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

Abstract

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 (f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> ) of different measured FBARs on a same wafer. Combined with the stack information of five cross section samples and the measured f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> , longitudinal acoustic velocities and densities of AlN and Mo is extracted. The fitted resonance frequency of the simplified model is compared to the measured f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> , 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 f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> , and the proposed method is useful for accurate frequency fitting and parameter extraction.