Highly-symmetric silicon dioxide shallow shell resonators with angstrom-level roughness

Abstract

A highly-symmetric silicon dioxide shallow shell resonator with angstrom-level roughness (Ra=4.3Å) is presented. Curvature discontinuities in shallow shells, at a controlled distance from the base anchor of the shell, provide acoustic decoupling and significantly reduce the anchor contribution to the frequency split in degenerate wineglass modes as well as their damping. The Finite Element Method (FEM) simulations, performed in COMSOL 4.4, show increasing strain energy density at the vicinity of curvature discontinuities, confirming acoustic decoupling. The fabricated resonant shells are symmetric structures with largely asymmetric supports to force the anchoring stem to be the main contributor to the frequency split. ConformalImaging Vibrometer (CIV) measurement characterization indicate that the fabricated shallow shell resonators have as-born sub-Hz frequency splits (∆f/f≈60ppm), without any electrical frequency tuning, for the lowest elliptical mode shapes, while having asymmetric anchoring stems.

Recent Advances in MEMS-Based 3D Hemispherical Resonator Gyroscope (HRG)—A Sensor of Choice

“…In CVGs, the resonating mass acts as the main sensing element and the geometry of it can be of different shapes. Based on the resonating mass, these types of gyroscopes can be in the form of a string [ 4 ], a single beam [ 5 , 6 ], U-shaped tuning forks (two parallel beams) [ 7 , 8 , 9 ], rocking-mass gyroscope systems (two perpendicular in-plane beams) [ 10 , 11 ], a butterfly [ 12 , 13 ], disks [ 14 , 15 , 16 , 17 , 18 , 19 ], cloverleaf-type disks [ 20 ], rings [ 21 , 22 , 23 ], rings with compliant spokes [ 24 ], non-continuous double rings (called folded-beam disks) [ 25 ], disks with special forms of supporting beams (called honeycomb disks) [ 26 ], cylinders [ 27 , 28 , 29 , 30 , 31 ], cupped cylinders [ 32 ], bell-shapes [ 33 , 34 , 35 ], 3D rectangular parallelepiped gyroscopes based on special vibratory modes of solid material (e.g., thickness-shear vibrating mode) [ 36 , 37 ], pierced shallow shells [ 38 ], shallow shells [ 39 ], microbubbles (spherical caps with a radius-over-height ratio larger than one) [ 40 ], cennospheres (hollow spheres) [ 41 ], quasi-spherical forms [ 42 ], spherical shell resonator gyroscopes [ 43 , 44 ,…”

Fabrication and characterisation of microscale hemispherical shell resonator with diamond electrodes on the Si substrate

“…Another study also reported an MEMS diamond hemispherical resonator that was fabricated by isotropically etching the glass (Corning 1715) as the hemispherical mould [8]. An Si dioxide shell resonator is presented in [9, 10] and a polySi microhemispherical resonating gyroscope is reported in [11, 12]. The material of Invar‐36 is also used to fabricate microhemispherical shell resonator in [13].…”

“…Meanwhile, most microhemisphere shell resonators studied were fabricated without the integrated electrodes. Many researches did not fully construct sensing and driving units for functioning resonating structures [4][5][6][7][8][9][10]. These approaches are limited by the lack of functional electrode structures with controllable capacitive gaps.…”