Restricted Relevance Vector Machine for Missing Data and Application to Virtual Metrology

Abstract

In semiconductor manufacturing, virtual metrology (VM) is a method of predicting physical measurements of wafer qualities using in-process information from sensors on production equipment. The relevance vector machine (RVM) is a sparse Bayesian kernel machine that has been widely used for VM modeling in semiconductor manufacturing. Missing values from equipment sensors, however, preclude training an RVM model due to missing kernels from incomplete instances. Moreover, imputation for such kernels can lead to a loss of model sparsity. In this work, we propose a restricted RVM (RRVM) that selects its basis functions from only complete instances to handle incomplete data for VM. We conduct the experiments using toy data and real-life data from an etching process for wafer fabrication. The results indicate the model's competitive prediction accuracy with massive missing data while maintaining model sparsity.