Achieving Sub-Hz Frequency Symmetry in Micro-Glassblown Wineglass Resonators

Abstract

We demonstrate, for the first time, sub-1 Hz frequency symmetry in micro-glassblown wineglass resonators with integrated electrode structures. A new fabrication process based on deep glass dry etching was developed to fabricate microwineglasses with self-aligned stem structures and integrated electrodes. The wineglass modes were identified by electrostatic excitation and mapping the velocity of motion along the perimeter using laser Doppler interferometry. A frequency split ( f ) of 0.15 and 0.2 Hz was demonstrated for n = 2 and n = 3 wineglass modes, respectively. To verify the repeatability of the results, a total of five devices were tested, three out of five devices showed f < 5 Hz. Frequency split stayed below 1 Hz for dc bias voltages up to 100 V, confirming that the low frequency split is attributed to high structural symmetry and not to capacitive tuning. High structural symmetry (<1 Hz) and atomically smooth surfaces (0.23 nm Sa) of the resonators may enable new classes of high performance 3-D MEMS devices, such as rate-integrating MEMS gyroscopes.

Modal Parameter Tuning of an Axisymmetric Resonator via Mass Perturbation

“…8. Overlaid on the data is the frequency response of the identified model (13) and analysis of this model reveals ω 1 = 13530.08 Hz, ω 2 = 13504.67 Hz, ψ 1 = 33.5…”

“…More recently, a number of fabrication results have been published on microscale threedimensional resonators. The effects of electrostatic biasing or outright modal frequency tuning has been reported for hemispheres [11], [12], hemitoroids [13], [14], and cylinders [15]. Few results, however, have been reported on the permanent modification of microscale resonators.…”

MEMS Micro-glassblowing Paradigm for Wafer-level Fabrication of Fused Silica Wineglass Gyroscopes

“…This leads to atomically smooth surfaces (0.23 nm Sa measured on glassblown shells using AFM [8]) and frequency splits ( ) that are uniformly low across the wafer. Table 1, shows summary of 5 borosilicate glass wineglasses on the same wafer, demonstrating ppm level frequency symmetry between the two degenerate n = 2 wineglass modes [9]. …”

Energy Dissipation Contribution Modeling of Vibratory Behavior for Silicon Micromachined Gyroscope

“…As for the structure topologies which mainly affect anchor damping, anchor loss models of simple cantilever beam have been established [46][47][48]. However, for some complex fully 3D resonators, contributions of another geometrical resonators including DETF [21], tether geometry [49][50][51], microsphere [52], cupped [52,53], wineglass [54], hemispherical [39], and disk shapes [55][56][57] to anchor loss are calculated hard by the analytical solution if no simplifying assumption is present. Damping loss model on accurately estimating the experiment results for these complex structure topology is very limited.…”