An alternative technique to Perfectly Matched Layers to model anchor losses in MEMS resonators with undercut suspensions

This paper presents and experimentally validates a new numerical approach to accurately model anchor losses in MEMS resonators with undercut suspensions. This method is an alternative to the use of Perfectly Matched Layers (PMLs) and excels at predicting Q for those cases in which highly reflective boundaries are present. The proposed finite element method (FEM) imposes fixed-constraints (FC) 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. This new approach is compared to the results obtained by using PML conditions and validated experimentally through measurement of 216 AlN resonators with resonance frequencies (f_r) around 60 MHz. The comparison shows that the proposed numerical technique has a similar accuracy to PML in predicting Q, but it is superior to it when reflections from the boundaries become relevant.