal frequency differences are reduced below 100 mHz from initial splits as large as 15 Hz for a pair of modes with 13.5 kHz nominal frequencies. [2016-0208]