## 2 Optimal Design Consideration and Analytical Modeling
### COMSOL Simulation of the Microheater  
A microheater was integrated adjacent to the sensor to maintain a stable surface temperature, thereby enhancing the sensor's sensitivity, response/recovery time, and selectivity. The operating principle of the microheater is that, when a voltage is applied, an electric field is generated inside the conductor. This electric field accelerates the electrons, which then collide with the lattice. The energy from these collisions is converted into thermal energy, proportional to the intensity of the electric field. As a result, heat is generated within the \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Number of input and output IDT pairs & 60 \\ Number of reflector pairs & 80 \\ Aperture length (\(\lambda\)) & 120 \\ Cavity length (\(\mu\)m) & 2000 \\ Wavelength \(\lambda\) (\(\mu\)m) & 17.6 \\ IDT Ti/Pt thickness (nm) & 10/100 \\ Acoustic velocity (m/s) of 128\({}^{\circ}\) YX LiNbO\({}_{3}\) & 3890 \\ Electromechanical coupling factor, \(K^{2}\) (\%) & 5.5 \\ Effective dielectric coefficient \(\varepsilon_{\text{P}}/\varepsilon_{0}\) & 55 \\ Sheet resistance (\(\Omega\)-m) & 0.939 \(\times\) 10\({}^{8}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The parameters of the two-port SAW delay line determined through COM modeling. Figure 2: **(a)** The detailed schematic of the developed SAW sensor and **(b)** its COM modeling results for S\({}_{21}\) vs. frequency, with and without the sensing materials. conductor, and simultaneously, the heat is transferred to the surrounding medium through thermal conduction, thermal radiation, and thermal convection. The maintenance of a stable temperature is not solely due to radiative heat loss but rather a balance between all heat transfer mechanisms, including conduction, convection, and radiation. In our system, the thermal energy generated by electron-lattice collisions reaches equilibrium with the heat dissipated through conduction (to the substrate and surrounding structures), convection (to the surrounding air), and radiation (to the environment). This balance ensures an almost stable temperature filed during operation. Using the COMSOL simulator (V6.3), a microheater was designed on a 128\({}^{\circ}\) YX LiNbO\({}_{3}\) substrate. The structural parameters of the microheater include the material, length, thickness, and width. By optimizing these parameters, the microheater's specifications were derived for optimal performance. Its placement and orientation were carefully designed to maximize heat transfer efficiency to the sensing area, ensuring stable and uniform thermal distribution (Figure 3). COMSOL thermal simulations served two primary purposes: (1) the modeling and visualizing the propagation of heat toward the cavity region (sensing area) under microheater activation, and (2) optimizing the heater design (e.g., length, width, placement) to maximize heat delivery efficiency. The temperature distribution demonstrates effective heat localization, achieving the necessary thermal conditions for enhanced sensor performance. Platinum (Pt) was selected as the material for the microheater due to its stable properties, even at very high temperatures over extended periods. Platinum (Pt) generally has a high melting point of 1768 \({}^{\circ}\)C. At driving temperatures below 90 \({}^{\circ}\)C, Pt degassing due to Joule heating is expected to be minimal. The microheater dimensions are 2 mm in length, 100 nm in thickness, and 500 \(\upmu\)m in width. The temperature sensor, located directly below the microheater in the same position as the sensing area, has dimensions of 1.5 mm in length, 100 nm in thickness, and 500 \(\upmu\)m in width. The heater exhibits a resistance of 50 ohms at room temperature. A DC voltage was applied to the designed microheater (Figure 3), leading to a temperature increase around the cavity of the SAW sensor.