Design and Fabrication of High-Q Birdbath Resonator for MEMS Gyroscopes

Sajal Singh Electrical and Computer

Engineering University of Michigan

Ann Arbor, Michigan, USA sajals@umich.edu

Tal Nagourney Electrical and Computer

Engineering University of Michigan

Ann Arbor, Michigan, USA taln@umich.edu

Jae Yoong Cho Electrical and Computer

Engineering University of Michigan

Ann Arbor, Michigan, USA jycho@umich.edu

Ali Darvishian Electrical and Computer

Engineering University of Michigan

Ann Arbor, Michigan, USA darvishi@umich.edu

Behrouz Shiari Electrical and Computer

Engineering University of Michigan

Ann Arbor, Michigan, USA bshiari@umich.edu

Khalil Najafi Electrical and Computer

Engineering University of Michigan

Ann Arbor, Michigan, USA najafi@umich.edu

Abstract—We present the design, fabrication, and measurement results of an axisymmetric 3D micro-shell resonator called the birdbath resonator. Three classes of birdbath resonators are studied; all exhibiting a record performance in terms of high-quality factor and long ring down time constants for their sizes. We also show that such high performing resonators have the potential to achieve low angle random walk and bias instability, achieving navigation-grade performance.

Keywords—High-Q resonator, shell resonator, MEMS gyroscope

I. INTRODUCTION

GPS navigation is commonly used in many applications including defense, autonomous vehicles, and robotics. However, absolute dependence on GPS can be unsafe due to its susceptibility to interference and unavailability. To make navigation more secure and reliable, inertial gyroscopes 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 size, cost and power requirements; however, their high bias instability (BI) and mechanical noise prevent MEMS gyroscopes from achieving navigation-grade performance. To mitigate these effects, it is imperative to design a resonator with a long ring-down time constant (τ) and high quality factor (Q). At the same time, these micro-devices should survive challenging and dynamic environmental conditions. To improve BI, it is critical to minimize asymmetric stiffness and damping. While asymmetric stiffness can be addressed using electronic frequency tuning; asymmetric damping can be improved by achieving long τ. The effect of mechanical noise or angle random walk (ARW) can be improved by achieving high Q. Finally, interference from environmental vibrations can be

avoided by positioning the n=2 wine-glass (WG) mode frequencies above the environmental noise frequency range. Recent advancements in MEMS gyroscopes have led to improved BI and ARW; however, achieving navigation-grade performance remains a challenge. As a result, designing a vibratory gyroscope that advances the performance on all fronts is needed for commercialization of MEMS vibratory gyroscopes for inertial navigation.

Different 2D and 3D resonators have been proposed for application as gyroscopes. A quad-mass silicon gyroscope was reported in [1] with τ ≈ 150 seconds at 2 kHz. While such a low operating frequency (f) reduces thermoelastic dissipation (TED), it can potentially have high vibration sensitivity due to its proximity to environmental noise frequencies. Other 2D gyroscopes including the DRG [2] and ring [3] structures have limited Q due to the large TED of Si at high f (> 10kHz). 3D shell resonators made of fused silica (FS) are attractive because they have excellent Q due to low TED even at high f. At the macro scale, HRGs [4] have achieved navigation-grade gyroscope performance. At the micro scale, [5] reported a Q ≈ 1

Fig. 1: Photograph of a BB-5 resonator mounted on a silicon substrate.

978-1-5386-1647-5/18/$31.00 ©2018 IEEE 15

million at frequency of 105 kHz. Reference [6] recently reported another micro-shell resonator with tailored stiffness and mass and achieved Q of 1.4 million at 17 kHz WG frequency. We previously reported birdbath (BB) shell resonator performance with long τ (>250 seconds) and high Q (> 4 million) at 5.5 kHz in [7]. In this work we report our latest results of three classes of BB resonators. One with radius of 2.5 mm (BB-2.5) that operate at ~10 kHz. Second with radius of 5 mm (BB-5) that operate at ~5 kHz and third of radius 5 mm (BB-5) that operate at ~10 kHz. We discuss the design, fabrication and the effects and mitigation methodology of energy losses for our resonators.

II. DESIGN OF BIRDBATH RESONATORS

To fabricate high-Q and long τ resonators, it is essential to minimize energy losses. Broadly, there are four major sources of energy dissipation, (a) anchor loss, which is due to propagation of elastic waves leading to losses from the resonator

to the substrate. (b) Different parts of the vibrating shell experiences compression and tension. This generates hot and cold regions. Thermal equilibrium is reached by irreversibly dissipating energy from the shell causing loss of energy known as TED. (c) Viscous loss which is due to the interaction of the resonating rim with the fluid particles resulting in loss of energy due to momentum transfer at collision. (d) Surface loss which is primarily due to the structure of the material and amplified by defects, roughness or presence of foreign particles and residues on the surface of a resonator. Our simulation studies have revealed that anchor loss and TED are not the dominant energy loss mechanisms for our shell resonators and the Q associated with these losses are usually >50 million, thanks to the FS material and the engineered design of our resonator [8]–[9]. Viscous damping is minimized by operating the resonator in high vacuum (~10 μTorr). Finally, we believe surface loss is the dominant energy loss mechanism limiting the performance of our resonators.

Fig. 2: Fabrication method of BB shells, (a) FS substrate sits on a machined graphite mold, (b) blowtorch softens the FS substrate and vacuum pull forms the shell. (c) Photograph and (d) schematic of a molded shell which is (e) coated with sacrificial protective metal and (f)-(g) set into a thick silicon wafer using thermoplastic. (h)-(i) The flat portion of the shell is lapped, and the rims are polished using CMP. Finally, the thermoplastic is dissolved, and metal is wet-etched to release the shells.

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Fig. 1 shows a photograph of a BB resonator mounted on a silicon test substrate. These shells are engineered to reduce the various vibrational losses and achieve high Q. The anchor of a BB shell is long which isolates it from the vibrating rim thus pumping less energy from the resonating rim to the anchor. They are fabricated monolithically ensuring they are self-aligned to the rest of the shell. Both these characteristics are important factors that determine losses from the anchor. These shells are made from FS which has inherently low material and thermoelastic losses. The surface of the shell is ultra-smooth due to our novel fabrication method discussed in the next section. Smooth surface further reduces surface loss. They have a thick rim which increases the modal mass and improves the gyroscope resolution. BB resonators operate in the n=2 WG modes at ~10 kHz for the BB-2.5 and ~5 and ~10 kHz for the BB-5 resonators which is higher than the bandwidth of noise from the environment.

III. FABRICATION OF BIRDBATH RESONATORS

BB resonators are fabricated from square FS substrates of side 15 mm for BB-2.5 (thickness ~100 µm) and 23 mm for BB-5 (thickness ~250 µm). The shells are formed by an in-house developed glass blowing technique called micro blowtorch reflow molding [10]. A FS substrate sits on a machined graphite mold that has a seat to automatically align the substrate to the anchor post. Since the BB shell is fabricated monolithically, the anchor is self-aligned. An oxygen-propane flame reaching temperature >1700 oC softens the substrate, which reflows under the vacuum pull from the mold forming a shell in 5–10 seconds.

The high temperature flame also smooths the shell surface with average roughness of the fabricated shell being less than 2 Å. The blowtorching parameters and the mold design allows the fabrication of shells of different radii and aspect ratios. After molding, the flat part of the shells needs to be removed. For this they are set into a thick silicon wafer with through holes and surrounded by a protective thermoplastic that rigidly holds the shells in the silicon wafer. As the wafer is lapped, the bottom of the shell is removed, separating the resonator from the flat FS substrate. The resonator rim is then polished with chemical mechanical planarization (CMP). Finally, the thermoplastic is chemically removed, and the shells are cleaned. We have noticed that the selection of a suitable thermoplastic is critical to the performance of our resonators. While some thermoplastics do not do a good job of holding the shell rigidly, others tend to leave residues on the shell even after aggressive acidic cleaning processes. To ensure that our resonators are free from any residue from the thermoplastic, we coat our shells with a sacrificial metal coating before setting them in the silicon wafer for lapping/CMP. Eventually, the thermoplastic is dissolved, and the sacrificial metals are wet-etched to have clean shells. The fabrication process is shown in Fig. 2. They are then rigidly attached to a silicon substrate with glass frit and tested for their resonant characteristics using a laser Doppler vibrometer (LDV) in vacuum as shown in Fig. 3. 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 vibration are allowed to freely decay. The ring-down constant is calculated by measuring the time taken for the maximum amplitude to decay by a factor of e. The Q is then calculated using the expression Q , where f is the frequency of vibration.

IV. RESULTS AND DISCUSSION

A. Resonator Performance Our BB-2.5 resonator exhibited a τ of 204 seconds and Q

of 5.87 million. Similarly, the BB-5 resonator operating at ~5 kHz has a τ of 495.54 seconds and Q of 7.97 million. Finally, BB-5 operating at ~10 kHz has a τ of 285 seconds and Q of 9.81 million. Table I tabulates the important resonant characteristics of these three shells. Fig. 4 shows the ring-down plots for the two sizes of BB shells. We believe that minimizing the surface loss has been instrumental in fabricating high-performance BB resonators. We have observed the performance of BB resonators to be greatly deteriorated by the presence of foreign particles, films, and residues on the shell surface. Optimization of the fabrication process to fabricate clean and residue free resonators has minimized surface loss, and this has proved to be important in achieving long τ and high-Qs. Pre-CMP sacrificial metal coating of the shells revealed the importance of residue-free resonators for achieving high-Q. We have seen a two-fold increase in τ and Q when a protective metal layer is used. We also believe that the lower surface-to-volume ratio of BB-5 is critical in reducing the surface loss thus increasing the quality factor [11]. At the same time, BB-5 resonators have lower frequency mismatch than BB-2.5. This is because of the fabrication imperfections that become less prominent as the shell size increases. To operate these shells as a gyroscope, they need to be coated with metal to make them conductive for electrostatic actuation and sensing. We have observed a ~45% reduction in Q when these shells are coated with conductive metal [12].

Fig. 3: The shells are mounted on a silicon substrate and tested for their resonance characteristics using LDV.

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B. Projected Gyroscope Performance Several parameters characterize the performance of a gyroscope. Among them are the mechanical noise known as the ARW (in o/hr/√Hz or o/√hr) and BI (in o/hr). ARW is contributed by mechanical noise and electrical noise. For a gyroscope with identical drive and sense mode frequencies and high Q, ARW is dominated by the mechanical noise. Also, when a gyroscope is maintained at a stable temperature and well-isolated from environmental vibration and shock, BI is dominated by the difference of 1/τ of the two WG modes. and bias (B) are governed by the equations,

°/√ – (1)

∆ sin 2 – (2)

here, is the displacement in the drive mode, is the effective mass, is the Boltzmann constant, T is the temperature, n is the mode number, is the angular gain and

is the angle of damping mismatch. We previously reported a

BB-2.5 gyroscope in [13] and [14] with an ARW of 1.26 mdeg/√ and BI of 39.1 mdeg/hr in [14] which is one the lowest noise MEMS gyroscope reported to date to the best of our knowledge. Using the same parameters (Table II) and assuming a 50% reduction in Q due to metal coating, our reported BB-2.5 resonator can achieve an ARW of 0.59 mdeg/√ as per Eq. (1). At the same time, τ of the two modes of the resonator used in [14] is 14.77 and 14.14 seconds. This device exhibited a BI of 39.1 mdeg/hr. Assuming a linear relationship of BI with 1/τ, the reported τ in this work can potentially exhibit a BI of 0.629 mdeg/hr. ARW and BI will further improve for BB-5 resonators due to their large effective mass, Q, and possibly large drive amplitude for large shells. Our achievement in fabricating resonators with high-Q on the order of several million and long τ of several hundred is an encouraging step forward towards fabricating high performing MEMS gyroscopes.

V. CONCLUSION

Achieving navigation-grade performance for a MEMS gyroscope requires long and high-Q resonators. We have demonstrated the fabrication of a 3D axially symmetric hemitoroidal resonator of two sizes operating at three different frequencies. All three classes of resonators have long and high Q. Our resonator design and blowtorching technique are efficient in minimizing energy losses and controlling the operating frequency. These resonators will be instrumental in producing MEMS gyroscopes that can reach competitive performance to their macro-counterparts for a commercial gyroscope. This will enable economical inertial navigation for different applications.

BB-2.5 BB-5 (5 kHz) BB-5 (10 kHz) WG1 WG2 WG1 WG2 WG1 WG2

f (kHz) 9.162 9.209 5.122 5.127 10.957 10.967 (s) 204 202 495.54 495 285 272.4

Q (million)

5.87 5.84 7.97 7.97 9.81 9.39

Δf (Hz) 47.61 5.74 10.30 Δ(1/ ) (Hz)

4.85x10-5 2.20x10-6 1.62x10-4

Parameter Symbol Value

Angular Gain 0.25

Drive Amplitude (µm) 2.2

Effective Mass (mg) 0.68

Frequency (kHz) 9.16

Quality Factor (million) Q 2.94

TABLE I. RESONANT CHARACTERISTICS OF BB RESONATORS.

TABLE II: GYROSCOPE TESTING PARAMETERS FOR BB-2.5 [14].

Fig. 4: Measured ring-down plot of a (a) BB-2.5, (b) 5 kHz BB-5 and (c) 10 kHz BB-5 resonator using LDV in vacuum.

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ACKNOWLEDGMENT

This research is supported by the DARPA:MRIG Program (Award#W31P4Q-11-1-0002) and DARPA:AIMS Program (Award #N66001-16-1-4029). The authors would like to thank the staff members at the Lurie Nanofabrication Facility (LNF); special thanks to Tom Latowski for help with the CMP tool. We thank Robert Gordenker for his help in the research lab.

REFERENCES [1] Prikhodko, Igor P., et al. "Foucault pendulum on a chip: Angle measuring

silicon MEMS gyroscope." Micro Electro Mechanical Systems (MEMS), 2011 IEEE 24th International Conference on. IEEE, 2011.

[2] Challoner, Anthony D., H. Ge Howard, and John Y. Liu. "Boeing disc resonator gyroscope." Position, Location and Navigation Symposium-PLANS 2014, 2014 IEEE/ION. IEEE, 2014.

[3] Putty, Michael William. A micromachined vibrating ring gyroscope. Diss. 1995.

[4] Loper Jr, Edward J., and David D. Lynch. "Vibratory rotation sensor." U.S. Patent No. 4,951,508. 28 Aug. 1990..

[5] Senkal, Doruk, et al. "MEMS micro-glassblowing paradigm for wafer-level fabrication of fused silica wineglass gyroscopes." Procedia Engineering 87 (2014): 1489-1492.

[6] Nagourney et al. “Fabrication of hemispherical fused silica micro-resonator with tailored stiffness and mass distribution.” Micro Electro Mechanical Systems (MEMS), 2018 IEEE 31st International Conference on. IEEE, 2018.

[7] Nagourney, Tal, et al. "259 second ring-down time and 4.45 million quality factor in 5.5 kHz fused silica birdbath shell resonator." Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS), 2017 19th International Conference on. IEEE, 2017.

[8] Darvishian, Ali, et al. "Thermoelastic Dissipation in Micromachined Birdbath Shell Resonators." Journal of Microelectromechanical Systems 26.4 (2017): 758-772.

[9] Darvishian, Ali, et al. "Anchor loss in hemispherical shell resonators." Journal of Microelectromechanical Systems 26.1 (2017): 51-66.

[10] Cho, Jae Yoong, et al. "3-dimensional blow torch-molding of fused silica microstructures." Journal of Microelectromechanical Systems 22.6 (2013): 1276-1284.

[11] Gretarsson, Andri M., and Gregory M. Harry. "Dissipation of mechanical energy in fused silica fibers." Review of scientific instruments 70.10 (1999): 4081-4087.

[12] Nagourney, Tal, et al. "Effect of metal annealing on the Q-factor of metal-coated fused silica micro shell resonators." Inertial Sensors and Systems (ISISS), 2015 IEEE International Symposium on. IEEE, 2015.

[13] Cho, Jae Yoong, et al. "Fused-Silica Micro Birdbath Resonator Gyroscope (µ-BRG)." Journal of Microelectromechanical Systems 23.1 (2014): 66-77.

[14] Boyd, Christopher, et al. "Effect of drive-axis displacement on MEMS Birdbath Resonator Gyroscope performance." Inertial Sensors and Systems (INERTIAL), 2017 IEEE International Symposium on. IEEE, 2017.

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