Understanding and Improving Virtual Metrology Systems Using Bayesian Methods

Abstract

Virtual Metrology (VM) is a method for monitoring semiconductor fabrication processes that estimates key device properties using sensor information recorded during processing. While useful, two common problems hinder virtual metrology performance. First, changes in the modeled system over time, i.e., concept drifts, decay model performance such that a static model no longer matches the underlying system once it has drifted. Second, limited sensor information, i.e., observability errors, further limit model performance, as an inability to infer the full state of the tool prevents optimal modeling. With these two sources of error in mind, we propose a system framework to better understand these systems. This framework relates recipe, chamber, sensor and wafer values, and incorporates both concept drift and observability errors. This framework synthesizes example system data that can then be used to develop more robust modeling techniques. Additionally, we use this synthetic system to propose a linear modeling technique using Bayesian methods that adapts to concept drift, and is less prone to overfitting. We test this proposed model on synthesized as well as manufacturing virtual metrology data, and demonstrate its superiority over traditional linear methods.