THE L<sub>∞</sub> VORONOI DIAGRAM OF SEGMENTS AND VLSI APPLICATIONS

Papadopoulou, Evanthia; Lee, D. T.

doi:10.1142/s0218195901000626

Cited by 48 publications

(50 citation statements)

References 15 publications

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“…The Voronoi diagram for open faults is a combinatorial structure interesting on its own right. Once the opens Voronoi diagram on a given layer is available the entire critical area integral can be computed analytically, in linear time, using the formulas given in [16,20,22].…”

Section: A Grid Based Methods Introduced Inmentioning

confidence: 99%

“…Once Voronoi regions of the opens Voronoi diagram are available, the critical area integral is extracted using the formulas given in [16,20,22]. Since this is a known technique presented in previous literature we refer the reader to [16,20,22] and we skip discussion in this paper.…”

Section: A Grid Based Methods Introduced Inmentioning

confidence: 99%

“…Since this is a known technique presented in previous literature we refer the reader to [16,20,22] and we skip discussion in this paper.…”

Section: A Grid Based Methods Introduced Inmentioning

confidence: 99%

“…The Voronoi method [5,16,18,20,22,28] which is using analytical formulas to extract the entire critical area after deriving a subdivision of the layout into regions that reveal the critical radius (size of smallest defect) of every point. The critical area integral is typically computed with no error in a single pass of the layout using O(n log n ) type of scan line algorithms.…”

Section: Iterative Shape-shifting Techniques That Compute A(r ) For Smentioning

confidence: 99%

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Net-Aware Critical Area Extraction for Opens in VLSI Circuits Via Higher-Order Voronoi Diagrams

Papadopoulou

2011

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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We address the problem of computing critical area for open faults (opens) in a circuit layout in the presence of multilayer loops and redundant interconnects. The extraction of critical area is the main computational bottleneck in predicting the yield loss of a VLSI design due to random manufacturing defects. We first model the problem as a geometric graph problem and we solve it efficiently by exploiting its geometric nature. To model open faults we formulate a new geometric version of the classic min-cut problem in graphs, termed the geometric min-cut problem. Then the critical area extraction problem gets reduced to the construction of a generalized Voronoi diagram for open faults, based on concepts of higher order Voronoi diagrams. The approach expands the Voronoi critical area computation paradigm [5, 16-19, 22, 28] with the ability to accurately compute critical area for missing material defects even in the presence of loops and redundant interconnects spanning over multiple layers. The generalized Voronoi diagrams used in the solution are combinatorial structures of independent interest. Report Info Published June 2010Number USI-INF-TR-2010-6 Institution Faculty of Informatics Università della Svizzera italiana Lugano, SwitzerlandOnline Access www.inf.usi.ch/techreports IntroductionCatastrophic yield loss of integrated circuits is caused to a large extent by random particle defects interfering with the manufacturing process resulting in functional failures such as open or short circuits. Yield loss due to random manufacturing defects has been studied extensively in both industry and academia and several yield models for random defects have been proposed (see e.g., [8,25,26]). The focus of all models is the concept of critical area, a measure reflecting the sensitivity of a design to random defects during manufacturing. Reliable critical area extraction is essential for today's IC manufacturing especially when DFM (Design for Manufacturability) initiatives are under consideration. The critical area of a circuit layout on a layer A is defined aswhere A(r ) denotes the area in which the center of a defect of radius r must fall in order to cause a circuit failure and D(r ) is the density function of the defect size. The defect density function has been estimated as follows [8,12,25,29]:where p,q are real numbers (typically p = 3,q = 1), c = (q + 1)(p − 1)/(q + p ), and r 0 is some minimum optically resolvable size. Using typical values for p,q , and c , the widely used defect size distribution is derived, 1

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Section: A Grid Based Methods Introduced Inmentioning

confidence: 99%

Section: A Grid Based Methods Introduced Inmentioning

confidence: 99%

“…Since this is a known technique presented in previous literature we refer the reader to [16,20,22] and we skip discussion in this paper.…”

Section: A Grid Based Methods Introduced Inmentioning

confidence: 99%

Section: Iterative Shape-shifting Techniques That Compute A(r ) For Smentioning

confidence: 99%

See 2 more Smart Citations

Net-Aware Critical Area Extraction for Opens in VLSI Circuits Via Higher-Order Voronoi Diagrams

Papadopoulou

2011

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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“…Our motivation for studying the min-max Voronoi diagram comes from an application in VLSI yield prediction, in particular the estimation of critical area, a measure reflecting the sensitivity of a VLSI design to spot defects during manufacturing [7,8,9,11,13]. In [12,11] the critical area computation problem for shorts, opens, and via-blocks was reduced to variations of L ∞ Voronoi diagrams of segments.…”

Section: Introductionmentioning

confidence: 99%

The Min-Max Voronoi Diagram of Polygons and Applications in VLSI Manufacturing

Papadopoulou¹,

Lee

2002

Algorithms and Computation

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Abstract. We study the min-max Voronoi diagram of a set S of polygonal objects, a generalization of Voronoi diagrams based on the maximum distance between a point and a polygon. We show that the min-max Voronoi diagram is equivalent to the Voronoi diagram under the Hausdorff distance function. We investigate the combinatorial properties of this diagram and give improved combinatorial bounds and algorithms. As a byproduct we introduce the min-max hull which relates to the minmax Voronoi diagram in the way a convex hull relates to the ordinary Voronoi diagram.

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