An analytical and numerical study of acoustic mismatch effects on internal dielectrically transduced MEMS resonators

This paper presents a supplement to the 1-D theory of internal dielectric transduction by including the effects of acoustic mismatch on the resonant frequency and motional impedance of internal dielectrically transduced micromechanical resonators. Analytical expressions for the mode shapes in said resonators are mathematically derived and verified for various dielectric and resonator body materials by comparing numerical simulation results with finite element analysis results using commercial software. Correction factors to the resonant frequencies and motional impedances predicted by the original theory are presented to provide designers a simple yet accurate model that takes into account the effects of acoustic mismatch. Our analysis shows that the ratio of Young´s moduli of the dielectric film and resonator body materials significantly impacts the motional impedance and thus must be considered when choosing the optimal dielectric material. This modified model will allow for precise and optimal design of internal dielectrically transduced micromechanical resonators for applications up to tens of gigahertz.