Direct Detection of Anchor Damping in MEMS Tuning Fork Resonators

Abstract

This paper presents the use of our approach to comprehensive measurements of the quality factor ( $Q$ ) of 1-MHz microelectromechanical system (MEMS) tuning fork resonators. We examined the most important mechanisms that are believed to limit the quality factor in MEMS tuning fork resonators (i.e., gas damping, thermoelastic dissipation (TED), anchor damping, and Akhiezer damping), and we were able to quantitatively account for each mechanism and to eliminate several from consideration. We take advantage of the elimination of TED at ~120 K, where the linear coefficient of thermal expansion (CTE) becomes 0. These observations enabled the first direct examination of the strength of anchor damping in megahertz tuning fork resonators, allowing the study of the effect of anchor design and other factors. In this megahertz frequency range, the wavelength of elastic waves far exceeds the dimensions of the die, so commonly used models cannot make predictions of anchor damping. Our results show that elastic energy can escape from the resonator through the anchor(s) and still be retained within the die. We find that anchor damping in these megahertz resonators is impacted more by die attach structures at the boundaries of the die than by the resonator anchor designs within the die. [2018-0038]