Calculus-like analysis method for analyzing bulk acoustic wave force sensors’ sensitivity

In order to analyze sensing mechanisms of bulk acoustic wave(BAW) force sensors based on the stress/strain effects and calculate their sensitivity accurately, a calculus-like analysis method is proposed. Drawing on the principles of calculus, the method replaces a full BAW resonator with numerous parallel resonator infinitesimals in the Mason equivalent circuit model. Thus, the finite element method(FEM) simulated stress/strain field across the BAW resonators active area can be associated with the mechanical characteristics of its piezoelectric film and electro-acoustic characteristics of its infinitesimals. Finally, the equivalent circuit is integrated in RF circuit simulation software to get the impedance characteristic curve and the series/parallel resonant frequency of the BAW resonator with an applied stress/strain field. When the resonator infinitesimals are sliced tiny enough, sensitivity analysis results will be accurate enough. Instanced with an embedded-FBAR quad-beam BAW accelerometer sensor-head, detailed application procedure of the method is introduced. Although only a single force sensing mechanism in a single stress/strain type BAW sensor is discussed in this case, the presented method is quite general. When the resonator infinitesimals are more close to the scale of crystal lattice of the piezoelectric material, the method might bridge the analysis with the first-principle calculated mechanic-acoustic-electronic characteristics of the piezoelectric film, enabling a multi-scale calculation from the microscopic materials characteristics to the mesoscopic devices physics.