Characteristics of the unique modes in HBARs

Simulation results for three kinds of HBARs with different piezo-film and substrate combinations are presented. Based on the distributions of the resonance frequency spacing and the effective coupling factor k_eff²(m) , which significantly rely on the acoustic impedance ratio of the piezo-film to substrate, a unique mode with maximum k_eff²(m) can be chosen. For the unique mode of the HBARs, the variations of the Q-value of the series resonance frequency, Q_s, the effective coupling factor k_eff²(m), the motional resistance R₁, the capacitance ratio r=C₀/C₁, the F.O.M.=Q_sC₁/2C₀, and Q_s·k_eff²(m), with the thickness of the substrate are calculated. Those data give some guidelines to choose the thickness of the substrate for compromising the parameters of the operating mode. Results showed that it is unnecessary to choose very thick substrate for obtaining high Q. Actually, high Q can be obtained when the thickness ratio to the film reaches about 50 to 150 for the three different kinds of samples.