Virtual Metrology (VM) predicts end-of-batch properties (metrology data) from measurable input data composed of pre-process metrology and fault detection and classi cation (FDC) system outputs. This dissertation aims at moving a step closer to the realization of VM in semiconductor manufacturing by providing solutions to the challenges that present VM technology faces. First, various VM methods are introduced and compared in terms of prediction accuracy using four industrial datasets collected from a plasma etch system at Texas Instruments, Inc.. Kalman lter estimation is employed in a novel way to serve as a VM model for predicting outputs of a static process. Recursive PLS regression (R-PLSR) and Kalman filter show the best prediction results as they update the model whenever new measurements are available. Next, two PLS variants (PLS with EWMA mean update and recursive PLS) are proposed as robust VM algorithms that can predict process outputs fairly accurately in the presence of unexpected process drifts and noise. The obtained results reinforce VM technology by suggesting appropriate prediction methods when unexpected process changes occur. For a successful implementation of VM, the data entering the VM model needs to be free from faults. Fault-free (reconstructed) data are obtained by performing fault detection, fault identi cation, and fault reconstruction. A novel fault detection method based on statistics pattern analysis (SPA) is presented. The SPA method provides better fault detection performance for diff erent types of faults as compared to the MPCA-based methods. Next, three well-known fault identi cation methods present in literature are implemented. An equation that relates the RBC with the SVI is derived. The contribution plot method identi es a smaller number of faults correctly as compared to the RBC and the SVI methods. Fairly good estimates of the fault magnitude are obtained when the faults are identi ed correctly. An approach that combines physical measurements with the VM estimates to develop a more robust approach than using VM alone is presented. EWMA-R2R control is implemented using three well-known sampling methods in order to demonstrate the superior performance of two novel control schemes: B-EWMA R2R control and VM-assisted EWMA-R2R control. A new reliance index, which is attractive from a mathematical and practical point of view, is proposed. The VM-assisted EWMA-R2R control yields the best control results among the control schemes employed in this study. The simulation results demonstrate that VM has the potential to reduce measurement costs signi cantly while promising better process control. / text

This thesis presents the modeling of tool data produced during ion implantation for the prediction of wafer sheet resistance. In this work, we will use various statistical techniques to address challenges due to the nature of equipment data: high dimensionality, colinearity, parameter interactions, and non-linearities. The emphasis will be data integrity, variable selection, and model building methods. Different variable selection and modeling techniques will be evaluated using an industrial data set. Ion implant processes are fast and depending on the monitoring frequency of the equipment, late detection of a process shift could lead to the loss of a significant amount of product. The main objective of the research presented in this thesis is to identify any ion implant parameters that can be used to formulate a virtual metrology model. The virtual metrology model would then be used for process monitoring to ensure stable processing conditions and consequent yield guarantees. / text

Predicting 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. / text

La thématique abordée porte sur la métrologie virtuelle (VM) pour estimer les données manquantes durant les processus de fabrications des semi-conducteurs. L'utilisation de la métrologie virtuelle permet également de fournir les mesures logicielles (estimations) des sorties pour alimenter les régulateurs run-to-run (R2R) mis en place pour le contrôle de la qualité des produits fabriqués. Pour remédier aux problèmes liés au retard de mesures causé par l'échantillonnage statique imposé par la stratégie et les équipements mis en place, notre contribution dans cette thèse est d'introduire la notion de l'échantillonnage dynamique intelligent. Cette stratégie est basée sur un algorithme qui prend en compte la condition de voisinage permettant d'éviter la mesure réelle même si l'échantillonnage statique l'exige. Cela permet de réduire le nombre de mesures réelles, le temps du cycle et le coût de production. Cette approche est assurée par un module de métrologie virtuelle (VM) que nous avons développé et qui peut être intégré dans une boucle de régulation R2R. Les résultats obtenus ont été validés sur des exemples académiques et sur des données réelles fournies par notre partenaire STMicroelectronics de Rousset concernant un processus chemical mechanical planarization (CMP). Ces données réelles ont permis également de valider les résultats obtenus de la métrologie virtuelle pour les fournir ensuite aux régulateurs R2R (ayant besoin de l'estimation de ces données). / The addressed work is about the virtual metrology (VM) for estimating missing data during semiconductor manufacturing processes. The use of virtual metrology tool also makes it possible to provide the software measurements (estimations) of the outputs to feed the run-to-run (R2R) controllers set up for the quality control of the manufactured products.To address these issues related to the delay of measurements caused by the static sampling imposed by the strategy and the equipments put in place, our contribution in this thesis is to introduce the notion of the dynamic dynamic sampling. This strategy is based on an algorithm that considers the neighborhood condition to avoid the actual measurement even if the static sampling requires it. This reduces the number of actual measurements, the cycle time and the cost of production. This approach is provided by a virtual metrology module (VM) that we have developed and which can be integrated into an R2R control loop. The obtained results were validated on academic examples and on real data provided by our partner STMicroelectronics of Rousset from a chemical mechanical planarization (CMP) process. This real data also enabled the results obtained from the virtual metrology to be validated and then supplied to the R2R regulators (who need the estimation of these data).

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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.