a convolutional autoencoder approach for feature extraction in virtual metrology

Abstract Exploiting the huge amount of data collected by industries is definitely one of the main challenges of the so-called Big Data era. In this sense, Machine Learning has gained growing attention in the scientific community, as it allows to extract valuable information by means of statistical predictive models trained on historical process data. In Semiconductor Manufacturing, one of the most extensively employed data-driven applications is Virtual Metrology, where a costly or unmeasurable variable is estimated by means of cheap and easy to obtain measures that are already available in the system. Often, these measures are multi-dimensional, so traditional Machine Learning algorithms cannot handle them directly. Instead, they require feature extraction, that is a preliminary step where relevant information is extracted from raw data and converted into a design matrix. Features are often hand-engineered and based on specific domain knowledge. Moreover, they may be difficult to scale and prone to information loss, affecting the effectiveness and maintainability of machine learning procedures. In this paper, we present a Deep Learning method for semi-supervised feature extraction based on Convolutional Autoencoders that is able to overcome the aforementioned problems. The proposed method is tested on a real dataset for Etch rate estimation. Optical Emission Spectrometry data, that exhibit a complex bi-dimensional time and wavelength evolution, are used as input

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

Smart Feature Selection to enable Advanced Virtual Metrology

The present dissertation enhances the research in computer science, especially state of the art Machine Learning (ML), in the field of process development in Semiconductor Manufacturing (SM) by the invention of a new Feature Selection (FS) algorithm to discover the most important equipment and context parameters for highest performance of predicting process results in a newly developed advanced Virtual Metrology (VM) system. In complex high-mixture-low-volume SM, chips or rather silicon wafers for numerous products and technologies are manufactured on the same equipment. Process stability and control are key factors for the production of highest quality semiconductors. Advanced Process Control (APC) monitors manufacturing equipment and intervenes in the equipment control if critical states occur. Besides Run-To-Run (R2R) control and Fault Detection and Classification (FDC) new process control development activities focus on VM which predicts metrology results based on productive equipment and context data. More precisely, physical equipment parameters combined with logistical information about the manufactured product are used to predict the process result. The compulsory need for a reliable and most accurate VM system arises to imperatively reduce time and cost expensive physical metrology as well as to increase yield and stability of the manufacturing processes while concurrently minimizing economic expenditures and associated data flow. The four challenges of (1) efficiency of development and deployment of a corporate-wide VM system, (2) scalability of enterprise data storage, data traffic and computational effort, (3) knowledge discovery out of available data for future enhancements and process developments as well as (4) highest accuracy including reliability and reproducibility of the prediction results are so far not successfully mastered at the same time by any other approach. Many ML techniques have already been investigated to build prediction models based on historical data. The outcomes are only partially satisfying in order to achieve the ambitious objectives in terms of highest accuracy resulting in tight control limits which tolerate almost no deviation from the intended process result. For optimization of prediction performance state of the art process engineering requirements lead to three criteria for assessment of the ML algorithm for the VM: outlier detection, model robustness with respect to equipment degradation over time and ever-changing manufacturing processes adapted for further development of products and technologies and finally highest prediction accuracy. It has been shown that simple regression methods fail in terms of prediction accuracy, outlier detection and model robustness while higher-sophisticated regression methods are almost able to constantly achieve these goals. Due to quite similar but still not optimal prediction performance as well as limited computational feasibility in case of numerous input parameters, the choice of superior ML regression methods does not ultimately resolve the problem. Considering the entire cycle of Knowledge Discovery in Databases including Data Mining (DM) another task appears to be crucial: FS. An optimal selection of the decisive parameters and hence reduction of the input space dimension boosts the model performance by omitting redundant as well as spurious information. Various FS algorithms exist to deal with correlated and noisy features, but each of its own is not capable to ensure that the ambitious targets for VM can be achieved in prevalent high-mixture-low-volume SM. The objective of the present doctoral thesis is the development of a smart FS algorithm to enable a by this advanced and also newly developed VM system to comply with all imperative requirements for improved process stability and control. At first, a new Evolutionary Repetitive Backward Elimination (ERBE) FS algorithm is implemented combining the advantages of a Genetic Algorithm (GA) with Leave-One-Out (LOO) Backward Elimination as wrapper for Support Vector Regression (SVR). At second, a new high performance VM system is realized in the productive environment of High Density Plasma (HDP) Chemical Vapor Deposition (CVD) at the Infineon frontend manufacturing site Regensburg. The advanced VM system performs predictions based on three state of the art ML methods (i.e. Neural Network (NN), Decision Tree M5’ (M5’) & SVR) and can be deployed on many other process areas due to its generic approach and the adaptive design of the ERBE FS algorithm. The developed ERBE algorithm for smart FS enhances the new advanced VM system by revealing evidentially the crucial features for multivariate nonlinear regression. Enabling most capable VM turns statistical sampling metrology with typically 10% coverage of process results into a 100% metrological process monitoring and control. Hence, misprocessed wafers can be detected instantly. Subsequent rework or earliest scrap of those wafers result in significantly increased stability of subsequent process steps and thus higher yield. An additional remarkable benefit is the reduction of production cycle time due to the possible saving of time consuming physical metrology resulting in an increase of production volume output up to 10% in case of fab-wide implementation of the new VM system

Computational Intelligence Techniques for OES Data Analysis

Semiconductor manufacturers are forced by market demand to continually deliver lower cost and faster devices. This results in complex industrial processes that, with continuous evolution, aim to improve quality and reduce costs. Plasma etching processes have been identified as a critical part of the production of semiconductor devices. It is therefore important to have good control over plasma etching but this is a challenging task due to the complex physics involved. Optical Emission Spectroscopy (OES) measurements can be collected non-intrusively during wafer processing and are being used more and more in semiconductor manufacturing as they provide real time plasma chemical information. However, the use of OES measurements is challenging due to its complexity, high dimension and the presence of many redundant variables. The development of advanced analysis algorithms for virtual metrology, anomaly detection and variables selection is fundamental in order to effectively use OES measurements in a production process. This thesis focuses on computational intelligence techniques for OES data analysis in semiconductor manufacturing presenting both theoretical results and industrial application studies. To begin with, a spectrum alignment algorithm is developed to align OES measurements from different sensors. Then supervised variables selection algorithms are developed. These are defined as improved versions of the LASSO estimator with the view to selecting a more stable set of variables and better prediction performance in virtual metrology applications. After this, the focus of the thesis moves to the unsupervised variables selection problem. The Forward Selection Component Analysis (FSCA) algorithm is improved with the introduction of computationally efficient implementations and different refinement procedures. Nonlinear extensions of FSCA are also proposed. Finally, the fundamental topic of anomaly detection is investigated and an unsupervised variables selection algorithm tailored to anomaly detection is developed. In addition, it is shown how OES data can be effectively used for semi-supervised anomaly detection in a semiconductor manufacturing process. The developed algorithms open up opportunities for the effective use of OES data for advanced process control. All the developed methodologies require minimal user intervention and provide easy to interpret models. This makes them practical for engineers to use during production for process monitoring and for in-line detection and diagnosis of process issues, thereby resulting in an overall improvement in production performance

Plasma Etch Process Virtual Metrology using Aggregative Linear Regression

To enhance product quality semiconductor manufacturing industries are increasing the amount of metrology information collected during manufacturing processes. This increase in information has provided companies with many opportunities for enhanced process monitoring and control. However, the increase in information also posses challenges as it is quite common now to collect many more measurements than samples from a process leading to ill-conditioned datasets. Illconditioned datasets are very common in semiconductor manufacturing industries where infrequent sampling is the norm. It is therefore critical to be able to quantify virtual metrology models developed from such data sets. This paper presents an aggregative linear regression methodology for modeling that allows the generation of confidence intervals on the predicted outputs. The aggregation enhances the robustness of the linear models in terms of process variation and model sensitivity towards prediction. Also, to deal with the large number of candidate process variables, variable selection methods are employed to reduce the dimensionality and computational efforts associated with building virtual metrology models. In the paper three methods for variable selection are evaluated in conjunction with aggregative linear regression (ALR). The proposed methodology is tested on a benchmark semiconductor plasma etch process dataset and the results are compared with state-ofart multiple linear regression (MLR) and Gaussian Process Regression (GPR) VM models

Plasma Etch Process Virtual Metrology using Aggregative Linear Regression

To enhance product quality semiconductor manufacturing industries are increasing the amount of metrology information collected during manufacturing processes. This increase in information has provided companies with many opportunities for enhanced process monitoring and control. However, the increase in information also posses challenges as it is quite common now to collect many more measurements than samples from a process leading to ill-conditioned datasets. Illconditioned datasets are very common in semiconductor manufacturing industries where infrequent sampling is the norm. It is therefore critical to be able to quantify virtual metrology models developed from such data sets. This paper presents an aggregative linear regression methodology for modeling that allows the generation of confidence intervals on the predicted outputs. The aggregation enhances the robustness of the linear models in terms of process variation and model sensitivity towards prediction. Also, to deal with the large number of candidate process variables, variable selection methods are employed to reduce the dimensionality and computational efforts associated with building virtual metrology models. In the paper three methods for variable selection are evaluated in conjunction with aggregative linear regression (ALR). The proposed methodology is tested on a benchmark semiconductor plasma etch process dataset and the results are compared with state-ofart multiple linear regression (MLR) and Gaussian Process Regression (GPR) VM models

Прикладна фізика : українсько-російсько-англійський тлумачний словник. У 4 т. Т. 2. З – Н

Словник охоплює близько 30 тис. термінів з прикладної фізики і дотичних до неї галузей знань та їх тлумачення трьома мовами (українською, російською та англійською). Багато термінів і визначень, наведених у словнику, якими послуговуються у відповідній галузі знань, досі не входили до жодного зі спеціалізованих словників. Словник призначений для викладачів, науковців, інженерів, аспірантів, студентів вищих навчальних закладів, перекладачів з природничих і технічних дисциплін