Modeling longitudinal leaky saw propagation under periodic electrode arrays (2006)

We have extended our earlier simple model for longitudinal leaky SAW (LLSAW) in isotropic elastic substrate (1) to account for periodic disturbance on the surface. In particular, periodic system of mechanical resonators on the surface is considered. The computed dispersion curves show Bragg stop- band for LLSAW as well as stopband due to backscattering of LLSAW to Rayleigh SAW. Furthermore, it is shown that the propagation loss can be made essentially to vanish with suitably chosen parameters of the resonators on the surface such that the radiation of shear bulk wave into the substrate is suppressed. It was recently shown that LLSAW modes with low propagation loss exist on YZ-cut LiNbO3 substrate for different thicknesses of the aluminum finger electrodes (2). These modes can be associated with higher order resonances of flexural waves in the electrodes. Here, simulation of infinite periodic IDT on YZ-LiNbO3 with gold electrodes is carried out using periodic FEM/BEM technique. It is found that, in addition to the flexural mode, other Lamb wave modes propagating in the gold electrode also support LLSAW with low losses. The computed dependence of Q-value (attenuation), LLSAW velocity and resonance-antiresonance-distance on electrode thickness is presented in detail. These dependencies can be exploited in resonator and, consequently, ladder filter design. I. INTRODUCTION The high phase velocity of longitudinal leaky SAW (LL- SAW) mode enables bandpass filter center frequencies above 5 GHz to be reached employing standard optical lithogra- phy (3). To better understand the characteristics of the LLSAW mode, earlier model for LLSAW on isotropic substrate (1) has been extended to incorporate loading by periodic array of resonating elements. In the direction parallel to the substrate surface, the electrode is taken to act as a resonator, whereas in the direction perpendicular to the substrate surface the electrode behaves as a mere mass load. The model takes into account scattering into BAW, as well as into forward and back- ward propagating higher harmonic SAW modes. The computed dispersion curves show Bragg stopbands due to LLSAW, as well as clear minimum in the propagation loss at frequencies close to the first Bragg reflection stopband. Hence, at certain frequency, the shear and longitudinal partial waves constituting the LLSAW solution in the substrate become decoupled, and the wave essentially contains only the longitudinal partial wave component, which decays exponentially into the substrate. SAW modes in thick ridge/electrode gratings have been earlier studied, e.g., by Baghai-Wadji et al. (4) and Laude et al. (5). Considering LLSAW, Solal et al. (2) studied its prop- agation properties under periodic system of thick aluminum (Al) electrodes on YZ-LiNbO3 substrate. They found that, in addition to Al electrode thickness of h/(2p )=8 % , LLSAW with low propagation loss exists for Al electrode thicknesses of h/(2p) = 24% and h/(2p) = 45%. The different optimal thicknesses were associated with the electrode resonances due to flexural wave (Lamb wave mode A0) propagating in the thickness direction of the electrode, such that the mechanical resonances at adjacent electrodes are coupled through the sub- strate. Here, numerical simulations of infinite IDTs with gold electrodes are carried out using the FEM/BEM technique with phased-periodic boundary conditions (periodic FEM/BEM in what follows). Equal to the case of Al electrodes, we find the LLSAW mode which can be associated with the resonance of the flexural wave in the gold electrode. In addition, high Q-values are obtained also for cases where the displacement profile within the electrode is more complex than that corre- sponding to the flexural wave.