# In-TFT-Array-Process Micro Defect Inspection Using Nonlinear Principal Component Analysis

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Results and Discussion

#### 2.1. Image Acquisition and Defect Analysis

#### 2.2. Inline Defect Inspection Scheme

#### 2.2.1. Layer 1: Image Preprocessing

#### 2.2.2. Layer 2: KPCA-Based Feature Extraction

#### Training

_{i}∈ R

^{n}}

_{i}

_{=1,...,}

_{M}(n =2500). The idea of KPCA is to map the input data x into a high-dimensional feature space F via a nonlinear mapping function φ and then perform PCA in F. Assume that the training data are centered to have a zero mean distribution in F, i.e., ${\sum}_{i=1}^{M}\phi ({x}_{i})=0$ (the centering method of data in F can be found in Appendix B of [12]). KPCA aims to diagonalize the estimate of the covariance matrix of the mapped data φ (x

_{i}):

_{i}),i = 1,..,M, there must exist the coefficients a

_{i},i = 1,...,M such that

_{ij}≡ k(x

_{i}, x

_{j}) = (φ (x

_{i}) ·φ (x

_{j})), where k(x

_{i}, x

_{j}) denotes the kernel function, then solving the eigenvalue problem λ v = Γv is equivalent to solving:

_{l}and eigenvectors ${a}^{l}={({a}_{1}^{l},\dots ,{a}_{M}^{l})}^{T}$ subject to the normalization condition λ

_{l}(a

^{l}a

^{l}) =1.

#### Feature extraction

^{k}in F is computed by:

^{k}is called its nonlinear principal components corresponding to φ. Since k=1,…,d, we can obtain d nonlinear principal components and they form a feature vector z = [z

^{1}, z

^{2},..., z

^{d}]

^{T}. The optimal number of principal components needs to be determined experimentally. Finally, after extracting the KPCA features, the PR features vectors are sent into Layer 3 for further classification, one at a time.

#### 2.2.3. Layer 3: Defect Inspection via ISVMs

#### Multi-class ISVMs for defect classification

#### ISVM

_{i}, y

_{i}}, i = 1,..., L, where z

_{i}∈ R

^{d}is the training data, and y

_{i}is its class label being either +1 or −1, let the weight vector and the bias of the separating hyperplane be w and b, the objective of SVM is to maximize the margin of separation and minimize the errors in the feature space, which is formulated as:

_{i}are slack variables representing the error measures of data. The error weight C is a free parameter; it measures the size of the penalties assigned to the errors.

^{+}and C

^{−}for the positive and the negative class. If the positive class is larger than the negative class, then set C

^{+}< C

^{−}; otherwise C

^{+}> C

^{−}, which induces a decision boundary which is more distant from the smaller class. Accordingly, the ISVM can be formulated as follows.

_{+}= {i | y

_{i}= +1}and I

_{−}= {i | y

_{i}= −1}, then the ISVM is formulated as the constrained optimization problem:

**1-Norm Soft Margin.**For k = 1 the primal Lagrangian is given by:

_{i}and β

_{i}are Lagrange multipliers. By taking partial differential to the Lagrangian with respect to the primal variables, the dual problem becomes:

**2-Norm Soft Margin.**For k=2 we obatin the Lagrangian:

_{[·]}is the indicator function. This can be viewed as a change in the Gram matrix G. Add 1/C

^{+}to the elements of the diagonal of G corresponding to examples of positive class and 1/C

^{−}to those corresponding to examples of the negative class:

_{i}≤ C

^{+}or 0< α

_{i}≤ C

^{−}, the corresponding data points are called support vectors (SVs). The solution for the weight vector is given by

_{s}is the number of SVs. In the case of 0 < α

_{i}< C

^{+}or 0 < α

_{i}< C

^{−}, we have ξ

_{i}= 0 according to the KT conditions. Hence, one can determine the optimal bias b

_{o}by taking any data point whose 0 < α

_{i}< C

^{+}or 0 < α

_{i}< C

^{−}. Once the optimal pair (w

_{o}, b

_{o}) is determined, the class label for an unseen data z can be obtained by the decision function:

^{2}is specified a priori by the user.

## 3. Experimental Section

^{+}and C

^{−}, while there is only one penalty weight in a SVM, i.e., C. Obviously, training an ISVM would be more complicated. If the number of free parameters of ISVM can be reduced, the parameter selection in the training stage can be sped up. Recall that ISVM suggests that one should assign a larger penalty weight to the larger class, and a smaller one to the smaller class. Hence, we assume that the size of the positive training set and the size of the negative training set are P and N, respectively. Then the following equations can let us reduce the number of penalty weights from 2 to 1:

^{+}and C

^{−}are obtained automatically. Equations in (19) indicate that if P > N, then C

^{+}< C

^{−}; if P < N, then C

^{+}> C

^{−}. The advantage is that the number of free parameters of an ISVM is reduced from 3 (C

^{+}, C

^{−}, σ) to 2 (C, σ).

## 4. Conclusions

## Acknowledgments

## References and Notes

- Lee, YJ; Yoo, SI. Automatic detection of region-mura defect in TFT-LCD. IEICE Inf Syst
**2004**, E87-D, 2371–2378. [Google Scholar] - Song, YC; Choi, DH; Park, KH. Multiscale detection of defect in thin film transistor liquid crystal display panel. Jpn. J. Appl. Phys
**2004**, 43, 5465–5468. [Google Scholar] - Tsai, DM; Lin, PC; Lu, CJ. An independent component analysis-based filter design for defect detection in low-contrast surface images. Pattern Recogn
**2006**, 39, 1679–1694. [Google Scholar] - Chen, LC; Kuo, CC. Automatic TFT-LCD mura defect inspection using discrete cosine transform-based background filtering and ‘just noticeable difference’ quantification strategies. Meas. Sci. Technol
**2008**, 19, 015507. [Google Scholar] - Liu, YH; Huang, YK; Lee, MJ. Automatic inline-defect detection for a TFT-LCD array process using locally linear embedding and support vector data description. Meas. Sci. Technol
**2008**, 19, 095501. [Google Scholar] - Roweis, ST; Saul, LK. Nonlinear dimensionality reduction by locally linear embedding. Science
**2000**, 290, 2323–2326. [Google Scholar] - Tax, D; Duin, R. Support vector data description. Mach. Learn
**2004**, 54, 45–66. [Google Scholar] - Chin, TJ; Suter, D. Out-of-sample extrapolation of learned manifolds. IEEE Trans. Pattern Anal
**2008**, 30, 1547–1556. [Google Scholar] - Kouropteva, O; Okun, O; Pietikäinen, M. Incremental locally linear embedding. Pattern Recogn
**2005**, 38, 1764–1767. [Google Scholar] - Liu, YH; Lin, SH; Hsueh, YL; Lee, MJ. Automatic target defect identification for TFT-LCD array process inspection using kernel fuzzy c-means based fuzzy SVDD ensemble. Expert Syst. Appl
**2009**, 36, 1978–1998. [Google Scholar] - Lu, J; Plataniotis, KN; Venetsanopoulos, AN. Face recognition using kernel direct discriminant analysis algorithms. IEEE Neural Netw
**2003**, 14, 117–126. [Google Scholar] - Schölkopf, B; Smola, A; Müller, KR. Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput
**1998**, 10, 1299–1319. [Google Scholar] - Kim, KI; Jung, K; Kim, HJ. Face recognition using kernel principal component analysis. IEEE Signal Proc. Lett
**2002**, 9, 40–42. [Google Scholar] - Vapnik, VN. Statistical Learning Theory; Springer: New York/Berlin Heidelberg, USA/Germany, 1998. [Google Scholar]
- Burges, CJC. A tutorial on support vector machines for pattern recognition. Data Min. Knowl. Disc
**1998**, 2, 121–167. [Google Scholar] - Haykin, S. Neural Networks: A Comprehensive Foundation; Prentice-Hall: Upper Saddle River, NJ, USA, 1999. [Google Scholar]
- Veropoulos, K; Campbell, C; Cristianini, N. Controlling the sensitivity of support vector machines. Proceedings of the IEEE International Joint Conference on Artificial Intelligence, Pasadena, CA, USA, July 11–17, 1999.
- Akbani, R; Kwek, S; Japkowicz, N. Applying support vector machines to imbalanced datasets. Proceedings of the 15th European Conference on Machine Learning, Pisa, Italy, September 20–24, 2004; pp. 39–50.
- Wu, G; Cheng, E. Class-boundary alignment for imbalanced dataset learning. ICML 2003 Workshop on Learning from Imbalanced Data Sets II, Washington, DC, USA, August 21, 2003.
- Japkowicz, N. The class imbalance problem: Significance and strategies. Proceedings of the IEEE International Conference on Artificial Intelligence: Special Track on Inductive Learning, Las Vegas, NV, USA, June 24–27, 2000; pp. 111–117.
- Ling, C; Li, C. Data mining for direct marketing problems and solutions. Proceedings of the 4th International Conference on Knowledge Discovery and Data Mining, New York, NY, USA, August 27–31, 1998.
- Chawla, N; Bowyer, K; Kegelmeyer, W. SMOTE: Synthetic minority over-sampling technique. J. Artif. Intel. Res
**2002**, 16, 321–357. [Google Scholar] - Liu, YH; Chen, YT. Face recognition using total margin-based adaptive fuzzy support vector machines. IEEE Neural Netw
**2007**, 18, 178–192. [Google Scholar] - Hsu, CW; Lin, CJ. A comparison of methods for multiclass support vector machines. IEEE Neural Netw
**2002**, 13, 415–425. [Google Scholar] - Witten, IH; Frank, E. Data Mining: Practical Machine Learning Tools and Techniques with JAVA Implementation; Morgan Kaufmann Publishers: San Francisco, CA, USA, 2000. [Google Scholar]
- Lee, K; Kim, DW; Lee, KH; Lee, D. Density-induced support vector data description. IEEE Neural Netw
**2007**, 18, 284–289. [Google Scholar] - Pang, SN; Kim, D; Bang, SY. Face membership authentication using SVM classification tree generated by membership-based LLE data partition. IEEE Neural Netw
**2005**, 16, 436–446. [Google Scholar]

**Figure 1.**An example of normal GE image. A normal GE pattern consists of three parts. The first part is the GE lines, which are the thicker lines appearing in the pattern periodically. The maximum width of a GE line is around 15 micro meters. The second part is the capacity storages (CSs), which are thinner than the GE lines. The third part is the rectangular regions surrounded by GE lines and CSs, called pixel regions (PRs).

**Figure 5.**Defective PRs. The PRs in the top row are CGC PRs. The second and the third rows display some APC and SCR PRs, respectively. The PRs in the bottom row are PAR PRs.

Inline Defects | Cause of generation |
---|---|

CGC (Connection between GE and CS) | It involves particles left on the thin film before photoresist coating. It would make the connected GE line and CS becomes a short circuit after the etching process. |

APC (Abnormal photo resist coating) | APC is caused by the staining of thinner drops on the thin film, which would produce drop-like photoresist holes. APC would make the pattern deformed after exposure. |

SCR (Scratch) | 1) when the robot arm for carrying glass substrates is biased in its position, substrates would get scratched; 2) when the cassette placing substrates deforms, substrates get scratched. |

PAR (Particle) | When the panels are carried to the inspection equipment by RGV, particles would fall on the surfaces of the panels. |

CGC | APC | SCR | PAR | Normal | Total | |
---|---|---|---|---|---|---|

# PRs | 88 | 60 | 102 | 680 | 200 | 1130 |

Methods | NN | PCA + NN | KPCA + NN |
---|---|---|---|

CR (%) | 84.07 | 89.02 | 92.03 |

Methods | KPCA + NN | KPCA + SVM | KPCA + 1N-ISVM | KPCA + 2N-ISVM |
---|---|---|---|---|

CR (%) | 92.03 | 94.69 | 95.40 | 96.28 |

Methods | NN | SVM | 1N-ISVM | 2N-ISVM |

CR (%) | 84.07 | 93.12 | 94.23 | 94.66 |

Classification results | CGC (44) | APC (30) | SCR (51) | PAR (340) | Normal (100) |
---|---|---|---|---|---|

CGC | 41 | 1 | 0 | 2 | 0 |

APC | 2 | 28 | 0 | 0 | 1 |

SCR | 0 | 0 | 48 | 8 | 0 |

PAR | 1 | 0 | 3 | 328 | 0 |

Normal | 0 | 1 | 0 | 2 | 99 |

© 2009 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

## Share and Cite

**MDPI and ACS Style**

Liu, Y.-H.; Wang, C.-K.; Ting, Y.; Lin, W.-Z.; Kang, Z.-H.; Chen, C.-S.; Hwang, J.-S.
In-TFT-Array-Process Micro Defect Inspection Using Nonlinear Principal Component Analysis. *Int. J. Mol. Sci.* **2009**, *10*, 4498-4514.
https://doi.org/10.3390/ijms10104498

**AMA Style**

Liu Y-H, Wang C-K, Ting Y, Lin W-Z, Kang Z-H, Chen C-S, Hwang J-S.
In-TFT-Array-Process Micro Defect Inspection Using Nonlinear Principal Component Analysis. *International Journal of Molecular Sciences*. 2009; 10(10):4498-4514.
https://doi.org/10.3390/ijms10104498

**Chicago/Turabian Style**

Liu, Yi-Hung, Chi-Kai Wang, Yung Ting, Wei-Zhi Lin, Zhi-Hao Kang, Ching-Shun Chen, and Jih-Shang Hwang.
2009. "In-TFT-Array-Process Micro Defect Inspection Using Nonlinear Principal Component Analysis" *International Journal of Molecular Sciences* 10, no. 10: 4498-4514.
https://doi.org/10.3390/ijms10104498