## 3 Results and Discussion  
To verify the parameter prediction performance of the trained CNN model, the position close to the trench center was through-focus scanned continually 10 times. The center lines of a series of microscope images were selected to construct prediction TSOM image sets, and the average of 10 measurement results was considered as the predicted value. Figure 7a-c show a comparison between the true (black triangles) and predicted (red circles) widths of HAR trenches with widths of around 2 \(\mu\)m, 10 \(\mu\)m, and 30 \(\mu\)m, respectively. Figure 7e shows a comparison between the actual (black triangles) and predicted (red circles) depths of HAR trenches with widths of 1.93 \(\mu\)m, 10.3 \(\mu\)m, and 30.3 \(\mu\)m, respectively. The comparison results show that the predicted value and true value match well. In order to further analyze the results shown in Figure 4, the standard deviation and error were used to evaluate the prediction performance. The definitions of the standard deviation and error are given in Equations (2) and (3), respectively:  
\[SD=\sqrt{\frac{1}{n-1}\sum_{i=1}^{n}\left(f_{i}-\overline{f}\right)^{2}} \tag{2}\]  
\[E=\left|\overline{f}-f_{i}\right| \tag{3}\]  
where \(f_{i}\) is the predicted value, \(\overline{f}\) is the average of the predicted values, \(f_{i}\) is the true value, and \(n\) is the number of measurements, which is 10 in this paper. Figure 7: Width and depth prediction results. Comparison between the actual (black triangles) and predicted (red circles) widths of HAR trenches with widths of around (**a**) 2 \(\mu\)m, (**b**) 10 \(\mu\)m, and (**c**) 30 \(\mu\)m; comparison between the actual (black triangles) and predicted (red circles) depths of HAR trenches with widths of (**d**) 1.93 \(\mu\)m, (**e**) 10.3 \(\mu\)m, and (**f**) 30.3 \(\mu\)m.  
The standard deviation and error of the width prediction results are shown in Figure 8. As a comparison, the results predicted by the traditional machine learning (ML) method demonstrated in Reference [22] are shown in order to verify the superiority of the CNN model. The adopted ML model is a support vector regression (SVR) model combined with a Histogram of Oriented Gradients (HOG) feature extractor [23, 24, 25]. The three trench sets for width prediction were irregularly spaced, with width intervals of a few hundred nanometers around 2 \(\upmu\)m, 10 \(\upmu\)m, and 30 \(\upmu\)m. The standard deviation and error were less than 10 nm for 2 \(\upmu\)m and 10 \(\upmu\)m wide trenches. The corresponding ML-predicted results were 40 nm and 180 nm for 2 \(\upmu\)m and 10 \(\upmu\)m wide trenches, which were much higher than the DL-predicted results, especially for 10 \(\upmu\)m wide trenches. For 30 \(\upmu\)m wide trenches, the standard deviation and error were significantly increased, but still less than 60 nm and 80 nm, respectively. The increase in the standard deviation and error was mainly due to the etching error, which increased as the width increased. Moreover, the depth of the 30 \(\upmu\)m wide trench was 443 \(\upmu\)m. A large scanning range was necessary for a deep trench to obtain the complete TSOM image. Incomplete TSOM images also led to poorer performance. The corresponding ML-predicted results were 170 nm and 250 nm, which were approximately three times the DL-predicted results. The comparison results confirmed the superior prediction ability of the DL model for width prediction. Figure 9 illustrates the standard deviation and error of the depth prediction results. The 1.93 \(\upmu\)m, 10.3 \(\upmu\)m, and 30.3 \(\upmu\)m wide trench sets for depth prediction were also irregularly spaced. As the depth increased, the depth interval also increased from a few tens of micrometers to more than 200 \(\upmu\)m. The standard deviation and error were 110 nm and 360 nm for 1.93 \(\upmu\)m wide trenches. For 10.3 \(\upmu\)m wide trenches, the results were 90 nm and 410 nm.