High-Q silicon flexural resonators for vibrating inertial sensors: Investigations of the limiting damping mechanisms

In designing micro-scale vibrating sensors, the achievement of very high quality factor (Q) resonators working in bending mode remains a major issue. Special attention has been paid in this work to explore the Q limitations of single-crystal silicon bending beam resonators and their dependences on geometry, temperatures and pressure for a large range of resonators. In order to preserve the resonating element from support damping, a system with high decoupling efficiency has been optimized using FEM analyses and implemented. Quality factor as a function of frequency shows the transition between thermoelastic damping (TED) and surface damping as limiting mechanism with the miniaturization of the resonators: At high vacuum, the thermoelastic theory is experimentally validated to be the main damping source for Q up to 4.0x10⁴. Beyond these values (Q > 1.4x10⁵) the surface effects are evidenced and characterized with thickness and frequency variations.