Window Discovery Research Articles

Inspection of Stochastic Defects With Broadband Plasma Optical Systems for Extreme Ultraviolet (EUV) Lithography

As extreme ultraviolet (EUV) lithography enters high volume manufacturing (HVM) to enable the sub-7nm scaling roadmap, characterizing and monitoring defects that print at wafer level are of critical importance to yield. This is especially true for defects coming from the EUV mask, due to multi-layer defects or added particles or growth on mask during its use, and for defects coming from the pattern formation process itself, which are known as stochastic printing defects or simply stochastic defects. In this paper we focus on developing inspection solutions for stochastic defects, which essentially are random local variations that occur between structures that should, in principle, print identically. These defects occur at significant frequencies with current state-of-the-art processes. Specifically, we discuss the importance of detecting these defects using KLA broadband plasma (BBP) optical inspection systems and the development of useful analysis methodologies. In addition, we describe use of traditional focus-dose process window discovery methodology developed on these optical inspection systems, for a foundry N5 equivalent M2 layer with both hybrid EUV and direct EUV patterning schemes. We highlight the impact of EUV stochastics to the overall process window.

Discovery of Anomalous Windows through a Robust Nonparametric Multivariate Scan Statistic (RMSS)

This paper studies unusual phenomena by discovering anomalous windows in multivariate spatial data. Such an anomalous window is a group of contiguous spatial objects indicating the occurrence of unusual phenomenon in terms of multiple variables. The paper presents a novel Robust non-parametric Multivariate Scan Statistic (RMSS). In contrast to the existing work, the authors’ approach is designed to deal with anomalous window discovery in multivariate data. They propose their multivariate scan statistic that employs the robust Mahalanobis distance which enables taking into account multiple behavioral attributes at the same time and their correlations for the discovery of significant anomalous windows. The proposed multivariate scan statistic is non-parametric such that it does not rely on any prior assumption about the data distribution. It is robust such that it can handle data with large amount of outliers, up to 50% of the overall data size. It is also affine equivariant such that affine transformation such as stretch or rotation of the data would not affect the results. The authors evaluate their approach with (a) real-world multivariate climate data for discovering natural disasters and climate changes, (b) real-world multivariate traffic accident data for identifying accident hubs, which are route segments with underlying accident-prone issues, and (c) synthetic data of both continuous and discrete multivariate distribution for identifying clusters of known outliers under different outlier percentage in data. They compare their results to state of the art multivariate scan statistic method (Kulldorff et al., 2007). The evaluation shows the detection power of the authors’ method, and the significant improvement over the existing methods.

Anomalous Window Discovery for Linear Intersecting Paths

The focus of this paper is to discover anomalous windows in linear intersecting paths. Anomalous windows are the contiguous groupings of data points. A linear path refers to a path represented by a line with a single dimensional spatial coordinate marking an observation point. In this paper, we propose an approach for discovering anomalous windows using a class of algorithms based on scan statistics, specifically 1) an Order invariant algorithm using Scan Statistics for Linear Intersecting Paths (SSLIP), 2) Brute force-SSLIP (BF-SSLIP), and 3) Central Brute Force-SSLIP (CBF-SSLIP). We further present two efficient variants of SSLIP: SSLIP* which employs a upper bound on the scan window size, and SSLIP-Acc, which adopts an accelerator function to speed up the scan process. The proposed approach for discovering anomalous windows along linear paths comprises the following distinct steps: 1) Cross Path Discovery: where we identify a subset of intersecting paths to be considered, 2) Anomalous Window Discovery: where we outline the various algorithms for the traversal of the cross paths to identify varying size directional windows along the paths. For identifying an anomalous window, an unusualness metric is computed, in the form of a likelihood ratio to indicate the degree of unusualness of this window with respect to the rest of the data. We identify the window with the highest likelihood ratio as our anomalous window, and 3) Monte Carlo Simulations: to ascertain whether this window is truly anomalous and not merely random occurrence, we perform hypothesis testing by computing a p-value using Monte Carlo Simulations. We present extensive experimental results in real world accident data sets for various highways with known issues (code and data available from [32], [27]). Additionally, we also perform comparisons with current approaches [18], [34] to show the efficacy of our approach. Our results show that our approach indeed is effective in identifying anomalous traffic accident windows along multiple intersecting highways.

Discovery of anomalous spatio‐temporal windows using discretized spatio‐temporal scan statistics

AbstractIn this paper, we address the discovery of anomalous spatio‐temporal windows using discretized spatio‐temporal scan (DSTS) Statistics. Anomalous spatio‐temporal window discovery is required in several key applications such as disease outbreaks in a region over a period of time, monitoring drinking water quality over time, identifying health risks to the population in a polluted region and urbanization patterns in a city, to name a few. In this paper, we address the issues arising out of the simultaneous effects of the properties of space and time in the discovery of anomalous windows. In such a framework, we identify (i) at what point in time the window changes, (ii) the spatial patterns of change over time, and (iii) a spatial extent in time which is completely or partially deviant with respect to the rest of the anomalous spatio‐temporal windows. None of the current approaches address all these issues in combination. We identify this knowledge keeping in mind the spatial and temporal autocorrelation, morphing shape of the window, and possible spatial or temporal discontinuities of the window. Subsequently, we perform experiments on several real‐world datasets, to validate our approach, while comparing with the established approaches. © 2011 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 2011