## 4 Evaluation  
### Accuracy Evaluation of Theoretical Model  
Using the established interdigital capacitive humidity sensor sensitivity and dynamic response theoretical model, the corresponding performance index can be quickly given according to the sensor structure. To better support the optimal design of the sensor structure, the COMSOL finite element analysis software is used to establish a humidity sensor model, calculate various performance indicators of the sensor, and compare it with the theoretical model to verify the accuracy of the model, as shown in Figure 6.  
In the evaluation of the steady-state sensitivity model, the initial parameters are set according to the common humidity sensor structure. The center values of each structure are \(\mu_{a}=5\,\upmu\)m, \(\mu_{b}=10\,\upmu\)m, \(\mu_{L}=1250\,\upmu\)m, \(\mu_{h_{1}}=3\,\upmu\)m and \(\mu_{h_{2}}=1\,\upmu\)m. The maximum allowable error variation coefficient is 0.4, so the variation range of each geometric structure parameter is \(a\in[3,7]\), \(b\in[6,14]\), \(L\in[750,1750]\), \(h_{1}\in[1.8,4.2]\) and \(h_{2}\in[0.6,1.4]\). We simulate the low temperature and low humidity environment where the sensor is located. The steady-state analysis sets the model ambient temperature as \(T=278.15\,\mathrm{K}\), ambient humidity as \(RH=10\%\). The geometric parameters of the sensor are changed by parametric scanning, and the sensor's performance under different geometric parameters is obtained. Figure 7 shows the comparison between the sensitivity calculated by the theoretical model and the results obtained by the finite element analysis at the same scale. The comparison results are verified by using the Pearson correlation coefficient. The correlation coefficient of the two methods in the thickness of the electrode layer \(h_{2}\) reaches 1, indicating that the established static sensitivity model has the same accuracy as the finite element simulation analysis for this structure. The correlation coefficient of \(a\), \(b\), \(L\), and \(h_{1}\) are also above 0.95, which can also meet the requirements of the optimization analysis. In the evaluation of dynamic response models. Although the extension of the inter-digital capacitive humidity sensor in the direction of length \(L\) can significantly improve the sensitivity of the sensor, it has little effect on the dynamic performance of the sensor. To improve the speed of finite element analysis and calculation and save computing resources, the model of the capacitive humidity sensor is simplified to a two-dimensional model on the y-z-plane. We set the effective diffusion coefficient of water molecules of the moisture-sensitive material as \(D=4.6\times 10^{-12}\) m\({}^{2}/\)s, the relative humidity of the  
Figure 6: (**a**) Finite element simulation of the sensor electric field. (**b**) Finite element simulation of sensor electric field mode. Figure 7: Sensitivity model accuracy evaluation. environment changes from 10% to 20% instantaneously at the beginning of the simulation, and the steady-state error of the analysis adjustment time \(t_{s}\) is less than 1%. Figure 8 shows the comparison between the response time calculated by the theoretical model and the results obtained by the finite element analysis at the same scale. Because the dynamic analysis process of the finite element analysis method is very complex, it is necessary to couple various physical fields and set multi-layer boundary conditions. Some subtle changes will affect the output results. At the same time, the accuracy of meshing will also affect the fluctuation of the dynamic response curve. In this case, the correlation coefficient between theory and simulation for each structure is higher than 0.98. It can be seen that the static sensitivity and dynamic response theoretical model of the interdigital capacitive humidity sensor established in this paper still has high accuracy in the low temperature and low humidity environment, which can well guide the optimal design of the sensor structure.