Longitudinal wave resonant frequency calculation and verification of the bulk acoustic resonator

Thickness and material of electrode, piezoelectric and supporting layer film of the Film Bulk Acoustic Resonator (FBAR) are main influence factors of resonant frequency, desired resonance frequency can be achieved by confirming thickness and material. A formula about thickness, material, frequency parameter and angular frequency has been achieved by deriving stress-equation of motion in longitudinal wave of film bulk acoustic resonator; frequency parameter has been get from Newton iteration of determinant of stress and displacement boundary conditions, continuity equations simulated by MATLAB. The resonant frequency of a certain FBAR whose thickness, material and frequency parameter are determined has been calculated by the formula, and the calculation value is 1.441 GHz. Equivalent circuit of longitudinal vibration Mason model which has the same thickness, material with formula calculation has been simulated by ADS, and resonant frequency of simulation model is 1.473GHz. Verification simulation of equivalent circuit of longitudinal vibration Mason model shows: resonant frequency calculation value by formula and the simulation value of model are very close, and we can use the formula to calculate longitudinal wave resonance frequency of FBAR.