3.1. Simulation of Resonators
Based on the advantages of fast and accurate simulations offered by the COM method, this work employs the COM method for the simulation and optimization of SAW resonators and DMS filters.
Figure 5 shows the calculated admittance of resonators for both bulk 36°YX−LT substrate and the 36°YX−LT/SiO
2/SiC multi-layered structure. The structural parameters of the resonator are shown in
Table 2. It can be observed that the multi-layered structure exhibits significantly higher
K2 and a larger oscillation amplitude. This can be attributed to the SiC substrate in the multi-layered structure, which has a higher velocity and thus offers an SAW energy confinement effect. This characteristic allows for the efficient conversion of electrical energy into mechanical vibration, enabling the high performance of SAW devices. Compared to the bulk LT substrate, the LT/SiO
2/SiC multi-layered substrate has advantages in terms of a higher
Q and improved temperature stability. From this point on, the 36°YX−LT/SiO
2/SiC multi-layered structure was further optimized in terms of different Euler angles and geometric structural parameters.
The advantages of the multi-layered structure over those of a bulk LT structure, in terms of SAW resonator fabrication, typically result in a higher Q and improved temperature stability. Therefore, in this study, the multi-layered structure is optimized and employed for the simulation of SAW devices.
Figure 6a presents the calculated velocities and electromechanical coupling coefficients of an SH wave mode on the LT/SiO
2/SiC structure versus different
β rotation angles of the LT layer. The maximum
K2 value of the device, which was approximately 13.88%, was achieved by setting the Euler angle of the LT layer in the COMSOL as (0°, 151°, 0°) when the LT layer thickness at 800 nm. In this configuration, the phase velocity reached around 4064 m/s.
Additionally,
Figure 6b illustrates the calculated velocities and electromechanical coupling coefficients versus different piezoelectric layer thicknesses on a 29°YX−LT/SiO
2/SiC structure. A
K2 value of 13.89% is obtained when the piezoelectric layer thickness is 0.2λ, with a corresponding phase velocity of 4060 m/s. This reduction in velocity is deemed acceptable compared to the case for a piezoelectric layer thickness of 0.1λ. In the case of a 0.2λ thick LT layer, a
K2 value of 13.91% is obtained when the electrode thickness is 0.06λ, as shown in
Figure 6c. It is worth noting that as the electrode thickness increases, the velocity of the SH wave mode gradually decreases due to the influence of mass loading. However, the velocity of 4085 m/s at the electrode thickness of 0.06λ is an acceptable value. Under the condition of a 0.2λ thick LT layer and 0.06λ thick Al electrodes, an optimized structure with a maximum
K2 of 13.92% and suitable phase velocity of 4122 m/s obtained simultaneously results when the metallization ratio is 0.4.
Figure 7a presents the simulation results of the optimized resonator compared to those of a resonator on a 36°YX−LT substrate. The optimized resonator on the 29°YX−LT/SiO
2/SiC structure exhibits significantly larger
K2 values and higher amplitudes compared to the resonator on a 36°YX−LT substrate.
Figure 7b illustrates the temperature characteristics of the optimized resonator on the 29°YX−LT/SiO
2/SiC structure. It is evident that as the temperature increases, the overall admittance gradually shifts to the left. The temperature coefficient of the resonance frequency (TCF
r) is −10.67 ppm/°C, while the temperature coefficient of the anti-resonance frequency (TCF
a) is −40.36 ppm/°C [
29,
30,
31].
Table 3 presents a comparison for the extracted COM parameters at different temperatures. As can be seen, these extracted temperature-dependent COM parameters vary with the temperature change. The performance comparison between the resonators on a 36°YX−LT substrate and a 29°YX−LT/SiO
2/SiC substrate is shown in
Table 4. The multi-layered structure demonstrates a significant improvement in temperature stability, which effectively mitigates the impact of temperature variations on SAW resonators and meets the requirements for precise and stable performance in practical applications.
3.2. Simulation of DMS Filters
The advantages of the optimized 29°YX−LT/SiO2/SiC structure over a 36°YX−LT structure typically imply a larger bandwidth and lower insertion loss for filters. Therefore, this work extends the optimization results of multi-layered SAW resonators and applies the optimized structure for a DMS filter simulation.
In order to obtain a wider bandwidth, the test DMS structure of three IDTs in which the lateral IDTs are symmetrically arranged with respect to the center IDT is used [
32].
Figure 8 presents the electrode configuration. The corresponding parameters of DMS filters are shown in
Table 5.
Figure 9 illustrates a comparison of the transmission spectrums between the filters on the 36°YX−LT and 29°YX−LT/SiO
2/SiC substrates. The DMS filter on the 29°YX−LT/SiO
2/SiC substrate exhibits a significantly wider bandwidth compared to that of the common filter. This expanded bandwidth enables the filter to transmit a broader range of frequencies, meeting the requirements for processing various frequency signals. Additionally, the 29°YX−LT/SiO
2/SiC structure demonstrates a flatter passband, ensuring uniform signal transmission and avoiding an uneven frequency response and distortion. This is crucial for applications that demand good signal quality and accuracy. Therefore, the DMS filter on the 29°YX−LT/SiO
2/SiC substrate provides more flexible and high-performance signal processing capabilities.
Figure 10 illustrates the computed temperature characteristics of the two DMS filters, indicating that the optimized 29°YX−LT/SiO
2/SiC structure exhibits superior temperature stability compared to that of the 36°YX−LT structure. Particularly, TCF suppression is evident at lower frequencies in the 29°YX−LT/SiO
2/SiC structure. TCF values at the lower edge (TCF
l) are reduced to −14.35 ppm/°C, while TCF values at the higher edge (TCF
h) are reduced to −22.02 ppm/°C compared to those of the DMS filter on a 36°YX−LT structure (TCF
l = −32.87 ppm/°C, TCF
h = −37.55 ppm/°C). The 29°YX−LT/SiO
2/SiC structure effectively suppresses the TCF to a satisfactory level, emphasizing its contribution to improved temperature stability.
Table 6 presents the specific performance of the two DMS filters. In addition to the improvement in TCF, in-band insertion loss is optimized from −3 dB to −2 dB, effectively enhancing the application potential of the filter at high temperatures and enabling the better performance of signal transmission. It can be inferred that by employing the improved method, it is possible in the early stages of designing SAW devices to simulate the propagation characteristics and temperature properties of DMS filters rapidly and accurately in the manufacturing process. This facilitates the identification of filters that meet the expected requirements, enabling mass production and reducing material wastage caused by inaccurate or incomplete simulations.