Extraction of Attenuation Parameter in Periodic Shorted Reflectors of One-Port SAW Resonator Using Scattering Matrix Approach

Abstract

In this work, the well-known scattering matrix approach to the design of one-port surface acoustic wave (SAW) resonators is adapted toward extraction of the coupling-of-modes (COM) attenuation parameter, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> for Rayleigh SAW propagation on a periodic shorted aluminum grating. The attenuation close to resonance inside the reflectors of the one-port SAW resonator is extracted by matching the measured conductance of the resonator to its version calculated from the experimentally measured interdigital transducer (IDT) scattering coefficients, intrinsic substrate parameters, and geometry of the resonator. Based on the extracted value of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> , it was observed that the proposed method could predict the unloaded <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -factor of the resonator at a minor discrepancy of ~7.02%. At the same time, since the proposed method utilizes the measured IDT scattering coefficients to consider the effect of IDT losses on the measured conductance of the resonator, it offers a convenient scheme to directly extract the attenuation of SAW contributed by the reflectors of the device through numerical means while operating purely in the frequency domain. The proposed method could be applied to quantify the increase in attenuation caused by viscous damping of SAW inside sensing film-coated reflectors of one-port SAW resonator sensors, and thereby, aid to optimize the sensing film thickness to deploy these devices for high-resolution frequency-based sensing applications.