Outliers detection by fuzzy classification method for model building

Mame Kouna Top; Yorick Trouiller; Vincent Farys; David Fuard; Emek Yesilada; Catherine Martinelli; Mazen Said; Franck Foussadier; Patrick Schiavone

doi:10.1117/12.812955

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23 March 2009 Outliers detection by fuzzy classification method for model building

Mame Kouna Top, Yorick Trouiller, Vincent Farys, David Fuard, Emek Yesilada, Catherine Martinelli, Mazen Said, Franck Foussadier, Patrick Schiavone

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Proceedings Volume 7272, Metrology, Inspection, and Process Control for Microlithography XXIII; 72721G (2009) https://doi.org/10.1117/12.812955
Event: SPIE Advanced Lithography, 2009, San Jose, California, United States

Abstract

Optical Proximity Correction (OPC) is used in lithography to increase the achievable resolution and pattern transfer fidelity for IC manufacturing. Nowadays, immersion lithography scanners are reaching the limits of optical resolution leading to more and more constraints on OPC models in terms of simulation reliability. The detection of outliers coming from SEM measurements is key in OPC [1]. Indeed, the model reliability is based in a large part on those measurements accuracy and reliability as they belong to the set of data used to calibrate the model. Many approaches were developed for outlier detection by studying the data and their residual errors, using linear or nonlinear regression and standard deviation as a metric [8]. In this paper, we will present a statistical approach for detection of outlier measurements. This approach consists of scanning Critical Dimension (CD) measurements by process conditions using a statistical method based on fuzzy CMean clustering and the used of a covariant distance for checking aberrant values cluster by cluster. We propose to use the Mahalanobis distance [2] in order to improve the discrimination of the outliers when quantifying the similarity within each cluster of the data set. This fuzzy classification method was applied on the SEM CD data collected for the Active layer of a 65 nm half pitch technology. The measurements were acquired through a process window of 25 (dose, defocus) conditions. We were able to detect automatically 15 potential outliers in a data distribution as large as 1500 different CD measurement. We will discuss about these results as well as the advantages and drawbacks of this technique as automatic outliers detection for large data distribution cleaning.

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Mame Kouna Top, Yorick Trouiller, Vincent Farys, David Fuard, Emek Yesilada, Catherine Martinelli, Mazen Said, Franck Foussadier, and Patrick Schiavone "Outliers detection by fuzzy classification method for model building", Proc. SPIE 7272, Metrology, Inspection, and Process Control for Microlithography XXIII, 72721G (23 March 2009); https://doi.org/10.1117/12.812955

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