Limits to Micromechanical Resonator Performance
Ilya Gurin and Clark Nguyen
Defense Advanced Research Projects Agency
This project aims to explore the ultimate performance attainable by micromechanical circuits (e.g., phase noise in oscillators, insertion loss in filters), as dictated by physical limitations. Initially, it will study energy loss from MEMS resonators by the propagation of waves through anchors and supporting structures. Energy transfer will be rigorously investigated with analytical models and finite-element simulation, followed by experimental verification on fabricated MEMS devices. This extensive model of anchor loss will be able to predict many performance limitations of micromechanical resonators for signal-processing applications such as filters and oscillators.
Mechanical resonators, such as quartz crystals and SAW devices, have been widely used for filters and oscillators in communication circuitry, but their further miniaturization and integration are limited. MEMS resonators, on the other hand, can be easily miniaturized, can be combined with CMOS processing, and can achieve low cost through batch fabrication. Recently, MEMS resonators, in particular silicon devices, have demonstrated excellent long-term and temperature stabilities, as well as resonant frequencies in the gigahertz range, and have started to replace quartz and SAW devices in industry.
One advantage that has enabled MEMS resonators to compete with quartz and SAW devices is their high quality factor (Q). This important parameter determines many circuit characteristics, such as phase noise and insertion loss. In the past decade, many energy loss mechanisms that determine the quality factor of MEMS resonators have been revealed, including air damping, surface loss, thermoelastic dissipation, motion of defects, carrier drift loss, and anchor loss. Among these, anchor loss often dominates, particularly in high–frequency, bulk-mode resonators such as disks and rings. Some attempts have been made to model and predict the anchor loss of MEMS resonators, but they have not produced convincing results. It is known that, for edge-supported resonators, quarter-wavelength supports yield high Q, but the magnitude of this effect cannot yet be predicted analytically with sufficient accuracy. This work aims to remedy this.
Figure 1: A 60-MHz wine-glass-mode disk resonator. This device was fabricated in the most recent Nguyen Group fabrication run. This layout aims to test different support beam dimensions (this device has support beams 1.5 μm by 4 μm).
Figure 2: ANSYS finite-element simulation of a wine-glass-mode disk with two supports. The heavy lines show the mode shape, and the light, dotted line shows the undeformed outline.