## 3 Experiment and Results
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Initial Frequency** & **Frequency Drift** & **Frequency Drift Percentage** & **Frequency Drift** & **Frequency Drift Percentage** & **Linearity** \\
**(kHz)** & **80 \({}^{\circ}\)C** & **200 \({}^{\circ}\)C** & **(kHz)** & **200 \({}^{\circ}\)C** & **Linearity** \\ \hline
62.73 & 69.6 & 11\% & 92.39 & 47.3\% & 0.19 \\
62.46 & 69.17 & 10.7\% & 92.03 & 47.3\% & 0.19 \\
61.07 & 65.68 & 7.5\% & 88 & 41.4\% & 0.186 \\
59.55 & 64.25 & 7.9\% & 86.86 & 45.9\% & 0.188 \\ \hline \end{tabular}
\end{table} 
Table 4: Frequency characteristics of four devices as temperature changes. Figure 7: Frequency characteristics of four devices with a back cavity size of 1000 \(\upmu\)m as temperature changes. temperatures. At 200 \({}^{\circ}\)C, the frequency increased from 181 kHz to 190.86 kHz, resulting in a frequency drift of 5.45%. The impedance phase also increased with temperature, changing from 12.9 at room temperature to 39.9 at 200 \({}^{\circ}\)C. In addition, in comparing the experimental results of the devices with back cavity sizes of 600 \(\upmu\)m and 1000 \(\upmu\)m with the simulation results mentioned above, it can be observed that the trends are generally consistent, confirming that increasing back cavity size affects the sensitivity to the temperature drift of the device. Figure 8: Impedance phase variation of four devices with temperature. Figure 9: Variation in electromechanical coupling coefficient of the devices with temperature. In addition, to validate the conclusion of the simulation on the effect of the top silicon thickness on the device, an experiment was carried out using devices with different top silicon thicknesses, while other structural parameters were kept the same, with a back cavity size of 600 \(\upmu\)m. The results are shown in Figure 11. The experimental results indicate that devices with a top silicon thickness of 3 to 5 \(\upmu\)m follow the trend of the simulation results, demonstrating that temperature drift is more pronounced when the top silicon is thinner. Similarly, when the top silicon thickness is smaller, the slope of the temperature drift change, appearing as a nearly linear interval at higher temperatures, is also significantly larger, which is consistent with the FEM analysis results. To investigate the macroscopic morphological changes of the devices under temperature influence, heating was performed using a heating plate due to the limitations of the  
Figure 11: Frequency variation with temperature for devices with a 600 \(\upmu\)m back cavity with different top Si thickness. Figure 10: Frequency and impedance phase variation with temperature for devices with a 600 \(\upmu\)m back cavity (**a**) Frequency (**b**) Impedance phase. 3D profilometer. Two devices with a back cavity of 600 \(\upmu\)m and two devices with a back cavity of 1000 \(\upmu\)m were placed on a soft bottom heating plate, and the entire setup was placed under the 3D profilometer to characterize device warpage. The heating plate was heated to 50 \({}^{\circ}\)C, 100 \({}^{\circ}\)C and 150 \({}^{\circ}\)C, and the warpage results are shown in Table 5. The results indicate that with increasing temperature, thermal expansion caused an increase in residual stress, leading to increased warpage of the devices, which in turn contributed to frequency drift and affected other performance parameters. To further explore the performance of the devices at high temperatures, a Micro System Analyzer MSA600 manufactured by Polytec GmbH (Baden-Wurttemberg, Germany). laser Doppler vibrometer (LDV) was used to characterize the mechanical vibration frequency and amplitude of the devices at different temperatures, with the results shown in Figure 12. The frequency change trend obtained from the LDV tests was consistent with that from electrical characterization, while the amplitude showed an initial increase followed by a decrease. The amplitude increased from 402.6 \(\upmu\)m at room temperature to 668.7 \(\upmu\)m at 160 \({}^{\circ}\)C, representing an increase of 66.1%.