An extended polynomial approach for modeling annular piezoelectric MEMS resonators: effects of inner-region metallization rate on resonance characteristics

Abstract

Abstract We have developed a semi-analytical method based on an extended polynomial approach to model the vibration characteristics of annular microelectromechanical systems (MEMSs) resonators with axisymmetric inner-region (partial) metallization. Due to variations in electrode distribution and electrical boundary conditions, the studied structure is divided into two distinct regions. The model incorporates specific window functions and expands the mechanical displacements and electrical potentials of each region into polynomial series to solve for wave propagation across the entire structure, capturing the differences between the regions. The results obtained using the proposed method through modal and harmonic analyses are validated against existing results from the literature. To evaluate this approach’s practical outcomes, the study examines how resonant frequencies, antiresonant frequencies, and dynamic electromechanical coupling coefficients ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>k</mml:mi> <mml:mrow> <mml:mtext>d</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> ) depend on the metallization rate. The findings reveal that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>k</mml:mi> <mml:mrow> <mml:mtext>d</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> can decrease to zero or increase by up to a factor of 8.47 compared to complete metallization depending on the electrode distribution. Detailed analyses of dispersion curves, impedance response patterns, and mechanical displacement field profiles further support these results, providing comprehensive insights into the electrical and mechanical behaviors of annular piezoelectric plates. These results provide valuable insights for optimizing the design of annular piezoelectric resonators, particularly for MEMS applications.