High-fidelity modeling of MEMS resonators. Part I. Anchor loss mechanisms through substrate

A computational model is developed for the prediction of wave propagation in the substrate of a MEMS resonator to study energy loss mechanisms from the vibrating beams to the substrate, viz., anchor loss. The model employs a modified classical Fourier transform method under periodic excitations at the anchor area. The present substrate model, when applied to a typical commercially fabricated substrate, estimates that the anchor loss of an ends-anchored resonator with its center frequency of 50 MHz can reach as high as 0.05% in terms of equivalent damping ratio. Anchor loss versus resonator center frequency is assessed by varying the beam dimension, which predicts that anchor loss increases a hundredfold for every tenfold increase in resonator center frequency in the case of two ends-anchored beam resonators. The substrate model has been integrated into a coupled beam-substrate-electrostatics model and validated with experimental data. Development of the detailed coupled-physics model and its validation is presented in Part II as a companion paper.