Fig. 1

Schematic of the piezoelectric layered structure with a rod resonator array (color online)"

Fig. 2

Schematic diagrams of the finite element models: (a) model for dispersion analysis; (b) model for frequency-domain analysis (color online)"

Table 1

Material properties of AlN, LiNbO3, and Si used in this study"

Fig. 3

Frequency-phase velocity dispersion curves of Rayleigh waves in the high-velocity bare layered structure for different piezoelectric layer thicknesses (h=5 μm, 10 μm, 15 μm). The solid lines represent the theoretical solutions, and the dots represent the results obtained from the finite element simulations (labeled as FEM in the figure). vRAlN and vRSi denote the theoretical Rayleigh wave velocities of the pure AlN layer and the pure Si substrate, respectively (color online)"

Fig. 4

Dispersion curves for the AlN-Si layered structure (h=10 μm): (a) wavenumber-frequency dispersion curves; (b) frequency-phase velocity dispersion curves. The solid lines represent the theoretical solutions, and the dots represent the results obtained from finite element simulations (labeled as FEM in the figure). vsSi and vRAlN denote the theoretical bulk shear wave velocity of the pure Si substrate and the Rayleigh wave velocity of the pure AlN layer, respectively. vmeta and vbare represent the SAW velocities of the metamaterial-covered and bare AlN-Si layered structures, respectively. The horizontal dashed lines in (a) and vertical ones in (b) indicate the resonant frequencies of the rod resonators (color online)"

Fig. 5

Dispersion curves and wave mode shapes of the AlN-Si layered structure (h=10 μm): (a) wavenumber-frequency dispersion curves, where vsSi denotes the theoretical bulk shear wave velocity of the pure Si substrate, and the horizontal dashed line indicates the second-order resonant frequency of the rod resonators; (b) wave mode shape corresponding to Point P1 labeled in (a); (c) wave mode shape corresponding to Point P2 labeled in (a) (color online)"

Fig. 6

Displacement fields of the AlN-Si layered structure (h=10 μm) at selected excitation frequencies: (a) positions at 423 MHz; (b) displacement fields at 423 MHz (within the bandgap); (c) positions at 600 MHz; (d) displacement fields at 600 MHz (outside the bandgap). vsSi denotes the theoretical bulk shear wave velocity of the pure Si substrate (color online)"

Fig. 7

Wave transmission characteristics of the AlN-Si layered structure (h=10 μm). The vertical dashed lines denote the resonant frequencies of the rod resonators (color online)"

Fig. 8

Frequency-phase velocity dispersion curves of Rayleigh waves in the low-velocity bare layered structure for different piezoelectric layer thicknesses: (a) h=5 μm; (b) h=10 μm; (c) h=15 μm. vsSi and vRSi denote the theoretical bulk shear wave velocity and Rayleigh wave velocity of the pure Si substrate, respectively. vsLN and vRLN denote the theoretical bulk shear wave velocity and Rayleigh wave velocity of the pure LiNbO3 layer, respectively (color online)"

Fig. 9

Dispersion curves of the LiNbO3-Si layered structure for different piezoelectric layer thicknesses: (a), (b) h=5 μm; (c), (d) h=10 μm; (e), (f) h=15 μm. The left column ((a), (c), (e)) shows the wavenumber-frequency dispersion curves, and the right column ((b), (d), (f)) shows the frequency-phase velocity dispersion curves. vsSi and vsLN denote the theoretical bulk shear wave velocities of the pure Si substrate and the pure LiNbO3 layer, respectively. vmeta and vbare represent the SAW velocities of the metamaterial-covered and bare LiNbO3-Si layered structures, respectively. The vertical dashed lines in (b), (d), and (f) indicate the resonant frequencies of the rod resonators (color online)"

Fig. 10

Dispersion curves and wave mode shapes of the LiNbO3-Si layered structure (h=10 μm): (a) wavenumber-frequency dispersion curves; (b), (c), (d), (e) wave mode shapes corresponding to P1, P2, P3, and P4 labeled in (a), respectively. vsSi and vsLN denote the theoretical bulk shear wave velocities of the pure Si substrate and the pure LiNbO3 layer, respectively. M0, M1, and M2 represent the dispersion curves of the fundamental Rayleigh wave, Sezawa wave, and second-order Rayleigh wave for the bare LiNbO3-Si structure, respectively (color online)"

Fig. 11

Displacement fields of the LiNbO3-Si layered structures at selected layer thicknesses h and excitation frequencies: (a) positions at 141 MHz for h=5 μm; (b) displacement fields at 141 MHz for h=5 μm; (c) positions at 423 MHz for h=5 μm; (d) displacement fields at 423 MHz for h=5 μm; (e) positions at 423 MHz for h=10 μm; (f) displacement fields at 423 MHz for h=10 μm; (g) positions at 423 MHz for h=15 μm; (h) displacement fields at 423 MHz for h=15 μm. vsSi and vsLN denote the theoretical bulk shear wave velocities of the pure Si substrate and the pure LiNbO3 layer, respectively (color online)"