# Kernel-Density-Based Particle Defect Management
## 5 Conclusions  
This study is significant because the proposed method utilizes the real data of the particles in the chamber of a semiconductor process. Novel monitoring statistics that efficiently identify the particles on the wafers in a chamber are proposed in this study. These new statistics are based on multivariate kernel density estimation and indicate the densities of the particles. Thorough management is essential for reducing the failures caused by particles in a semiconductor manufacturing process. This study presents a particle defect management method using a kernel-density-based particle map for improving the conventional method of monitoring the number of particles. In particular, the main contribution of this study is the development of new monitoring statistics. The new statistics that consider the distribution of particles, when applied to an actual process, produce the following three effects. Firstly, the proposed method can reduce the number of unnecessary replacements. Secondly, according to a field internal review, when this study is applied to an actual process, a reduction of approximately 30% in the meantime to repair (MTTR), i.e., the time to find the cause of a failure, is expected. Third, regardless of the number of particles, dense particles increase the possibility of further failures. Therefore, using the proposed particle maps, it is possible to detect defects and predict future failures.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Dataset** & **PD** & **KDPD** \\ \hline Dataset 1 & 0.79 & 0.92 \\ Dataset 2 & 0.81 & 0.93 \\ Dataset 3 & 0.84 & 0.98 \\ Dataset 4 & 0.99 & 0.97 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Area under the ROC (AUROC) (If AUROC = 1, then the test is perfect. If AUROC = 0.5, then the test is worthless) 1.  
Figure 11: Receiver operating characteristic (ROC) curves of the four datasets including each fault type.  
Since the semiconductor manufacturing processes are becoming finer, particle defect management becomes increasingly important. If the proposed kernel-density-based particle map can be applied to an actual process, it is expected to improve both the yield and the quality of the semiconductor product. The size of particle defect has a large influence on yield. The current wafer size is 300 mm, but the wafer size will grow and the defect rate will increase as the process is refined. Therefore, in the future, it is necessary to identify the relationship between the particle map and both the yield and quality of the wafer.  
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2016R1A2B4013678). This work was also supported by the BK21 Plus (Big Data in Manufacturing and Logistics Systems, Korea University) and by the Samsung Electronics Co., Ltd.  
[PERSON] and [PERSON] contributed equally to this work as co-first authors. They designed and implemented the algorithm to solve the defined industrial problem. [PERSON] validated the proposed algorithm and guided the research. All authors read and approved the final manuscript.  
The authors declare no conflict of interest.