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 based on the stress/strain effects and calculate their sensitivity accurately,a calculus-like analysis method is proposed.Drawing on the principles of calcu-lus,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 resonator’s active area can be asso-ciated 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/paral-lel 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 sin-gle stress/strain type BAW sensor is discussed in this case,the presented method is quite general.When the resonator infinitesi-mals 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.
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