Wineglass Modes Research Articles

The Effect of the Anisotropy of Single Crystal Silicon on the Frequency Split of Vibrating Ring Gyroscopes.

This paper analyzes the effect of the anisotropy of single crystal silicon on the frequency split of the vibrating ring gyroscope, operated in the wineglass mode. Firstly, the elastic properties including elastic matrices and orthotropic elasticity values of (100) and (111) silicon wafers were calculated using the direction cosines of transformed coordinate systems. The (111) wafer was found to be in-plane isotropic. Then, the frequency splits of the mode ring gyroscopes of two wafers were simulated using the calculated elastic properties. The simulation results show that the frequency split of the (100) ring gyroscope is far larger than that of the (111) ring gyroscope. Finally, experimental verifications were carried out on the micro-gyroscopes fabricated using deep dry silicon on glass technology. The experimental results are sufficiently in agreement with those of the simulation. Although the single crystal silicon is anisotropic, all the results show that compared with the (100) ring gyroscope, the frequency split of the ring gyroscope fabricated using the (111) wafer is less affected by the crystal direction, which demonstrates that the (111) wafer is more suitable for use in silicon ring gyroscopes as it is possible to get a lower frequency split.

Fully Differential Piezoelectric Button-Like Mode Disk Resonator for Liquid Phase Sensing.

We present a unique lateral shear resonance mode excited in a microelectromechanical (MEM) disk resonator. We refer to this proposed mode as the button-like (BL) mode. The BL mode has a characteristic lateral strain profile (based on the sum of orthogonal strain components in the plane of fabrication) which resembles a shirt button, hence our choice of name for this mode. The strain profile of the BL mode is highly suited for piezoelectric transduction. Like the more widely reported wine-glass (WG) or elliptical mode, the BL mode offers feedthrough cancellation through fully differential transduction. However, compared to the WG mode, the BL mode possesses a higher coupling coefficient ( [Formula: see text]) and a higher quality ( Q ) factor for the same disk radius. These advantages make the BL mode highly attractive for realizing electrically addressed MEM resonators for liquid-phase sensing. This paper examines various design aspects pertaining to the BL mode: tether geometry, characterization setup, size of disk, and even the effect of the gap around the disk on the Q factor. The highest Q factor measured in water is 410 based on a disk with a radius of [Formula: see text]. The lowest motional resistance in water is 1.36 [Formula: see text] based on a disk with a radius of [Formula: see text].

Application of micro-blowtorching process with whirling platform for enhancing frequency symmetry of microshell structure

This paper proposes and demonstrates an improved process to fabricate fused silica (FS) microshell structures using a whirling platform and femtosecond laser ablation. The micro-blowtorching process is modeled analytically to analyze the final geometry and thickness of the microshell structure. After the factors that affect frequency symmetry are analyzed, the whirling platform is presented to enhance the structural symmetry in the molding process. Femtosecond laser ablation is used to improve the processing quality in the releasing process. The FS microshell structures are fabricated by the micro-blowtorching process using the whirling platform. The surface roughness is measured with an atomic force microscope (AFM), showing a sub-nanometer smooth surface quality (0.404 nm Ra). A roundness measuring instrument was employed to characterize the geometric parameter error. The 4th harmonic error was effectively suppressed, which contributed to the improvement in the frequency symmetry. The microshell resonator with T-shaped masses was released with femtosecond laser ablation, which revealed good ablation quality on the side wall. The wineglass modes were verified with electrostatic actuation and capacitive detection using out-of-plane electrodes. The experimental results reveal a relatively good frequency symmetry (Δfn= 2/fn= 2) ranging from 0.07%–0.83%. The minimum frequency mismatch was tuned to 0.02 Hz by applying a DC voltage. The maximum measured Q-factor was 95.27 k.

Compensation of frequency split by directional lapping in fused quartz micro wineglass resonators

We present, for the first time, a permanent structural asymmetry compensation method for fused quartz micro wineglass resonators. Using the technique, we demonstrated a near six times reduction of structural asymmetry (n = 2 wineglass mode), culminating in reduction of the frequency split from 41 to 7 Hz. This is an iterative process. In each iteration, the structural asymmetry was first identified by measuring the mode shape of the resonators. Then, directional lapping was performed with specially designed lapping fixtures to accurately control the lapping angle down to 1°. Analytical predictions and numerical simulations were conducted to study the structural asymmetry phenomenon and the effects of compensation on the quality factor of the structure, showing the ability of this process to reduce the structural asymmetry, while not affecting the overall quality factor of the resonators.

Dependency of the Splitting of Resonance Frequency of a Hemispherical Shell on Its Structural Parameters

The main component of a hemispherical resonating gyroscope is its hemispherical shell. This project will attempt to study the dependency of the splitting of eigen-frequencies of the degenerate wine glass mode, on the shells sphericity, surface roughness and other structural parameters.

Piezoelectric-on-Silicon Square Wine-Glass Mode Resonator for Enhanced Electrical Characterization in Water

We describe a piezoelectric square wine-glass (SWG) mode micromechanical resonator as a unique device topology for liquid phase sensing applications that offers enhanced quality (Q)-factor in water over other common contour modes. We show a Q-factor in water of 377 for 14.08-MHz SWG mode resonator (mean of multiple measurements), which is one of the highest Q-factors among piezoelectric resonators tested when covered in a fluid. We show that the Q-factor in water of the SWG mode increases much more significantly with a reduction in resonator size relative to the square-extensional (SE) mode, such that the Q-factor the SWG mode can be almost twice of the SE mode. We present an analytical model for the mode shape of the proposed SWG resonators and their effective electromechanical coupling factor $({k}_{\text {eff}}^{{2}})$ . Due to the enhanced Q-factor in water, reasonable ${k}_{\text {eff}}^{{2}}$ , and feedthrough cancelation (using fully differential transduction with the fluid loaded from the backside of the device), we show that a strong resonant peak of 29.8 dB is obtainable in water.

Microsacle PolySilicon Hemispherical Shell Resonating Gyroscopes with Integrated Three-dimensional Curved Electrodes

A novel approach for fabrication of polysilicon hemispherical resonator gyroscopes with integrated 3-D curved electrodes is developed and experimentally demonstrated. The 3-D polysilicon electrodes are integrated as a part of the hemispherical shell resonator’s fabrication process, and no extra assembly process are needed, ensuring the symmetry of the shell resonator. The fabrication process and materials used are compatible with the traditional semiconductor process, indicating the gyroscope has a high potential for mass production and commercial development. Without any trimming or tuning of the n=2 wineglass frequencies, a 28 kHz shell resonator demonstrates a 0.009% frequency mismatch between two degenerate wineglass modes, and a 13.6 kHz resonator shows a frequency split of 0.03%. The ring-down time of a fabricated resonator is 0.51 s, corresponding to a Q of 22000, at 0.01 Pa vacuum and room temperature. The prototype of the gyroscope is experimentally analyzed, and the scale factor of the gyro is 1.15 mV/°/s, the bias instability is 80 °/h.

Frequency Tuning of a Disk Resonator Gyroscope via Stiffness Perturbation

This paper introduces a utility algorithm to reduce the permanent frequency mismatch of the primary wineglass modes in a disk resonator gyroscope via stiffness perturbation. In this algorithm, each tuning electrode is regarded as two rows of radial springs with negative stiffness. On the basis of the tuning model for a ring with radial springs, we can obtain the functional relation between equivalent stiffness or voltage of each tuning electrode and the frequency split. Corresponding simulations are conducted to demonstrate the performance of the algorithm. Finally, the electrostatic tuning experiment is presented to further verify the algorithm and illustrate the use of the tuning procedure. Results of experiment show that the frequency split of resonator is decreased to smaller than 0.03 Hz from original about 15 Hz.

Modeling the Effect of Imperfections in Glassblown Micro-Wineglass Fused Quartz Resonators

In this paper, we developed an analytical model, supported by experimental results, on the effect of imperfections in glassblown micro-wineglass fused quartz resonators. The analytical model predicting the frequency mismatch due to imperfections was derived based on a combination of the Rayleigh's energy method and the generalized collocation method. The analytically predicted frequency of the n = 2 wineglass mode shape was within 10% of the finite element modeling results and within 20% of the experimental results for thin shells, showing the fidelity of the predictive model. The postprocessing methods for improvement of the resonator surface quality were also studied. We concluded that the thermal reflow of fused quartz achieves the best result, followed in effectiveness by the RCA-1 surface treatment. All the analytical models developed in this paper are to guide the manufacturing methods to reduce the frequency and damping mismatch, and to increase the mechanical quality factor of the device.

Piezoelectric Bulk Mode Disk Resonator Post-Processed for Enhanced Quality Factor Performance

This paper presents a bulk-mode disk resonator utilizing a transverse piezoelectric actuation technique to drive the single crystalline silicon disk structure in its wine-glass bulk mode of resonance. The device is fabricated by post-processing dies from a commercial microelectromechanical systems process and combines high quality factor and relatively low motional resistance. Post-process fabrication steps are used to reduce the width of the anchor beam supports, and consequently reduce the anchor losses. This results in a factor of 3 increase in the quality factor. Post-processed resonators were measured to have resonance frequencies of 23 MHz and quality factors of 13000 in atmospheric pressure, increasing to 31000 in 1 mTorr vacuum. The devices also demonstrate motional resistances of 21 kQ in atmospheric pressure, reducing to 8.8 kQ in 1 mTorr vacuum without requiring any dc voltage for operation.

Design of spurious mode-free elliptical ring resonators

Spurious modes suppression to retain the purity of the main resonance in lateral-extensional contour modes is one of the most important requirements for commercializing vibrating RF MEMS resonators. This issue becomes much more critical for ring-shaped micromechanical resonators that are normally susceptible to both out-of-plane flexural modes and in-plane torsional modes at frequencies adjacent to that of the desired lateral-extensional mode. However, this kind of lateral-extensional mode resonators hold unique ability to achieve GHz frequencies without excessive scaling of its key dimensions, such as inner and outer radius, to facilitate strong electromechanical coupling coefficient by either capacitive or piezoelectric transducers while exhibiting high Q’s on the orders of a few thousands. This paper presents a new type of ring resonators based on a hollow ellipsoid structure operating in the extensional wine-glass mode. Due to the mode shape matching to the resonator body shape, vibration amplitude at this strategically-designed mode becomes much larger than those for other modes. Moreover, a harmonic analysis to verify the basic design principles and further discussions towards design optimization have been presented.

Anchor Loss Variation in MEMS Wine-Glass Mode Disk Resonators Due to Fluctuating Fabrication Process

With increasing demand for high-frequency, high-quality factor ( $Q$ -factor) mechanical resonators, the $Q$ -factor declining issue at high-frequency becomes increasingly prominent. This paper studies the performance variations of disk resonators under the wine-glass vibration mode due to the support beam offset that are caused by process deviations. The formula of the $Q$ -factor in terms of the support loss is derived to further illustrate the change of the $Q$ -factor caused by the beam offset. It is found that the impact of the extensional mode on the performance is more serious than that of the flexural mode, since the extensional mode may destruct the mode shape and decrease the radial size (i.e., amplitude) of the disk. Finally, some design methods on how to improve the $Q$ -factor of the resonator are given. The numerical results show that there are, respectively, 0.07% and 13.7% increase in the resonant frequency and the disk radial size when the support beam offset is 4°, whereas the increase in the resonant frequency and the disk radial size becomes 0.96% and 69.8%, respectively, when the support beam offset reaches 16°. For the $Q$ -factor, although the flexural-mode $Q$ -factor, $Q_{\mathrm {\mathrm {f}}}$ , increases with increasing support beam offset, the overall $Q$ -factor of the resonator still decreases due to the dominant extensional-mode loss. In the worst case, the largest decline reaches 27.11% from the zero offset position (where there is only flexural-mode loss) to the 16° offset position.

Bulk Mode Disk Resonator With Transverse Piezoelectric Actuation and Electrostatic Tuning

This paper presents a wine-glass bulk mode disk resonator based on a novel transverse piezoelectric actuation technique to achieve bulk mode resonance of the single crystalline silicon disk structure. The device is fabricated in a commercial microelectromechnical systems (MEMS) process, and combines reasonable quality factor and superior motional resistance in a low-cost technology. External capacitive electrodes are used for electrostatic tuning of the resonance frequency, relying on the electrostatic spring softening effect. The resonator was measured to have a resonance frequency of ~15 MHz and a quality factor of ~2000 in atmospheric pressure, increasing to ~5000 in 100-mtorr vacuum. The temperature co-efficient for the frequency of the device was also measured to be about -40 ppm/°C. The resonator requires no dc voltage for operation, but its resonance frequency can be tuned by varying the applied dc voltage on the capacitive electrodes with a factor of 1 ppb/V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> .

Microcrystalline diamond cylindrical resonators with quality-factor up to 0.5 million

We demonstrate high quality-factor 1.5 mm diameter batch-fabricated microcrystalline diamond cylindrical resonators (CR) with quality-factors limited by thermoelastic damping (TED) and surface loss. Resonators were fabricated 2.6 and 5.3 μm thick in-situ boron-doped microcrystalline diamond films deposited using hot filament chemical vapor deposition. The quality-factor (Q) of as-fabricated CR's was found to increase with the resonator diameter and diamond thickness. Annealing the CRs at 700 °C in a nitrogen atmosphere led to a three-fold increase in Q, a result we attribute to thinning of the diamond layer via reaction with residual O2 in the annealing furnace. Post-anneal Q exceeding 0.5 million (528 000) was measured at the 19 kHz elliptical wineglass modes, producing a ring-down time of 8.9 s. A model for Q versus diamond thickness and resonance frequency is developed including the effects of TED and surface loss. Measured quality factors are shown to agree with the predictions of this model.

Reducing anchor loss In thin-film aluminum nitride-on-diamond contour mode MEMS resonators with support tethers based on phononic crystal strip and reflector

In this paper, we report on (1) the proposed support tether configuration based on phononic crystal (PnC) strip to reduce the anchor loss in the thin-film piezoelectric-on-diamond (TPoD) contour mode microelectromechanical systems (MEMS) resonators, namely the $$100^0$$1000 oriented thin-film aluminum nitride (AlN)-on-diamond wine glass (WG) and width shear (WS) mode MEMS resonators, (2) impacts of the geometrical dimensions on the band gaps of the proposed PnC structure, (3) evaluation of the performance of the Q improvement between the proposed support tether configuration and the one based on the reflector presented by B P Harrington and R Abdolvand. The designed resonators operate at approximately 115 and 156 MHz corresponding with the WG and WS modes. The band gap width covering these two operating frequencies is 30.2 and 20.6 MHz, respectively. The maximum Q of the WG mode resonator with five-unit cell PnC strip based support tethers achieves up to 398.5 % over that of the same resonator with reflector based support tethers. Similar to the WS mode one with three-unit cell PnC strip based support tethers, this Q is up to 591.1 %. The average Q of the WG mode resonator with PnC strip based support tethers over the maximum Q of the same one with different reflectors is enhanced about 964.4, 952.9, 364.2 and 4599.5 %. For the WS mode resonator, these Q values are up to 2388.8, 1830.4, 528.2 and 2384.5 %. The finite element (FE) analysis in COMSOL Multiphysics software (COMSOL) is utilized to simulate the proposed PnC strip as well as the WG and WS mode resonators.

High Q diamond hemispherical resonators: fabrication and energy loss mechanisms

We have fabricated polycrystalline diamond hemispheres by hot-filament CVD (HFCVD) in spherical cavities wet-etched into a high temperature glass substrate CTE matched to silicon. Hemispherical resonators 1.4 mm in diameter have a Q of up to 143 000 in the fundamental wineglass mode, for a ringdown time of 2.4 s. Without trimming, resonators have the two degenerate wineglass modes frequency matched as close as 2 Hz, or 0.013% of the resonant frequency (~16 kHz). Laser trimming was used to match resonant modes on hemispheres to 0.3 Hz. Experimental and FEA energy loss studies on cantilevers and hemispheres examine various energy loss mechanisms, showing that surface related losses are dominant. Diamond cantilevers with a Q of 400 000 and a ringdown time of 15.4 s were measured, showing the potential of polycrystalline diamond films for high Q resonators. These resonators show great promise for use as hemispherical resonant gyroscopes (HRGs) on a chip.

Modal Parameter Tuning of an Axisymmetric Resonator via Mass Perturbation

This paper reports the permanent frequency mismatch reduction of the primary wineglass modes in a planar axisymmetric resonator by strategic mass loading. The resonator consists of a set of concentric rings that are affixed to neighboring rings by a staggered system of spokes. The outer layers of spokes are targets for mass deposition. This paper develops modified ring equations that guide the mass perturbation process, and despite the fact that the deposited mass and deposition locations are quantized, it is possible to systematically reduce the frequency difference of the wineglass modes to effective degeneracy such that two modes cannot be distinguished in a frequency response plot. Results on five resonators are reported with nominal wineglass modes near 14 kHz, quality factors of 50k, and frequency mismatches exceeding 30 Hz in some cases, but with postperturbation mismatches smaller than 80 mHz. Furthermore, it is also shown that the quality factors remain unchanged. [2014-0227]

Bulk disc resonators radial and wineglass mode resonance characterization for mass sensing applications

This paper reports the design and fabrication of bulk mode micromechanical disc resonators operating in radial and wine-glass modes of excitation. The reported structures are fabricated utilizing a single crystal SOI wafer through micromachining processes. Both resonators are fabricated on a device layer with a thickness of 20 µm and a gap size of 1.75 µm between the resonant beam and surrounding electrodes. Four anchors support the resonant disc using a T-shaped connection stem. The designed structures resonate at 2.87 and 3.99 MHz, in wine glass and radial modes respectively, and are electrostatically actuated by a DC voltage of 110 V between the disc and electrodes. The designed resonators show high quality factors while operating in air, 1,1876.2 for wine-glass and 7380 for radial. In addition, the resonators are used for distributed and point mass measurements of a sputtered gold metal layer. The wine glass resonator shows a frequency down shift of 1 kHz for a 44 ngr gold point mass, and a frequency shift of 22 kHz for a distributed mass of 83 µgr. Same test is performed on radial mode resonator and a resonance frequency shift of 1.24 and 25.54 kHz was observed for point and distributed mass, respectively in air and at room temperature.

Mode-Matching of Wineglass Mode Disk Resonator Gyroscope in (100) Single Crystal Silicon

In this paper, we present four design methods to overcome (100) silicon crystalline anisotropy and achieve mode-matching in wineglass-mode disk resonator gyroscope (DRG). These methods were validated through experimental characterization of more than 145 different devices that arose from simulations. With the proposed methods, the frequency split of the 250-kHz DRG wineglass modes in (100) silicon was reduced from >10 kHz to as low as 96 Hz (<0.04% of 250-kHz resonant frequency) without any electrostatic tuning. Perfect mode-matching is then achieved using electrostatic tuning. Mode-matching was maintained within ±10 Hz over a temperature range from −20 °C to 80 °C. The temperature dependence of quality factor is also discussed in this paper. These results allow for the development of high-performance miniature DRGs tuned for degenerate wineglass mode operation from high-quality crystalline silicon material. [2013-0303]

Solid-gap wine-glass mode disks VB-FET resonators applied to biomass sensing

The working principle of an electromechanical resonator for mass sensing applications is based on monitoring the characteristic resonance frequency downshift due to the particles attachment on the surface of the device. Solid-Gap Vibrating-Body Field Effect Transistor (VB-FET) resonators offer an interesting solution for extreme biomass sensing due to their high motional current at resonance, their compatibility with Complementary Metal-Oxide-Semiconductor (CMOS) circuits, high reproducibility of characteristics and the possibility to have exploitable values of the quality factor (Q-factor) in air and liquid operation. In this work a detailed micromechanical analysis of VB-FET disk resonators is carried out, considering geometrical design parameters, geometrical variability, motional resistance for air and solid-gaps, Q-factor and variable particle-resonator sensing cases, permitting quantitative discussions on their suitability for biosensing.