Outliers detection by fuzzy classification method for model building

International audienceOptical 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

Computational Analysis of Distance Operators for the Iterative Closest Point Algorithm

The Iterative Closest Point (ICP) algorithm is currently one of the most popular methods for rigid registration so that it has become the standard in the Robotics and Computer Vision communities. Many applications take advantage of it to align 2D/3D surfaces due to its popularity and simplicity. Nevertheless, some of its phases present a high computational cost thus rendering impossible some of its applications. In this work, it is proposed an efficient approach for the matching phase of the Iterative Closest Point algorithm. This stage is the main bottleneck of that method so that any efficiency improvement has a great positive impact on the performance of the algorithm. The proposal consists in using low computational cost point-to-point distance metrics instead of classic Euclidean one. The candidates analysed are the Chebyshev and Manhattan distance metrics due to their simpler formulation. The experiments carried out have validated the performance, robustness and quality of the proposal. Different experimental cases and configurations have been set up including a heterogeneous set of 3D figures, several scenarios with partial data and random noise. The results prove that an average speed up of 14% can be obtained while preserving the convergence properties of the algorithm and the quality of the final results