Thermoelastic Damping in the Electrodes Determines $Q$ of AlN Contour Mode Resonators

This paper experimentally verifies the impact of thermoelastic damping (TED) in metal electrodes on the quality factor (<inline-formula> <tex-math notation="LaTeX">$Q_{\text {ted}})$ </tex-math></inline-formula> of 1 GHz Aluminum Nitride (AlN) contour mode resonators (CMRs). A semianalytical approach that treats the electrodes as standard anelastic solids and models their displacement through a 1-D wave equation is followed to predict the dependence of <inline-formula> <tex-math notation="LaTeX">$Q_{\text {ted}}$ </tex-math></inline-formula> on geometrical, thermal, and mechanical parameters. To verify <inline-formula> <tex-math notation="LaTeX">$Q_{\text {ted}}$ </tex-math></inline-formula> experimentally, resonators having top electrodes with different coverage ratios (0.75, 0.5, 0.25) and materials (Au, Pt, Al), but identical vibrating body (made out of AlN) and anchor design have been fabricated and tested. Moreover, resonators having distinct electrode metals are measured under different temperature conditions ranging from 50 to 300 K. All the experiments follow the predicted trend, which confirm that TED can be considered as the main source of intrinsic material damping in AlN CMRs and the dominant damping mechanism when anchor losses are mitigated. [2016-0189]