## 3 Simulation Performance Analysis
### Resonator Design and Simulation  
As both SAW-related sensors and filters are fundamentally constructed based on resonators, the analysis of resonator performance impacts becomes crucial. Figure 10 illustrates a schematic diagram of a single-port resonator structure. Single-port resonators typically consist of the IDT and reflecting grating (RG). The IDT refers to metal electrodes arranged in a crossed pattern on a piezoelectric substrate, divided into an input port and a ground port. The portion of the interdigital electrode's crossed arrangement length is referred to as the acoustic aperture. This section concludes with the design of a SAW resonator with the coexistence of Rayleigh and Sezawa modes using this laminated structure. The Q, as an important indicator of resonators, is primarily determined by the pairs of the RG, IDT, and the aperture width (W). In this section, we will investigate the influence of the number of the IDT pairs (Nt) and the W on the Q value of the resonator. This study fixes the number of the RG at 25 pairs and then explores the impact of different Nt and W values on the electrical performance of the IDT/ZnO/SiO\({}_{2}\)/diamond multilayer resonator structure. The thickness of each layer in the resonator is determined based on the results from the previous section. When studying the impact of Nt, we utilized the array functionality of COMSOL, gradually increasing Nt from 70 pairs to 150 pairs while keeping W fixed at 20 \(\lambda\) to simulate the effects of different Nt values on the resonator. The simulation results are presented  
Figure 10: Schematic structure of single-port SAW resonator. Figure 9: Designed device’s displacement against substrate depth in both Rayleigh and Sezawa modes: (a) Rayleigh wave; (b) Sezawa wave. in terms of the Y11 parameter. As seen in Figure 11a, with the increase in Nt, the peaks at the resonance and anti-resonance frequencies of the Sezawa wave show a significant rise, indicating an increase in admittance values. This phenomenon is attributed to the better confinement of energy within the resonator as Nt increases. Simultaneously, there is minimal change in the resonance and anti-resonance frequencies, i.e., \(k^{2}\) shows no significant variation. To assess the changes in Q values, this study employs the \(-3\) dB bandwidth method [32]. Figure 11b illustrates the magnitudes and trends of Qs and Qp values obtained for different Nt values. As Nt increases from 70 pairs to 150 pairs, the corresponding Q values at the resonance (Qs) and anti-resonance (Qp) points both show improvement, with Qs changing from 835.2 to 987.1, and Qp changing from 1486.7 to 1627.5. Clearly, the change in Qp is more pronounced. To achieve a higher Qs and Qp while avoiding excessively large device sizes, this study maintains the IDT pairs at a constant value of 130 and proceeds to investigate the impact of W on the resonator. Utilizing the finite element method for parameterized simulations, W is varied in increments of 20 \(\lambda\), ranging from 20 \(\lambda\) to 100 \(\lambda\). Figure 12a depicts a schematic of Y11 under different W values, showing an increase in the peaks of Sezawa wave resonance and anti-resonance frequencies, representing an increase in admittance values. Furthermore, \(k^{2}\) remains relatively unchanged. Figure 12b illustrates the magnitudes and trends of Qp and Qs values for different W values. The results indicate a slight increase in Qp, rising from 1591.3 to 1645.8. Conversely, Qs decreases from 964.8 to 408.6, which is attributed to the increased electrode resistance resulting from the larger W.  
Figure 11: Effect of Nt on Y11 performance and Q value: (**a**) Effect of Nt on Y11 performance; (**b**) the values of Qs and Qp vary with Nt. Figure 12: Effect of W on Y11 performance and Q value: (**a**) effect of W on Y11 performance; (**b**) the values of Qs and Qp vary with W/\(\lambda\).