Micromachined polycrystalline diamond hemispherical shell resonators

Abstract

The hemispherical resonator gyro (HRG) is low loss and high stability, spurring recent interest in micro-scale hemispherical resonators. To achieve mode-matching and high-Q performance in a hemispherical resonator, geometric symmetry in combination with low thermoelastic damping structural material are critical. In this work, we describe the development of millimeter scale 3D hemispherical shell resonators fabricated from polycrystalline diamond, a material with low thermoelastic damping and very high stiffness. The relation between the fourth harmonic (4θ) in a Fourier analysis of the resonator's radius r(θ) and frequency mismatch (Δf) of the 2θ elliptical vibration modes of the shell resonator is demonstrated.

Demonstration of 1 Million <inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula>-Factor on Microglassblown Wineglass Resonators With Out-of-Plane Electrostatic Transduction

“…Since the volume of the wineglass will continuously change during the transient solution, (4) can not be used to calculate V wineglass . Instead, a surface integral for the inner surface of the wineglass is used:…”

“…For example, Q-factor of 19.1k have been demonstrated on poly-silicon shell structures deposited in preetched cavities [3]. Q-factors up to 24k [4] were measured on poly-diamond wineglass shells deposited in pre-etched cavities and up to 20k were measured on sputtered Ultra Low Expansion (ULE) glass shells deposited on precision ball lenses [5]. Q-factors as high as 7.8k was demonstrated on blow-molded bulk metallic glass shells [6] and 1 million on fused silica shells [7].…”

“…For thin film devices this is accomplished by defining electrode structures within the pre-etched cavity by placing a sacrificial layer in between the electrode and the device [4], [8]. For glassblown devices a wide variety architectures have been demonstrated, including deep glass dry etching of the capacitive gaps [9] (>30μm), utilization of thermal mismatch between the shell and the mold to create the capacitive gaps [6] (∼15μm), and various assembly techniques [10], [11] (∼15μm).…”

Design and Fabrication of Micro Hemispheric Shell Resonator with Annular Electrodes

“…Several methods for the fabrication of MEMS wineglass resonators have been published in the literature. These methods include: thermally growing oxide in isotropically etched cavities [8], micro crystalline diamond deposition on hemispherical molds [18], and utilizing a sphere mold on which polysilicon and ultra low expansion titania silicate glass are deposited and releasing the hemispherical shell [19]. However, these methods involve complicated processes, and the roughness of hemispheric shells is difficult to reduce down to 10 nm due to fabrication precision of the molds.…”

Out-of-plane electrode architecture for fused silica micro-glassblown 3-D wineglass resonators

“…For example, Qfactor of 19.1k have been demonstrated on poly-silicon shell structures deposited in pre-etched cavities [1]. Q-factors up to 24k [2] were measured on poly-diamond wineglass shells deposited in pre-etched cavities and up to 20k were measured on sputtered ultra low expansion (ULE) glass shells deposited on precision ball lenses [3]. Q-factors as high as 7.8k was demonstrated on blow-molded bulk metallic glass shells [4] and 1 million on fused silica shells [5].…”