Article

An Effective Chemical Mechanical Polishing Fill Insertion Approach

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Abstract

To reduce chip-scale topography variation, dummy fill is commonly used to improve the layout density uniformity. Previous works either sought the most uniform density distribution or sought to minimize the inserted dummy fills while satisfying certain density uniformity constraint. However, due to more stringent manufacturing challenges, more criteria, like line deviation and outlier, emerge at newer technology nodes. This article presents a joint optimization scheme to consider variation, total fill, line deviation, outlier, overlap, and running time simultaneously. More specifically, first we decompose the rectilinear polygons and partition fillable regions into rectangles for easier processing. After decomposition, we insert dummy fills into the fillable rectangular regions optimizing the fill metrics simultaneously. We propose three approaches, Fast Median approach, LP approach, and Iterative approach, which are much faster with better quality, compared with the results of the top three contestants in the ICCAD Contest 2014.

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... Geometric structures such as the Voronoi diagram [29,30] and the Delaunay triangulation [5] partition the underlying space into regions based on proximity. There are various applications in chip manufacturing [19], geoinformatics [23], and pattern recognition [1,27]. ...
Preprint
We investigate the problem of partitioning a rectilinear polygon $P$ with $n$ vertices and no holes % with no holes into rectangles using disjoint line segments drawn inside $P$ under two optimality criteria. In the minimum ink partition, the total length of the line segments drawn inside $P$ is minimized. We present an $O(n^3)$-time algorithm using $O(n^2)$ space that returns a minimum ink partition of $P$. In the thick partition, the minimum side length over all resulting rectangles is maximized. We present an $O(n^3 \log^2{n})$-time algorithm using $O(n^3)$ space that returns a thick partition using line segments incident to vertices of $P$, and an $O(n^6 \log^2{n})$-time algorithm using $O(n^6)$ space that returns a thick partition using line segments incident to the boundary of $P$. We also show that if the input rectilinear polygon has holes, the corresponding decision problem for the thick partition problem using line segments incident to vertices of the polygon is NP-complete. We also present an $O(m^3)$-time $3$-approximation algorithm for the minimum ink partition for a rectangle containing $m$ point holes.
Chapter
The rectangular partitioning of a digital object, A (without holes) is presented here. The partitioning is obtained in such a way that the set of connected output rectangles are related to the straight skeleton of the corresponding digital object. The given digital object, A is imposed on background grid of size, g (say) and its inner isothetic cover, P is obtained which is the maximum area orthogonal polygon inside the digital object. The combinatorial rules are formulated to apply those on P to partition it into a set of rectangles such that it is related to the straight skeleton of P. The partitioning algorithm discussed here runs in where n being the number of pixels on the periphery of digital object and g being the grid size. The experimental result shows the efficiency of the algorithm.
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We investigate the problem of partitioning a rectilinear polygon P with n vertices and no holes into rectangles using disjoint line segments drawn inside P under two optimality criteria. In the minimum ink partition, the total length of the line segments drawn inside P is minimized. We present an O(n3)-time algorithm using O(n2) space that returns a minimum ink partition of P. In the thick partition, the minimum side length over all resulting rectangles is maximized. We present an O(n3log2⁡n)-time algorithm using O(n3) space that returns a thick partition using line segments incident to vertices of P, and an O(n6log2⁡n)-time algorithm using O(n6) space that returns a thick partition using line segments incident to the boundary of P. We also show that if the input rectilinear polygon has holes, the corresponding decision problem for the thick partition problem using line segments incident to vertices of the polygon is NP-complete. We also present an O(m3)-time 3-approximation algorithm for the minimum ink partition for a rectangle containing m point holes.
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Computing partitions of rectilinear polygons with minimum stabbing number
  • Stephane Durocher
  • Saeed Mehrabi