Query:  Using the k-Nearest Neighbor Rule for Semiconductor Manufacturing Processes.

Candidate papers:

abstract: It has been recognized that effective fault detection techniques can help semiconductor manufacturers reduce scrap, increase equipment uptime, and reduce the usage of test wafers. Traditional univariate statistical process control charts have long been used for fault detection. Recently, multivariate statistical fault detection methods such as principal component analysis (PCA) based methods have drawn increasing interest in the semiconductor manufacturing industry. However, the unique characteristics of the semiconductor processes, such as nonlinearity in most batch processes, multimodal batch trajectories due to product mix, and process steps with variable durations, have posed some difficulties to the PCA based methods. To explicitly account for these unique characteristics, a fault detection method using the k nearest neighbor rule (FD kNN) is developed in this paper. Because in fault detection faults are usually not identified and characterized beforehand, in this paper the traditional kNN algorithm is adapted such that only normal operation data is needed. Because the developed method makes use of the kNN rule, which is a nonlinear classifier, it naturally handles possible nonlinearity in the data. Also, because the FD kNN method makes decisions based on small local neighborhoods of similar batches, it is well suited for multimodal cases. Another feature of the proposed FD kNN method, which is essential for online fault detection, is that the data preprocessing is performed automatically without human intervention. These capabilities of the developed FD kNN method are demonstrated by simulated illustrative examples as well as an industrial example.
author_names: Q Peter He

Jin Wang
title: Fault Detection Using the k Nearest Neighbor Rule for Semiconductor Manufacturing Processes
venue: IEEE Transactions on Semiconductor Manufacturing
year: 2007

abstract: Fault detection technique is essential for improving overall equipment efficiency of semiconductor manufacturing industry. It has been recognized that fault detection based on k nearest neighbor rule (kNN) can effectively deal with some characteristics of semiconductor processes, such as multimode batch trajectories and nonlinearity. However, the computation complexity and storage space involved in neighbors searching of k NN prevent it from online monitoring, especially for high dimensional cases. To deal with this difficulty, principal component based k NN has also been presented in literature, in which dimension reduction is done by principal component analysis (PCA) before k NN rule implemented to fault detection. However, dimension reduction by PCA may distort the distances between pairs of samples (trajectories) Thus the false alarm and missing detection of k NN for fault detection may increase in principal component subspace because PCA fails to preserve pairwise distances in subspace. To overcome this drawback, we propose a new fault detection method based on random projection and k NN rule, which combines the advantages of random projection in distance preservation (in the expectation) and k NN rule in dealing with the problems of multimodality and nonlinearity that often coexist in semiconductor manufacturing processes. An industrial example illustrates the performance of the proposed method.
author_names: Zhe Zhou

Chenglin Wen

Chun-jie Yang
title: Fault Detection Using Random Projections and k Nearest Neighbor Rule for Semiconductor Manufacturing Processes
venue: IEEE Transactions on Semiconductor Manufacturing
year: 2015

abstract: Aiming at nonlinearity and multimodal batch trajectories in semiconductor manufacturing processes, principal component analysis and k nearest neighbor (kNN) related methods were previously presented. However, these methods require data unfolding and are not capable of extracting crucial features, which affects the performance of fault detection. In this paper, an automated fault detection method using convolutional auto encoder (CAE) and k nearest neighbor rule is proposed. Firstly, data collected in one batch is considered as a two dimensional gray scale image, and is input to CAE for feature unsupervised learning, with no need of data preprocessing and data labels. Secondly, kNN rule is incorporated into CAE to construct the monitoring index and perform fault detecting. Finally, the effectiveness of the proposed method is verified with a benchmark semiconductor manufacturing process.
author_names: Haili Zhang

Pu Wang

Xuejin Gao

Huihui Gao

Yongsheng Qi
title: Automated Fault Detection Using Convolutional Auto Encoder and k Nearest Neighbor Rule for Semiconductor Manufacturing Processes
venue: 2020 3rd International Conference on Intelligent Autonomous Systems (ICoIAS)
year: 2020

abstract: Fault detection (FD) utilizing "principal component based k nearest neighbor rule" (PC kNN) has been previously studied. However, these studies do not explicitly account for the distribution of process variables in the manufacturing process. In addition, they do not incorporate the expert's domain knowledge. To account for these issues, we introduced a new technique, FD using human machine co construct intelligence (FD HMCCI) that explicitly accounts for the distribution of process variables and integrates the expert's knowledge in the principal subspace. In this technique, the expert knowledge is represented as expert envelopes, which are the range of values variables can take within which the expert believes that the process is acceptable. Similarly, the range of values of the variables within which the PC kNN classifies the process as acceptable are represented as kNN envelopes. FD HMCCI calibrates the parameters such that the aggregate score, which combines agreement (overlapping area between the expert and kNN envelope) disagreement (the non overlapping area) and tail risk (the conditional expectation of the variables' distribution outside the kNN envelope) is maximized. For demonstration, the technique is implemented to calibrate p of PC kNN that is used for FD in Varian E500 implanter, operated in a semi conductor foundry.
author_names: Manish Ranjit

Harshvardhan Gazula

Simon M Hsiang

Yang Yu

Marcus Borhani

Sonny Spahr

Leyikun Taye

Chad Stephens

Bart Elliott
title: Fault Detection Using Human Machine Co Construct Intelligence in Semiconductor Manufacturing Processes
venue: IEEE Transactions on Semiconductor Manufacturing
year: 2015

abstract: Metal etching process is considered to be a bottleneck step in semiconductor manufacturing, and many parameters of etchers can be monitored with sensor systems. So, an effective fault detection algorithm for the etching process is particularly important. Recently, some classification methods that only need positive samples such as principal component analysis based methods and k nearest neighbor rule based methods have been used for fault detection and achieved some meaningful results. But the requirement that the distribution of the monitored parameters obeys certain structure is hard to satisfy due to product mix. Our method fault detection via sparse representation is based on the assumption that there exists a similar pattern to the testing sample in the training set, while the fault is exotic to the training set. So, normal samples can be linearly represented well (a low representation error) using few training samples while the fault cannot reach the same error precision, which is independent of the distribution of the samples. Once the representation of the testing sample is determined using sparse representation model, the distance between the original sample and its representation using few high weighted basis can be used to detect the fault. The illustrative and industry experiments have verified the efficiency of our method.
author_names: Likun Ren

Weimin Lv
title: Fault Detection via Sparse Representation for Semiconductor Manufacturing Processes
venue: IEEE Transactions on Semiconductor Manufacturing
year: 2014

abstract: Fault detection and classification (FDC) has been recognized as an integral component of the advanced process control (APC) framework in the semiconductor industry, as it helps to improve overall equipment efficiency (OEE) However, some unique characteristics of semiconductor manufacturing processes have posed challenges for FDC applications, such as nonlinearity in most batch processes, and multimodal batch trajectories due to product mix. To explicitly account for these unique characteristics, a pattern recognition based fault detection method utilizing the k nearest neighbor rule (FD kNN) was previously developed. In FD kNN, historical data are used directly as the reference of normal process operation to determine whether a new measurement is a fault. Therefore, for processes with a large number of variables, it can be computation and storage intensive, and may be difficult for online process monitoring. To address this difficulty, we propose a fast pattern recognition based fault detection method, termed principal component based kNN (PC kNN) which takes advantages of both principal component analysis (PCA) for dimensionality reduction and FD kNN for nonlinearity and multimode handling. Two simulation examples and an industrial example are used to demonstrate the performance of the proposed PC kNN method in fault detection.
author_names: Qinghua Peter He

Jin Wang
title: Large Scale Semiconductor Process Fault Detection Using a Fast Pattern Recognition Based Method
venue: IEEE Transactions on Semiconductor Manufacturing
year: 2010

abstract: It has been recognized that the <inline formula> <tex math notation="LaTeX"{k} /tex math>/inline formula> nearest neighbors rule <inline formula> <tex math notation="LaTeX"{k} /tex math>/inline formula>NNs) is effective for fault detection of processes with multimode characteristics. When the variance structures of different mode data sets are similar, <inline formula> <tex math notation="LaTeX"{k} /tex math>/inline formula>NN can indeed detect faults accurately. However, once the variance structures change markedly, some weak faults deviating from a dense mode fail to be detected using <inline formula> <tex math notation="LaTeX"{k} /tex math>/inline formula>NN. The main reason is that <inline formula> <tex math notation="LaTeX"{k} /tex math>/inline formula>NN statistic values of these weak faults are usually submerged by those of normal samples in some sparse modes. In order to overcome the above shortcomings of <inline formula> <tex math notation="LaTeX"{k} /tex math>/inline formula>NN, a new fault detection strategy based on weighted distance of <inline formula> <tex math notation="LaTeX"{k} /tex math>/inline formula>NNs (FD <inline formula> <tex math notation="LaTeX"\text{w}{k} /tex math>/inline formula>NNs) is proposed. In FD <inline formula> <tex math notation="LaTeX"\text{w}{k} /tex math>/inline formula>NN, the weighted parameter of distance of a sample to its <inline formula> <tex math notation="LaTeX"$j /tex math>/inline formula>th nearest neighbor is the reciprocal of the mean distance of the <inline formula> <tex math notation="LaTeX"{j} /tex math>/inline formula>th nearest neighbor to its <inline formula> <tex math notation="LaTeX"{k} /tex math>/inline formula> nearest neighbors. Compared with the statistic in <inline formula> <tex math notation="LaTeX"{k} /tex math>/inline formula>NN, the new statistic in FD <inline formula> <tex math notation="LaTeX"\text{w}{k} /tex math>/inline formula>NN can both eliminate the influence of variance structure in multimodal processes and reduce the autocorrelation of statistic values. As a single model method, FD <inline formula> <tex math notation="LaTeX"\text{w}{k} /tex math>/inline formula>NN is more suitable for monitoring multimode processes than <inline formula> <tex math notation="LaTeX"{k} /tex math>/inline formula>NN. The efficiency of FD <inline formula> <tex math notation="LaTeX"\text{w}{k} /tex math>/inline formula>NN is implemented in a simulated multimode case and in the semiconductor manufacturing processes. The experimental results indicate that the proposed method outperforms FD <inline formula> <tex math notation="LaTeX"{k} /tex math>/inline formula>NN, principal component analysis (PCA) and kernel PCA.
author_names: Cheng Zhang

Xianwen Gao

Yuan Li

Liwei Feng
title: Fault Detection Strategy Based on Weighted Distance of $k$ Nearest Neighbors for Semiconductor Manufacturing Processes
venue: IEEE Transactions on Semiconductor Manufacturing
year: 2019

abstract: Abstract In the semiconductor industry, traditional multivariate statistical process monitoring methods and pattern classification based detection methods have been developed to detect the semiconductor process faults. However, they do not show superior performance due to the limits of these methods and the unique characteristics of semiconductor processes such as non linearity and multimodal batch trajectories. This paper presents a novel diffusion maps based k nearest neighbor rule (DM kNN) technique that can reduce data storage costs and enhance the performance of fault detection by integrating diffusion maps analysis with k nearest neighbor rule. DM kNN takes full advantage of the dimensionality reduction and information preserving properties of DM to extract the low dimensional manifold feature that optimally preserves the intrinsic nonlinear structure of the data set. Then the adapted kNN rule based fault detection method is applied to the low dimensional manifold feature space to detect potential faults. The effectiveness and robustness of DM for dimensionality reduction and feature extraction are verified in simulation experiments compared with other linear and nonlinear dimensionality reduction methods. In addition, DM kNN is applied to monitor the semiconductor manufacturing process. The fault detection results of the proposed method are demonstrated to be superior to those of the MPCA, FD kNN, PC kNN and FS kNN approaches.
author_names: Yuan Li

Xinmin Zhang
title: Diffusion maps based k nearest neighbor rule technique for semiconductor manufacturing process fault detection
year: 2014

abstract: Abstract Defective wafer detection is essential to avoid loss of yield due to process abnormalities in semiconductor manufacturing. For most complex processes in semiconductor manufacturing, various sensors are installed on equipment to capture process information and equipment conditions, including pressure, gas flow, temperature, and power. Because defective wafers are rare in current practice, supervised learning methods usually perform poorly as there are not enough defective wafers for fault detection (FD) The existing methods of anomaly detection often rely on linear excursion detection, such as principal component analysis (PCA) k nearest neighbor (kNN) classifier, or manual inspection of equipment sensor data. However, conventional methods of observing equipment sensor readings directly often cannot identify the critical features or statistics for detection of defective wafers. To bridge the gap between research based knowledge and semiconductor practice, this paper proposes an anomaly detection method that uses a denoise autoencoder (DAE) to learn a main representation of normal wafers from equipment sensor readings and serve as the one class classification model. Typically, the maximum reconstruction error (MaxRE) is used as a threshold to differentiate between normal and defective wafers. However, the threshold by MaxRE usually yields a high false positive rate of normal wafers due to the outliers in an imbalanced data set. To resolve this difficulty, the Hampel identifier, a robust method of outlier detection, is adopted to determine a new threshold for detecting defective wafers, called MaxRE without outlier (MaxREwoo) The proposed method is illustrated using an empirical study based on the real data of a wafer fabrication. Based on the experimental results, the proposed DAE shows great promise as a viable solution for on line FD in semiconductor manufacturing.
author_names: Shu-Kai S Fan

Chia-Yu Hsu

Chih-Hung Jen

Kuan-Lung Chen

Li-Ting Juan
title: Defective wafer detection using a denoising autoencoder for semiconductor manufacturing processes
venue: Adv. Eng. Informatics
year: 2020

abstract: Fault detection and classification (FDC) has been recognized in the semiconductor industry as an integral component of advanced process control (APC) framework in improving overall equipment efficiency (OEE) To explicitly account for the unique characteristics of the semiconductor processes, such as nonlinearity in most batch processes, multimodal batch trajectories due to product mix, the fault detection method based on the k nearest neighbor rule (FD kNN) has been developed previously for fault detection in semiconductor manufacturing. However, because FD kNN does not generate a classifier offline, it is computational and storage intensive, which could make it difficult for online process monitoring. To take the advantages of principal component analysis (PCA) in dimensionality reduction and FD kNN in nonlinearity and multimode handling, a principal component based kNN (PC kNN) is proposed. Two simulated examples and an industrial example are used to demonstrate the performance of the proposed PC kNN method in fault detection.
author_names: Q Peter He

Jin Wang
title: Principal component based k nearest neighbor rule for semiconductor process fault detection
venue: 2008 American Control Conference
year: 2008