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Advanced Process Control is an important research area in Semiconductor Manufacturing to improve process stability crucial for product quality. Especially in low-volume-high-mixture fabrication plants, knowledge discovery in databases is extremely challenging due to complex technology mixtures and reduced availability of data for comparable process steps. Thus, actual research focuses on Data Mining using Machine Learning methods to model unknown functional interrelations. High Density Plasma Chemical Vapor Deposition appears to be a process area in semiconductor manufacturing predestinated for application of Data Mining. Promising results have been achieved by implementing statistical models to predict the thickness of dielectric layers deposited onto a metallization layer of the manufactured wafer. This paper describes the approach to predict the layer thickness using a state-of-the-art Machine Learning regression algorithm: Support Vector Regression. The recent extension of Support Vector Machines overcomes pure classification and deals with multivariate nonlinear input data for regression.