Multilevel Kernel Methods for Virtual Metrology in Semiconductor Manufacturing

Abstract In 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.

[1]  Mario Bertero,et al.  The Stability of Inverse Problems , 1980 .

[2]  D. Harville.  Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems , 1977 .

[3]  A. L. Barker,et al.  Bayesian Estimation and the Kalman Filter , 1994 .

[4]  Gunnar Rätsch,et al.  An introduction to kernel-based learning algorithms , 2001, IEEE Trans. Neural Networks.

[5]  Fan-Tien Cheng,et al.  Accuracy and Real-Time Considerations for Implementing Various Virtual Metrology Algorithms , 2008, IEEE Transactions on Semiconductor Manufacturing.

[6]  M. Aizerman,et al.  Theoretical Foundations of the Potential Function Method in Pattern Recognition Learning , 1964 .

[7]  Fan-Tien Cheng,et al.  NN-Based Key-Variable Selection Method for Enhancing Virtual Metrology Accuracy , 2009, IEEE Transactions on Semiconductor Manufacturing.

[8]  Nello Cristianini,et al.  Kernel Methods for Pattern Analysis , 2003, ICTAI.

[9]  James Moyne,et al.  Virtual metrology and feedback control for semiconductor manufacturing processes using recursive partial least squares , 2008 .

[10]  Fan-Tien Cheng,et al.  Developing a dual-stage indirect virtual metrology architecture , 2010, 2010 IEEE International Conference on Robotics and Automation.

[11]  Russ Wolfinger,et al.  Computing Gaussian Likelihoods and Their Derivatives for General Linear Mixed Models , 1994, SIAM J. Sci. Comput..

[12]  Cheng-Ching Yu,et al.  On the interaction between measurement strategy and control performance in semiconductor manufacturing , 2008 .

[13]  Hyoungjoo Lee,et al.  Virtual metrology for run-to-run control in semiconductor manufacturing , 2011, Expert Syst. Appl..

[14]  Rich Caruana,et al.  Multitask Learning , 1998, Encyclopedia of Machine Learning and Data Mining.