CMP and Dummy Fill

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Supported by MARCO GSRC
Compression Schemes for "Dummy Fill" VLSI Layout
Data
Robert Ellis, Andrew B. Kahng and Yuhong Zheng (
Texas AM University and UCSD) http//vlsicad.ucs
d.edu
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Outline

• Dummy Fill and Fill Compression Problem
• Our Contributions
• JBIG Standards
• Loss/Lossless Compression Algorithms
• Experimental Results
• Conclusion and Future Research

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CMP and Dummy Fill

• Uneven features cause polishing pad to deform in
  Chemical-Mechanical Polishing (CMP)

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

• Dummy feature explodes layout data volume,
  creates a bottleneck in the design-to-manufacturin
  g handoff
• Dummy fill data compression is required

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Fill Compression Problem

• A fill pattern can be expressed as a binary (0-1)
  matrix

Problem Given a 0-1 matrix B m?n digitized
from a dummy fill layout, compress it with the
objective of minimizing output data size h
Compression ratio r m?n/h

• One-sided loss
• Limited loss can improve compressibility
• Asymmetric loss
• 1?0 okay! (fill geometry disappears)
• 0?1 not allowed (fill geometry appears)

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General Flow for Compression Heuristics
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Our Contribution

• New compression heuristic algorithms on JBIG
  methods
• JBIG1
• JBIG2-Pattern Matching and Substitution (PMS)
• JBIG2-Soft Pattern Matching (SPM)
• Two loss mechanisms
• Proportional loss relative fraction of 1s
  allowed to be changed to 0s
• Fixed speckle loss absolute number of 1s
  allowed to be changed to 0s
• Asymmetric cover method that comprehends
  one-sided loss and improves the compression ratio

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General Flow for Compression Heuristics
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JBIG Standard

• JBIG (Joint Bi-level Image Experts Group) is an
  experts group of ISO, IEC and CCITT (JTC1/SC2/WG9
  and SGVIII). Its goal is to define a compression
  standard for bi-level image coding
• JBIG1 international standard for lossless
  compression of bi-level images (ITU-T T.82)
  (1993)
• JBIG2 the first International standard that
  provides for both lossless and lossy compression
  of bi-level images (1999)
• JBIG methods are based on Arithmetic Coding and
  Context-based Statistical Modeling

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JBIG2 PMS

• PMS Pattern Matching and Substitution
• Dictionary reference blocks that used to match
  data blocks
• Extract and encode repeatable patterns

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JBIG2 SPM

• SPM Soft Pattern Matching
• Dictionary reference blocks that used to match
  and coding data blocks
• Estimate bits probabilities based on data block
  and matched reference block, codes data in
  arithmetic coding

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Dictionary Construction

• To achieve better compression ratio
• Dictionary should contain as few reference
  blocks as possible to match a much larger number
  of data blocks
• Reference indices (pointing from data blocks to
  reference blocks) as shorter as possible
• Removing singletons from the dictionary will
  reduce the size of dictionary
• Asymmetric cover approach is applied to construct
  a dictionary for loss compression

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General Flow for Compression Heuristics
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Asymmetric Cover Heuristic

• The problem of building a cover for a set of data
  blocks is an instance of the Set Cover Problem
  (SCP)
• Asymmetric cover allows number of 1s can be
  changed to 0s, yet 0s can not be changed to 1s
• Our heuristic for constructing cover views the
  data blocks as vertices of a graph with edge
  weights defined as
• w(D1, D2) min(t(D1) HD(D1, D1 D2),
  t(D2)-HD(D2, (D1 D2))
• D data block, bit-wise AND t(D) the
  total allowable loss for D
• D1 and D2 covered by the same cover iff w(D1, D2)
  ? 0
• Cover D D1 D2.

Clustering data blocks 111111 and 111101
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Description of Algorithm Pieces
Index Description A1 A2.1 A2.2 A2.3 A3
  Benchmark Compress matrix using JBIG1 ?
  Loss introduction Proportional loss ? ?
  Loss introduction Fixed speckle loss ?
JBIG lossless components JBIG2 PMS ? ? ? ?
JBIG lossless components JBIG2 SPM (lossless) ? ? ?
JBIG lossless components Singleton exclusion singleton data blocks compression by JBIG1 ? ? ? ?
Compress dictionary JBIG1 on reference blocks compression ? ? ? ?
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General Compression Algorithm
Segment data matrix into blocks
Yes

• (A2.2)

No
Asymmetric cover heuristic for one-sided loss

• (A2.3)

• (A3)

• Exclude Singleton
• (A2, A3)

Perform lossless compression (JBIG1, JBIG2 PMS,
and JBIG2 SPM) on data matrix

• JBIG2 PMS (A2, A3)

• JBIG2 SPM (A2)

• Dictionary Compression using JBIG1 (A2,
  A3)

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Experimental Results

• A2.1 is the best lossless fill compression
  methods, with an average of 29.93 improvement to
  the Bzip2
• A1 gives competitive compresstion ratios, with an
  average of 28.7 improvement to the Bzip2
• A2.2 and A3 performs similar in all test cases
• Large loss yields better compression ratios.

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Dictionary Fits SREFs
111000101 111000111 111000111 000101000 000101000
000101000 101000000 111000000 101000000
M
F
loss
101000101 101000101 101000101 000101000 000101000
000101000 101000000 101000000 101000000
M
F
Dictionary entry
SREF
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Geometry Compression Operators
OASIS Repetition Types
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Conclusion and Future Research

• We have implemented algorithms based on JBIG
  methods in combination with the new concept of
  one-sided loss to compress binary data files of
  dummy fill features.
• JBIG1 is quite effective. Our new heuristics
  A2-A3 and the fixed speckle loss heuristic offer
  better compression with slower runtime,
  especially as data files become larger
• Ongoing research examines synergies between fill
  generation and compression, as well as
  compression techniques that exploit constructs in
  the GDSII standard (AREF and SREF) and the new
  OASIS format (8 repetitions) for layout data.

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Thank You!
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Experimental Results (Contd)

• For lossless compression, A1 is the most
  cost-effective method, taking only 2.7? longer
  than Bzip2 on average. A2.1 is nearly as cost
  effective, but takes 5.9? longer than Bzip2 on
  average.
• A3 is the most cost-effective proportional loss
  method, taking 3.7 ? longer than Bzip2 on
  average. The running time of A2.2 is 9.4 ? longer
  than Bzip2 on average with proportional loss
  ratio k0.2 and 10.3 ? longer with k0.4.