偏场下薄膜体声波谐振器频率偏移的摄动分析
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摘要
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.
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.
引文
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[17]SINHA B K,TIERSTEN H F.On the temperature dependence of the velocity of surface waves in quartz[J].Journal of Applied Physics,1980,51(9):4659-4665.
[18]KOSINSKI J A.The fundamental nature of acceleration sensitivity[C]//Proc of IEEE International Frequency Control Symposium,1996.
[19]MASSON J,REINHARDT A,BALLANDRAS S.Simulation of stressed FBAR thanks to a perturbation method[C]//Proc of IEEE Mtt-s International Microwave Symposium Digest,2005.
[20]PANDEY D K,SINGH D,YADAV R R.Ultrasonic wave propagation inⅢrd group nitrides[J].Applied Acoustics,2007,68(7):766-777.
[21]BRUGGER,K.Pure modes for elastic waves in crystals[J].Journal of Applied Physics,1965,36(3):759-0.
[22]WANG Z,ZHAO J,GAO Y,et al.First-principle studies on the influence of anisotropic pressure on the physical properties of aluminum nitride[J].Materials Research Express,2017,4(1):016303.
[2]GAO J N,LIU G R,LI J,et al.Recent developments of film bulk acoustic resonators[J].Functional Materials Letters,2016,9(3):1630002.
[3]唐宁,常烨,刘晶,等.新型便携式薄膜体声波谐振气体传感器的研制与应用[J].纳米技术与精密工程,2016(5):331-336.
[4]PANG W,ZHAO H,KIM E S,et al.Piezoelectric microelectromechanical resonant sensors for chemical and biological detection[J].Lab on a Chip,2012,12(1):29-44.
[5]CHIU K H,CHEN H R,HUANG R S.High-performance film bulk acoustic wave pressure and temperature sensors[J].Japanese Journal of Applied Physics,2007,46(4A):1392-1397.
[6]NAGARAJU M B,LINGLEY A R,SRIDHARAN S,et al.27.4 A 0.8 mm 3±0.68 psi single-chip wireless pressure sensor for TPMS applications[C]//Proc of IEEE International SolidState Circuits Conference,2015.
[7]ZHANG H,KIM E S.Micromachined acoustic resonant mass sensor[J].Journal of Microelectromechanical Systems,2005,14(4):699-706.
[8]CAMPANELLA H,PLAZA J A,MONTSERRAT J,et al.Accelerometer Based on Thin-Film Bulk Acoustic Wave Resonators[C]//Proceedings of IEEE Ultrasonics Symposium,2007.
[9]CAMPANELLA H,PLAZA J A,MONTSERRAT J,et al.High-frequency sensor technologies for inertial force detectionbased on thin-film bulk acoustic wave resonators(FBAR)[J].Microelectronic Engineering,2009,86(4):1254-1257.
[10]CAMPANELLA H,CAMARGO C J,ESTEVE J,et al.Sensitivity of thin-film bulk acoustic resonators(FBAR)to localized mechanical forces[J].Journal of Micromechanics and Microengineering,2013,23(6):065024.
[11]DELICADO A,CLEMENT M,OLIVARES J,et al.Influence of induced stress on AlN-solidly mounted resonators[C]//Proc of IEEE European Frequency&Time Forum,2016.
[12]高杨,赵坤丽,赵俊武.体声波换能器灵敏度的微分-综合分析法[J].强激光与粒子束,2016,28(6):1-7.
[13]赵俊武.FBAR的应力负载效应研究[D].绵阳:西南科技大学,2017.
[14]TIERSTEN H F.On the nonlinear equations of thermoelectroelasticity[J].International Journal of Engineering Science,1971,9(7):587-604.
[15]TIERSTEN H F.Perturbation theory for linear electroelastic equations for small fields superposed on a bias[J].Journal of the Acoustical Society of America,1978,64(3):832-837.
[16]SINHA B K,TIERSTEN H F.First temperature derivatives of the fundamental elastic constants of quartz[J].Journal of Applied Physics,1979,50(4):2732.
[17]SINHA B K,TIERSTEN H F.On the temperature dependence of the velocity of surface waves in quartz[J].Journal of Applied Physics,1980,51(9):4659-4665.
[18]KOSINSKI J A.The fundamental nature of acceleration sensitivity[C]//Proc of IEEE International Frequency Control Symposium,1996.
[19]MASSON J,REINHARDT A,BALLANDRAS S.Simulation of stressed FBAR thanks to a perturbation method[C]//Proc of IEEE Mtt-s International Microwave Symposium Digest,2005.
[20]PANDEY D K,SINGH D,YADAV R R.Ultrasonic wave propagation inⅢrd group nitrides[J].Applied Acoustics,2007,68(7):766-777.
[21]BRUGGER,K.Pure modes for elastic waves in crystals[J].Journal of Applied Physics,1965,36(3):759-0.
[22]WANG Z,ZHAO J,GAO Y,et al.First-principle studies on the influence of anisotropic pressure on the physical properties of aluminum nitride[J].Materials Research Express,2017,4(1):016303.