A model-based clustering approach to the recognition of the spatial defect patterns produced during semiconductor fabrication

Defects on semiconductor wafers tend to cluster and the spatial defect patterns of these defect clusters contain valuable information about potential problems in the manufacturing processes. This study proposes a model-based clustering algorithm for automatic spatial defect recognition on semiconductor wafers. A mixture model is proposed to model the distributions of defects on wafer surfaces. The proposed algorithm can find the number of defect clusters and identify the pattern of each cluster automatically. It is capable of detecting defect clusters with linear patterns, curvilinear patterns and ellipsoidal patterns. Promising results have been obtained from simulation studies.     

Wafer yield prediction using derived spatial variables

Unreliable chips tend to form spatial clusters on semiconductor wafers. The spatial patterns of these defects are largely reflected in functional testing results. However, the spatial cluster information of unreliable chips has not been fully used to predict the performance in field use in the literature. This paper proposes a novel wafer yield prediction model that incorporates the spatial clustering information in functional testing. Fused LASSO is first adopted to derive variables based on the spatial distribution of defect clusters. Then, a logistic regression model is used to predict the final yield (ratio of chips that remain functional until expected lifetime) with derived spatial covariates and functional testing values. The proposed model is evaluated both on real production wafers and in an extensive simulation study. The results show that by explicitly considering the characteristics of defect clusters, our proposed model provides improved performance compared to existing methods. Moreover, the cross‐validation experiments prove that our approach is capable of using historical data to predict yield on newly produced wafers.     

A Spatial‐EWMA Framework for Detecting Clustering

Spatial surveillance is critical to health systems, manufacturing industries, and in many other domains. For example, determining hotspots of infectious diseases and detecting defect patterns on semiconductor wafers require sensitive spatial analysis tools. The goal of this paper is to detect spatial clusters with mean shifts. Conventional multivariate analysis methods may ignore spatial structure among data and lead to inefficient inspection. Several likelihood ratio‐based scan statistics have been designed for spatial surveillance. However, there is no most powerful test when parameters like shift magnitude and coverage are unknown. This paper proposes a spatial exponentially weighted moving average (spatial‐EWMA) approach that can detect the existence and locate the potential centers of shift clusters. The test procedure assigns different weights to the data with different radius levels from the investigated shift center. The efficiency of the spatial‐EWMA approach is shown by simulation. Lastly, an example of detecting the counties with high incidence of male thyroid cancer in New Mexico is provided to show the effectiveness of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.     

Automatic identification of spatial defect patterns for semiconductor manufacturing

This research proposes an on-line diagnosis system based on denoising and clustering techniques to identify spatial defect patterns for semiconductor manufacturing. Today, even with highly automated and precisely monitored facilities used in a near dust-free clean room and operated with well-trained process engineers, the occurrence of spatial signatures on the wafer still cannot be avoided. Typical defect patterns shown on the wafer, including edge ring, linear scratch, zone type and mixed type, usually contain important information for quality engineers to remove their root causes of failures. In this paper, a spatial filter is simultaneously used to judge whether the input data contains any systematic cluster and to extract it from the noisy input. Then, an integrated clustering scheme combining fuzzy C means (FCM) with hierarchical linkage is adopted to separate various types of defect patterns. Furthermore, a decision tree based on two cluster features (convexity and eigenvalue ratio) is applied to a separated pattern to provide decision support for quality engineers. Experimental results show that both real dataset and synthetic dataset have been successfully extracted and classified. More importantly, the proposed method has potential to be further applied to other industries, such as liquid crystal display (LCD) and plasma display panel (PDP).     

A generalised uncertain decision tree for defect classification of multiple wafer maps

Classification of defect chip patterns is one of the most important tasks in semiconductor manufacturing process. During the final stage of the process just before release, engineers must manually classify and summarise information of defect chips from a number of wafers that can aid in diagnosing the root causes of failures. Traditionally, several learning algorithms have been developed to classify defect patterns on wafer maps. However, most of them focused on a single wafer bin map based on certain features. The objective of this study is to propose a novel approach to classify defect patterns on multiple wafer maps based on uncertain features. To classify distinct defect patterns described by uncertain features on multiple wafer maps, we propose a generalised uncertain decision tree model considering correlations between uncertain features. In addition, we propose an approach to extract uncertain features of multiple wafer maps from the critical fail bit test (FBT) map, defect shape, and location based on a spatial autocorrelation method. Experiments were conducted using real-life DRAM wafers provided by the semiconductor industry. Results show that the proposed approach is much better than any existing methods reported in the literature.     

Multi-step ART1 algorithm for recognition of defect patterns on semiconductor wafers

The integrated circuits (ICs) on wafers are highly vulnerable to defects generated during the semiconductor manufacturing process. The spatial patterns of locally clustered defects are likely to contain information related to the defect generating mechanism. For the purpose of yield management, we propose a multi-step adaptive resonance theory (ART1) algorithm in order to accurately recognise the defect patterns scattered over a wafer. The proposed algorithm consists of a new similarity measure, based on the p-norm ratio and run-length encoding technique and pre-processing procedure: the variable resolution array and zooming strategy. The performance of the algorithm is evaluated based on the statistical models for four types of simulated defect patterns, each of which typically occurs during fabrication of ICs: random patterns by a spatial homogeneous Poisson process, ellipsoid patterns by a multivariate normal, curvilinear patterns by a principal curve, and ring patterns by a spherical shell. Computational testing results show that the proposed algorithm provides high accuracy and robustness in detecting IC defects, regardless of the types of defect patterns residing on the wafer.     

Markov Random Fields in Pattern Recognition for Semiconductor Manufacturing

Under the most general conditions of an anisotropic Markov random field, we model the two-dimensional spatial distribution of microchips on a silicon wafer. The proposed model improves on its predecessors as it stipulates the spatial correlation of different strengths in all eight directions. Its canonical parameters represent the intensity of failures, main effects, and interactions of neighboring chips. Explicit forms of conditional distributions are derived, and maximum pseudo-likelihood estimates of canonical parameters are obtained. This numerical characteristic summarizes general patterns of clusters of failing chips on a wafer, capturing their size, shape, direction, density, and thickness. It is used to classify incoming wafers to known root-cause categories by matching them to the closest pattern.     

纸塑复合袋表面缺陷图像分割算法的设计与实现

目的 纸塑复合袋表面缺陷图像受到噪声、光照不均以及自身缺陷等因素的影响,在对图像缺陷区域进行分割时会造成过分割或欠分割.针对此现象提出一种将边缘检测和自适应区域生长法相结合的纸塑复合袋表面缺陷图像的分割算法.方法 首先利用Sobel算子和形态学运算对双边滤波后的缺陷图像进行第1次分割;然后对缺陷区域进行最小外接矩形标记并计算其形状特征,通过判定形状特征大小来决定是否继续分割;最后将符合继续分割的图像缺陷区域质心作为初始种子点,在原始图像上进行自适应区域生长,形成第2次分割结果,完成缺陷图像分割.结果 与其他算法相比,该算法对各类常见缺陷均能取得较好的分割效果,Dice系数均在0.93以上.结论 该算法分割精度较高,有较强的鲁棒性,可以满足工业上的生产需求.     

Algorithmic Scheme for Concurrent Detection and Classification of Printed Circuit Board Defects

An ideal printed circuit board (PCB) defect inspection system can detect defects and classify PCB defect types. Existing defect inspection technologies can identify defects but fail to classify all PCB defect types. This research thus proposes an algorithmic scheme that can detect and categorize all 14-known PCB defect types. In the proposed algorithmic scheme, fuzzy c-means clustering is used for image segmentation via image subtraction prior to defect detection. Arithmetic and logic operations, the circle hough transform (CHT), morphological reconstruction (MR), and connected component labeling (CCL) are used in defect classification. The algorithmic scheme achieves 100% defect detection and 99.05% defect classification accuracies. The novelty of this research lies in the concurrent use of CHT, MR, and CCL algorithms to accurately detect and classify all 14-known PCB defect types and determine the defect characteristics such as the location, area, and nature of defects. This information is helpful in electronic parts manufacturing for finding the root causes of PCB defects and appropriately adjusting the manufacturing process. Moreover, the algorithmic scheme can be integrated into machine vision to streamline the manufacturing process, improve the PCB quality, and lower the production cost.     

Locating Steganalysis of LSB Matching Based on Spatial and Wavelet Filter Fusion

For the case of that only a single stego image of LSB (Least Significant Bit) matching steganography is available, the existing steganalysis algorithms cannot effectively locate the modified pixels. Therefore, an algorithm is proposed to locate the modified pixels of LSB matching based on spatial and wavelet filter fusion. Firstly, the validity of using the residuals obtained by spatial and wavelet filtering to locate the modified pixels of LSB matching is analyzed. It is pointed out that both of these two kinds of residuals can be used to identify the modified pixels of LSB matching with success rate higher than that of randomly guessing. Then, a method is proposed to measure the correlation between the results of two locating algorithms. Statistical results show that there are low correlations between the locating results of spatial filter based algorithm and wavelet filter based algorithm. Then these two kinds of residuals are fused by the voting method to improve the locating performance. The experimental results show that the proposed fusion algorithm can effectively improve the locating accuracy for the modified pixels of LSB matching.     

A novel hybrid resampling for semiconductor wafer defect bin classification

Generally, defective dies on semiconductor wafer maps tend to form spatial clusters in distinguishable patterns which contain crucial information on specific problems of equipment or process, thus it is highly important to identify and classify diverse defect patterns accurately. However, in practice, there exists a serious class imbalance problem, that is, the number of the defective dies on semiconductor wafer maps is usually much smaller than that of the non-defective dies. In various machine learning applications, a typical classification algorithm is, however, developed under the assumption that the number of instances for each class is nearly balanced. If the conventional classification algorithm is applied to a class imbalanced dataset, it may lead to incorrect classification results and degrade the reliability of the classification algorithm. In this research, we consider the semiconductor wafer defect bin data combined with wafer warpage information and propose a new hybrid resampling algorithm to improve performance of classifiers. From the experimental analysis, we show that the proposed algorithm provides better classification performance compared to other data preprocessing methods regardless of classification models.     

Image processing based on seeded spontaneous optical pattern formation by optoelectronic feedback

Spontaneous optical pattern formation from an initial seed optical pattern in an optoelectronic system with optical diffractive feedback is investigated experimentally. We demonstrate that the temporal evolution of the spontaneously formed patterns exhibits a contrast enhancement effect, a spatial filtering effect, and filling of vacant space while the surrounding structures are maintained. These effects allow us to perform image processing of natural fringe patterns, i.e., in our experiments, fingerprint patterns. We also demonstrate image processing with defect invariance for fingerprint patterns.     

Fiducial markers for increasing the versatility of optical correlation in the measurement of faults on integrated-circuit wafers

A microscope-coherent optical processor is used for the measurement of the registration errors on integrated-circuit wafers. The measurements are obtained from the optical correlation of wafers with reference wafer patterns by use of matched spatial filters. Previously, the intricate pattern of the active circuit area of wafers has been used in the correlation process, and a new matched spatial filter had to be created for each different integrated circuit. Here, the results of using comparatively plain fiducial markers on a wafer for the registration-error measurement are presented, and these show that the measurements can be made independent of the design of the integrated circuit while maintaining the advantages and accuracy of the optical correlation technique.     

Edge-Mediated Annihilation of Vacancy Clusters in Monolayer Molybdenum Diselenide (MoSe2) under Electron Beam Irradiation

Annihilation of vacancy clusters in monolayer molybdenum diselenide (MoSe₂) under electron beam irradiation is reported. In situ high-resolution transmission electron microscopy observation reveals that the annihilation is achieved by diffusion of vacancies to the free edge near the vacancy clusters. Monte Carlo simulations confirm that it is energetically favorable for the vacancies to locate at the free edge. By computing the minimum energy path for the annihilation of one vacancy cluster as a case study, it is further shown that electron beam irradiation and pre-stress in the suspended MoSe₂ monolayer are necessary for the vacancies to overcome the energy barriers for diffusion. The findings suggest a new mechanism of vacancy healing in 2D materials and broaden the capability of electron beam for defect engineering of 2D materials, a promising way of tuning their properties for engineering applications.     

A reversible data-hiding method for palette-based images with capacity optimization

This study presents a reversible data-hiding scheme based on palette image histogram characteristics, in which the least frequent color entries and the most frequent color entries are identified to imbed data. Data are concealed by sacrificing many sets of the least frequent colors, and placing one of the most frequent colors in their positions in the palette to make a ‘cluster’ for each set. Different bits of data can be imbedded using different sized clusters. A capacity optimization scheme is then developed to obtain the maximum capacity by estimating all possible combinations of clusters. For image reconstruction, making the host image reversible requires saving the overhead information caused by sacrificing the least frequent colors. Effectiveness of the proposed method is also demonstrated on test images by showing the capacity and distortion. Importantly, the proposed method has a high imbedding capacity and excellent marked image quality.     

PCA-based feature selection scheme for machine defect classification

The sensitivity of various features that are characteristic of a machine defect may vary considerably under different operating conditions. Hence it is critical to devise a systematic feature selection scheme that provides guidance on choosing the most representative features for defect classification. This paper presents a feature selection scheme based on the principal component analysis (PCA) method. The effectiveness of the scheme was verified experimentally on a bearing test bed, using both supervised and unsupervised defect classification approaches. The objective of the study was to identify the severity level of bearing defects, where no a priori knowledge on the defect conditions was available. The proposed scheme has shown to provide more accurate defect classification with fewer feature inputs than using all features initially considered relevant. The result confirms its utility as an effective tool for machine health assessment.     

Classification: Methods for the Exploratory Analythi of Multivariate Data

A fuzzy clustering strategy is used to identify subsets of influential observations in regression. As part of the fuzzy clustering strategy, the analyst can explore the uniqueness of selected subsets and the degree of belonging of observations to selected subsets. This is accomplished by either varying a fuzzy parameter or the number of clusters. Once the observations or subsets have been identified, the analyst can then compute regression diagnostics to confirm their degree of influence in regression. Bootstrapping and high-breakdown procedures were used to confirm the influence of the previously identified subsets. This fuzzy clustering strategy is applied to the modified data on wood-specific gravity and an augmented production dataset. Both datasets have been previously presented in the literature.     

Integrated color defect detection method for polysilicon wafers using machine vision

For the typical color defects of polysilicon wafers,i.e.,edge discoloration,color inaccuracy and color non-uniformity,a new integrated machine vision detection method is proposed based on an HSV color model.By transforming RGB image into three-channel HSV images,the HSV model can efficiently reduce the disturbances of complex wafer textures.A fuzzy color clustering method is used to detect edge discoloration by defining membership function for each channel image.The mean-value classifying method and region growing method are used to identify the other two defects,respectively.A vision detection system is developed and applied in the production of polysilicon wafers.     

Capacity planning with sequential two-level time constraints in the back-end process of wafer fabrication

A time constraint is a queue-time boundary that is set between particular sequential operations to ensure final product yield. These time boundaries, called ‘sequential time constraints’, can be found in a series of operations on the back-end of wafer fabrication. Wafers exceeding the time constraints are traced through the fabrication process, but generally pass through the remaining processes. Nonetheless, it is a waste of capacity to continue processing wafers with unacceptable yield. Unfortunately, these unacceptable wafers cannot be identified before the wafer acceptance test using the current control policy. This work proposes a control rule for two-level time constraints with capacity planning methodology under this rule. Wafers exceeding the lower time constraints will be treated as normal wafers; however, once wafers exceed the upper time constraint, they will be scrapped immediately. In the capacity planning model, a GI/G/m queuing network is applied to determine the required number of machines. By pre-setting target yields, the rates of wafers being marked or scrapped can be controlled. Furthermore, a novel scheme–regarding machine failures as irregular customers–is introduced to describe the effect of service interruptions. The results show that the proposed control rule and capacity planning model can more effectively resolve the issues of sequential time constraints. Moreover, the results of the analysis indicate that the current capacity expansion policy of the semiconductor industry should be re-examined.     

Analysis of hyperspectral fluorescence images for poultry skin tumor inspection

We present a hyperspectral fluorescence imaging system with a fuzzy inference scheme for detecting skin tumors on poultry carcasses. Hyperspectral images reveal spatial and spectral information useful for finding pathological lesions or contaminants on agricultural products. Skin tumors are not obvious because the visual signature appears as a shape distortion rather than a discoloration. Fluorescence imaging allows the visualization of poultry skin tumors more easily than reflectance. The hyperspectral image samples obtained for this poultry tumor inspection contain 65 spectral bands of fluorescence in the visible region of the spectrum at wavelengths ranging from 425 to 711 nm. The large amount of hyperspectral image data is compressed by use of a discrete wavelet transform in the spatial domain. Principal-component analysis provides an effective compressed representation of the spectral signal of each pixel in the spectral domain. A small number of significant features are extracted from two major spectral peaks of relative fluorescence intensity that have been identified as meaningful spectral bands for detecting tumors. A fuzzy inference scheme that uses a small number of fuzzy rules and Gaussian membership functions successfully detects skin tumors on poultry carcasses. Spatial-filtering techniques are used to significantly reduce false positives.