Methods for improving the reliability of semiconductor fault detection and diagnosis with principal component analysis

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Cherry, Gregory Allan

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This dissertation presents several methods for improving multivariate monitoring capabilities, with an emphasis on semiconductor manufacturing operations. Although many alternative algorithms have been proposed for multivariate statistical process control, principal component analysis (PCA) remains the most commonly used, and therefore serves as a core component of all of the methods that are developed within this work. Recent developments of PCA-based methodologies are reviewed, including the combined index for fault detection, multiblock analysis and variable contributions for fault diagnosis, and adaptive methods for handling drifting processes. The multiblock approach is extended to the combined index in this work, with the objective of simplifying the fault diagnosis task. The new approach is evaluated with site-level critical dimension metrology data and plasma stripper processing tool data. The issue of non-normally distributed data is also addressed through the application of density estimation for evaluating the quality of the principal component scores. Although kernel density estimation has been previously cited as a method for monitoring such data, mixture models are proposed in order to reduce model complexity and computational effort. Furthermore, several adaptation strategies for the density estimators are developed and suggestions are provided on their use. A rapid thermal anneal case study demonstrates how the estimators outperform the traditional Hotelling’s T02 statistic due to the presence of a first wafer effect. Several methods of data conditioning and preprocessing are presented to improve the fault detection and diagnosis results. Conditioning refers to the removal of unreliable and unimportant information, while preprocessing transforms batch data into consistent vectors for multi-way PCA. A comparative analysis of summary statistic, linear interpolation, and dynamic time warping preprocessing is performed on data collected from a plasma etcher. As multivariate monitoring is proliferated, the maintenance of the deployed models can become a challenge due to the substantial multiplicity of products and equipment throughout the fabrication facility. Although it has previously been applied for fault classification, Fisher discriminant analysis (FDA) is applied here to characterize differences between etch and rapid thermal anneal processing tools and to track the historical evolution of an adaptive PCA model for a plasma stripper.