Perturbation analysis of frequency shift in a thin film bulk acoustic wave resonator under biasing field

Abstract

In order to accurately predict the sensitivity of thin film bulk acoustic wave resonator (FBAR) sensors for measuring mechanical or thermal field, a combined perturbation and finite element method based on the theory for small field superposed on the finite biasing field is proposed. Firstly, the average biasing stress of piezoelectric layer AlN of FBAR sensors under external load is calculated by COMSOL finite element software. Then, the resonant frequency and corresponding mode shape of FBAR are calculated in COMSOL. Finally, the calculated data of the finite element are substituted into the perturbation integral formula to obtain the frequency sensitivity of the FBAR sensor. The frequency sensitivity obtained by the perturbation and finite element method is 41.3 MHz/N, which is close to the reported experimental result of 50 MHz/N. The feasibility of this method is verified.