Direct Detection of Akhiezer Damping in a Silicon MEMS Resonator

Janna Rodriguez,Grant M Glaze,Christopher A Watson,Thomas W Kenny,Eldwin J Ng,C H Ahn,Yushi Yang,Saurabh A Chandorkar

doi:10.1038/s41598-019-38847-6

Abstract

Silicon Microelectromechanical Systems (MEMS) resonators have broad commercial applications for timing and inertial sensing. However, the performance of MEMS resonators is constrained by dissipation mechanisms, some of which are easily detected and well-understood, but some of which have never been directly observed. In this work, we present measurements of the quality factor, Q, for a family of single crystal silicon Lamé-mode resonators as a function of temperature, from 80–300 K. By comparing these Q measurements on resonators with variations in design, dimensions, and anchors, we have been able to show that gas damping, thermoelastic dissipation, and anchor damping are not significant dissipation mechanisms for these resonators. The measured f · Q product for these devices approaches 2 × 1013, which is consistent with the expected range for Akhiezer damping, and the dependence of Q on temperature and geometry is consistent with expectations for Akhiezer damping. These results thus provide the first clear, direct detection of Akhiezer dissipation in a MEMS resonator, which is widely considered to be the ultimate limit to Q in silicon MEMS devices.

Highlights

Q limited by thermomechanical noise arising from energy dissipation[4]
It is defined as the ratio of energy stored in the system to the energy dissipated per vibration cycle (Eq 1); higher Q values correspond to resonators with slower energy dissipation mechanisms: Q = 2π Energy stored in the system
The most important dissipation mechanisms have generally been identified as Gas damping, Thermo-Elastic Dissipation (TED), Anchor damping, and Akhiezer damping

Summary

Introduction

Q limited by thermomechanical noise arising from energy dissipation[4]. it is increasingly important to understand the fundamental limits to energy dissipation in these devices. The quality factor, Q, of a resonator is a dimensionless parameter that indicates the rate at which energy stored in the resonant mode is lost. It is defined as the ratio of energy stored in the system to the energy dissipated per vibration cycle (Eq 1); higher Q values correspond to resonators with slower energy dissipation mechanisms:. The most important dissipation mechanisms have generally been identified as Gas damping, Thermo-Elastic Dissipation (TED), Anchor damping, and Akhiezer damping. Akhiezer damping is expected to be important only for resonators operating at frequencies above 10 MHz with modes that are not expected to cause strong TED8,9. Many of these dissipation mechanisms have unique “signatures” in their temperature dependence that can be used to help identify the presence and magnitude of their contributions[12], as discussed below

Methods

Findings

Discussion

Conclusion