Fused Silica Micro Birdbath Shell Resonators With 1.2 Million Q and 43 Second Decay Time Constant
Abstract
We report a micro-scale fused silica (FS) birdbath (BB) shell resonator with a high mechanical quality factor (Q = 1.2 million), long decay time constant (! = 43.6 s), a resonant frequency of 8.8 kHz for wineglass modes, and excellent symmetry resulting in a frequency split of only 6.7 Hz between two wineglass modes. The resonator has a volume of 41 mm 3 (radius = 2.5 mm, anchor radius = 0.5 mm, height ~ 2.1 mm). The resonator is useful in a wide range of applications, including inertial sensors, timing devices, and chemical and biological sensors.
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- However, the sapphire material has intrinsic anisotropy and high stress, which will induce frequency mismatch for resonators. It is also worth mentioning that, while various micro cylinder or hemispherical cylinder resonators have been reported recently with Q factors of 5 ˆ 10 5 ~1.2 ˆ 10 6 [16][17][18], these resonators have much higher mode frequency, resulting in much shorter ring-down time. Although some notable experimental results have been reported, these technologies are still premature for high-accuracy gyroscopic applications.
[Show abstract] [Hide abstract] ABSTRACT: The cylindrical resonator gyroscope (CRG) is a typical Coriolis vibratory gyroscope whose performance is determined by the Q factor and frequency mismatch of the cylindrical resonator. Enhancing the Q factor is crucial for improving the rate sensitivity and noise performance of the CRG. In this paper, for the first time, a monolithic cylindrical fused silica resonator with a Q factor approaching 8 × 105 (ring-down time over 1 min) is reported. The resonator is made of fused silica with low internal friction and high isotropy, with a diameter of 25 mm and a center frequency of 3974.35 Hz. The structure of the resonator is first briefly introduced, and then the experimental non-contact characterization method is presented. In addition, the post-fabrication experimental procedure of Q factor improvement, including chemical and thermal treatment, is demonstrated. The Q factor improvement by both treatments is compared and the primary loss mechanism is analyzed. To the best of our knowledge, the work presented in this paper represents the highest reported Q factor for a cylindrical resonator. The proposed monolithic cylindrical fused silica resonator may enable high performance inertial sensing with standard manufacturing process and simple post-fabrication treatment.- The staircase and cone designs are primarily intended to demonstrate the capabilities of the blowtorch technique. The birdbath resonator previously achieved a 43 second ring-down time [6] and the guided birdbath may improve its design both by improving geometric repeatability and by enabling precise control over the sidewall curvature. The guided birdbath has rounder sidewalls that we expect may improve Q.
[Show abstract] [Hide abstract] ABSTRACT: We present a high level of control over complex profile curvature in micro fused silica shell resonators achieved through a blowtorch molding process. The graphite mold geometry is imparted on the shell without transferring the texture, preserving the 2.4 Å surface roughness of the reflowed fused silica. A variety of shapes are possible using this technique, including a bell shape with a height-to-radius ratio of 1.2. The shell will gently curve around sharp corners but can also follow a curvature prescribed by a rounded or conical sidewall. We offer an explanation for the mechanism that enables this process. We also discuss simulation results on anchor loss and thermoelastic damping and measure ring-down times of 6.7 seconds at ∼12.9 kHz for both n = 2 wineglass modes of a bell resonator.- Micro BB resonators have a ~16.1 times larger S/V ratio than the HRG, so it is expected that their Q is very sensitive to metal coating conditions and surface quality. Recently, we reported ~2ímprovement~2ímprovement in Q compared to previous versions of metalcoated BB resonators due to thinner sputtered Cr/Au metal layers and the use of a short BHF etching step [7]. This work proved the importance of surface loss with respect to Q of the BB resonator, but further studies are necessary on the relationship between treatment of thin metal coatings and Q.
[Show abstract] [Hide abstract] ABSTRACT: This paper reports on the effect of annealing thin metal films coated on high-Q fused silica shell resonators. While the ring-down time of some resonators improves with annealing, others degrade. Investigations include the effect of annealing on metal film stress, roughness, and elemental composition, as well as the effect of film thickness and roughness on quality factor. Increased tensile stress and film roughness are observed after annealing; it is suspected that these changes are due to formation of intermetallic grain boundaries that result in film densification and the formation of hillocks. Increasing film thickness reduces Q, though it is unlikely due to thermoelastic damping. Surface roughness tends to increase with film thickness, but does not appear to have a direct correlation with Q.- Q-factors up to 24k [4] were measured on poly-diamond wineglass shells. Blow molding was used to demonstrate Q-factors as high as 7.8k on bulk metallic glass shells [5] and above 1 million on fused silica shells [6]. We explore an alternative fabrication paradigm under the hypothesis that surface tension and pressure driven micro-glassblowing process may serve as an enabling mechanism for wafer-scale fabrication of extremely symmetric and atomically smooth degenerate mode CVGs,Fig 1. Micro-glassblowing process relies on viscous deformation of the device layer under the influence of surface tension and pressure forces to define the 3-D shell structure as opposed to conventional deposition, molding, or etching techniques, this leads to levels of smoothness and structural symmetry that is not available through conventional fabrication techniques.
[Show abstract] [Hide abstract] ABSTRACT: In this paper, we report latest developments in wafer-level micro-glassblowing paradigm for fabrication of highly symmetric, high Q-factor fused silica wineglass gyroscopes. Q-factors over 1 million have been demonstrated on both n = 2 wineglass modes with a high frequency symmetry (Δf/f) of 132 ppm. High Q-factor is enabled by a high aspect ratio, self-aligned glassblown stem structure, careful surface treatment of the perimeter area, and low internal loss fused silica material. Low frequency split is provided by the self-correcting behavior of the surface tension based micro-glassblowing process. Micro- glassblowing may enable batch-fabrication of high performance fused silica wineglass gyroscopes on a wafer surface at a significantly lower cost than their precision-machined macro-scale counterparts.- One of the main challenges of fabricating micro-wineglass resonators is the definition of electrode structures in a manner compatible with batch-fabrication, Fig. 2. 3-D side-walls of the wineglass geometry makes it challenging to fabricate radial electrodes with small capacitive gaps and to keep the gap uniform across the height of the structure. Even though post-fabrication assembly techniques have been successfully demonstrated [10], [11], these approaches create a bottle-neck in batch-fabrication of the devices at wafer level. Fig. 3. Out-of-plane electrode architecture consists of a micro-glassblown fused silica (FS) wineglass resonator and planar Cr/Au electrodes defined on fused silica, enabling batch-fabrication.
[Show abstract] [Hide abstract] ABSTRACT: In this paper, for the first time, we report Q-factor over 1 million, on both modes, and high frequency symmetry of 132 ppm on wafer-level micro-glassblown 3-D fused silica wineglass resonators at a compact size of 7 mm diameter and center frequency of 105 kHz. In addition, we demonstrate for the first time, out-of plane capacitive transduction on MEMS wineglass resonators. High Q-factor is enabled by a high aspect ratio, self-aligned glassblown stem structure, careful surface treatment of the perimeter area, and low internal loss fused silica material. Electrostatic transduction is enabled by detecting the spatial deformation of the 3-D wineglass structure using a new out-of-plane electrode architecture. To the best of our knowledge, work presented in this paper is the highest reported Q-factor on a degenerate mode device at 7 mm diameter or smaller. Micro-glassblowing may enable batch-fabrication of high performance fused silica wineglass gyroscopes at a significantly lower cost than their precision-machined macro-scale counterparts- [Show abstract] [Hide abstract] ABSTRACT: In this paper, we report an out-of-plane electrode architecture for micro-glassblown fused silica wineglass gyroscopes. Transduction is enabled by the 3-D mode shape of the wineglass resonator, which allows one to drive and sense the wineglass modes using the out-of-plane component of the vibratory motion. The transduction architecture has been succesfully demonstrated on fused silica wineglass resonators with Q-factor over 1 million, on both modes, and high frequency symmetry (Δf=f) of 132 ppm at a compact size of 7 mm diameter and center frequency of 105 kHz. Out-of-plane electrode architecture enables the use of sacrifical layers to define the capacitive gaps, which enables wafer-level integration, mitigates alignment issues and provides uniformly small gaps. 10 μm capacitive gaps have been demonstrated on a 7 mm shell, resulting in over 9 pF of active capacitance within the device. Wafer-level scalability of out-of-plane electrode architecture may enable batch-fabrication of high performance fused silica micro-glassblown wineglass gyroscopes at a significantly lower cost than their precisionmachined macro-scale counterparts.
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