Reliable formulas for accurately determining the resonance and antiresonance frequencies of thin film bulk acoustic resonators

Expanding upon Lakin’s theory by considering the phase shift of the acoustic waves in the metallic layers, we have developed an impedance formula for a piezoelectric layer covered by a finite thickness of metal layers, enabling the precise determination of its resonant and anti-resonant frequencies. Compared to experimental data and 3D finite element simulations, our formula can accurately and quickly predict resonant, anti-resonant frequencies, and bandwidth across a wide range of piezoelectric and metallic layer thickness combinations.