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 (<inline-formula> <tex-math notation="LaTeX">${f} _{\mathrm{ p}}$ </tex-math></inline-formula>) of different measured FBARs on a same wafer. Combined with the stack information of five cross section samples and the measured <inline-formula> <tex-math notation="LaTeX">${f} _{\mathrm{ p}}$ </tex-math></inline-formula>, longitudinal acoustic velocities and densities of AlN and Mo is extracted. The fitted resonance frequency of the simplified model is compared to the measured <inline-formula> <tex-math notation="LaTeX">${f} _{\mathrm{ p}}$ </tex-math></inline-formula>, 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 <inline-formula> <tex-math notation="LaTeX">${f} _{\mathrm{ p}}$ </tex-math></inline-formula>, and the proposed method is useful for accurate frequency fitting and parameter extraction.