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<p>Film bulk acoustic resonators (FBARs) are essential in RF front-end applications due to their high performance, microsize, and ease of integration. This paper presents a one-dimensional analytical model for predicting the nonlinear forced vibrations of thickness–extensional AlN FBARs based on nonlinear piezoelectric theory. The model incorporates geometric and material nonlinearities, viscous damping, and electrode mechanical effects. Analytical expressions are derived to describe the excitation frequency–current relationship, including the effects of an external circuit. The influences of driving voltage, higher-order elastic constants, viscous damping, and electrode materials on the nonlinear frequency response are examined. Results indicate that increasing voltage strengthens nonlinear effects, leading to resonance frequency hardening and response multi-stability. The critical voltage marking the transition from linear to nonlinear behavior is also identified. Additionally, electrode properties, fourth-order elastic constants, and damping significantly affect the nonlinear response. Proper electrode and circuit design can mitigate nonlinear effects and extend the linear operating range. The proposed analytical model serves as an efficient tool for predicting nonlinear FBAR vibrations, providing valuable insights for device optimization.</p>

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One-dimensional analytical model for nonlinear forced vibrations in thickness–extensional film bulk acoustic resonators

  • 期刊论文

  • 发表日期：

    2025年7月27日

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  • Ruoqian Lin,
  • Zinan Zhao,
  • Guangyao lv,
  • Qiaozhen Zhang,
  • Xiangyong Zhao,
  • Weiqiu Chen

摘要

Film bulk acoustic resonators (FBARs) are essential in RF front-end applications due to their high performance, microsize, and ease of integration. This paper presents a one-dimensional analytical model for predicting the nonlinear forced vibrations of thickness–extensional AlN FBARs based on nonlinear piezoelectric theory. The model incorporates geometric and material nonlinearities, viscous damping, and electrode mechanical effects. Analytical expressions are derived to describe the excitation frequency–current relationship, including the effects of an external circuit. The influences of driving voltage, higher-order elastic constants, viscous damping, and electrode materials on the nonlinear frequency response are examined. Results indicate that increasing voltage strengthens nonlinear effects, leading to resonance frequency hardening and response multi-stability. The critical voltage marking the transition from linear to nonlinear behavior is also identified. Additionally, electrode properties, fourth-order elastic constants, and damping significantly affect the nonlinear response. Proper electrode and circuit design can mitigate nonlinear effects and extend the linear operating range. The proposed analytical model serves as an efficient tool for predicting nonlinear FBAR vibrations, providing valuable insights for device optimization.