Analytical and Numerical Methods to Model Anchor Losses in 65-MHz AlN Contour Mode Resonators

Abstract

This paper presents and experimentally validates two different approaches to describe the quality factor ( $Q$ ) due to anchor losses in 65-MHz aluminum nitride (AlN) contour mode resonators (CMRs). The first method is an approach that can be considered qualitative in nature, as it consists of a simplified analytical model that assumes quasi-static anchor conditions and a semi-infinite substrate. Despite its simplicity, it effectively provides designers with some guidelines on how to layout resonator anchors. The second approach is quantitative and consists of a numerical technique that can be considered as an alternative to the use of perfectly matched layers (PMLs). The new finite-element method imposes fixed-constraint (FC) boundary conditions at the edges of the released regions, and the $Q$ is calculated as the ratio of strain energy in both resonator and anchors and the total acoustic energy transferred to the substrate. The two approaches (analytical and numerical) are experimentally validated through measurements of 216 AlN CMRs operating at their fundamental resonance frequency (around 65 MHz). The proposed numerical approach is also compared with the results obtained using PML. This comparison shows that the FC technique has a similar accuracy to PML in predicting $Q$ , but it is superior to the latter when reflections from the clamped boundaries become relevant. [2015-0336]