The Impact of Damping on Flicker Frequency Noise of AlN Piezoelectric MEMS Resonators

This paper presents a detailed study on the effect of damping on flicker frequency (1/f) noise of 1.1-GHz aluminum nitride (AlN) contour mode resonators (CMRs). A total of 52 different AlN CMRs with different sizes, electrode designs, and anchor types are systemically designed and fabricated to give a wide range of quality factors ( $Q)$ from 300 to 3500, allowing the study of how two major damping mechanisms in AlN CMRs: 1) anchor losses; and 2) thermoelastic damping affect the resonator 1/f noise. In total, we have measured 1/f noise of 104 CMRs using the modified homodyne noise measurement setup and the results confirm that 1/f noise shows a clear power law dependency ranging from 1/ $Q^{2.7}$ to 1/ $Q^{3.5}$ , depending on the main nature of the damping mechanism. Additionally, we have measured 1/f noise of 25 CMRs at 10 K and the results follow the trend observed at ambient temperature. Understanding and accounting for the effect of damping on 1/f noise are crucial for building ultra-low noise microelectromechanical systems resonators for sensing, timing, and frequency applications. [2016-0204]