Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences


UC Berkeley


2008 Research Summary

Dynamic Virtual Metrology in Semiconductor Manufacturing

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Dekong Zeng and Costas J. Spanos

Virtual metrology has become a critical component of semiconductor manufacturing control. The idea is to construct predictive models that can forecast the electrical and physical parameters of wafers, based on data collected from the relevant processing tools. In this way, direct measurements from the wafer can be minimized or eliminated altogether, hence the term "virtual" metrology. Challenges include the selection of the appropriate modeling method, the pre-treatment [1] of the raw data, and the deployment of a VMM that can track an aging manufacturing process.

We are focusing on constructing dynamic VMM for on-line process monitoring and yield prediction based on the integration of linear partial least squares [2], principal components, and neural network methods. Principal component analysis and partial least squares are explored as direct modeling methods. They also serve as dimension reduction pretreatment for neural networks [3] training. Feed-forward neural networks with back-propagation training are applied for studying non-linear relationships between the inputs and outputs.

Data pretreatment is critical to the overall VMM performance, due to the high dimensionality and co-linearity of the raw process data. Pretreatment methods fall into three categories: outlier detection, data scaling, and data classification. Outliers can cause large prediction error variance in the model, thus detecting and removing the outlier is essential. Data scaling prevents variables with large numeric values from dominating. Data classification helps in determining whether different VMMs should be deployed for different production tools, products, or production periods. We are examining a variety of techniques including k-means clustering, SVM (support vector machine), and correlation analysis based on intuitive understanding about the process variables.

C. C. Aggarwal and P. S. Yu, "Outlier Detection for High Dimensional Data," ACM SIGMOD Conf., 2001.
P. Geladi and R. B. Kowalski, "Partial Least-Squares Regression: A Tutorial," Anal. Chem. Acta., Vol. 185, 1986, pp. 1-17.
P. Baldi and K. Hornik, "Neural Networks and Principal Component Analysis: Learning from Examples without Local Minima," Neural Networks, Vol. 2, No. 53, 1989.