Dimensionality reduction methods in virtual metrology

The objective of this work is the creation of predictive models that can forecast the electrical or physical parameters of wafers using data collected from the relevant processing tools. In this way, direct measurements from the wafer can be minimized or eliminated altogether, hence the term "virtual" metrology. Challenges include the selection of the appropriate process step to monitor, the pre-treatment of the raw data, and the deployment of a Virtual Metrology Model (VMM) that can track a manufacturing process as it ages. A key step in any VM application is dimensionality reduction, i.e. ensuring that the proper subset of predictors is included in the model. In this paper, a software tool developed with MATLAB is demonstrated for interactive data prescreening and selection. This is combined with a variety of automated statistical techniques. These include step-wise regression and genetic selection in conjunction with linear modeling such as Principal Component Regression (PCR) and Partial Least Squares (PLS). Modeling results based on industrial datasets are used to demonstrate the effectiveness of these methods.

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