## 2 Design and Simulation
### Simulation of the Relative Sensitivity with Different Loaded Areas on Surface of SAWR  
In order to extract the areas where the SAWR has higher sensitivity to particle mass loading effect and minor response differences, the frequency response generated by the mass loading effect on each area of the device surface was obtained through simulation. In this contribution, we used high-performance dual-port SAWRs constructed with three IDTs and two shorted grating reflectors as a sensing core of our sensor for a sizeable sensitive area. The schematic of our chip is shown in Figure 3. The aluminum interdigital transducer and shorted reflectors were patterned on ST-X quartz, the common electrical port of lateral IDTs (IDT\({}_{2}\) and IDT\({}_{3}\)) was designated as an input port, and the electrical port of central IDT (IDT\({}_{1}\)) as an output port. The density \(\rho\) of aluminum material is 2700 kg/m\({}^{3}\), and elastic stiffness constants \(C_{12}\) and \(C_{44}\) are 5.11 and 2.63 [20]. The structure parameters of our SAWR are shown in Table 2.  
Figure 3: The schematic of a two-port SAWR with three IDTs. Figure 2: Schematic diagram of cascaded impactor with SAW sensors. First, the non-loaded and loaded 3D finite element models were simulated by the commercial software COMSOL MULTIPHYSICS. The coupling model parameters were extracted and put into the P-matrix for calculation [21]. In order to save model computing resources, the periodic model of the electrodes on the piezoelectric substrate was simplified to a half-period model imposed with periodic boundary conditions for obtaining numerical results of infinitely large periodic structures. Figure 4 shows the schematic diagram and mesh geometry of the half-period model of electrodes on the piezoelectric substrate. Table 3 shows the coupling-of-modes (COM) parameters extracted from the simulation before and after mass loaded on the interdigital transducer. We simulated the situation of particles loaded on the surface of the SAWR by loading the IDT with a 300 nm thick SiO\({}_{2}\) layer [22]. \begin{table}
\begin{tabular}{c c} \hline
**Structural Parameter** & **Value** \\ \hline Electrical period \(\lambda\) (\(\mu\)m) & 10 \\ Finger width \(a\) (\(\mu\)m) & 2.5 \\ Metallization ratio \(\eta\) & 0.5 \\ Acoustic aperture \(W\) & 150\(\lambda\) \\ Finger thickness \(h\) (nm) & 250 \\ Grid period \(p_{g}\) (\(\mu\)m) & 5 \\ Length between IDT\({}_{1}\) and IDT\({}_{2}\)\(g_{1}\) & 22.5\(\lambda\) \\ Length between IDT and reflector \(g_{2}\) & \(\lambda\) \\ number of IDT\({}_{1}\) finger pairs & 45 \\ number of IDT\({}_{2}\) and IDT\({}_{3}\) finger pairs & 23 \\ number of reflector finger pairs & 200 \\ \hline \end{tabular}
\end{table} 
Table 2: Structure parameters of SAWR. Figure 4: Schematic diagram (**a**) and mesh geometry (**b**) of the periodic model. \begin{table}
\begin{tabular}{c c c} \hline
**COM-Parameter** & **Value (Non-Loaded)** & **Value (Loaded)** \\ \hline SAW Velocity (m/s) & 3146.045 & 3124.873 \\ Normalized static capacitance \(C_{n}\) (F/m) & 4.290 \(\times\) 10\({}^{-11}\) & 5.150 \(\times\) 10\({}^{-11}\) \\ Normalized reflectivity \(\kappa\lambda_{0}\) & \(-\)0.023 & \(-\)0.031 \\ Normalized transduction coefficient \(\alpha\) (\(\Omega^{-1/2}\)) & 2.570 \(\times\) 10\({}^{-5}\) & 2.282 \(\times\) 10\({}^{-5}\) \\ \hline \end{tabular}
\end{table} 
Table 3: Extraction results of COM parameters before and after being loaded. The non-loaded center frequency of dual-port SAWR with three IDTs we used was 311 MHz. A comparison of the simulated amplitude-frequency response and phase-frequency response curve with the actual response measurement was shown in Figure 5, and the simulated response corresponded in shape between testing results, especially the peak and slope at the center frequency. In order to optimize the impactor design parameters and chip placement, we obtained the areas on the surface of SAWR that are sensitive to the mass loading effect while having a minor variation in response.