An Investigation on Extraction of Material Parameters in Longitudinal Mode of FBAR

A generalized method for the extraction of longitudinal parameters of materials in a film bulk acoustic resonator (FBAR) is proposed in this brief. Based on the simplification of the equivalent circuit of a Mason model, a compact step impedance resonator (SIR) model without loss resistors or static capacitors is obtained. The resonance of the acoustic layer is also expressed through the resonance condition of a SIR model analytically. Innovatively, the simplified model is used to fit the parallel resonance frequency (fp) of different measured FBARs on a same wafer. Combined with the stack information of five cross section samples and the measured fp, longitudinal acoustic velocities and densities of AlN and Mo is extracted. The fitted resonance frequency of the simplified model is compared to the measured fp, and the maximum frequency offset is controlled within 6 MHz. In addition, the extracted material parameters are compared with the reference values and show great matching. This brief analytically reveals the correlation between material parameters and fp, and the proposed method is useful for accurate frequency fitting and parameter extraction.