Area Fill Generation With Inherent Data Volume Reduction

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Area Fill Generation With Inherent Data Volume
Reduction
Supported by Cadence Design Systems, Inc., NSF,
the Packard Foundation, and State of Georgias
Yamacraw Initiative
Yu Chen, Andrew B. Kahng, Gabriel Robins,
Alexander Zelikovsky and Yuhong Zheng (UCLA,
UCSD, UVA, GSU) http//vlsicad.ucsd.edu/
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CMP and Interlevel Dielectric Thickness

• Chemical-Mechanical Planarization (CMP)
• wafer surface planarization
• Uneven features cause polishing pad to deform

Post-CMP ILD thickness
Features

• Interlevel-dielectric (ILD) thickness ? feature
  density
• Insert dummy features to decrease variation

Post-CMP ILD thickness
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Fill Compression Problem

• Compressible Fill Generation Problem (CFGP)
• Given a design rule-correct layout, create the
  minimum number of GDSII AREFs to represent area
  fill features such that the window density
  variation is within the given bounds (L,U)

Filled layout with 82 area features
Original layout
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Fill Compression in Fixed-Dissection Regime

• Fixed CFGP in Fixed-Dissection Regime
• Given a design rule-correct layout consisting of
  tiles, the site arrays for each tile,
  and fill requirement for each tile, create
  the minimum number of AREFs to represent area
  fill features such that each tile contains
  exactly area fill features

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Linear Programming Based Methods

• Main idea
• Find minimum AREFs in free sites for given fill
  requirements
• Single-Tile Integer LP Formulations

site in position (p,q) in tile (i,j)
feasible AREF in layout
is covered by AREF
AREF is chosen
otherwise
otherwise
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Compressible Fill Generation with AREF

• Multiple-Tile Integer LP Formulations
• Ideally consider fill compression on entire
  layout at one time
• Multiple-tile compression as a tradeoff

• Ranged Fill Compression
• Exploit allowed range of fill features for each
  tile
• Single-Tile
• Multiple-Tile

for tiles
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Greedy Speedup Approaches

• Motivation of Speedup
• Strict greedy heuristic
• O(n4) time complexity
• Provide good solutions but is impractical
• Greedy speedup schemes
• Trade-off between time complexity and compression
  performance
• Pick acceptable AREFs instead of maximal AREFs

• Greedy Speedup Approach 1 (GS-1)
• Find the largest AREFs originating from each free
  site
• Pick the AREF that fills the maximum number of
  free sites but does not overfill the tiles if
  such an AREF exists
• Otherwise, select the maximum AREF from the
  largest AREFs, and take one of its sub-AREFs
  which do not overfill the tiles
• Time complexity of the algorithm is reduced to
  O(n3)

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Greedy Speedup Approaches (contd)

• Greedy Speedup Approach 2 (GS-2)
• Pick the acceptable AREFs originating from each
  free site
• Criteria of an acceptable AREF
• Size is smaller than K ? L
• Fill maximum free sites but does not overfill the
  tiles
• Time complexity of the algorithm is reduced to
  O(KLn2)

• GS-1 vs. GS-2
• Compared to GS-1, GS-2 achieves better tradeoff
  between compression results and time complexity.
  While KL ltlt n, GS-2 results are just 4 worse
  but 39 faster than GS-1 based on our
  experiments.
• GS-1 cannot guarantee better behavior with
  multiple-tile option than with single-tile option
  because the sets of the largest AREFs are
  different for the single-tile option and the
  multiple-tile option
• GS-2 does guarantee better behavior with
  multiple-tile option

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Experiments Greedy Speedup Approaches

• Greedy approach can achieves very large
  compression ratios, especially when the fill
  features are small
• GS-1 gets better results for single-tile than for
  multiple-tile
• GS-2 results are always better for multiple-tile
  than for single-tile

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Experiments Greedy Speedup Approaches

• GS-2 achieves better tradeoff between
  performance and runtime
• GS-2 is much faster than GS-1, with only small
  quality degradation

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Comparison of fill compression methods

• Performance of GS-1 is very close to optimal ILP
  method

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Conclusions Future Works

• Contributions
• New compressed fill strategies with AREF to
  reduce data volume
• Linear programming based methods
• Greedy based optimization methods

• Future Works
• Improve compression ratios and scalability
• Exploit new standard layout format
• Open Artwork System Interchange Standard (OASIS)
• Compressible fill generation problem with
  underlying layout hierarchy

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Thank You!