Feature extraction

In order to prove the Hough transform for lines detection, we involved the real failure of scratch pattern, as shown in Figure 3.7 (a), in semiconductor manufacturing.

Figure 3.7 Line detection of Hough transform (a) Wafer with a scratch signature (b) Filter out random failures (c) Transformed into r-θ parameter space. (d) Frequency histogram of the signature

Afterward, we managed a filter algorithm to filter out the random failures from the original Line spatial pattern and obtained the identified cluster, as shown in Figure 3.7 (b). This procedure can reduce the number of wafers and dies that must be analyzed.

When transformed the signature pattern from image space into the r-θ parameter

38

space, all the dies in the same line are intersected to a point at the angle 135 degree, as shown in Figure 3.7 (c). To automate the classification process, we count the number of die with the identical values of (r ,θ) for the cluster, the result can be visualized as a 2-dimensional frequency histogram, as shown in Figure 3.7 (d). Thus, from the frequency data we automatically identify this pattern as a potential diagonal scratch.

Any other cluster composed of lines, scratches can be identified at the angles of 0, 45, 90 and 135 degrees, as shown in Figure 3.8.

Pattern r-θ parameter space 3D histogram

(a)

(b)

(c)

(d)

Figure 3.8 Four angle line detection of Hough transform (a) 0 degree (b) 45 degree (c) 90 degree (d) 135 degree

In the following, we could notice that the frequency histogram for the cluster composed of ring signature, as shown in Figure 3.9 (a), is not be so characterized and

39

average distributed at the angles of 0, 45, 90 and 135 degrees. This result of frequency histogram caused us to confuse with Bull eye, Ring and Edge signature, as shown in Figure 3.9 (b) (c) (d). This result is presenting that the linear Hough transform is not enough to determine the signature without Line signature pattern. Therefore, we further employed the circular Hough transform method to distinguish the kind of Bull eye and Blob spatial pattern.

Pattern r- θ parameter space 3D histogram

(a)

(b)

(c)

(d)

Figure 3.9 Linear Hough transform for variant shape (a) Bull eye (b) Blob. (c) Ring (d) Edge

The circle is similar to represent in parameter space, compared to the line. As we described in section 2.4.2, each edge point we draw a circle with center in the point with the desired radius, when the edge points in the xy-plane are located on the same

40

perimeter then the circles with center in these points must be intersected to a point, as shown in Figure 3.10 (a). At the coordinates which belong to the perimeter of the drawn circle we increment the value in our accumulator matrix. In this way we sweep over every edge point in the input image drawing circles with the desired radii and incrementing the values (or score) in our accumulator. When every edge point and ever desired radius is used, we can turn our attention to the accumulator, as shown in Figure 3.10 (b). The accumulator matrix which is three dimensional, if the radius is not held constant, can quite fast grow large. In order to simplify the parametric representation of the circle, the radius can be limited to number of known radii, such as 1 < r < R where R is the wafer radius.

(a)

(b)

Figure 3.10 Circle detection using circular Hough transform (a) 4 points are located on the same perimeter with radius r in the xy-plane and 4 circles are intersected to a

41

point (b) Sample of the accumulator matrix

In general, the signatures of Bull eye and Blob spatial pattern on wafers could not be representing in completely circular shape. It could be in elliptic or arbitrary shape.

Thus the maximum score in the accumulator will not be the optimal selection. To find the optimal selection in the accumulator we defined an equation named cover ratio as following:

Therefore, based on the accumulator matrix we created previously, finding a set of center (x, y) and radius of circle in the accumulator and calculated the CR. Once the CR has been exceeded the threshold value (for instance, CR=0.9) then we could pick up this set of center and radius for our optimal parameter. The procedure result shown in Figure 3.11.

Figure 3.11 Finding optimal CR

There is a situation should be noticed that the circle we found by circular Hough transform could be located in small area of failed dies (Figure 3.12). Thus, we must set a criteria to eliminate this situation occur. The criteria set as following:

42

Figure 3.12 Circle detection in Ring and Blob spatial pattern

After we found a set of optimal center and radius, we further distinguish the spatial pattern between Bull eye and Blob by calculated the distance form wafer center to optimal center as shown in Figure 3.13. When the distance is large enough, the spatial pattern could correspond to the characteristic values of Blob spatial pattern.

43

Otherwise, there failure shape could be Bull eye spatial pattern.

Figure 3.13 The distance of Bull eye and Blob spatial pattern

The final portion of the feature extraction divided the wafer map into two zones as show in Figure 10, which zone1 occupied 4/5 of the wafer and zone2 occupied 1/5 of the wafer as shown in Figure 3.14.

Figure 3.14 Wafer splitting

In order to extract the features of ring and edge shapes, we only consider the number of failed dies in zone2, so we defined the Zone Ratio as:

44

For instance, in Figure 11, if the failed pattern represent in ring signature, the calculated values of zone ratio showing a high percentage. If the failed pattern represent in edge signature, the calculated value of zone ratio showing a moderate percentage. Of course, when the failed patterns represent in Blob signature which is very close to the boundary of wafer map, it could also has a moderate percentage values of zone ratio. However, the Blob spatial pattern will be detected by CHT and calculated a distance between detected circle and wafer center, but edge spatial patterns will not. So, it can still effectively identify the edge spatial pattern.

Figure 3.15 Failed ratio in zone

All of the features that we discussed previously can be summarized in Table7. When the linear HT feature has an obvious intersection in a certain angle, we can almost determine the spatial pattern has Line signature. The CHT distance can detect whether there is a circular signature distribution on the wafer and the Zone ratio can detect

45

ring and edge signature similarly.

Table 3.2 Relationship between features and patterns

46