Design and Fabrication of High-Q Birdbath Shell Resonators for MEMS Gyroscopes
Sajal Singh, Tal Nagourney, Jae Yoong Cho, Ali Darvishian, Behrouz Shiari, Khalil Najafi, University of Michigan Ann Arbor
Location: Big Sur
GPS navigation is commonly used in many applications including defense, autonomous vehicles, and robotics. However, absolute dependence on GPS is unreliable due to its susceptibility to interference. To make navigation more secure and reliable gyroscope-based inertial measurement units (IMU) are used to sense the rotation rate and angle with high precision. However, their large sizes, high costs and power requirements limit their use in many applications. MEMS-based vibratory gyroscopes are attractive candidates for reducing IMU size and cost. However, their high bias instability and mechanical noise limits MEMS gyroscope from achieving navigation-grade performance. To mitigate these effects, it is imperative to design a resonator with a long ring-down time constant and high quality-factor (Q). Long ring-down time constant improves bias instability by reducing bias drift due to asymmetric damping. At the same time, high Q reduces mechanical noise and increases gyroscope sensitivity leading to lower angle random walk.
In this work, we design and fabricate fused silica (FS) 3D shell resonators known as birdbath (BB) resonators of radius 2.5 mm (BB-2.5) and 5 mm (BB-5) exhibiting long ring-down time constants and high Q. We previously reported BB-2.5 resonator characteristics in  and BB-5 performance in . [3,4] demonstrated a BB resonator as a gyroscope. Here, we present our latest results on the performance of BB resonators with BB-2.5 resonator exhibiting ring-down time constant of 207 seconds and Q of 5.99 million. Similarly, BB-5 resonator exhibited ring-down time constant of 495 seconds and Q of 7.97 million. These results are unprecedented in their class of resonators.
BB resonators have hollow and self-aligned anchors that makes the shells symmetric in shape and minimizes anchor loss. They have a gradually thickening sidewall profile from the anchor to the resonating rim. The large mass at the rim helps increase the modal mass and in turn the Coriolis force which improves the gyroscope resolution. BB resonators operate in the degenerate n=2 wine-glass (WG) modes with frequencies of ~10 kHz for the BB-2.5 and ~5 kHz for the BB-5 resonators which are higher than that of environmental noise. This makes the BB resonator gyroscope tolerant to ambient vibration. Due to fabrication imperfections, the two modes are not exactly matched, and the shells exhibit a small difference in resonant frequencies (df) between the two modes. After depositing a conductive metal layer and packaging the BB resonator with electrodes, df can be reduced to the mHz range with electrostatic tuning.
BB shells are fabricated using FS, which has inherently lower thermoelastic damping (TED) loss. The shells are formed by an in-house developed glass blowing technique called blowtorch molding, where a flat FS substrate sits on a machined graphite mold. An oxygen-propane flame reaching temperature >1700C softens the substrate, which reflows under the vacuum pull from the mold forming hemitoroidal shells in 5–20 seconds . The high temperature flame also smooths the shell surface with average roughness of the fabricated shell being less than 2 angstroms. This ultra-smooth surface is important for reducing losses from the surface. The blowtorching parameters and the mold design allows the fabrication of shells of different radii and aspect ratios. After molding, the BB shells are encapsulated in a thick silicon wafer with holes using a thermoplastic. The silicon wafer containing the shells is lapped to isolate the shells from the substrate they were molded from. Subsequently, the rims are polished using chemical-mechanical planarization (CMP) .
Post-isolation, the shells are attached from the anchor on a silicon substrate using glass-frit and tested for their resonant characteristics using a laser Doppler vibrometer (LDV) in vacuum. The shells are excited using a piezoelectric actuator and the motion of the rim is measured using the LDV. The FFT of the response reveals the two n=2 WG mode frequencies. In turn, each mode is driven into resonance; the drive signal is then cut-off and the vibrations are allowed to freely decay. The ring-down constant is calculated by measuring the time taken to decay the amplitude by a factor of e as compared to the initial vibration amplitude. We have fabricated BB-2.5 shell which exhibits ring-down time constant of 207 seconds and Q of 5.99 million at the resonance frequency of 9.209 kHz with a df of 47.5 Hz. Similarly, BB-5 shell has exhibited ring-down time constant of 495 seconds and Q of 7.97 million at the resonance frequency of 5.127 kHz with a df of 6.5 Hz.
Conclusion and Significance
We believe that minimizing the surface loss has been instrumental in fabricating high-performance micro-shell resonators. We have observed the performance of BB resonators to be greatly deteriorated by the presence of foreign particles, films, residues on the shell surface. We have optimized our fabrication process to minimize the surface loss and this has proved to be important in achieving long ring-down time constant and high Q. We also believe that higher volume-to-surface ratio of BB-5 is critical in reducing the surface loss thus increasing the quality factor. At the same time, BB-5 resonators have lower df than BB-2.5. This is because of the fabrication imperfections which becomes less prominent as the shell size increases. Nevertheless, both sizes of resonators have long ring-down time and Qs and we believe they will prove to be instrumental in producing MEMS gyroscopes that can reach the performance level of modern commercial macro-gyroscopes, enabling affordable inertial navigation for a wide range of applications.
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