A predictive method to forecast spatial variability of stochastic processes for deep nanoscale semiconductor manufacturing

Yijian Chen

doi:10.1117/12.710986

5 April 2007 A predictive method to forecast spatial variability of stochastic processes for deep nanoscale semiconductor manufacturing

Yijian Chen

Author Affiliations +

Proceedings Volume 6518, Metrology, Inspection, and Process Control for Microlithography XXI; 65182O (2007) https://doi.org/10.1117/12.710986
Event: SPIE Advanced Lithography, 2007, San Jose, California, United States

Abstract

A general predictive method based on Canonical Correlation Analysis (CCA) is developed to identify globally correlated process modes that are responsible for the spatial variability in deep nanoscale semiconductor manufacturing. This multivariate statistical method overcomes the limitations of ordinary multiple linear regression technique by introducing canonical variates with certain properties which allow us to construct a transfer matrix to relate the predictand vector to the predictor vector directly. Principal Component Analysis (PCA), another multivariate statistical technique, is introduced to find the orthogonal modes that explain the larger fraction of the total process variations. We also discuss the constraint of sample number in CCA and propose using the leading principal components (PCAs) to replace the original raw data in correlation analysis.

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Yijian Chen "A predictive method to forecast spatial variability of stochastic processes for deep nanoscale semiconductor manufacturing", Proc. SPIE 6518, Metrology, Inspection, and Process Control for Microlithography XXI, 65182O (5 April 2007); https://doi.org/10.1117/12.710986

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KEYWORDS

Principal component analysis

Simulation of CCA and DLA aggregates

Matrices

Critical dimension metrology

Semiconductor manufacturing

Canonical correlation analysis

Stochastic processes

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