2.4 ZnO thin film based SAW devices on silicon
2.4.7 Results of ZnO/Si SAW resonator
The phase velocity in the layered structure ranges in between the surface wave velocity of substrate and the surface wave velocity of bulk ZnO, which is surface wave velocity in (100) silicon (4921 m/s) and in ZnO (2507 m/s) [54]. The
phase velocity dispersion is higher in case of large acoustic impedance difference between piezoelectric thin film and substrate [3]. At smaller thicknesses of ZnO film the surface wave exhibits the properties of substrate with high phase velocity and as the thickness increase the phase velocity tend to reach the velocity bulk ZnO. From the K2 characteristics, we observed that the position of IDT and inclusion of metal layers affects the values significantly. From Fig. 2.16, M/ZnO/IDT/Si configuration exhibits relative high K2 of 4.5% at h/λ = 0.4, which requires a thick ZnO film and also compatibility and characterization difficulties arises due to presence of metal layer above ZnO. Relative high K2 of 1.5% at h/λ = 0.1 with phase velocity of 4252 m/s is exhibited by IDT/ZnO/Si configuration. Relative high K2 of 3% at h/λ = 0.32 with phase velocity of 3248 m/s is observed from ZnO/IDT/Si configuration.
IDT electrode
ΓL2
≈ ≈
ΓR2
p
Silicon y
x z
IDT
PML ΓL3
≈ ≈
ΓR3
ΓL1≈ ZnO ≈ΓR1
Fig. 2.15. 2D Geometry of the periodic section used for the simulation.
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IDT/ZnO/M/Si configuration exhibits relative maximum K2 of 2.75% at h/λ = 0.5 with low phase velocity of 2668 m/s.
The IDT is designed with an admittance of 0.02 mho at center frequency. The center frequency can be obtained using eigenmode analysis or frequency dependent analysis. One port SAW resonator is designed using equivalent circuit model for all the configurations, the number of finger pairs in IDT and resonance frequency, coupling coefficient, and ZnO thicknesses are summarized in Table 2.4. The thicknesses of ZnO are considered to obtain high frequency of operation with K2 at that h/λ.
𝑘𝑘=𝑗𝑗|0.5∗ 𝐾𝐾2|∗ �𝜋𝜋
2� ∗ �(−𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐) +�𝑃𝑃0.5(𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐)
𝑃𝑃−0.5(𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐)�� (2.41) where Δ = nπ, P0.5(cos Δ)= 1.5061 and P-0.5(cos Δ)= 1.3280 are the Legendre polynomials adapted from Nordin [26].
Total reflectivity of grating is given by
|𝛤𝛤| = tanh𝑁𝑁|𝑘𝑘| (2.42)
Where N is number of reflector gratings, using the reflectivity k the penetration length of the generated surface wave is calculate using
𝐿𝐿𝑝𝑝=𝜆𝜆/|4𝑟𝑟| (2.43)
Fig. 2.16. The phase velocity and electromechanical coupling coefficient dispersion characteristics of four ZnO/Si configurations.
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Further, we carried out eigenmode analysis to study the generation of higher order modes in ZnO/IDT/Si structure, as it exhibit high coupling coefficient at smaller thickness of ZnO compared with other configurations as well as small device size. The phase velocity and coupling coefficient dispersion of curves of first four modes generated in the ZnO/IDT/Si layered structure are shown in Fig. 2.17. From (a) we observe the maximum velocity attained by the modes generated is near to shear bulk wave velocity of silicon which is 5653 m/s and as the thickness of ZnO increases the phase velocity tends to SAW velocity of bulk ZnO. In case of layered structures the maximum phase velocity attain by higher order modes is the shear bulk velocity of the substrate [3], [47]. From Fig. 2.17(b), we observe the 0th Rayleigh mode exhibits relative maximum coupling coefficient at h/λ = 0.3. 1st higher order Rayleigh wave is observed at h/λ = 0.2 having phase velocity of 5285 m/s with K2 = 0.92%
which is the relative maximum exhibited by 1st mode. 2nd mode starts at h/λ = 0.55 with phase velocity of 5328 m/s with a K2 value of 0.27% and reaches a relative maximum value of 0.33% with a phase velocity of 5275 m/s. Mode 3 starts from h/λ = 0.875 with phase velocity of 5317 m/s and K2 value of 0.29%. As mode 0 exhibiting maximum coupling coefficient, we carried out the harmonic analysis to obtain total displacement and harmonic admittance characteristics of modes generated in ZnO/IDT/Si one port SAW resonator structure. The obtained frequency dependent results are shown in Fig. 2.18 and the surface displacement profiles of two modes generated in the structure are show in Fig. 2.19.
Table 2.4 Dimensions of one port SAW resonator obtained using equivalent circuit model.
Configuration ZnO (µm) K2 (%) f0 (MHz) Nt k (per one finger) N
(a) IDT/ZnO/Si 0.8 1.392 508.6653 81 0.0028 348
(b) IDT/ZnO/M/Si 0.4 1.95 549.2043 66 0.0016 608
(c) ZnO/IDT/Si 2.6 2.95 389.3882 63 0.011 88
(d) M/ZnO/IDT/Si 0.4 1.53 556.3627 74 0.01 0.01
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(a) (b)
Fig. 2.17. The variation of phase velocities of 0th, 1st, 2nd, and 3rd Rayleigh modes with respect to ZnO film thickness ratio in conventional ZnO/Si structure.
(a) (b)
Fig. 2.18. (a) Normalized admittance and (b) normalized displacement characteristics of Rayleigh surface modes generated in conventional ZnO/IDT/Si configured SAW resonator at h/λ = 0.3.
(a) (b) (c) (d) (e) (f)
Fig. 2.19. (a) Total displacement, (b) x-displacement, (c) y-displacement profiles of fundamental Rayleigh mode, and (d) total displacement profile, (e) x-displacement, (c) y-displacement profiles of first higher order Rayleigh modes generated in the ZnO/IDT/Si structure at h/λ = 0.3, displacement scale in µm.
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A few literature has been reported on the FE simulation of thin film SAW device on silicon using ZnO film and many researchers reported the simulation of conventional piezoelectric substrate based SAW delay lines [46], [57], and [58]. In this section, ZnO/IDT/Si structure SAW delay is simulated to compare the simulation results with the proposed SAW delay line on silicon described in the next chapter. A delay line with 4λ distance between the centers of input and output IDT’s. The dimensions used in the simulation are as follows: pitch of 4 µm, metallization ratio of 0.5, and thickness of IDT electrodes 0.1 µm and substrate depth of 5λ. The 2D schematic of ZnO/IDT/Si SAW delay line with subdomain conditions are shown in Fig. 2.20. Fixed boundary condition is applied to bottom boundaries of the geometry and rest all boundaries are assumed stress free. Rayleigh damping boundary conditions are applied to absorb medium, which is extend to one wavelength on the both sides of the delay line to absorb the unwanted reflections form the edges of the device. The electrical boundary conditions are as follows: the alternate fingers of input port are grounded and a 1V sinusoidal driven voltage of its resonance frequency (367.9581 MHz) of is given to remaining electrodes [59]. Meshing is optimized in such way that extreme fine meshing is obtained at active surface region of structure and fine mesh into the substrate.
The transient analysis is carried out using the direct solver available in COMSOL multiphysics for 30 ns with a time interval of 1 ps. The displacements and potential at the receiver electrode are recorded at every step.