272 IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 21, NO. 2, MAY 2008 Classification of Defect Clusters on Semiconductor Wafers Via the Hough Transformation K. Preston White, Jr., Senior Member, IEEE, Bijoy Kundu, and Christina M. Mastrangelo Abstract—The Hough transformation employing a normal line-to-point parameterization is widely applied in digital image processing for feature detection. In this paper, we demonstrate how this same transformation can be adapted to classify defect signatures on semiconductor wafers as an aid to visual defect metrology. Given a rectilinear grid of die centers on a wafer, we demonstrate an efficient and effective procedure for classifying defect clusters composed of lines at angles of 0 , 45 , 90 , and 135 from the horizontal, as well as adjacent compositions of such lines. Included are defect clusters representing stripes, scratches at arbitrary angles, and center and edge defects. The principle advantage of the procedure over current industrial practice is that it can be fully automated to screen wafers for further engineering analysis. Index Terms—Defect metrology, Hough transformation, image processing, process control, spatial defect analysis and classifica- tion, wafer maps. I. INTRODUCTION V ISUAL defect metrology is an in-line process-monitoring technique used to assess process capability in semicon- ductor manufacturing. It is well known that spatial patterns in the distribution of defects on a die can be related to the potential causes of these defects in the manufacturing process. Given the considerable time, effort, and expense of detecting and classi- fying spatial defect signatures manually, there has been consid- erable interest over the past decade in automating the process (Chen and Liu [1], Gleason et al. [2], Hansen and Thyregod [3], Jun et al. [4], Karnowski et al. [5], Ken et al. [6], Tobin et al. [7], Shankar and Zhong [8], Hwang and Kuo [9], Wang et al. [10], and Yuan and Kuo [11]). In this paper, we demonstrate how a well-known, pattern- recognition algorithm can be incorporated into visual defect metrology systems to improve process control. Specifically, we develop a procedure that can be used to classify clusters of de- fective die on semiconductor wafer. This procedure builds upon the defect clustering methodology developed by Kundu et al. [12]–[14], which integrates a test for spatial randomness [15], [16] with filtering [17] and clustering algorithms [18] to reduce the number of wafers and die that must be analyzed. The pro- cedure then applies the Hough transformation (HT) [19], [20] Manuscript received September 5, 2006; revised December 20, 2007. K. P. White, Jr., is with the Department of Systems and Information Engi- neering, University of Virginia, Charlottesville, VA 22904-4747 USA. B. Kundu is with the Department of Radiology, University of Virginia, Char- lottesville, VA 22904 USA. C. M. Mastrangelo is with the Department of Industrial Engineering, Univer- sity of Washington, Seattle, WA 98195-2650 USA. Digital Object Identifier 10.1109/TSM.2008.2000269 for spatial pattern recognition and a frequency count to iden- tify lines or sets of lines which represent stripes, scratches, and center and edge defects. Section II provides a brief tutorial on parameter planes and a description of the HT. In Section III we describe the classifi- cation procedure incorporating the HT algorithm for scratches at arbitrary angles on semiconductor wafers. The applicability of the procedure to other types of defect clusters is explored in Section IV. Section V provides the conclusions of this research. II. HOUGH TRANSFORMATION The HT figures prominently in digital image processing. Originally proposed by Hough in 1959, the HT can be applied to detect arbitrary shapes in images, given a parameterized description of the shape in question. Specifically as applied in this research, the HT is used to detect collinear arrangement of defective die on a semiconductor wafer. The motivating idea behind the HT for line detection is that each input measurement (e.g., coordinate point) indicates its contribution to a globally consistent solution (e.g., the physical line which gave rise to that image point). A. -Parameter Plane To understand the HT, we need first to introduce the con- cept of a parameter plane (or parameter space) for an analytical function. As throughout in this research, we restrict our consid- eration here to the simplest (but most useful) case of a straight line. Consider a fixed point defined in terms of its Carte- sian coordinates in the -plane. Any line through this point is the set of all points in the -plane (1) where and , respectively, are the slope and intercept of , as shown in Fig. 1. Note that the slope-intercept parameter pair uniquely defines this line, while the fixed point serves to define a fixed relationship the between these two parameters such that the line includes this point. Thus, the line in the -plane is completely defined by the single point in the slope-intercept or parameter plane, as shown in Fig. 1(b). The economy of description provided by this line-to-point transformation is the basis for its usefulness. Now consider a (possibly infinite) set of lines, all of which intersect at the fixed point (2) 0894-6507/$25.00 © 2008 IEEE