The Multi-Mode Resonance in AlN Lamb Wave Resonators

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
_p
), group velocity (v
_g
), effective coupling coefficient (k
_eff
²
), 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
₀
mode and S
₁
mode specifically: the S
₀
mode is more contourlike and exhibits the largest k
_eff
²
when h
_AlN
/λ is close to 0.5; the S
₁
mode is strong in vertical direction and can enable high resonance frequency (f
_s
) and large k
₂
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.