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Energy trapping of thickness-extensional modes in thin film bulk acoustic wave resonators

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Abstract

We perform a theoretical analysis on a rectangular trapped-energy piezoelectric resonator operating with thickness-extensional modes of a thin zinc oxide film on a silicon layer. The driving electrode covers the central part of the resonator only. The two-dimensional scalar differential equation for such a structure derived by Tiersten and Stevens is employed which can describe in-plane mode variations. A variational formulation is developed which provides the theoretical foundation for the Ritz method used in our analysis. Free vibration frequencies and modes are obtained and examined. Modes with vibrations trapped under the driving electrode are found. An approximation used to obtain the classical result of the resonator by Tiersten and Stevens, i.e., the neglect of the four corner regions of the resonator, is removed in our variational analysis. It is shown that their approximation causes a frequency difference on the order of dozens of parts per million for the fundamental thickness-extensional operating mode, quite significant in resonator design and operation.

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Authors and Affiliations

  1. State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Zinan Zhao, Zhenghua Qian & Bin Wang

  2. Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE, 68588-0526, U.S.A.

    Jiashi Yang

Authors
  1. Zinan Zhao
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  2. Zhenghua Qian
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  3. Bin Wang
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  4. Jiashi Yang
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Corresponding author

Correspondence to Zhenghua Qian.

Additional information

Recommended by Editor Yeon June Kang

Zinan Zhao received his B.E. in engineering mechanics in 2014 from Nanjing University of Aeronautics and Astronautics, China. Since 2014, he has been a master student of solid mechanics in the State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, China. His current research interest is mainly on the vibration analysis of various acoustic wave devices.

Zhenghua Qian received his B.E. in engineering mechanics in 2002 and Ph.D. in solid mechanics in 2007 from Xi’an Jiaotong University, China. From 2007 to 2012, he worked as a JSPS researcher and G-COE researcher in Tokyo Institute of Technology, Japan. Since 2012, he has been a Professor at the State key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, China. Qian has over 50 papers on the wave propagation of electromechanical materials and structures. His current research focus is mainly placed on the structural analysis and design of piezoelectric acoustic wave devices.

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Zhao, Z., Qian, Z., Wang, B. et al. Energy trapping of thickness-extensional modes in thin film bulk acoustic wave resonators. J Mech Sci Technol 29, 2767–2773 (2015). https://doi.org/10.1007/s12206-015-0605-0

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  • DOI: https://doi.org/10.1007/s12206-015-0605-0

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