Uncertainty Aware Virtual Metrology (VM) Framework Enabling Optimized Physical Metrology Policy and VM Model Adaptations

Accuracy of Virtual Metrology (VM) models, selection of wafers for physical metrology, and VM model adaptation are all vital areas of semiconductor manufacturing research which share a complex interdependence between each other. These interdependencies dictate the need for a unified framework which addresses VM modeling, uncertainty-aware selection of wafers for physical metrology, and adaptations of that model based on the newly obtained physical metrology results. In this paper, we propose a linear Gaussian dynamic model-based framework which models and tracks the behavior of VM model parameters over time, quantifies the uncertainty of VM model parameters and the VM model itself, and provides a theoretical framework for optimization of the selection of wafers which need to be physically inspected. We demonstrate the efficacy and superiority of this integrated VM modeling and upkeeping framework over the existing heuristic solutions using a uniquely large dataset obtained from an industrial plasma etch process performed on 114,774 wafers in a major 300 mm wafer semiconductor fab.