## 2 Materials and Methods  
The schematic of conventional IDTs/ZnO/SiC configuration and our proposed structure are depicted in Figure 1a,b. Compared to the traditional multi-layer structure in SAW devices, piezoelectric thin film between the adjacent top interdigitated electrodes is partially removed in this work, as depicted in Figure 1b. The commercial finite element method (FEM) software COMSOL Multiphysics was used to obtain the SAW characteristics of the proposed structure. A three-dimensional model that uses a periodic component of the practical resonator's structure was established The width of the model was one wavelength, and the wavelength \(\lambda\) was fixed at 2 \(\upmu\)m. The thicknesses of the total ZnO piezoelectric film and the etching depth were \(h\) and \(d\), respectively. The etching ratio \(d/h\) was used to express the proportion of the etched part to the whole piezoelectric film. The electrode's width was represented by \(w\), and the retained ZnO pillars' width was consistent with the electrode. The model's size at the \(y\)-axis was set as 0.25\(\upmu\). The periodic boundary condition was applied in both the \(x\)- and \(y\)- direction to assume infinite length. The PMLwas fixed at the bottom of SiC substrate to eliminate the reflection of acoustic waves at the bottom boundary. The material constants of ZnO and SiC were obtained from Ref. [16]. The influences of Al, Cu, Pt, Mo, W, and Au as electrode materials were also investigated, and their properties were from COMSOL database.  
All parts except the two electrodes were included in the electrostatics. One electrode was set as the terminal electrical condition with voltage +1 V, and the other one was ground. The \(\mid\)Y(S)\(\mid\) spectra were derived through the frequency domain calculation.  
The effective phase velocity (\(V_{\text{P}}\)) of the resonator is estimated through the formula [24]:  
\[V_{p}=\lambda\frac{f_{r}+f_{a}}{2} \tag{1}\]  
The effective electromechanical coupling coefficient \(K^{2}\) is calculated by [11; 30]:  
\[K^{2}=\frac{\pi f_{r}}{2f_{a}}/\tan(\frac{\pi f_{r}}{2f_{a}}) \tag{2}\]  
where \(f_{r}\) and \(f_{a}\) are the resonant frequency and anti-resonant frequency corresponding to the local maximum and local minimum in the \(\mid\)Y(S)\(\mid\) spectra, respectively.  
Figure 2 shows a typical input admittance curve and phase curve of the partially etched ZnO/SiC configuration when the ZnO piezoelectric film normalized thickness h is 0.6\(\lambda\) and the etching ratio \(d/h\) is 0.7. There are two resonant modes in the admittance spectrum, and the center frequency of each mode is 1.12 GHz and 2.77 GHz. The insets depict the simulated mode shape diagrams of the above two modes at their resonant frequencies. It was found that both of their propagation characteristics are similar to those of the Rayleigh and Sezawa modes of the conventional structure. As observed from the deformation shape, different from conventional SAW structure, the SAW propagation is not obvious in this structure. This is because when the piezoelectric films are etched to the pillars, each pillar works as a BAW resonator. The vibration of the BAW in the \(z\) direction dominates the resonance, and only a small part of acoustic energy is transformed into a SAW. Similar results have been reported by [PERSON] et al. [31] and [PERSON] et al. [27]. In order to distinguish the conventional structure modes, it is better to call the first order mode quasi-Rayleigh and the second order mode quasi-Sezawa mode [31].  
Figure 1: The structure schematic of (**a**) traditional multi-layer structure and (**b**) IDTs/partially etched ZnO/SiC structure.