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

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

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 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

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

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

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

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