Multilevel Kernel Methods for Virtual Metrology in Semiconductor Manufacturing

Abstract

AbstractIn semiconductor manufacturing, Virtual Metrology (VM) methodologies aim to obtain reliable estimates of process results without actually performing measurement operations, that are cost-intensive and time-consuming. This goal is usually achieved by means of statistical models, linking (easily collectible) process data to target measurements. In this paper, we tackle two of the most important issues in VM: function regression in high-dimensional spaces and data heterogeneity caused by inhomogeneous production and equipment logistics. We propose a hierarchical framework based on kernel methods and solved by means of multitask learning strategies and mixed-effects statistical models to improve the quality of estimates. The proposed methodology is validated on actual process and measurement data from the semiconductor manufacturing.