# Numerical Simulation-Based Study of Controlled Particle Deposition Technology for Wafer Surfaces
## 3 Results and Discussion
### Standard Wafer Sample  
The deposition efficiency is defined as the ratio of the number of deposited particles to the number of incident particles and can be expressed as  
\[\eta=\frac{N_{\text{D}}}{N_{\text{in}}}=\frac{C_{\text{D}}V_{\text{D}}}{N_{\text{ in}}}=\frac{C_{\text{D}}\cdot H_{\text{spot}}\cdot S_{\text{spot}}}{Q_{\text{in}} \cdot C_{\text{p}}\cdot t} \tag{1}\]  
where \(Q_{\text{in}}\): fluid flow rate; \(C_{\text{p}}\): aerosol particle concentration; \(t\): deposition time; \(C_{\text{D}}\): deposition concentration; \(H_{\text{spot}}\): height of the boundary layer above the sediment spot; \(S_{spot}\): deposition spot area.  
Figure 11 presents the SSIS scans of wafer samples with four different particle sizes, while Table 3 summarizes the number of deposited particles and deposition efficiency for each sample. The results indicate that, except for the 70 nm wafer samples, each wafer contains approximately 2000 to 3000 deposited particles, with a deposition efficiency of around 28%. This level of deposition meets the particle quantity requirements for SSIS calibration.  
Under the optimized experimental conditions--namely, a nozzle diameter of 4 mm, a deposition height of 15 mm, a chamber volume exceeding 657 cm\({}^{3}\), and a rotation speed of 0.314 rad/s--Figure 11 presents the SSIS scans of wafer samples with four different particle sizes, while Table 3 summarizes the corresponding particle counts and deposition efficiencies. The results show that, with the exception of the 70 nm samples, each wafer  
Figure 11: SSIS scanning results of standard wafers with different particle sizes. \({}^{\#}\) indicates the number of defects observed.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Particle Size/nm** & **Number of Deposited Particles/\#** & **Deposition Efficiency/\%** \\ \hline
70 & 502 & 6.5\% \\
100 & 2470 & 27.4\% \\
140 & 2031 & 29.6\% \\
200 & 3069 & 28.4\% \\ \hline \hline \end{tabular} Note: \({}^{\#}\) indicates the number of defects observed.  
\end{table}
Table 3: Deposition number and deposition efficiency of standard wafers with different particle sizes.  
contained approximately 2000 to 3000 deposited particles, corresponding to a deposition efficiency of approximately 28%. This level of particle loading satisfies the requirements for SSIS calibration.  
It should be noted that the SSIS result images do not include a scale bar. This is due to two main reasons: (1) SSIS operates by analyzing light scattering signals and converting them into particle size information based on the system's internal calibration curves; as such, the output images typically do not represent real physical dimensions or include scale references. (2) The particle dots in SSIS images are visually enlarged to enhance visibility, and their sizes do not directly correspond to the actual dimensions on the wafer. Therefore, including a scale bar could be misleading.  
Figure 12 compares the deposition efficiency between simulation and experiment for different particle sizes. The data analysis shows that the trend of deposition efficiency with increasing particle size is consistent between the two. However, the simulated results are consistently higher than the experimental results across all particle sizes, with differences ranging from 9.1% to 11.62%. This discrepancy primarily stems from the simplified treatment of kinetic behavior in the numerical simulation compared to actual working conditions.  
The deposition efficiency is highly dependent on particle size, with the 70 nm wafer samples exhibiting lower deposition efficiency than other particle sizes. This discrepancy aligns with the numerical simulation results. Overall, the four wafer samples with different particle sizes demonstrated good monodispersity and uniform deposition during the SSIS scan calibration process. This confirms that the generation-deposition system is capable of producing standard wafers that meet the requirements for SSIS calibration.