Gaussian process regression for virtual metrology of microchip quality and the resulting strategic sampling scheme

Manufacturing of integrated circuits involves many sequential processes, often ex- ecuted to nanoscale tolerances, and the yield depends on the often unmeasured quality of intermediate steps. In the high-throughput industry of fabricating microelectronics on semi-conducting wafers, scheduling measurements of product quality before the electrical test of the complete IC can be expensive. We therefore seek to predict metrics of product quality based on sensor readings describing the environment within the relevant tool during the processing of each wafer, or to apply the concept of virtual metrology (VM) to monitor these intermediate steps. We model the data using Gaussian process regression (GPR), adapted to simultaneously learn the nonlinear dynamics that govern the quality characteristic, as well as their operating space, expressed by a linear embedding of the sensor traces’ features. Such Bayesian models predict a distribution for the target metric, such as a critical dimension, so one may assess the model’s credibility through its predictive uncertainty. Assuming measurements of the quality characteristic of interest are budgeted, we seek to hasten convergence of the GPR model to a credible form through an active sampling scheme, whereby the predictive uncertainty informs which wafer’s quality to measure next. We evaluate this convergence when predicting and updating online, as if in a factory, using a large dataset for plasma-enhanced chemical vapor deposition (PECVD), with measured thicknesses for ~32,000 wafers. By approximately optimizing the information extracted from this seemingly repetitive data describing a tightly controlled process, GPR achieves ~10% greater accuracy on average than a baseline linear model based on partial least squares (PLS). In a derivative study, we seek to discern the degree of drift in the process over the several months the data spans. We express this drift by how unusual the relevant features, as embedded by the GPR model, appear as the in- puts compensate for degrading conditions. This method detects the onset of consistently unusual behavior that extends to a bimodal thickness fault, anticipating its flagging by as much as two days.Mechanical Engineerin

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

A review of data mining applications in semiconductor manufacturing

The authors acknowledge Fundacao para a Ciencia e a Tecnologia (FCT-MCTES) for its financial support via the project UIDB/00667/2020 (UNIDEMI).For decades, industrial companies have been collecting and storing high amounts of data with the aim of better controlling and managing their processes. However, this vast amount of information and hidden knowledge implicit in all of this data could be utilized more efficiently. With the help of data mining techniques unknown relationships can be systematically discovered. The production of semiconductors is a highly complex process, which entails several subprocesses that employ a diverse array of equipment. The size of the semiconductors signifies a high number of units can be produced, which require huge amounts of data in order to be able to control and improve the semiconductor manufacturing process. Therefore, in this paper a structured review is made through a sample of 137 papers of the published articles in the scientific community regarding data mining applications in semiconductor manufacturing. A detailed bibliometric analysis is also made. All data mining applications are classified in function of the application area. The results are then analyzed and conclusions are drawn.publishersversionpublishe

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

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

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

Real-time virtual metrology and control for plasma etch

Plasma etch is a semiconductor manufacturing process during which material is removed from the surface of semiconducting wafers, typically made of silicon, using gases in plasma form. A host of chemical and electrical complexities make the etch process notoriously difficult to model and troublesome to control. This work demonstrates the use of a real-time model predictive control scheme to control plasma electron density and plasma etch rate in the presence of disturbances to the ground path of the chamber. Virtual metrology (VM) models, using plasma impedance measurements, are used to estimate the plasma electron density and plasma etch rate in real time for control, eliminating the requirement for invasive measurements. The virtual metrology and control schemes exhibit fast set-point tracking and disturbance rejection capabilities. Etch rate can be controlled to within 1% of the desired value. Such control represents a significant improvement over open-loop operation of etch tools, where variances in etch rate of up to 5% can be observed during production processes due to disturbances in tool state and material properties

Virtual metrology for semiconductor manufacturing applications

Per essere competitive nel mercato, le industrie di semiconduttori devono poter raggiungere elevati standard di produzione a un prezzo ragionevole. Per motivi legati tanto ai costi quanto ai tempi di esecuzione, una strategia di controllo della qualità che preveda la misurazione completa del prodotto non è attuabile; i test sono eettuati su un ristretto campione dei dati originali. Il traguardo del presente lavoro di Tesi è lo studio e l'implementazione, attraverso metodologie di modellistica tipo non lineare, di un algoritmo di metrologia virtuale (Virtual Metrology) d'ausilio al controllo di processo nella produzione di semiconduttori. Infatti, la conoscenza di una stima delle misure non realmente eseguite (misure virtuali) può rappresentare un primo passo verso la costruzione di sistemi di controllo di processo e controllo della qualità sempre più ranati ed ecienti. Da un punto di vista operativo, l'obiettivo è fornire la più accurata stima possibile delle dimensioni critiche a monte della fase di etching, a partire dai dati disponibili (includendo misurazioni da fasi di litograa e deposizione e dati di processo - ove disponibili). Le tecniche statistiche allo stato dell'arte analizzate in questo lavoro comprendono: - multilayer feedforward networks; Confronto e validazione degli algoritmi presi in esame sono stati possibili grazie ai data-set forniti da un'industria manifatturiera di semiconduttori. In conclusione, questo lavoro di Tesi rappresenta un primo passo verso la creazione di un sistema di controllo di processo e controllo della qualità evoluto e essibile, che abbia il ne ultimo di migliorare la qualità della produzione.ope