## 3 Bin2 Vec: A Convolutional Neural Network-Based WBM Coloring Scheme
### Word2 Vec and Bin2 Vec
#### 3.2.2 Bin2 Vec  
In this study, the original WBMs have the size \(301\times 301\) pixels. Each pixel in a WBM can have a value between \(-2\) and \(9999\). Although the nine product groups have the same raw WBM size, the actual number of dies on the wafer along the horizontal and vertical axes are different. Table 2 lists the number of unique bin codes, the number of dies along the horizontal/vertical axis, as well as the number of total, good, and bad wafers and their proportions. Group 1 has the largest number of WBMs, containing 5464 WBMs with \(23\times 27\) dies. In contrast, Group 9 has the smallest number of WBMs, containing 1715 WBMs with \(47\times 51\) dies. For the current manufacturing process of the company, a total of 10,002 bin codes are possible for the dies, as explained with Table 1. However,  
Figure 3: The Skip-Gram model architecture. only a small portion of them actually appeared: Group 1 has the largest number of unique bin codes (401), whereas only eight bin codes appear for Group 6. Although the size of raw WBMs is 301 \(\times\) 301 pixels, each die is represented by 3 \(\times\) 3, 4 \(\times\) 3, or 4 \(\times\) 4 pixels according to the product type, and the same bin codes are assigned to the pixels for the same die. Hence, we resized the original WBM by aggregating the pixels for the same die so that a die is presented by a \(1\times 1\) pixel in the reduced WBM as shown in Figure 4.  
Currently, WBMs are colorized by the random RGB scheme in which a randomly selected RGB code is assigned to each bin code so that different bin codes can be distinguished on the WBM to help engineers identify meaningful bin patterns. The main drawback of this coloring scheme is that the relationships between bin codes are not preserved. In practice, some bin codes are closely related while others are completely unrelated. This relationship information is completely ignored by the current WBM coloring scheme. Encouraged by process engineers' domain knowledge that nearby dies often fail the same test together, we propose a new WBM coloring scheme called Bin2 Vec by considering the location information of dies on the wafer. The proposed Bin2 Vec transforms a one-dimensional scalar bin code into a three-dimensional embedding vector by employing the learning mechanism of the Word2 Vec embedding model. Once the bin code is converted into a three-dimensional vector, it can be used not only to assign an RGB code, which can also be considered a three-dimensional vector, but also to compute the similarity between any two pairs of bin codes. For engineers who actually investigate WBM patterns, Bin2 Vec can also provide the following information compared with random RGB coloring, i.e., the more similar the color, the more frequently the bin codes appear together in a local area on the wafer. To train the Bin2 Vec model, a total of 25 bin codes with size \(5\times 5\) are taken to make a training instance, as shown in Figure 4(a). This square matrix is then reshaped into a 25-dimensional vector: the first column becomes the first five elements and the last column becomes the last five elements, as shown in Figure 4(b). This sampling and reshaping process for a single wafer is repeated by sliding the \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Group** & **No. Wafers** & **No. Good** & **No. Bad** & **Good (\%)** & **Bad (\%)** & **No. Bins** & **No. Dies (Horizontal)** & **No. Chips (Vertical)** \\ \hline
1 & 5464 & 4156 & 1308 & 76.06 & 23.94 & 401 & 23 & 27 \\
2 & 5449 & 4771 & 678 & 87.56 & 12.44 & 77 & 29 & 50 \\
3 & 3261 & 2621 & 640 & 80.37 & 19.63 & 43 & 41 & 36 \\
4 & 2781 & 2578 & 203 & 92.70 & 7.30 & 108 & 47 & 62 \\
5 & 2543 & 2145 & 398 & 84.35 & 15.65 & 371 & 29 & 26 \\
6 & 2101 & 850 & 1251 & 40.46 & 59.54 & 8 & 32 & 38 \\
7 & 1958 & 1403 & 555 & 71.65 & 28.35 & 82 & 33 & 58 \\
8 & 1799 & 1535 & 264 & 85.33 & 14.67 & 206 & 26 & 26 \\
9 & 1715 & 1542 & 173 & 89.91 & 10.09 & 108 & 47 & 51 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Raw data information of WBM.