The Multi-Mode Resonance in AlN Lamb Wave Resonators

Abstract

The characteristics of the multi-mode resonance behavior of AlN Lamb wave resonators (LWRs) are theoretically and experimentally investigated for the first time in this paper. Adler's approach and finite element method (FEM) are used to calculate the dispersive characteristics of the phase velocity (v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> ), group velocity (v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> ), effective coupling coefficient (k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eff</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), and temperature coefficient of frequency for the first eight Lamb wave modes with different transducer configurations. The FEM is performed to take an insight into the mode shapes of the S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> mode and S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> mode specifically: the S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> mode is more contourlike and exhibits the largest k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eff</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> when h <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">AlN</sub> /λ is close to 0.5; the S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> mode is strong in vertical direction and can enable high resonance frequency (f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> ) and large k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> simultaneously when AlN thickness is very thin. Experimentally, AlN LWRs with different AlN thicknesses are designed and fabricated. The measured results are fitted into the multi-resonance BVD model so that the device performance parameters, as well as the equivalent, lumped element values are extracted and compared. By choosing different normalized AlN thicknesses, the performance of different Lamb wave modes varies largely due to the dispersive characteristics and agrees well with theoretically predicted acoustic characteristics. This paper lays the foundation for characterizing the multi-resonance behaviors of AlN LWRs and gives guidance on choosing the optimal design parameters and Lamb wave modes for different applications.