Tal Nagourney

INVESTIGATION OF THERMOELASTIC LOSS MECHANISM IN SHELL RESONATORS

Maximizing quality (Q) factor is key to enhancing the performance of micro mechanical resonators, which are used in a wide range of applications such as gyroscopes, filters, and clocks. There are several energy loss mechanisms commonly associated with micro resonators including anchor loss through the substrate, squeeze film damping, thermoelastic dissipation (TED), and surface loss. This work focuses on the thermoelastic loss as one of the major energy dissipation mechanisms of micro shell resonators.In this article, the effects of material properties, thickness, conductive coating and operating temperature on the Q-factor of micro shell resonators are investigated. Numerical simulation shows shell resonators have higher Q-factors when they are operating at lower temperatures. Although, the magnitude of the simulated Q-factors of an uncoated bare resonator made from fused silica is more than 70 million and so it is too high to have a remarkable effect on the total Q-factor, our study shows that even a thin layer of some conductive coatings like gold on the surface of a bare shell reduces Q-factor significantly. The sensitivity of the coated shell resonator design to the TED phenomenon provides useful information for the development of new micro shell resonators with improved performance and Q-factors.Copyright

Anchor Loss in Hemispherical Shell Resonators

Micromachined hemispherical shell resonators (HSRs) can be used in high accuracy vibratory gyroscopes. These resonators need to have very low energy loss to achieve very high quality factor. Energy might be lost through the anchor, fluid-structure interaction, thermoelastic dissipation, phonon–phonon and phonon–electron interactions, and the resonator surface. This paper investigates energy loss through the anchor of HSRs using a numerical approach. To numerically determine wave radiation from the anchor to the infinite substrate, a perfectly matched layer is used around a finite substrate. Anchor loss investigations in HSRs are classified into four categories. First, the effects of shell properties—material, geometry, and imperfections—are investigated. Second, the relationships between anchor loss and properties of the stem, such as material, geometry, and stem-shell misalignments, are studied. Third, the effects of substrate characteristics—substrate material, attachment material between the stem and substrate, and attachment configuration of the substrate and stem—are investigated. Finally, the effects of external motions, such as shock and rotation, are analyzed. It is found that anchor loss in HSRs strongly depends on the shell, stem, and substrate properties. This study also shows that any imperfection in the shell or any misalignment between the shell and stem increases anchor loss by orders of magnitude. [2016-0115]

Effect of metal annealing on the Q-factor of metal- coated fused silica micro shell resonators

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.

A comparison between experiments and fem predictions for blowtorch reflow of fused silica micro-shell resonators

We report a non-isothermal model and FEM results for prediction of geometries of fused silica micro-shell resonators fabricated by blowtorch molding process. The model is successfully applied to investigate the production details of 3-D hemi-ellipsoidal shells of revolutions with eccentricity, such as bird-bath shell resonators. The advantages of the present numerical model are that the shell geometry and thickness can be optimized by changing different fabrication parameters such as surface heat flux, conductivity of mold material and initial temperature of the mold. The model brings out the blowtorch molding capabilities and limitations for fabrication of hollow 3-D shell resonators.

Micromachined high-Q fused silica bell resonator with complex profile curvature realized using 3D micro blowtorch molding

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.

259 Second ring-down time and 4.45 million quality factor in 5.5 kHz fused silica birdbath shell resonator

The fused silica birdbath (BB) resonator is an axisymmetric 3D shell resonator that could be used in high-performance MEMS gyroscopes. We report a record quality factor (0 for a 5-mm-radius resonator, which is expected to reduce gyroscope bias drift. We present measurement results for two sizes of resonators with long vibratory decay time constants (τ), high Qs, and low damping asymmetry (Δτ−1) between their n = 2 wine-glass (WG) modes. We find a reduction in damping for larger resonators and a correlation between higher Q and lower as well as evidence of a lower bound on Q for resonators with low damping asymmetry.

Simulation of Blowtorch Reflow of Fused Silica Micro-Shell Resonators

Fabrication of high-precision micro-shell 3-D resonators is a challenging task. We report a non-isothermal model and finite-element simulation results for the prediction of geometries of fused silica micro-shell resonators fabricated with a blowtorch molding process. The model considers coupling between thermal and mechanical aspects of the reflowing process and heat transfer at the fused silica/mold interface, which dramatically controls the final shape of the resonator. The model is successfully applied to investigate the production details of 3-D hemi-ellipsoidal shells of revolutions with eccentricity, such as birdbath shell resonators. Comparisons of numerical results with experimental observations demonstrate that the model can predict an overall trend of thickness distribution. The numerical model can be used to optimize shell geometry and thickness by changing different fabrication parameters, such as surface heat flux, conductivity of the mold material, and initial temperature of the mold. The simulation technique also allows the mold shape and design to be optimized to fabricate different micro-shell geometries and dimensions. The model clarifies the blowtorch molding capabilities and limitations for fabrication of hollow 3-D shell resonators. [2016-0251]

Effect of drive-axis displacement on MEMS Birdbath Resonator Gyroscope performance

We report the latest experimental results from a fused-silica Birdbath Resonator Gyroscope (BRG) with a quality factor of 419k and a resonant frequency of 9030 Hz. The BRG and its readout/control system achieve an angle random walk (ARW) of 0.00126 deg/√hr and a bias stability of 0.0391 deg/hr. These results were obtained using a force-rebalanced control architecture without temperature control or additional compensation. The ARW and bias stability are further improved by driving the resonator at displacements near 10% of the nominal electrostatic gap. The low gyroscope noise is attributed to a relatively large measured scale factor of 100 mV/deg/s.

Numerical study of impact of surface roughness on thermoelastic loss of micro-resonators

In this work, a numerical investigation on thermoelastic damping (TED) in micro-resonators with surface roughness has been reported. A numerical approach using the finite element method (FEM) is implemented for creating surface roughness on the top and bottom of beam resonators. Quality (Q) factor for fundamental flexural mode is numerically obtained using eigenfrequency analysis. The results of the simulations reveal that the local thermodynamic balance becomes upset in the presence of asperities on the surfaces of the rough resonators and the restoration of this balance is accompanied by many local irreversible heat flow processes that give rise to the bulk TED of the resonator. The effect of the resonator thickness and surface asperity height on the surface QTED is investigated.

Numerical prediction of stress evolution during blowtorch reflow of fused silica micro-shell resonators

Micro-blowtorching is a new, fast and reliable fabrication process to form 3D hollow fused silica shell structures such as high Q-factor birdbath resonators. The performance of the fabricated shell as a resonator can be significantly degraded due to the thermal residual stress during the early cooling phase after fabrication. A multi-step finite element analysis is developed for a qualitative prediction of residual stresses and deformation of the birdbath shells. First, a novel non-isothermal model is used to simulate the reflow and molding process. In the next step, the calculated temperature field is used to conduct a transient heat transfer analysis to mimic the cooling phase up to a designated temperature. Finally, the non-uniform temperature field from the heat transfer simulation is used to conduct a thermoelastic analysis to predict the residual stresses and deformation that would exist at ambient temperature in the birdbath shell structure. The predicted internal stresses can usefully be employed to optimize the coarse and fine annealing processes to reduce the stresses in a fabricated shell to a desired level.