Amy Duwel

Engineering MEMS Resonators With Low Thermoelastic Damping

This paper presents two approaches to analyzing and calculating thermoelastic damping in micromechanical resonators. The first approach solves the fully coupled thermomechanical equations that capture the physics of thermoelastic damping in both two and three dimensions for arbitrary structures. The second approach uses the eigenvalues and eigenvectors of the uncoupled thermal and mechanical dynamics equations to calculate damping. We demonstrate the use of the latter approach to identify the thermal modes that contribute most to damping, and present an example that illustrates how this information may be used to design devices with higher quality factors. Both approaches are numerically implemented using a finite-element solver (Comsol Multiphysics). We calculate damping in typical micromechanical resonator structures using Comsol Multiphysics and compare the results with experimental data reported in literature for these devices

Impact of geometry on thermoelastic dissipation in micromechanical resonant beams

Thermoelastic dissipation (TED) is analyzed for complex geometries of micromechanical resonators, demonstrating the impact of resonator design (i.e., slots machined into flexural beams) on TED-limited quality factor. Zener first described TED for simple beams in 1937. This work extends beyond simple beams into arbitrary geometries, verifying simulations that completely capture the coupled physics that occur. Novel geometries of slots engineered at specific locations within the flexural resonator beams are utilized. These slots drastically affect the thermal-mechanical coupling and have an impact on the quality factor, providing resonators with quality factors higher than those predicted by simple Zener theory. The ideal location for maximum impact of slots is determined to be in regions of high strain. We have demonstrated the ability to predict and control the quality factor of micromechanical resonators limited by thermoelastic dissipation. This enables tuning of the quality factor by structure design without the need to scale its size, thus allowing for enhanced design optimization

Energy loss in MEMS resonators and the impact on inertial and RF devices

In this paper, we review the current understanding of energy loss mechanisms in micromachined (MEMS and NEMS) devices. We describe the importance of high quality factor (Q) to the performance of MEMS gyros and MEMS resonators used in radio-frequency applications.

Multimode thermoelastic dissipation

In this paper, we investigate thermoelastic dissipation (TED) in systems whose thermal response is characterized by multiple time constants. Zener [Phys. Rev. 52, 230 (1937)] analyzed TED in a cantilever with the assumption that heat transfer is one dimensional. He showed that a single thermal mode was dominant and arrived at a formula for quantifying the quality factor of a resonating cantilever. In this paper, we present a formulation of thermoelastic damping based on entropy generation that accounts for heat transfer in three dimensions and still enables analytical closed form solutions for energy loss estimation in a variety of resonating structures. We apply this solution technique for estimation of quality factor in bulk mode, torsional, and flexural resonators. We show that the thermoelastic damping limited quality factor in bulk mode resonators with resonator frequency much larger than the eigenfrequencies of the dominant thermal modes is inversely proportional to the frequency of the resonator un...

Quality factors of MEMS gyros and the role of thermoelastic damping

In this paper, we present new experimental data illustrating the importance of thermoelastic damping in MEMS resonant sensors. We have used MEMS gyroscopes to demonstrate that both the choice of materials and variations in device design can lead to significant differences in the measured Quality (Q) factors of the device. These differences in Q factor can be explained by including the contribution of thermoelastic damping (TED), which varies strongly between the different silicon etch-stop compositions used in this study. Known damping mechanisms such as fluid damping, anchor damping, and electronics damping are minimized and held fixed in this experiment so that materials effects can be isolated.

Quick Switch: Strongly Correlated Electronic Phase Transition Systems for Cutting-Edge Microwave Devices

The authors discuss an overview of strongly correlated electron systems and metal-insulator transition (MIT) oxide materials. Microwave applications of MIT materials are also introduced. This overview offers a vision for future microwave devices with adaptive capabilities.

Oscillator phase noise: systematic construction of an analytical model encompassing nonlinearity

This paper offers a derivation of phase noise in oscillators resulting in a closed-form analytic formula that is both general and convenient to use. This model provides a transparent connection between oscillator phase noise and the fundamental device physics and noise processes. The derivation accommodates noise and nonlinearity in both the resonator and feedback circuit, and includes the effects of environmental disturbances. The analysis clearly shows the mechanism by which both resonator noise and electronics noise manifest as phase noise, and directly links the manifestation of phase noise to specific sources of noise, nonlinearity, and external disturbances. This model sets a new precedent, in that detailed knowledge of component-level performance can be used to predict oscillator phase noise without the use of empirical fitting parameters.

Particle Swarm Optimization for Design of Slotted MEMS Resonators With Low Thermoelastic Dissipation

The geometry of a slotted MEMS resonator was optimized using a binary particle swarm optimization technique to reduce energy dissipation from thermoelastic dissipation (TED). The optimization technique combines fundamental physics with bio-inspired algorithms to navigate the complicated design space that arises from multiphysical problems. Fully-coupled thermomechanical simulations were used for optimization of QTED, and a weakly-coupled approach was used for design analysis. Through this approach, a TED-limited Q of 56000 was simulated, showing a 40% improvement over previous designs that were generated from the conventional intuitive design approach. The discovery of non-intuitive designs with these techniques also leads to new insight about the behavior of TED. The design algorithm used in this paper can be readily adapted to a variety of MEMS design problems.

Verification of the phase-noise model for MEMS oscillators operating in the nonlinear regime

We experimentally verify the phase-noise model for oscillators operating in a nonlinear regime by testing a micromechanical resonator-based oscillator (MEMS oscillator). Operation of oscillators in the nonlinear regime had been believed to induce instability [1] - a belief we have demonstrated to be mistaken [2]. As a result of this misunderstanding, little study has been devoted to the phase-noise performance of oscillators in the nonlinear regime. In this study, we compare measurements of the phase noise of MEMS oscillators far into the nonlinear regime and compare them with a recent prediction [3]. This paper provides confirmation that low phase-noise performance is possible in the nonlinear regime, and confirms that models can be used to predict and optimize performance.

Thermal energy loss mechanisms in micro- to nano-scale devices

In micro- and nano-scale resonators, a key performance metric is the quality factor (Q), which is the ratio of stored mechanical energy to the energy dissipated. In well-optimized designs, Q is limited by thermal physics and specific energy loss mechanisms including thermoelastic, Akhieser, and Landau-Rumer damping. The relative importance of each effect depends on the time and length scales dominating the device. Most published analyses focus on special regimes where only one mechanism dominates, though real devices may operate in regimes that are not the limiting case. This paper presents thermal damping across the range of frequency and length scales. Data on acoustic loss is compared with theory.