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基于局部与非局部线性判别分析和高斯混合模型动态集成的晶圆表面缺陷探测与识别

余建波 卢笑蕾 宗卫周

余建波, 卢笑蕾, 宗卫周. 基于局部与非局部线性判别分析和高斯混合模型动态集成的晶圆表面缺陷探测与识别. 自动化学报, 2016, 42(1): 47-59. doi: 10.16383/j.aas.2016.c150311
引用本文: 余建波, 卢笑蕾, 宗卫周. 基于局部与非局部线性判别分析和高斯混合模型动态集成的晶圆表面缺陷探测与识别. 自动化学报, 2016, 42(1): 47-59. doi: 10.16383/j.aas.2016.c150311
YU Jian-Bo, LU Xiao-Lei, ZONG Wei-Zhou. Wafer Defect Detection and Recognition Based on Local and Nonlocal Linear Discriminant Analysis and Dynamic Ensemble of Gaussian Mixture Models. ACTA AUTOMATICA SINICA, 2016, 42(1): 47-59. doi: 10.16383/j.aas.2016.c150311
Citation: YU Jian-Bo, LU Xiao-Lei, ZONG Wei-Zhou. Wafer Defect Detection and Recognition Based on Local and Nonlocal Linear Discriminant Analysis and Dynamic Ensemble of Gaussian Mixture Models. ACTA AUTOMATICA SINICA, 2016, 42(1): 47-59. doi: 10.16383/j.aas.2016.c150311

基于局部与非局部线性判别分析和高斯混合模型动态集成的晶圆表面缺陷探测与识别

doi: 10.16383/j.aas.2016.c150311
基金项目: 

上海市教育委员会科研创新项目 13YZ002

国家自然科学基金项目 51375290, 71001060

详细信息
    作者简介:

    卢笑蕾 同济大学机械与能源工程学院硕士研究生.主要研究方向为图像处理,机器学习,模式识别.E-mail:lanmingdt@163.com

    宗卫周 同济大学机械与能源工程学院硕士研究生.主要研究方向为信号处理.E-mail:zongweizhou@163.com

    通讯作者:

    余建波 博士,同济大学副教授.主要研究方向为统计分析,智能维护和机器学习.本文通信作者.E-mail:jianboyu.bob@gmail.com

Wafer Defect Detection and Recognition Based on Local and Nonlocal Linear Discriminant Analysis and Dynamic Ensemble of Gaussian Mixture Models

Funds: 

Innovation Program of Shanghai Municipal Education Commission 13YZ002

Supported by National Natural Science Foundation of China 51375290, 71001060

More Information
    Author Bio:

    Master student at the School of Mechanical Engineering, Tongji University. Her research interest covers image processing, machine learning and pattern recognition

    Master student at the School of Mechanical Engineering, Tongji University. His research interest covers signal processing

    Corresponding author: YU Jian-Bo Ph.D. and associate professor at the School of Mechanical Engineering, Tongji University. His research interest covers statistical analysis, intelligent condition-based maintenance and machine learning. Corresponding author of this paper
  • 摘要: 在复杂的半导体制造过程中,晶圆生产经过薄膜沉积、蚀刻、抛光等多项复杂的工序,制造过程中的异常波动都可能导致晶圆缺陷产生.晶圆表面的缺陷模式通常反映了半导体制造过程的各种异常问题,生产线上通过探测和识别晶圆表面缺陷,可及时判断制造过程故障源并进行在线调整,降低晶圆成品率损失.本文提出了基于一种流形学习算法与高斯混合模型动态集成的晶圆表面缺陷在线探测与识别模型.首先该模型开发了一种新型流形学习算法——局部与非局部线性判别分析法(Local and nonlocal linear discriminant analysis, LNLDA),通过融合数据局部/非局部信息以及局部/非局部惩罚信息,有效地提取高维晶圆特征数据的内在流形结构信息,以最大化数据不同簇样本的低维映射距离,保持特征数据中相同簇的低维几何结构.针对线上晶圆缺陷产生的随机性和复杂性,该模型对每种晶圆缺陷模式构建相应的高斯混合模型(Gaussian mixture model, GMM),提出了基于高斯混合模型动态集成的晶圆缺陷在线探测与识别方法.本文提出的模型成功地应用到实际半导体制造过程的晶圆表面缺陷在线探测与识别,在WM-811K晶圆数据库的实验结果验证了该模型的有效性与实用性.
  • 图  1  晶圆表面缺陷探测与识别方法

    Fig.  1  Framework of the wafer defect detection and recognition method

    图  2  晶圆图中值滤噪结果

    Fig.  2  Median filtering on wafer map

    图  3  霍夫变换检测直线

    Fig.  3  Line detection by using Hough transform

    图  4  晶圆缺陷模式图与对应的Randon变换

    Fig.  4  Wafer defect patterns and their corresponding Radon transform

    图  5  内嵌数据结构图

    Fig.  5  Intrinsic data structure graph

    图  6  提出方案的实施流程图

    Fig.  6  The flow chart of the proposed method

    图  7  不同子空间维数下的晶圆缺陷识别率变化

    Fig.  7  The recognition rate of wafer defect pattern with different reduced dimensionality

    图  8  晶圆缺陷NLLP监控图

    Fig.  8  Defect pattern detection by NLLP control chart

    图  9  判定为缺陷模式的正常晶圆样本

    Fig.  9  Examples of normal wafer that incorrectly predicted as defect pattern

    图  10  误识别为Local模式的缺陷晶圆样本

    Fig.  10  Defect pattern that incorrectly predicted as local pattern

    图  11  晶圆新缺陷模式(Local) NLLP检测图

    Fig.  11  New defect pattern (local) detection by NLLP control chart

    图  12  晶圆Local缺陷模式的NLLP识别图

    Fig.  12  Local defect pattern recognition by NLLP control chart

    表  1  晶圆缺陷特征集

    Table  1  Features of defect wafer pattern

    特征类别特征集
    几何特征 区域特征、线性特征、Hu不变矩
    灰度特征 平均值、方差、歪斜度、峰值、能量、熵
    纹理特征 能量、对比度、相关性、均匀度、熵
    投影特征 峰值、平均幅值、均方根幅值、投影波形特征
    投影峰值、投影脉冲
    下载: 导出CSV

    表  2  基于各种投影算法的1NN最佳识别率(%)及相应输入维度

    Table  2  Best recognition rate(%) of 1NN and subspace dimensionality based on the five data projection algorithms

    Algorithm train:test=2:1 train:test=1:1 train:test=1:2
    Baseline 66.60 (53) 63.71 (53) 62.38 (53)
    PCA 66.81 (11) 63.71 (14) 62.49 (12)
    LDA 56.75 (3) 57.57 (21) 64.20 (3)
    LPP 80.51 (24) 77.71 (30) 77.06 (29)
    LFDA77.94 (6) 80.29 (5) 79.42 (5)
    LNLDA 85.44 (6) 84.71 (10) 84.46 (10)
    下载: 导出CSV

    表  3  晶圆缺陷探测率(%)

    Table  3  The defect detection rate (%)

    缺陷模式 Center Donut Edge-ring Edge-local Random Local
    缺陷探测率 97.0 100 100 99.0 100 100
    下载: 导出CSV

    表  4  两套特征集对应的晶圆缺陷识别率(%)

    Table  4  The recognition rate based on two different feature sets (%)

    缺陷模式 特征集A 特征集B
    Center 86 87
    Donut 86 87
    Edge-ring 100 100
    Local 65 76
    Random 92 93
    Edge-local 67 75
    Average 84.0 87.5
    下载: 导出CSV

    表  5  晶圆缺陷模式识别率(%)

    Table  5  The recognition rate of different defect patterns (%)

    缺陷模式Center Donut Edge-ring Local Random Edge-local
    Center 87 0 0 12 01
    Donut 0 94 0 6 00
    Edge-ring 0 0 100 0 00
    Local 8 3 0 76 013
    Random 0 2 0 2 93 3
    Edge-local 67 75 9 14 175
    下载: 导出CSV

    表  6  各种分类器的晶圆缺陷识别率比较(%)

    Table  6  Comparison of recognition rates of the five classifiers (%)

    分类器GMM KNN SVM BPN C4.5
    Center 8792 979593
    Donut 9498 100 9896
    Edge-ring 100 100100 100 100
    Local 7669 685665
    Random 9393 929494
    Edge-local 7566 667856
    Average87.50 86.33 87.17 86.83 84.0
    下载: 导出CSV
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出版历程
  • 收稿日期:  2015-05-18
  • 录用日期:  2015-09-17
  • 刊出日期:  2016-01-01

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