Virtual metrology modeling of time-dependent spectroscopic signals by a fused lasso algorithm

• We propose to use a fused lasso model to construct a reliable virtual metrology (VM) model of spectroscopic signals.
• The fused lasso-based VM model is useful for analyzing spectroscopic signals with features that can be ordered in some meaningful way.
• The fused lasso-based VM model can robustly identify significant features in spectroscopic signals.
• We examine the usefulness and robustness of the fused lasso-based VM model compared to the original lasso- and elastic net-based VM models.
• The present work is the first attempt to use the fused lasso for purposes of VM.

This paper proposes a fused lasso model to identify significant features in the spectroscopic signals obtained from a semiconductor manufacturing process, and to construct a reliable virtual metrology (VM) model. Analysis of spectroscopic signals involves combinations of multiple samples collected over time, each with a vast number of highly correlated features. This leads to enormous amounts of data, which is a challenge even for modern-day computers to handle. To simplify such complex spectroscopic signals, dimension reduction is critical. The fused lasso is a regularized regression method that performs automatic variable selection for the predictive modeling of highly correlated datasets such as those of spectroscopic signals. Furthermore, the fused lasso is especially useful for analyzing high-dimensional data in which the features exhibit a natural order, as is the case in spectroscopic signals. In this paper, we conducted an experimental study to demonstrate the usefulness of a fused lasso-based VM model and compared it with other VM models based on the lasso and elastic-net models. The results showed that the VM model constructed with features selected by the fused lasso algorithm yields more accurate and robust predictions than the lasso- and elastic net-based VM models. To the best of our knowledge, ours is the first attempt to apply a fused lasso to VM modeling.