Two-Dimensional Coupling Vibration Analysis of Laterally Acoustically Coupled Two-Port Thin-Film Bulk Acoustic Resonators

  • Haoyu Huang
  • Nian Li
  • Bin Wang
  • Zhenghua QianEmail author
  • Bin Huang
  • Tingfeng Ma
  • Iren Kuznetsova


In this paper, we present an approach to studying the mode coupling vibrations in two-port thin-film bulk acoustic wave resonator (FBAR) devices with two pairs of electrodes deposited on the zinc oxide film. The two-dimensional plate theory established in our previous work is employed, which takes into account the coupling of the operating thickness-extensional mode with the extensional, flexural, fundamental and second-order thickness-shear modes. The propagation of straight-crested waves in the plate is studied, and the state-vector approach is successfully used to simplify the derivation process. For a structurally symmetric device, the modes are separated into quasi symmetric and antisymmetric ones. Frequency spectra and corresponding mode shapes are obtained under the stress-free boundary conditions, respectively, and then coupling effects and energy trapping phenomenon are discussed in detail. Some results for structures with asymmetric electrode distributions are also shown. It is found that the choice of aspect ratio has a great effect on mode couplings of FBAR devices. This study will be useful for the design of FBAR filters and sensors.


FBAR RF filter Two-dimensional theory Mode coupling Trapped energy 



This work was supported by the State Key Laboratory of Mechanics and Control of Mechanical Structures at NUAA [Grant No. MCMS-I-0518K02], the National Natural Science Foundation of China [Grant Nos. 11502108, 1611530686] and the Natural Science Foundation of Jiangsu Province [Grant No. BK20140037]. Iren Kuznetsova thanks Russian Foundation Basic Research Grant #18-29-23042 and Russian Ministry of Science and Education for partial financial support.


  1. 1.
    Lee PCY, Yu JD, Lin WS. A new two-dimensional theory for vibrations of piezoelectric crystal plates with electroded faces. J Appl Phys. 1998;83(3):1213–23.CrossRefGoogle Scholar
  2. 2.
    Beaver WD. Analysis of elastically coupled piezoelectric resonators. J Acoust Soc Am. 1968;43(5):972–81.CrossRefGoogle Scholar
  3. 3.
    Li N, Qian Z, Yang J. Effects of nonlinearity on transient processes in AT-cut quartz thickness-shear resonators. Acta Mech Solida Sin. 2015;28(4):347–52.CrossRefGoogle Scholar
  4. 4.
    He H, Nie G, Liu J, et al. Energy trapping of thickness-shear and thickness-twist modes in a partially electroded AT-cut quartz resonator. Acta Mech Solida Sin. 2012;25(6):579–85.CrossRefGoogle Scholar
  5. 5.
    Iriarte GF, Engelmark F, Katardjiev IV. Reactive sputter deposition of highly oriented AlN films at room temperature. J Mater Res. 2002;17(6):1469–75.CrossRefGoogle Scholar
  6. 6.
    Martin F, Jan ME, ReyMermet S, et al. Shear mode coupling and tilted grain growth of AlN thin films in BAW resonators. IEEE Trans Ultrason Ferroelectr Freq Control. 2006;53(7):1339–43.CrossRefGoogle Scholar
  7. 7.
    Satoh Y, Nishihara T, Yokoyama T, et al. Development of piezoelectric thin film resonator and its impact on future wireless communication systems. Jpn J Appl Phys. 2005;44(5A):2883–94.CrossRefGoogle Scholar
  8. 8.
    Ruby RC, Bradley P, Oshmyansky Y, et al. Thin film bulk wave acoustic resonators (FBAR) for wireless applications. In: IEEE ultrasonics symposium 2001 (vol. 1, p. 813–821).Google Scholar
  9. 9.
    Gabl R, Green E, Schreiter M, et al. Novel Integrated FBAR sensors: a universal technology platform for bio- and gas-detection. In: Sensors Proceedings of IEEE. 2003 (vol. 2 no. 2, p. 1184–8).Google Scholar
  10. 10.
    Tukkiniemi K, Rantala A, Nirschl M, et al. Fully integrated FBAR sensor matrix for mass detection. Procedia Chem. 2009;1(1):1051–4.CrossRefGoogle Scholar
  11. 11.
    Fu YQ, Luo JK, Du XY, et al. Recent developments on ZnO films for acoustic wave based bio-sensing and microfluidic applications: a review. Sens Actuators B Chem. 2010;143(2):606–19.CrossRefGoogle Scholar
  12. 12.
    Kim EK, Lee TY, Jeong YH, et al. Air gap type thin film bulk acoustic resonator fabrication using simplified process. Thin Solid Films. 2006;496(2):653–7.CrossRefGoogle Scholar
  13. 13.
    Ueda M, Hara M, Taniguchi S, Yokoyama T, Nishihara T, Hashimoto K, Satoh Y. Development of an X-band filter using air-gap-type film bulk acoustic resonators. Jpn J Appl Phys. 2008;47(5S):4007–10.CrossRefGoogle Scholar
  14. 14.
    Link M, Schreiter M, Weber J, Primig R, Pitzer D, Gabl R. Solidly mounted ZnO shear mode film bulk acoustic resonators for sensing applications in liquids. IEEE Trans Ultrason Ferroelectr Freq Control. 2006;53(2):492–6.CrossRefGoogle Scholar
  15. 15.
    Lin RC, Chen YC, Chang WT, et al. Highly sensitive mass sensor using film bulk acoustic resonator. Sens Actuators A Phys. 2008;147(2):425–9.CrossRefGoogle Scholar
  16. 16.
    Larson JD, et al. Modified Butterworth-Van Dyke circuit for FBAR resonators and automated measurement system. In: Ultrasonics Symposium. 2000 (vol. 1, p. 863–8).Google Scholar
  17. 17.
    Tiersten HF, Stevens DS. An analysis of thickness-extensional trapped energy resonant device structures with rectangular electrodes in the piezoelectric thin film on silicon configuration. J Appl Phys. 1983;54(10):5893–910.CrossRefGoogle Scholar
  18. 18.
    Zhao Z, Qian Z, Wang B. Energy trapping of thickness-extensional modes in thin film bulk acoustic wave filters. AIP Adv. 2016;6(1):993–5.Google Scholar
  19. 19.
    Li N, Qian Z, Yang J. Two-dimensional equations for piezoelectric thin-film acoustic wave resonators. Int J Solids Struct. 2017;110:170–7.CrossRefGoogle Scholar
  20. 20.
    Li N, Qian Z, Yang J. Effects of aspect ratio on the mode couplings of thin-film bulk acoustic wave resonators. AIP Adv. 2017;7(5):055113.CrossRefGoogle Scholar
  21. 21.
    Li N, Qian Z, Wang B. Forced coupling vibration analysis of FBAR based on two-dimensional equations associated with state-vector approach. AIP Adv. 2018;8(9):095306.CrossRefGoogle Scholar
  22. 22.
    Meltaus J, Pensala T, Kokkonen K. Parametric study of laterally acoustically coupled bulk acoustic wave filters. IEEE Trans Ultrason Ferroelectr Freq Control. 2012;59(12):2742–51.CrossRefGoogle Scholar
  23. 23.
    Pensala T, Meltaus J, Kokkonen K, et al. 2-D modeling of laterally acoustically coupled thin film bulk acoustic wave resonator filters. IEEE Trans Ultrason Ferroelectr Freq Control. 2010;57(11):2537–49.CrossRefGoogle Scholar
  24. 24.
    Zhu F, Zhang Y, Wan B, et al. An elastic electrode model for wave propagation analysis in piezoelectric layered structures of film bulk acoustic resonators. Acta Mech Solida Sin. 2017;30(3):46–53.CrossRefGoogle Scholar
  25. 25.
    Shen F, Lee KH, O’Shea SJ, et al. Frequency interference between two quartz crystal microbalances. Sensors. 2003;3(3):274–81.CrossRefGoogle Scholar
  26. 26.
    Shen F, Lu P. Influence of interchannel spacing on the dynamical properties of multichannel quartz crystal microbalance. IEEE Trans Ultrason Ferroelectr Freq Control. 2004;51(2):249–53.MathSciNetCrossRefGoogle Scholar
  27. 27.
    Li H, Du H, Xu L, et al. Analysis of multilayered thin-film piezoelectric transducer arrays. IEEE Trans Ultrason Ferroelectr Freq Control. 2009;56(11):2571–7.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace EngineeringNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.Faculty of Mechanical Engineering and MechanicsNingbo UniversityNingboChina
  3. 3.Kotelnikov Institute of Radio Engineering and Electronics of RASMoscowRussia

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