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Compression Schemes for "Dummy Fill" VLSI Layout Data

Robert Ellis, Andrew B. Kahng and Yuhong Zheng

( Texas A&M University and UCSD) ( Texas A&M University and UCSD)

http://vlsicad.ucsd.eduhttp://vlsicad.ucsd.edu

Supported by MARCO GSRC

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

Post-CMP ILD thicknessFeatures

CMP and Dummy Fill

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

Dummy features Post-CMP ILD thickness

Dummy feature explodes layout data volume, creates a bottleneck in the design-to-manufacturing handoff

Dummy fill data compression is required

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Fill Compression Problem

1 1 0 0 0 0 0 00 0 0 0 0 1 1 11 0 1 0 0 0 0 01 0 0 0 0 0 0 01 0 0 0 0 0 0 11 0 0 0 0 0 0 10 0 1 0 0 0 1 10 0 1 1 1 1 0 1

Compressed Layout Data

1: With features 0: Without features

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

Problem: Given a 0-1 matrix B [mn] digitized from a dummy fill layout, compress it with the objective of minimizing output data size h Compression ratio r = mn/h One-sided loss

• Limited loss can improve compressibility• Asymmetric loss:

• 10 okay! (fill geometry disappears); • 01 not allowed (fill geometry appears)

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General Flow for Compression Heuristics

Segment data matrix into blocks

Loss allowed?

Applied one-sided loss to original data matrix

Perform lossless compression on data matrix

END

YesNo

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Our Contribution

New compression heuristic algorithms on JBIG methods• JBIG1• JBIG2-Pattern Matching and Substitution (PM&S)• JBIG2-Soft Pattern Matching (SPM)

Two loss mechanisms• Proportional loss: relative fraction of 1’s allowed to be

changed to 0’s• Fixed “speckle” loss: absolute number of 1’s allowed to

be changed to 0’s

Asymmetric cover method that comprehends one-sided loss and improves the compression ratio

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General Flow for Compression Heuristics

Segment data matrix into blocks

Loss allowed?

Perform lossless compression (JBIG1, JBIG2 PM&S, and JBIG2 SPM) on data matrix

END

YesNo

Applied one-sided loss to original data matrix

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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 PM&S

PM&S: 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

Segment data matrix into blocks

Loss allowed?

Asymmetric cover heuristic for one-sided loss

Perform lossless compression (JBIG1, JBIG2 PM&S, and JBIG2 SPM) on data matrix

END

YesNo

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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 1’s can be changed to 0’s, yet 0’s can not be changed to 1’s

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

Fixed speckle loss

JBIG* lossless

components

JBIG2 PM&S

JBIG2 SPM (lossless)

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

Asymmetric cover heuristic for one-sided loss

Perform lossless compression (JBIG1, JBIG2 PM&S, and JBIG2 SPM) on data matrix

END

Yes

No•(A2.2)

•(A2.3)

•(A3)•Exclude Singleton (A2, A3)

•JBIG2 PM&S (A2, A3)

•Dictionary Compression using JBIG1 (A2, A3)

•JBIG2 SPM (A2)

Loss allowed?

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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 casesLarge loss yields better compression ratios.

Compression ratio of fill compression heuristics

0

20

40

60

80

100

1 2 3 4 5Test cases

Com

pres

sion

rat

io

Bzip2

A1

A2.1

A2.2@20%loss

A2.2@40%loss

A3@20%loss

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Dictionary Fits SREFs 111000101111000111111000111000101000000101000000101000101000000111000000101000000

101000101101000101101000101000101000000101000000101000101000000101000000101000000

loss

Dictionary entrySREF

F

F’

M

M’

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Geometry Compression Operators

TYPE 1TYPE 2

TYPE 3

equivalent to “GDSII AREF”

TYPE 4

TYPE 5

TYPE 6

TYPE 7

TYPE 8

equivalent to “GDSII SREF”

OASIS Repetition Types

Original layout Filled layout with area features in 9 repetitions

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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!Thank You!

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Experimental Results (Cont’d)Run time of fill compression heuristics

0100200300400500600700

1 2 3 4 5Test cases

Run

time

(s)

Bzip2

A1

A2.1

A2.2@20%loss

A2.2@40%loss

A3@20%loss

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 k=0.2 and 10.3 longer with k=0.4.