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Area Fill Generation With

Inherent Data Volume Reduction

Yu Chen, Andrew B. Kahng, Gabriel Robins, Yu Chen, Andrew B. Kahng, Gabriel Robins,

Alexander Zelikovsky and Yuhong ZhengAlexander Zelikovsky and Yuhong Zheng

(UCLA, UCSD, UVA, GSU)(UCLA, UCSD, UVA, GSU)

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

Supported by Cadence Design Systems, Inc.,Supported by Cadence Design Systems, Inc.,NSF, the Packard Foundation, and NSF, the Packard Foundation, and

State of Georgia’s Yamacraw InitiativeState of Georgia’s Yamacraw Initiative

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CMP and Interlevel Dielectric Thickness

Chemical-Mechanical Planarization (CMP) = wafer surface planarization

Uneven features cause polishing pad to deform

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

Post-CMP ILD thicknessFeatures

Area fillfeatures

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)

Original layout Filled layout with 82 area features

Filled layout with area features in 9 AREFs

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Fill Compression in Fixed-Dissection Regime

Original layout infixed-dissection regime

windows

tile

Tile with original featuresGrid the tile with feature size Satisfy fixed fill requirement (e.g., 56fill features) with minimum number of AREFs (e.g., 4 AREFs)

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

nm

ijT ijF

ijF

Tile with original featuresGrid the tile with feature size Satisfy ranged fill requirement (e.g., 50 ~ 60 fill features) with minimum number of AREFs (e.g., 3 AREFs)

),( ijij UBLBnm

),( ijij UBLBijT

Ranged CFGP in Fixed-Dissection Regime Given a design rule-correct layout consisting of tiles, the

site arrays for each tile, and fill requirement range for each tile, create the minimum number of AREFs to represent area fill features such that each tile contains a number of area fill features in the range

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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

0

1pqs

0

1a

pqijS , site in position (p,q) in tile (i,j) A feasible AREF in layout

is covered by AREFpqijS ,

otherwise otherwiseAREF is chosen A

AREFsfeasibleall

a

1

0

1

0

k

p

l

qpqij sF

pqseringAREFsall

pq ascov

0pqs pqijS ,if is occupied by original features

pqseringAREFsall

pqpq asncov

Minimize:

# covered slack sites = given # fill features

all sites covered by AREF are filled

only the sites covered by AREF can be filled

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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

1)1(

'

1)1(

''' 1,,1;1,,0

ki

kip

lj

Bjqqpij BjAisF for tilesBA

Ranged Fill Compression Exploit allowed range of fill features for each tile

Single-Tile

Multiple-Tile

1

0

1

0

k

p

l

qijpqij UBsLB

1)1(

'

1)1(

''' 1,,1;1,,0

ki

kipij

lj

Bjqqpij BjAiUBsLB for tilesBA

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Greedy Speedup Approaches

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)

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

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Greedy Speedup Approaches (cont’d)

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 K·L << 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 Compression Ratios: GS-1 vs. GS-2

0

5

10

15

20

25

30

35

Testcases

Co

mp

res

sio

n R

ati

oGS-1 Ranged Single-Tile GS-2 Ranged Single-Tile GS-1 Ranged Multiple-Tile GS-2 Ranged Multiple-Tile

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

Run Time: GS-1 vs. GS-2

1

10

100

1000

10000

100000

T1/1500 T1/1000 T1/500 T1/250 T2/1500 T2/1000 T2/500 T2/250 T3/1500 T3/1000 T3/500 T3/250

Test cases

Ru

n T

ime

GS-1 Ranged Single-Tile GS-2 Ranged Single-Tile GS-1 Ranged Multiple-Tile GS-2 Ranged Multiple-Tile

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Comparison of fill compression methodsPerformance of the fill compression methods

0

1000

2000

3000

4000

5000

6000

7000

T1/80K/4/1500 T2/80K/4/1500 T3/80K/4/1500 T4/12K/4/200 T5/12K/4/200 T6/12K/4/200

Testcases

# o

f A

RE

Fs

Fixed Fill: ILP Fixed Fill: GS-1 Fixed Fill: GS-2 Ranged Fill: ILP Ranged Fill: GS-1 Ranged Fill: GS-2

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

GS-1 is more efficient in run time than ILP method

Run time of the fill compression methods

1

10

100

1000

10000

100000

T1/80K/4/1500 T2/80K/4/1500 T3/80K/4/1500 T4/12K/4/200 T5/12K/4/200 T6/12K/4/200

Test cases

Ru

n t

ime

Fixed Fill: ILP Fixed Fill: GS-1 Fixed Fill: GS-2 Ranged Fill: ILP Ranged Fill: GS-1 Ranged Fill: GS-2

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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!Thank You!