Statistical Methods for Semiconductor Manufacturing (2013)

In this thesis techniques for non-parametric modeling, machine learning, filtering and prediction and run-to-run control for semiconductor manufacturing are described.\nIn particular, algorithms have been developed for two major applications area:\n- Virtual Metrology (VM) systems;\n- Predictive Maintenance (PdM) systems.\nBoth technologies have proliferated in the past recent years in the semiconductor industries, called fabs, in order to increment productivity and decrease costs.\nVM 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 âcostlyâ to be measured in economic or temporal terms: the prediction is based on process variables and/or logistic information on the production that, instead,\nare always available and that can be used for modeling without further costs.\nPdM 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\nmethods and on the availability of process/logistic data, is in contrast with other classical approaches:\n- 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;\n- Preventive Maintenance (PvM), where the maintenances are scheduled in advance based on temporal intervals or on production iterations.\nBoth 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.\nThe 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\none, where lots of data are recorded and can be employed to build mathematical models.\nWe present several original contributions, both in the form of applications and methods.\nThe introduction of this thesis will be an overview on the semiconductor fabrication process: the most common practices on Advanced Process Control (APC) systems\nand the major issues for engineers and statisticians working in this area will be presented.\nFurthermore we will illustrate the methods and mathematical models used in the applications.\nWe will then discuss in details the following applications:\n- 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.\n- A new VM module for multi-step (CVD, Etching and Litography) line is proposed, where Multi-Task Learning techniques have been employed.\n- A new Machine Learning algorithm based on Kernel Methods for the estimation of scalar outputs from time series inputs is illustrated.\n- 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.\n- 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.\n- A PdM system based on Elastic Nets for the maintenance predictions in Ion Implantation tool is described.\nSeveral 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.