为了分析基于应力/应变效应的体声波(BAW)力传感器的敏感机理、准确计算其灵敏度, 提出了一种用于BAW力传感器灵敏度分析的微分-综合分析法。该方法借鉴了微积分的原理, 在Mason等效电路模型中将一个完整的BAW谐振器替换为多个谐振器微元的并联, 从而将谐振器有源区面积A上应力/应变场的有限元计算结果与压电薄膜材料的力学特性、谐振器微元的电声学特性关联起来; 最后, 在射频电路仿真软件中进行等效电路的综合, 得到整个BAW谐振器在应力/应变场作用下的阻抗特性曲线及其串/并联谐振频率。当BAW谐振器微元的划分足够细密时, 获得的灵敏度分析结果将足够精确。为了论证该方法的原理, 给出了一个直观的校核案例。以一个嵌入式FBAR结构的四梁BAW加速度计表头为例, 介绍了该方法用于BAW力传感器灵敏度分析的详细过程。虽然案例中只讨论了一种应力/应变型BAW力传感器的单一力敏机理, 但该方法具有普适性。并且, 当谐振器微元小到接近其压电材料晶格的尺度时, 就能与压电薄膜的力-声-电特性的第一性原理计算结果关联起来, 实现从微观材料特性到介观器件物理的多尺度计算。

In order to analyze sensing mechanisms of bulk acoustic wave(BAW) force sensors which based on the stress/strain effects and calculate their sensitivity accurately, a calculus-like analysis method for BAW force sensors’ sensitivity analyzing purpose is proposed. The novel method draws on the principles of calculus, replaced a full BAW resonator with numerous parallel connected resonator infinitesimals in the Mason equivalent circuit model. Thus, the Finite element method(FEM) simulated stress/strain field across the BAW resonator’s 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 stress field. When the resonator infinitesimals are sliced tiny enough, sensitivity analysis results will be accurate enough. Principle of the method is demonstrated, and an intuitive validation case is given. Instanced with an embedded-FBAR quad-beam BAW accelerometer sensor-head case, detailed application procedures of the method for BAW force sensor sensitivity analysis 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. Furthermore, when the resonator infinitesimals are more close to the scale of crystal lattice of its piezoelectric material, which might bridge to 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.