Growing Structure Multiple Model System for Quality Estimation in Manufacturing Processes

A new virtual metrology (VM) method for estimation of product quality characteristics will be presented using the recently introduced growing structure multiple model system (GSMMS) approach for modeling of non-linear dynamic systems. The underlying concept of local linear models enables representation of non-linear dependencies with non-Gaussian and non-stationary noise characteristics. In addition, localized analysis of VM inputs within the GSMMS framework enables detection of situations when the model is not adequate and needs to be improved. The newly proposed method was applied to an extensive dataset gathered from a plasma enhanced chemical vapor deposition tool operating in a major semiconductor manufacturing fab, with tool signatures being used to predict the mean film thicknesses on the wafers. The GSMMS-based VM significantly decreased the number of measurements necessary for prediction, while improving VM accuracy, as compared to several linear and nonlinear benchmark VM methodologies. These beneficial results are credited to the GSMMS being able to store local models within its growing network of local VM models corresponding to various operating regimes of the underlying manufacturing machine, as well as to recognize situations when new physical measurements need to be taken and when new local VM models need to be added.