Integrated performance prediction and quality control in manufacturing systems

textPredicting the condition of a degrading dynamic system is critical for implementing successful control and designing the optimal operation and maintenance strategies throughout the lifetime of the system. In many situations, especially in manufacturing, systems experience multiple degradation cycles, failures, and maintenance events throughout their lifetimes. In such cases, historical records of sensor readings observed during the lifecycle of a machine can yield vital information about degradation patterns of the monitored machine, which can be used to formulate dynamic models for predicting its future performance. Besides the ability to predict equipment failures, another major component of cost effective and high-throughput manufacturing is tight control of product quality. Quality control is assured by taking periodic measurements of the products at various stages of production. Nevertheless, quality measurements of the product require time and are often executed on costly measurement equipment, which increases the cost of manufacturing and slows down production. One possible way to remedy this situation is to utilize the inherent link between the manufacturing equipment condition, mirrored in the readings of sensors mounted on that machine, and the quality of products coming out of it. The concept of Virtual Metrology (VM) addresses the quality control problem by using data-driven models that relate the product quality to the equipment sensors, enabling continuous estimation of the quality characteristics of the product, even when physical measurements of product quality are not available. VM can thus bring significant production benefits, including improved process control, reduced quality losses and higher productivity. In this dissertation, new methods are formulated that will combine long-term performance prediction of sensory signatures from a degrading manufacturing machine with VM quality estimation, which enables integration of predictive condition monitoring (prediction of sensory signatures) with predictive manufacturing process control (predictive VM model). The recently developed algorithm for prediction of sensory signatures is capable of predicting the system condition by comparing the similarity of the most recent performance signatures with the known degradation patterns available in the historical records. The method accomplishes the prediction of non-Gaussian and non-stationary time-series of relevant performance signatures with analytical tractability, which enables calculations of predicted signature distributions with significantly greater speeds than what can be found in literature. VM quality estimation is implemented using the recently introduced growing structure multiple model system paradigm (GSMMS), based on the use of local linear dynamic models. The concept of local models enables representation of complex, non-linear dependencies with non-Gaussian and non-stationary noise characteristics, using a locally tractable model representation. Localized modeling enables a VM that can detect situations when the VM model is not adequate and needs to be improved, which is one of the main challenges in VM. Finally, uncertainty propagation with Monte Carlo simulation is pursued in order to propagate the predicted distributions of equipment signatures through the VM model to enable prediction of distributions of the quality variables using the readily available sensor readings streaming from the monitored manufacturing machine. The newly developed methods are applied to long-term production data coming from an industrial plasma-enhanced chemical vapor deposition (PECVD) tool operating in a major semiconductor manufacturing fab.Mechanical Engineerin

Virtual metrology for plasma etch processes.

Plasma processes can present dicult control challenges due to time-varying dynamics and a lack of relevant and/or regular measurements. Virtual metrology (VM) is the use of mathematical models with accessible measurements from an operating process to estimate variables of interest. This thesis addresses the challenge of virtual metrology for plasma processes, with a particular focus on semiconductor plasma etch. Introductory material covering the essentials of plasma physics, plasma etching, plasma measurement techniques, and black-box modelling techniques is rst presented for readers not familiar with these subjects. A comprehensive literature review is then completed to detail the state of the art in modelling and VM research for plasma etch processes. To demonstrate the versatility of VM, a temperature monitoring system utilising a state-space model and Luenberger observer is designed for the variable specic impulse magnetoplasma rocket (VASIMR) engine, a plasma-based space propulsion system. The temperature monitoring system uses optical emission spectroscopy (OES) measurements from the VASIMR engine plasma to correct temperature estimates in the presence of modelling error and inaccurate initial conditions. Temperature estimates within 2% of the real values are achieved using this scheme. An extensive examination of the implementation of a wafer-to-wafer VM scheme to estimate plasma etch rate for an industrial plasma etch process is presented. The VM models estimate etch rate using measurements from the processing tool and a plasma impedance monitor (PIM). A selection of modelling techniques are considered for VM modelling, and Gaussian process regression (GPR) is applied for the rst time for VM of plasma etch rate. Models with global and local scope are compared, and modelling schemes that attempt to cater for the etch process dynamics are proposed. GPR-based windowed models produce the most accurate estimates, achieving mean absolute percentage errors (MAPEs) of approximately 1:15%. The consistency of the results presented suggests that this level of accuracy represents the best accuracy achievable for the plasma etch system at the current frequency of metrology. Finally, a real-time VM and model predictive control (MPC) scheme for control of plasma electron density in an industrial etch chamber is designed and tested. The VM scheme uses PIM measurements to estimate electron density in real time. A predictive functional control (PFC) scheme is implemented to cater for a time delay in the VM system. The controller achieves time constants of less than one second, no overshoot, and excellent disturbance rejection properties. The PFC scheme is further expanded by adapting the internal model in the controller in real time in response to changes in the process operating point

Doctor of Philosophy

dissertationIn order to ensure high production yield of semiconductor devices, it is desirable to characterize intermediate progress towards the final product by using metrology tools to acquire relevant measurements after each sequential processing step. The metrology data are commonly used in feedback and feed-forward loops of Run-to-Run (R2R) controllers to improve process capability and optimize recipes from lot-to-lot or batch-to-batch. In this dissertation, we focus on two related issues. First, we propose a novel non-threaded R2R controller that utilizes all available metrology measurements, even when the data were acquired during prior runs that differed in their contexts from the current fabrication thread. The developed controller is the first known implementation of a non-threaded R2R control strategy that was successfully deployed in the high-volume production semiconductor fab. Its introduction improved the process capability by 8% compared with the traditional threaded R2R control and significantly reduced out of control (OOC) events at one of the most critical steps in NAND memory manufacturing. The second contribution demonstrates the value of developing virtual metrology (VM) estimators using the insight gained from multiphysics models. Unlike the traditional statistical regression techniques, which lead to linear models that depend on a linear combination of the available measurements, we develop VM models, the structure of which and the functional interdependence between their input and output variables are determined from the insight provided by the multiphysics describing the operation of the processing step for which the VM system is being developed. We demonstrate this approach for three different processes, and describe the superior performance of the developed VM systems after their first-of-a-kind deployment in a high-volume semiconductor manufacturing environment

Virtual metrology for plasma etch processes.

Plasma processes can present dicult control challenges due to time-varying dynamics and a lack of relevant and/or regular measurements. Virtual metrology (VM) is the use of mathematical models with accessible measurements from an operating process to estimate variables of interest. This thesis addresses the challenge of virtual metrology for plasma processes, with a particular focus on semiconductor plasma etch. Introductory material covering the essentials of plasma physics, plasma etching, plasma measurement techniques, and black-box modelling techniques is rst presented for readers not familiar with these subjects. A comprehensive literature review is then completed to detail the state of the art in modelling and VM research for plasma etch processes. To demonstrate the versatility of VM, a temperature monitoring system utilising a state-space model and Luenberger observer is designed for the variable specic impulse magnetoplasma rocket (VASIMR) engine, a plasma-based space propulsion system. The temperature monitoring system uses optical emission spectroscopy (OES) measurements from the VASIMR engine plasma to correct temperature estimates in the presence of modelling error and inaccurate initial conditions. Temperature estimates within 2% of the real values are achieved using this scheme. An extensive examination of the implementation of a wafer-to-wafer VM scheme to estimate plasma etch rate for an industrial plasma etch process is presented. The VM models estimate etch rate using measurements from the processing tool and a plasma impedance monitor (PIM). A selection of modelling techniques are considered for VM modelling, and Gaussian process regression (GPR) is applied for the rst time for VM of plasma etch rate. Models with global and local scope are compared, and modelling schemes that attempt to cater for the etch process dynamics are proposed. GPR-based windowed models produce the most accurate estimates, achieving mean absolute percentage errors (MAPEs) of approximately 1:15%. The consistency of the results presented suggests that this level of accuracy represents the best accuracy achievable for the plasma etch system at the current frequency of metrology. Finally, a real-time VM and model predictive control (MPC) scheme for control of plasma electron density in an industrial etch chamber is designed and tested. The VM scheme uses PIM measurements to estimate electron density in real time. A predictive functional control (PFC) scheme is implemented to cater for a time delay in the VM system. The controller achieves time constants of less than one second, no overshoot, and excellent disturbance rejection properties. The PFC scheme is further expanded by adapting the internal model in the controller in real time in response to changes in the process operating point

Statistical Methods for Semiconductor Manufacturing

In this thesis techniques for non-parametric modeling, machine learning, filtering and prediction and run-to-run control for semiconductor manufacturing are described. In particular, algorithms have been developed for two major applications area: - Virtual Metrology (VM) systems; - Predictive Maintenance (PdM) systems. Both technologies have proliferated in the past recent years in the semiconductor industries, called fabs, in order to increment productivity and decrease costs. VM systems aim of predicting quantities on the wafer, the main and basic product of the semiconductor industry, that may be physically measurable or not. These quantities are usually ’costly’ to be measured in economic or temporal terms: the prediction is based on process variables and/or logistic information on the production that, instead, are always available and that can be used for modeling without further costs. PdM systems, on the other hand, aim at predicting when a maintenance action has to be performed. This approach to maintenance management, based like VM on statistical methods and on the availability of process/logistic data, is in contrast with other classical approaches: - Run-to-Failure (R2F), where there are no interventions performed on the machine/process until a new breaking or specification violation happens in the production; - Preventive Maintenance (PvM), where the maintenances are scheduled in advance based on temporal intervals or on production iterations. Both aforementioned approaches are not optimal, because they do not assure that breakings and wasting of wafers will not happen and, in the case of PvM, they may lead to unnecessary maintenances without completely exploiting the lifetime of the machine or of the process. The main goal of this thesis is to prove through several applications and feasibility studies that the use of statistical modeling algorithms and control systems can improve the efficiency, yield and profits of a manufacturing environment like the semiconductor one, where lots of data are recorded and can be employed to build mathematical models. We present several original contributions, both in the form of applications and methods. The introduction of this thesis will be an overview on the semiconductor fabrication process: the most common practices on Advanced Process Control (APC) systems and the major issues for engineers and statisticians working in this area will be presented. Furthermore we will illustrate the methods and mathematical models used in the applications. We will then discuss in details the following applications: - A VM system for the estimation of the thickness deposited on the wafer by the Chemical Vapor Deposition (CVD) process, that exploits Fault Detection and Classification (FDC) data is presented. In this tool a new clustering algorithm based on Information Theory (IT) elements have been proposed. In addition, the Least Angle Regression (LARS) algorithm has been applied for the first time to VM problems. - A new VM module for multi-step (CVD, Etching and Litography) line is proposed, where Multi-Task Learning techniques have been employed. - A new Machine Learning algorithm based on Kernel Methods for the estimation of scalar outputs from time series inputs is illustrated. - Run-to-Run control algorithms that employ both the presence of physical measures and statistical ones (coming from a VM system) is shown; this tool is based on IT elements. - A PdM module based on filtering and prediction techniques (Kalman Filter, Monte Carlo methods) is developed for the prediction of maintenance interventions in the Epitaxy process. - A PdM system based on Elastic Nets for the maintenance predictions in Ion Implantation tool is described. Several of the aforementioned works have been developed in collaborations with major European semiconductor companies in the framework of the European project UE FP7 IMPROVE (Implementing Manufacturing science solutions to increase equiPment pROductiVity and fab pErformance); such collaborations will be specified during the thesis, underlying the practical aspects of the implementation of the proposed technologies in a real industrial environment

매개분포근사를 통한 공정시스템 공학에서의 확률기계학습 접근법

학위논문(박사) -- 서울대학교대학원 : 공과대학 화학생물공학부, 2021.8. 이종민.With the rapid development of measurement technology, higher quality and vast amounts of process data become available. Nevertheless, process data are ‘scarce’ in many cases as they are sampled only at certain operating conditions while the dimensionality of the system is large. Furthermore, the process data are inherently stochastic due to the internal characteristics of the system or the measurement noises. For this reason, uncertainty is inevitable in process systems, and estimating it becomes a crucial part of engineering tasks as the prediction errors can lead to misguided decisions and cause severe casualties or economic losses. A popular approach to this is applying probabilistic inference techniques that can model the uncertainty in terms of probability. However, most of the existing probabilistic inference techniques are based on recursive sampling, which makes it difficult to use them for industrial applications that require processing a high-dimensional and massive amount of data. To address such an issue, this thesis proposes probabilistic machine learning approaches based on parametric distribution approximation, which can model the uncertainty of the system and circumvent the computational complexity as well. The proposed approach is applied for three major process engineering tasks: process monitoring, system modeling, and process design. First, a process monitoring framework is proposed that utilizes a probabilistic classifier for fault classification. To enhance the accuracy of the classifier and reduce the computational cost for its training, a feature extraction method called probabilistic manifold learning is developed and applied to the process data ahead of the fault classification. We demonstrate that this manifold approximation process not only reduces the dimensionality of the data but also casts the data into a clustered structure, making the classifier have a low dependency on the type and dimension of the data. By exploiting this property, non-metric information (e.g., fault labels) of the data is effectively incorporated and the diagnosis performance is drastically improved. Second, a probabilistic modeling approach based on Bayesian neural networks is proposed. The parameters of deep neural networks are transformed into Gaussian distributions and trained using variational inference. The redundancy of the parameter is autonomously inferred during the model training, and insignificant parameters are eliminated a posteriori. Through a verification study, we demonstrate that the proposed approach can not only produce high-fidelity models that describe the stochastic behaviors of the system but also produce the optimal model structure. Finally, a novel process design framework is proposed based on reinforcement learning. Unlike the conventional optimization methods that recursively evaluate the objective function to find an optimal value, the proposed method approximates the objective function surface by parametric probabilistic distributions. This allows learning the continuous action policy without introducing any cumbersome discretization process. Moreover, the probabilistic policy gives means for effective control of the exploration and exploitation rates according to the certainty information. We demonstrate that the proposed framework can learn process design heuristics during the solution process and use them to solve similar design problems.계측기술의 발달로 양질의, 그리고 방대한 양의 공정 데이터의 취득이 가능해졌다. 그러나 많은 경우 시스템 차원의 크기에 비해서 일부 운전조건의 공정 데이터만이 취득되기 때문에, 공정 데이터는 ‘희소’하게 된다. 뿐만 아니라, 공정 데이터는 시스템 거동 자체와 더불어 계측에서 발생하는 노이즈로 인한 본질적인 확률적 거동을 보인다. 따라서 시스템의 예측모델은 예측 값에 대한 불확실성을 정량적으로 기술하는 것이 요구되며, 이를 통해 오진을 예방하고 잠재적 인명 피해와 경제적 손실을 방지할 수 있다. 이에 대한 보편적인 접근법은 확률추정기법을 사용하여 이러한 불확실성을 정량화 하는 것이나, 현존하는 추정기법들은 재귀적 샘플링에 의존하는 특성상 고차원이면서도 다량인 공정데이터에 적용하기 어렵다는 근본적인 한계를 가진다. 본 학위논문에서는 매개분포근사에 기반한 확률기계학습을 적용하여 시스템에 내재된 불확실성을 모델링하면서도 동시에 계산 효율적인 접근 방법을 제안하였다. 먼저, 공정의 모니터링에 있어 가우시안 혼합 모델 (Gaussian mixture model)을 분류자로 사용하는 확률적 결함 분류 프레임워크가 제안되었다. 이때 분류자의 학습에서의 계산 복잡도를 줄이기 위하여 데이터를 저차원으로 투영시키는데, 이를 위한 확률적 다양체 학습 (probabilistic manifold learn-ing) 방법이 제안되었다. 제안하는 방법은 데이터의 다양체 (manifold)를 근사하여 데이터 포인트 사이의 쌍별 우도 (pairwise likelihood)를 보존하는 투영법이 사용된다. 이를 통하여 데이터의 종류와 차원에 의존도가 낮은 진단 결과를 얻음과 동시에 데이터 레이블과 같은 비거리적 (non-metric) 정보를 효율적으로 사용하여 결함 진단 능력을 향상시킬 수 있음을 보였다. 둘째로, 베이지안 심층 신경망(Bayesian deep neural networks)을 사용한 공정의 확률적 모델링 방법론이 제시되었다. 신경망의 각 매개변수는 가우스 분포로 치환되며, 변분추론 (variational inference)을 통하여 계산 효율적인 훈련이 진행된다. 훈련이 끝난 후 파라미터의 유효성을 측정하여 불필요한 매개변수를 소거하는 사후 모델 압축 방법이 사용되었다. 반도체 공정에 대한 사례 연구는 제안하는 방법이 공정의 복잡한 거동을 효과적으로 모델링 할 뿐만 아니라 모델의 최적 구조를 도출할 수 있음을 보여준다. 마지막으로, 분포형 심층 신경망을 사용한 강화학습을 기반으로 한 확률적 공정 설계 프레임워크가 제안되었다. 최적치를 찾기 위해 재귀적으로 목적 함수 값을 평가하는 기존의 최적화 방법론과 달리, 목적 함수 곡면 (objective function surface)을 매개화 된 확률분포로 근사하는 접근법이 제시되었다. 이를 기반으로 이산화 (discretization)를 사용하지 않고 연속적 행동 정책을 학습하며, 확실성 (certainty)에 기반한 탐색 (exploration) 및 활용 (exploi-tation) 비율의 제어가 효율적으로 이루어진다. 사례 연구 결과는 공정의 설계에 대한 경험지식 (heuristic)을 학습하고 유사한 설계 문제의 해를 구하는 데 이용할 수 있음을 보여준다.Chapter 1 Introduction 1 1.1. Motivation 1 1.2. Outline of the thesis 5 Chapter 2 Backgrounds and preliminaries 9 2.1. Bayesian inference 9 2.2. Monte Carlo 10 2.3. Kullback-Leibler divergence 11 2.4. Variational inference 12 2.5. Riemannian manifold 13 2.6. Finite extended-pseudo-metric space 16 2.7. Reinforcement learning 16 2.8. Directed graph 19 Chapter 3 Process monitoring and fault classification with probabilistic manifold learning 20 3.1. Introduction 20 3.2. Methods 25 3.2.1. Uniform manifold approximation 27 3.2.2. Clusterization 28 3.2.3. Projection 31 3.2.4. Mapping of unknown data query 32 3.2.5. Inference 33 3.3. Verification study 38 3.3.1. Dataset description 38 3.3.2. Experimental setup 40 3.3.3. Process monitoring 43 3.3.4. Projection characteristics 47 3.3.5. Fault diagnosis 50 3.3.6. Computational Aspects 56 Chapter 4 Process system modeling with Bayesian neural networks 59 4.1. Introduction 59 4.2. Methods 63 4.2.1. Long Short-Term Memory (LSTM) 63 4.2.2. Bayesian LSTM (BLSTM) 66 4.3. Verification study 68 4.3.1. System description 68 4.3.2. Estimation of the plasma variables 71 4.3.3. Dataset description 72 4.3.4. Experimental setup 72 4.3.5. Weight regularization during training 78 4.3.6. Modeling complex behaviors of the system 80 4.3.7. Uncertainty quantification and model compression 85 Chapter 5 Process design based on reinforcement learning with distributional actor-critic networks 89 5.1. Introduction 89 5.2. Methods 93 5.2.1. Flowsheet hashing 93 5.2.2. Behavioral cloning 99 5.2.3. Neural Monte Carlo tree search (N-MCTS) 100 5.2.4. Distributional actor-critic networks (DACN) 105 5.2.5. Action masking 110 5.3. Verification study 110 5.3.1. System description 110 5.3.2. Experimental setup 111 5.3.3. Result and discussions 115 Chapter 6 Concluding remarks 120 6.1. Summary of the contributions 120 6.2. Future works 122 Appendix 125 A.1. Proof of Lemma 1 125 A.2. Performance indices for dimension reduction 127 A.3. Model equations for process units 130 Bibliography 132 초 록 149박

Improving process monitoring and modeling of batch-type plasma etching tools

Manufacturing equipments in semiconductor factories (fabs) provide abundant data and opportunities for data-driven process monitoring and modeling. In particular, virtual metrology (VM) is an active area of research. Traditional monitoring techniques using univariate statistical process control charts do not provide immediate feedback to quality excursions, hindering the implementation of fab-wide advanced process control initiatives. VM models or inferential sensors aim to bridge this gap by predicting of quality measurements instantaneously using tool fault detection and classification (FDC) sensor measurements. The existing research in the field of inferential sensor and VM has focused on comparing regressions algorithms to demonstrate their feasibility in various applications. However, two important areas, data pretreatment and post-deployment model maintenance, are usually neglected in these discussions. Since it is well known that the industrial data collected is of poor quality, and that the semiconductor processes undergo drifts and periodic disturbances, these two issues are the roadblocks in furthering the adoption of inferential sensors and VM models. In data pretreatment, batch data collected from FDC systems usually contain inconsistent trajectories of various durations. Most analysis techniques requires the data from all batches to be of same duration with similar trajectory patterns. These inconsistencies, if unresolved, will propagate into the developed model and cause challenges in interpreting the modeling results and degrade model performance. To address this issue, a Constrained selective Derivative Dynamic Time Warping (CsDTW) method was developed to perform automatic alignment of trajectories. CsDTW is designed to preserve the key features that characterizes each batch and can be solved efficiently in polynomial time. Variable selection after trajectory alignment is another topic that requires improvement. To this end, the proposed Moving Window Variable Importance in Projection (MW-VIP) method yields a more robust set of variables with demonstrably more long-term correlation with the predicted output. In model maintenance, model adaptation has been the standard solution for dealing with drifting processes. However, most case studies have already preprocessed the model update data offline. This is an implicit assumption that the adaptation data is free of faults and outliers, which is often not true for practical implementations. To this end, a moving window scheme using Total Projection to Latent Structure (T-PLS) decomposition screens incoming updates to separate the harmless process noise from the outliers that negatively affects the model. The integrated approach was demonstrated to be more robust. In addition, model adaptation is very inefficient when there are multiplicities in the process, multiplicities could occur due to process nonlinearity, switches in product grade, or different operating conditions. A growing structure multiple model system using local PLS and PCA models have been proposed to improve model performance around process conditions with multiplicity. The use of local PLS and PCA models allows the method to handle a much larger set of inputs and overcome several challenges in mixture model systems. In addition, fault detection sensitivities are also improved by using the multivariate monitoring statistics of these local PLS/PCA models. These proposed methods are tested on two plasma etch data sets provided by Texas Instruments. In addition, a proof of concept using virtual metrology in a controller performance assessment application was also tested.Chemical Engineerin

2022 Review of Data-Driven Plasma Science

Data-driven science and technology offer transformative tools and methods to science. This review article highlights the latest development and progress in the interdisciplinary field of data-driven plasma science (DDPS), i.e., plasma science whose progress is driven strongly by data and data analyses. Plasma is considered to be the most ubiquitous form of observable matter in the universe. Data associated with plasmas can, therefore, cover extremely large spatial and temporal scales, and often provide essential information for other scientific disciplines. Thanks to the latest technological developments, plasma experiments, observations, and computation now produce a large amount of data that can no longer be analyzed or interpreted manually. This trend now necessitates a highly sophisticated use of high-performance computers for data analyses, making artificial intelligence and machine learning vital components of DDPS. This article contains seven primary sections, in addition to the introduction and summary. Following an overview of fundamental data-driven science, five other sections cover widely studied topics of plasma science and technologies, i.e., basic plasma physics and laboratory experiments, magnetic confinement fusion, inertial confinement fusion and high-energy-density physics, space and astronomical plasmas, and plasma technologies for industrial and other applications. The final section before the summary discusses plasma-related databases that could significantly contribute to DDPS. Each primary section starts with a brief introduction to the topic, discusses the state-of-the-art developments in the use of data and/or data-scientific approaches, and presents the summary and outlook. Despite the recent impressive signs of progress, the DDPS is still in its infancy. This article attempts to offer a broad perspective on the development of this field and identify where further innovations are required

Unsupervised Feature Extraction Techniques for Plasma Semiconductor Etch Processes

As feature sizes on semiconductor chips continue to shrink plasma etching is becoming a more and more critical process in achieving low cost high-volume manufacturing. Due to the highly complex physics of plasma and chemical reactions between plasma species, control of plasma etch processes is one of the most di±cult challenges facing the integrated circuit industry. This is largely due to the di±culty with monitoring plasmas. Optical Emission Spectroscopy (OES) technology can be used to produce rich plasma chemical information in real time and is increasingly being considered in semiconductor manufacturing for process monitoring and control of plasma etch processes. However, OES data is complex and inherently highly redundant, necessitating the development of advanced algorithms for e®ective feature extraction. In this thesis, three new unsupervised feature extraction algorithms have been proposed for OES data analysis and the algorithm properties have been explored with the aid of both arti¯cial and industrial benchmark data sets. The ¯rst algorithm, AWSPCA (AdaptiveWeighting Sparse Principal Component Analysis), is developed for dimension reduction with respect to variations in the analysed variables. The algorithm gener- ates sparse principle components while retaining orthogonality and grouping correlated variables together. The second algorithm, MSC (Max Separation Clustering), is devel- oped for clustering variables with distinctive patterns and providing e®ective pattern representation by a small number of representative variables. The third algorithm, SLHC (Single Linkage Hierarchical Clustering), is developed to achieve a complete and detailed visualisation of the correlation between variables and across clusters in an OES data set. The developed algorithms open up opportunities for using OES data for accurate pro- cess control applications. For example, MSC enables the selection of relevant OES variables for better modeling and control of plasma etching processes. SLHC makes it possible to understand and interpret patterns in OES spectra and how they relate to the plasma chemistry. This in turns can help engineers to achieve an in-depth under- standing of underlying plasma processes