# Defect Detection and Error Source Tracing in Laser Marking of Silicon Wafers with Machine Learning
## 4 Discussion  
Defect detection in the laser marking of silicon wafers relies on a combination of high-resolution imaging, laser-based scattering/reflection analysis, and real-time process monitoring. These quality control measures are essential to ensure the accuracy, durability, and traceability of wafer markings while also safeguarding the functional integrity of semiconductor devices. The new barcode laser marking on the wafers cannot be detected by traditional OCR methods but can be inspected by this pixel-matching technique.  
Random forest algorithms have the disadvantage of being computationally intensive: training many trees can be resource-intensive, especially with large datasets and many features; less interpretability: while they are more interpretable than some black-box models, random forests are less transparent than a single decision tree because of their ensemble nature. Because defect checking of laser marking on a wafer is a supervised classification, the defect model of one routine is only suitable for a single case. This means that when the marker character is altered, the model must be retrained. Therefore, there is no need to introduce complex algorithms that require longer processing time and high-end hardware. Nevertheless, the proposed technique offers a low-cost and high-efficiency approach to inspect the defect product of laser marking with approximately 97.0% accuracy, and offers the cause of the error with 91.6% overall accuracy. The F\({}_{1}\) score of the defect inspection is 0.974, which means an almost perfect accuracy and recall; the 0.889 kappa value in the error cause tracing has demonstrated almost perfect agreement in separating the error cause. This finding ensures the defect model constructed by random forest algorithms with 100 accurate imagery laser markings on wafers could offer high accuracy for defect detection via unpretentious pixel overlapping methods.  
Conceptualization, T.-T.Y. and H.-C.W.; methodology, T.-T.Y., W.-F.P., and H.-C.W.; software, W.-F.P. and H.-C.W.; validation, W.-F.P. and H.-C.W.; formal analysis, H.-C.W.; resources, T.-T.Y.; writing--original draft preparation, H.-C.W.; writing--review and editing, T.-T.Y. All authors have read and agreed to the published version of the manuscript.  
This study received no external funding.  
This research article did not involve humans.  
This data are available upon request from the corresponding author.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Product** & **Improper** & **Missing Marks** & **Excessive or Insufficient** & **Blurred or** & \\
**Result** & **Alignment of Marks** & **Marking Depth** & **Illlegible Marks** & \\ \hline Improper & & & & & \\ alignment of & 94 & 1 & 4 & 9 & 108 \\ marks & & & & & \\ \hline Missing & 2 & 96 & 2 & 1 & 101 \\ marks & & & & & \\ \hline Excessive or & & & & & \\ insufficient & 3 & 0 & 93 & 3 & 99 \\ marking depth & & & & & \\ \hline Blurred or illegible & & & & & \\ marks & 5 & 0 & 4 & 92 & 101 \\ \hline  & 104 & 97 & 103 & 105 & 409 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The confusion matrix of error source tracing result.