Planarization of metal layers in a chip based on Voronoi diagram
01 Dec 2012-pp 1-4
TL;DR: A Voronoi diagram-based tessellation for better selection of the positions where metal fills need to be inserted to improve the uniformity criteria is proposed and compared with an existing Monte-Carlo based fast heuristic using windows on ISCAS'85 benchmarks.
Abstract: Dummy metal fills are inserted in the upper metal layers of a chip to restore planarity of the metal layers and to ensure mechanical robustness of the chip, thereby its performance Existing tile and window-based metal fill synthesis techniques typically check the metal density of a layer within a square tile window, insert dummy metal shapes in the tile if required, and shift the window by a distance related to the side of the tile to cover the entire layer As a large number of window positions have to be checked for accuracy, these window based approaches are not efficient In this paper, we propose a Voronoi diagram-based tessellation for better selection of the positions where metal fills need to be inserted to improve the uniformity criteria Our method is compared with an existing Monte-Carlo (MC) based fast heuristic using windows on ISCAS'85 benchmarks Experimental results demonstrate that our method guarantees the same minimum metal density with smaller variation in metal density variation and less coupling capacitance between the metals
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01 Jan 1992
TL;DR: In this paper, the Voronoi diagram generalizations of the Voroni diagram algorithm for computing poisson Voroni diagrams are defined and basic properties of the generalization of Voroni's algorithm are discussed.
Abstract: Definitions and basic properties of the Voronoi diagram generalizations of the Voronoi diagram algorithms for computing Voronoi diagrams poisson Voronoi diagrams spatial interpolation models of spatial processes point pattern analysis locational optimization through Voronoi diagrams.
133 citations
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Book•
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01 Jan 1969
16,023 citations
"Planarization of metal layers in a ..." refers background in this paper
...The geometric dual graph [9] of the Voronoi diagram is a triangulated graph, with the points in S as vertices....
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TL;DR: The Voronoi diagram as discussed by the authors divides the plane according to the nearest-neighbor points in the plane, and then divides the vertices of the plane into vertices, where vertices correspond to vertices in a plane.
Abstract: Computational geometry is concerned with the design and analysis of algorithms for geometrical problems. In addition, other more practically oriented, areas of computer science— such as computer graphics, computer-aided design, robotics, pattern recognition, and operations research—give rise to problems that inherently are geometrical. This is one reason computational geometry has attracted enormous research interest in the past decade and is a well-established area today. (For standard sources, we refer to the survey article by Lee and Preparata [19841 and to the textbooks by Preparata and Shames [1985] and Edelsbrunner [1987bl.) Readers familiar with the literature of computational geometry will have noticed, especially in the last few years, an increasing interest in a geometrical construct called the Voronoi diagram. This trend can also be observed in combinatorial geometry and in a considerable number of articles in natural science journals that address the Voronoi diagram under different names specific to the respective area. Given some number of points in the plane, their Voronoi diagram divides the plane according to the nearest-neighbor
4,236 citations
"Planarization of metal layers in a ..." refers background in this paper
...the Voronoi diagram are called Voronoi edges, and the corner points of Voronoi cells where Voronoi edges meet are called Voronoi vertices [7][8]....
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Book•
01 Jan 1992TL;DR: In this article, the Voronoi diagram generalizations of the Voroni diagram algorithm for computing poisson Voroni diagrams are defined and basic properties of the generalization of Voroni's algorithm are discussed.
Abstract: Definitions and basic properties of the Voronoi diagram generalizations of the Voronoi diagram algorithms for computing Voronoi diagrams poisson Voronoi diagrams spatial interpolation models of spatial processes point pattern analysis locational optimization through Voronoi diagrams.
4,018 citations
TL;DR: The authors achieve near-optimal filling for flat layouts with respect to each of these objectives, and indicate that the hybrid hierarchical filling approach is efficient, scalable, accurate, and highly competitive with existing methods for hierarchical layouts.
Abstract: Chemical-mechanical polishing (CMP) and other manufacturing steps in very deep submicron very large scale integration have varying effects on device and interconnect features, depending on local characteristics of the layout. To improve manufacturability and performance predictability, the authors seek to make a layout uniform with respect to prescribed density criteria, by inserting "area fill" geometries into the layout. In this paper, they make the following contributions. First, the authors define the flat, hierarchical, and multiple-layer filling problems, along with a unified density model description. Secondly, for the flat filling problem, they summarize current linear programming approaches with two different objectives, i.e., the Min-Var and Min-Fill objectives. They then propose several new Monte Carlo-based filling methods with fast dynamic data structures. Thirdly, they give practical iterated methods for layout density control for CMP uniformity based on linear programming, Monte Carlo, and greedy algorithms. Fourthly, to address the large data volume and inherent lack of scalability of flat layout density control, the authors propose practical methods for hierarchical layout density control. These methods smoothly trade off runtime, solution quality, and output data volume. Finally, they extend the linear programming approaches and present new Monte Carlo-based methods for the multiple-layer filling problem. Comparisons with previous filling methods show the advantages of the new iterated Monte Carlo and iterated greedy methods for both flat and hierarchical layouts and for both density models (spatial density and effective density). The authors achieve near-optimal filling for flat layouts with respect to each of these objectives. Their experiments indicate that the hybrid hierarchical filling approach is efficient, scalable, accurate, and highly competitive with existing methods (e.g., linear programming-based techniques) for hierarchical layouts.
82 citations
"Planarization of metal layers in a ..." refers background or methods in this paper
...In [1], square shapes are suggested, and later on in [2], guidelines on choice of fill size, and the number of fill rows and columns are given, but the same fill insertion algorithm as in [1] is followed....
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...The authors in [1] worked on two objectives separately: (i) minimizing variation of metal density with a upper bound on density, and (ii) minimizing the amount of fills used to maintain metal density within a certain range....
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...However, algorithms for determining the locations of fills are merely a handful [1]....
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...In [1], different types of algorithms have been applied for determining the locations of metal fills....
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...in [1] formulated the metal filling problem to determine the locations of fills in tile-window based fixed dissection scenario....
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TL;DR: The concept of design-driven fill synthesis that seeks to optimize CMP fill with respect to objectives beyond mere density uniformity is discussed, which minimizes the impact of C MP fill on design performance and parametric yield while still satisfying the density criteria that are motivated by manufacturing models.
Abstract: We survey recent research and practice in the area of chemical-mechanical polishing (CMP) fill synthesis, in terms of both problem formulations and solution approaches We review the CMP as the planarization technique of choice for multilevel very large-scale integration metallization processes Post-CMP wafer topography varies according to pattern density We review density-analysis methods and density-control objectives that are used in today's fill-synthesis algorithms In addition, we discuss the concept of design-driven fill synthesis that seeks to optimize CMP fill with respect to objectives beyond mere density uniformity Design-driven fill synthesis minimizes the impact of CMP fill on design performance and parametric yield while still satisfying the density criteria that are motivated by manufacturing models We conclude with a discussion of where CMP fill synthesis may be naturally integrated within future design and manufacturing flows
81 citations
"Planarization of metal layers in a ..." refers background or methods in this paper
...We address the filling problem by inserting floating dummy fills with rectangular shape, which outperforms other shapes [2]....
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...Analysis of several guidelines [2] for reducing coupling effect of metal filling reveals that while runtime increases for finding appropriate positions of fills with reduced coupling effect, accuracy in terms of uniformity may need to be sacrificed to achieve such reduction....
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...The paper [2] shows that rectangular fill shape outperforms other shapes in minimizing the effect on interconnect capacitance....
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...In [1], square shapes are suggested, and later on in [2], guidelines on choice of fill size, and the number of fill rows and columns are given, but the same fill insertion algorithm as in [1] is followed....
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