Voronoi Diagram of a Polygon in Chessboard Metric and Maskless Lithographic Applications Hayong Shin * , Eonjin Park ** , Deok-Soo Kim *** * Department of Industrial Engineering, KAIST, hyshin@kaist.ac.kr ** Department of Industrial Engineering, KAIST, parkeonjin@kaist.ac.kr *** Department of Industrial Engineering, Hanyang Univ., dskim@hanyang.ac.kr ABSTRACT Lithography using photomasks has been the major workhorse in printed circuit boards, semiconductors, and flat panel display device manufacturing. However, the cost of photomask is so high that it often becomes the bottleneck, especially when the production volume is low. Recently, maskless lithography technology is gaining more attention, and hence, the computation of efficient lithography path becomes of greater importance than ever in order to obtain high throughput of lithography process. The target machine in mind has a numerically controlled XY table on which a substrate is located and a variable size (square-shape) aperture in front of the light source. In this paper, we present an approach to direct lithography path generation using Voronoi diagram and medial axis transform in chessboard metric. The properties and construction method of Voronoi diagram of a polygonal object in chessboard metric is examined. Then, lithography path generation scheme is explained. The proposed idea can also be applied to the fabrication of photomask itself and the rapid prototyping of a 3D model via layered lithography. Keywords Chessboard metric, Voronoi diagram, Medial axis transform, Maskless lithography 1. Introduction Though lithography was originally invented as a precise printing method using a stone or metal plate at the end of 18 th century, it has been the workhorse in printed circuit board, VLSI, and flat panel display devices, and MEMS/NEMS device manufacturing. However, the cost and time of making the photomask used in optical projection lithography process is so large that it often becomes the major cost driver, especially when the production volume is low [1]. Recently, maskless lithography technology, which does not use physical photomask, is gaining more attention, and hence, the computation of efficient lithography path becomes of greater importance than ever in order to obtain high throughput of lithography process. Many types of maskless lithography equipments are being developed, including ZPAL of MIT [2] and HiRes-MLS of Ball Semiconductor [3]. Basically, maskless lithography is to selectively expose the desired region of substrate coated with photoresist by guiding the light with software control. The above mentioned maskless lithography equipments use scan-conversion type of region filling, with a big array of individually controlled light beams in order to achieve high-throughput productivity. Another type of maskless lithograph machine uses a vector-stroke type movement of light beam with varying aperture size. In this paper, we focus on the latter type machine, which has a numerically controlled XY table on which a substrate is located and a variable size aperture of square shape in front of the light source. This machine can also be used for the in-line repair of defects on flat panel display device such as LCD, PDP, or OLED. Another application can be found in the rapid prototyping of a 3D model via layered lithography. Though the basic task (region filling) is similar to that of pocket milling, the main differences are : (1) the light beam is of axis-aligned square shape, and (2) the size of square can vary continuously during the movement. Considering these differences, we found that L ∞ metric medial axis transform of the target polygonal region suits the purpose perfectly. Hereafter we will denote Voronoi diagram in L p metric by VD p , and medial axis transform in L p metric by MAT p . The next two sections are devoted to VD ∞ and MAT ∞ . Section 4 explains how to compute