# The Wettability and Numerical Model of Different Silicon Microstructural Surfaces
## 2 Surface Properties of Silicon Prepared by PIII Technology
### Theoretical Value of Static Contact Angle  
The structural parameters corresponding to the theoretical model of the contact angle were extracted from the SEM and AFM characterization results. In addition, the static contact angles of the sample surface were calculated by the [PERSON] and Cassie-Baxter theoretical models, respectively. According to the [PERSON] theory, the [PERSON]'s contact angle (\(\theta_{W}^{*}\)) on the microstructural surfaces can be calculated based on Equation (2), where r was obtained by the AFM characterization results and the [PERSON]'s contact angle was 54\({}^{\circ}\), which was obtained from the experiment with sample 1. Photoshop software (Adobe, Inc., CA, USA) was applied to extract the pixels of the different shades of gray from Figure 3. The proportion of the pixels in the lighter color region to the total number of pixels in the whole image was calculated, wherein the projection area of the protruding structure accounted for the percentage of the total projection area of the picture, namely, the solid-liquid fractional surface area (\(f_{S}\)). According to the [PERSON] theory, the [PERSON]'s contact angle (\(\theta_{C}^{*}\)) on the microstructural surfaces can be calculated based on Equation (3) for a [PERSON]'s contact angle of 54\({}^{\circ}\). Table 2 presents the microstructural characteristic parameters of the sample surfaces and the contact angles of the corresponding theoretical models. Variations in the contact angle of experimental measurements (\(\theta_{E}\)), the theoretical Cassie-Baxter contact angle (\(\theta_{C}^{*}\)), and the theoretical [PERSON] contact angle (\(\theta_{W}^{*}\)) with the mixing ratio of the gases are presented in Figure 7, wherein the graph indicates that the trend of the theoretical [PERSON]'s contact angle (\(\theta_{W}^{*}\)) is the opposite of that of the contact angle of the experimental measurement (\(\theta_{E}\)). The presence of microstructures generated an obvious increase in the area ratio (r) of the sample surface, thereby resulting in a significant reduction in the contact angle. It was obvious that Equation (2) was not suitable for predicting the static contact angle of the sample. The trend of the theoretical [PERSON]'s contact angle (\(\theta_{C}^{*}\)) was the same as that of the contact angle of the experimental measurement (\(\theta_{E}\)), wherein an increase of the static contact angle caused an increase of the mixing ratio of the gases. When the mixing ratio of the gases was 1:1, the [PERSON]'s contact angle in Equation (3) still used the contact angle of the untreated silicon surface, which did not consider the change in the [PERSON]'s contact angle due to the chemical reaction. Therefore, a significant difference was observed between \(\theta_{E}\) and \(\theta_{C}^{*}\) when the mixing ratio of the gases was 1:1, though this was not observed in the theoretical model. However, when the mixing ratio of the gases was greater than 3:1, \(\theta_{C}^{*}\) continued to increase due to both the continuous decrease of \(f_{S}\) and the increased deviation between \(\theta_{C}^{*}\) and  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Mixing Ratio of the Gases (SF\({}_{6}\)/O\({}_{2}\))** & **0** & **1:1** & **2:1** & **3:1** & **4:1** & **5:1** & **6:1** \\ \hline \(r\) & 1 & 1.104 & 1.440 & 1.632 & 1.736 & 2.076 & 2.232 \\ \(\theta_{W}^{*}\) & 54 & 49 & 32 & 16 & – & – & – \\ \(f_{S}\) & 1 & 0. \(\theta_{E}\). On one hand, these results indicated that the calculation method of \(f_{S}\) greatly influenced the contact-angle calculation results. On the other hand, it also indicated that \(f_{S}\) was not the only factor that affected the static contact angle. According to the analysis of the contact angle of the experimental measurements in the last section, the contact angle was co-influenced by the roughness and area ratio. However, the Cassie-Baxter theory unified all the influence factors of the contact angle to parameter \(f_{S}\).