Multiparametric Virtual Metrology Model Building by Job-Shop Data Fusion Using a Markov Chain Monte Carlo Method

This paper proposes a generic methodology for building a multiparametric virtual metrology (VM) model that predicts the chemical-mechanical polishing (CMP) rate in the mass production of many different products in small quantities using multiple tools in a job shop. The VM model must handle inter-individual differences in both products and tools, with multiple parameters. To identify the multiparametric VM model from datasets of small samples collected from the tools in the early stages of mass production, all the datasets are fused together using a Markov chain Monte Carlo method for a hierarchical Bayesian model. The proposed method is validated by simulation experiments using real manufacturing data collected from six tools for seven mixed products. In particular, the 18 parameters of the VM model are identifiable even from a fusion of the datasets with just 10 samples from each of the tools. The root mean square of errors (RMSE) of the variation in the polished amount decreases to 41% when using the APC with the VM model.