# Defect Detection and Error Source Tracing in Laser Marking of Silicon Wafers with Machine Learning
## 3 Results  
Four laser configurations were applied during the testing procedure: laser speed, power, frequency, and path. Four examples from the various settings are shown in Figure 4. This indicates that both the laser speed and power are the primary controls on the marking results. The effects of various frequencies and paths cannot be distinguished visually. For machine examination purposes, all the testing pictures were transformed into grayscale, and then the image portion that contained characters was obtained using the edge detection technique. The pixel value within the selected portion was then compared to the standard product at the exact location to obtain the brightness difference and then this difference was contoured to create charts, as shown in Figure 5.  
The testing dataset contained 100 pictures of laser marking on wafers with various settings, 70% of which were randomly chosen for model training, and the remaining 30% served as model validation. The predicted and observed brightness values and regression results are listed in Figure 6, where the R\({}^{2}\) value of 0.94 denotes a very high agreement of this model prediction outcome and suggests that 25% difference values are the minimum acceptable product threshold. From the three samples shown in Figure 7, the clearest image has the lowest pixel value differencing index of 15 and the two products with such index values greater than 25 are ambiguous then been identified as defects. The ink density shown in Figure 6 also affects the pixel value differencing index, when the actual ink density exceeded than 25, the disagreement between the observed and predicted values is increased then jeopardizes the quality of engraving characters. Therefore, the pixel value differencing index of 25 is a reasonable threshold for defect detection at this configuration. Figure 4: Photographs of four different laser marking settings. (**a**) Laser frequency: 30 KHz; laser path: type1; laser speed: 50 mm/s; laser power: 100 W; (**b**) 40, type 3, 100, 80; (**c**) 30, type 1, 50, 80; (**d**) 40, type 3, 200, 60. Figure 5: Brightness contour chart of wafer images with various laser marking configurations. Figure 6: Model validation with random forest using four parameters: speed, power, frequency, and path. The R\({}^{2}\) value of the regression was 0.94, and the MSE was 0.99. By examining the detailed distribution of pixel value differencing, as shown in Figure 8, a pattern of geometry variation can be observed. With this corresponding match for each type of defect, error source tracing becomes possible. A shaking table for simulating the laser marking procedure under the effect of an earthquake and its products is shown in Figure 9. The shaking intensity, frequency, and many other factors can lead to various outcomes. The pixel grid overlap ratio method was applied to represent the degree of alteration, as shown in Figure 10. The overlap ratio is the percentage of the detected character pixel grid in the test image relative to that in standard product images. For perfect matching, 100% produces a lower blur ratio in the marking. When the laser power or frequency was increased, the width of the marking increased, and thus, the overlap ratio declined. Figure 8: (**left**) Defect product image, (**right**) corresponding pixel value differencing index. Figure 7: Sample images of the pixel value differencing index for a standard product: (**left**) 15, (**middle**) 25, (**right**) 32. Four types of defective patterns acquired from 100 marking samples were introduced to generate 409 synthetic images of laser marking on wafers with various external causes. Because the degree of influence was randomly assigned, the ground truth information was validated by human inspection. There were 104 cases of improper alignment of marks, 97 cases of missing marks, 103 cases of excessive or insufficient marking depth, and 105 cases of blurred or illegible marks to validate the accuracy of the error tracing analysis.