Multilevel Lasso applied to Virtual Metrology in semiconductor manufacturing

In semiconductor manufacturing, the state of the art for wafer quality control is based on product monitoring and feedback control loops; the related metrology operations, that usually involve scanning electron microscopes, are particularly cost-intensive and time-consuming. It is therefore not possible to evaluate every wafer: commonly, a small subset of a productive lot is measured at the metrology station and delegated to represent the whole lot. Virtual Metrology (VM) methodologies aim to obtain reliable estimates of metrology results without actually performing measurement operations; this goal is usually achieved by means of statistical models, linking process data and context information to target measurements. In this paper, we tackle two of the most important issues in VM: (i) regression in high dimensional spaces where few variables are meaningful, and (ii) data heterogeneity caused by inhomogeneous production and equipment logistics. We propose a hierarchical framework based on ℓ1-penalized machine learning techniques and solved by means of multitask learning strategies. The proposed methodology is validated on actual process and measurement data from the semiconductor manufacturing industry.