偏场下薄膜体声波谐振器频率偏移的摄动分析

Perturbation analysis of frequency shift in a thin film bulk acoustic wave resonator under biasing field

为准确预测测量力、热场的薄膜体声波谐振器(FBAR)传感器的灵敏度,采用叠加于有限偏场之上的小增量场理论描述,提出一种摄动与有限元联合求解方法。该方法利用COMSOL有限元软件计算FBAR传感器受外界载荷下其压电层AlN的平均偏置应力,进一步在COMSOL中计算FBAR的谐振频率与相应的振型,将有限元的计算数据代入摄动积分公式中,得到FBAR传感器的频率灵敏度。并以一个圆膜片FBAR为案例,介绍该方法用于计算圆膜片FBAR频率-集中力灵敏度的详细过程。采用摄动与有限元联合求解方法得到的频率灵敏度为41.3 MHz/N,与文献报道的实验结果 50 MHz/N接近,验证了方法的可行性。

In order to accurately predict the sensitivity of thin film bulk acoustic wave resonator(FBAR)sensors for measuring mechanical or thermal field, a combined perturbation and finite element method is proposed based on the theory for small field superposed on the finite bias. Firstly, the average biasing stress of piezoelectric layer AlN of FBAR sensor under external load is calculated by COMSOL finite element software.Then, the resonant frequency and corresponding mode shape of FBAR are calculated in COMSOL. Finally, the calculated data of the finite element are substituted into the perturbation integral formula to obtain the frequency sensitivity of the FBAR sensor. The frequency sensitivity obtained by the perturbation and finite element method is 41.3 MHz/N, which is close to the reported experimental result of 50 MHz/N. The feasibility of this method is verified.