Modified BVD-equivalent circuit of FBAR by taking electrodes into account

A modified BVD-equivalent circuit model is developed when taking the thin electrodes as mass loading. It is shown that the mass of the electrodes can be directly added onto the mass of the piezoelectric film to form a series inductor and a capacitance is added to the capacitance of the film in parallel. The results implied that the traditional BVD model could be applied to the three-layer resonators with thick electrodes. Numerical simulations for three-layer FBAR consisting of AlN film with thick electrodes were carried out, and results showed that a simple L₁-C-₁-R₁ and C₀ model is perfectly applicable for thick electrodes when the two electrodes have similar thickness. If the thickness of the two electrodes is very different, the simple BVD model can´t be simply used.