Efficient Process-Hotspot Detection Using Range Pattern Matching in Routing Stage

1
Efficient Process-Hotspot Detection UsingRange
Pattern Matching in Routing Stage

• Hailong Yao1 Subarna Sinha2 Charles
  Chiang2
• Xianlong Hong1 Yici Cai1
• 1Department of Computer Science and Technology
• Tsinghua University, Beijing, P.R. China
• 2Synopsys ATG, Mountain View, CA
• This work is done during the authors internship
  at Synopsys ATG

2
Outline

• Motivation
• Range Patterns and Matching
• Process-Hotspot Detection System
• Experimental Results
• Conclusion

3
Motivation

• Manufacturability-aware physical design is
  becoming a necessity
• Certain layout configurations susceptible to
  stress and lithographic process fluctuations
  affect yield
• Process-hotspots layout configurations most
  susceptible to process issues
• Remove process-hotspots and replace them with
  more yield-friendly configurations

4
Limitations of Recommended Rules

• Fabs use design rules (like recommended rules) to
  represent process-hotspots
• Limitations
• Some effects are non-local
• Difficult to represent relationships between
  large group of non-neighboring objects with a
  small set of rules
• Explosion of design rules slows down the router
• DRC tools are being supplemented with accurate
  process simulators (for instance, for lithography)

5
Limitations of Process Models

• Lida Huang, et al at DAC04 1 and J. Mitra, et
  al at DAC05 2 proposed embedding an aerial
  image simulator in the router to identify
  process-hotspots
• Limitations
• Lack of knowledge of downstream steps and
  over-estimation of process-hotspots
• Huge computational expense

1 L.-D. Huang and M. D. F. Wong, Optical
proximity correction (OPC)-friendly maze
routing, In DAC, pages 186191, June 2004. 2
J. Mitra, P. Yu, and D. Z. Pan, RADAR Ret-aware
detailed routing using fast lithography
simulations, In DAC, pages 369372, June 2005.
6
Represent Process-hotspots with Patterns

• A good representation of process-hotspots would
  be a 2D layout of rectangles, i.e. a pattern
• Can be built off-line using test-structures or
  more accurate simulation tools
• Process-hotspot detection during routing would
  complement current advances in yield enabling
  steps

7
Why Range Pattern?

• Layouts/patterns are quite similar with minor
  variations
• Exact pattern multiple similar patterns
• Range pattern a group of similar layouts with
  allowable variations in length, width and/or
  spacing
• Ranges on the pattern parameters enable compact
  representation

S1?S2
8
Process-hotspot Detection

• Collaborate with a fab or in-house accurate
  simulation and mask synthesis flows to build
  range patterns
• Score the patterns in the set based on yield
  impact
• Scores can be used by the router to give higher
  priority during correction
• Represent process-hotspots as a library of range
  patterns
• Process-hotspot detection find all the locations
  where the layout is identical to one of the
  patterns contained in a range pattern

9
Outline

• Motivation
• Range Patterns and Matching
• Range Pattern Definitions
• Layout Representation
• Range Pattern Representation
• Process-Hotspot Detection System
• Experimental Results
• Conclusion

10
Range Pattern Definitions

• Range pattern DRC-correct two-dimensional layout
  of rectangles with additional specifications
• Widths and lengths of the rectangles can vary
  within certain user-specified bounds
• Spacings between pairs of rectangles can vary
  within certain user-specified bounds
• Optimal widths and lengths of the rectangles and
  optimal spacings between pairs of rectangles can
  be specified
• Constraints can be specified over linear
  combinations of the widths, lengths and spacings
  of the rectangles

11
Range Pattern Example
Rectangle 1
Rectangle 2
Rectangle 3

• Range pattern Staircase with the following
  specifications
• Optimal width of each rectangle 90 nm
• Optimal spacing between adjacent rectangles 90
  nm
• Range of width of all rectangles (90, 150) nm
• Range of spacing between adjacent rectangles
  (90, 150) nm
• Range of length of central rectangle (200, 500)
  nm
• Distance between the right edge of rectangle 1
  and the left edge of rectangle 3 cannot exceed 50
  nm
• A range pattern contains a multitude of exact
  patterns

12
Range Pattern Matching Problem

• The Range Pattern Matching (RPM) problem
• Given a layout and a range pattern, determine
  all occurrences of the range pattern in the
  layout and score these occurrences using the
  scoring mechanism for the range pattern

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Outline

• Motivation
• Range Patterns and Matching
• Range Pattern Definitions
• Layout Representation
• Range Pattern Representation
• Process-Hotspot Detection System
• Experimental Results
• Conclusion

14
Layout Representation

• Layout is represented by a two-dimensional matrix
  LN1?N2 where Li,j 0 or 1 (0 ? i lt N1, 0 ? j lt
  N2)
• Conversion If a rectangle overlaps a grid
  location, the value at that location is set to 1.
  Otherwise, it is set to 0
• Different grid sizes result in different layout
  matrix

15
Outline

• Motivation
• Range Patterns and Matching
• Range Pattern Definitions
• Layout Representation
• Range Pattern Representation
• Process-Hotspot Detection System
• Experimental Results
• Conclusion

16
Cutting-slice Representation

• Horizontal (vertical) slice 2D matrix where all
  the rows (columns) are equal
• Fragment of a slice sub-matrix where all the
  elements are equal
• Cutting-slice a set of horizontal (vertical)
  slices S0, , Sn-1 with the following
  specifications
• Adjacent slices are not equal, i.e. Si ? Si1, 0
  ? i lt n-1
• Each slice Si is decomposed into fragments Fi,0,
  , Fi,m-1, where Fi,j ? Fi,j1, 0 ? j lt m-1
• If applicable, optimal values are specified for
  the fragments in each slice and for the slices
  themselves
• If applicable, ranges are specified for each
  slice and/or fragments within the slice
• If applicable, constraints between different
  fragments and/or slices are specified as linear
  functions

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Cutting-slice of Range Pattern Staircase

• Totally 5 slices S0,,S4
• Fragments in the ith slice have the same width as
  Si
• Fragment length and slice width can vary
• Si slice width
• Fi,j fragment length
• Item 6 translates to F0,0 - F4,0 ? 50

R1
R2
R3

1. Optimal width of each rectangle 90 nm
2. Optimal spacing between adjacent rectangles 90
   nm
3. Range of width of all rectangles (90, 150) nm
4. Range of spacing between adjacent rectangles
   (90, 150) nm
5. Range of length of central rectangle (200, 500)
   nm
6. Distance between the right edge of rectangle 1
   and the left edge of rectangle 3 cannot exceed 50
   nm

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Slicing Direction

• Slicing direction direction used to generate the
  slices
• Slicing direction affects the number of
  cutting-slices
• The total number of cutting-slices is calculated
  by enumerating all the range overlapping cases
• Choose the slicing direction with less
  cutting-slices

Staircase
slicing direction V
3 cutting-slices
slicing direction H
1 cutting-slice
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Outline

• Motivation
• Range Patterns and Matching
• Process-Hotspot Detection System
• Overview
• Range Pattern Matching Sub-problem
• Scalability and Runtime Optimization
• Experimental Results
• Conclusion

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Overview

• Hierarchical dual-grid scheme with matching done
  on two grid sizes
• The grid sizes are used to generate the layout
  matrices and the cutting-slices of the range
  pattern
• Matching with the coarse grid identifies
  locations that are potential matches
• Match locations are verified on the finer grid
  size
• Fine grid size is equal to the manufacturing grid
  size

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Outline

• Motivation
• Range Patterns and Matching
• Process-Hotspot Detection System
• Overview
• Range Pattern Matching Sub-problem
• Scalability and Runtime Optimization
• Experimental Results
• Conclusion

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Worm-like Movement of the Layout Block

• Matching is done block by block
• Layout matrix LN1N2, Block BhN2, where
  min ? h ? max
• min (max) the minimum (maximum) possible number
  of rows of the range pattern
• Enumerate all the blocks whose heights are
  between min and max on each row of the layout
  matrix
• Worm-like enumeration only the top and the
  bottom rows are changed each time to reuse work
  done in encoding the previous block
• Enables incremental encoding and greatly improves
  runtime

max
min
max
min
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KMP-based Filter

• Basic idea Encode both the block B and the
  cutting-slice C as 1D strings BE and CE,
  respectively. Search CE in BE to find all
  potential matches. All locations that are not
  matches are filtered out. The potential matches
  are examined more closely
• The run-length compression of a column CjN is
  equal to b0, b1, , bn-1, where
• bi ? bi1 (0 ? i lt n-1)
• CjN can be represented as a concatenation of
  n segments, i.e. b0 repeated ?0 times, b1
  repeated ?1 times, and so on
• Example 111001111011000011 is compressed to
  13021401120412
• Binary encoding with 1 added at the top to
  distinguish between 01 and 1 11010101 213

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Matching Example
N2
1
1
1
1
1
1
0
0
1
1
h
0
1
1
1
2
10
10
2
3
5
13
5
3
2
10
10
2
3
13
3
5
5

• Encode the slices in the cutting-slice 1D
  string 3, 5, 13, 5, 3
• Identify the slices in the block
• Run-length compression on each slice and encode
  the slices 2, 10, 10, 2, 3, 5, 13, 5, 3, 2, 10,
  10, 2
• Search the encoded cutting-slice 3, 5, 13, 5, 3
  in the encoded block by KMP string matching
  algorithm
• Columns 5-14 of the block are examined more
  closely for a true match and the remaining
  locations are filtered out

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Complexity Analysis of the RPM Algorithm

• Layout matrix LN1N2 , Layout block BhN2
  where min ? h ? max
• Slice identification O(N2)
• Let the number of identified slices be s (1 ? s ?
  N2), run-length compression takes O(s ? U), where
  U is the average time for updating the run-length
  compression of each slice
• Incremental binary encoding O(s)
• KMP string matching O(s)
• The verification process for each potential
  match O(1)
• RPM algorithm for one layout block max(N2, s?U)
• Total number of different blocks in the layout
  matrix LN1N2 is less than (N1-min1)?(max-min
  1)
• Total time complexity O(max(N2, s?U) ?
  (N1-min1) ?(max-min1))
• Key factors Size of the layout (N1, N2), the
  variation range in the height of the
  cutting-slice (min, max)

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Outline

• Motivation
• Range Patterns and Matching
• Process-Hotspot Detection System
• Overview
• Range Pattern Matching Sub-problem
• Scalability and Runtime Optimization
• Experimental Results
• Conclusion

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Scalability and Runtime Optimization

• Scalability window-by-window matching
• Consecutive windows overlap to avoid loss of
  matches
• Runtime matching on a fine grid size is slow
• Hierarchical matching strategy dual grid
  matching scheme of coarse grid matching followed
  by fine grid matching

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Outline

• Motivation
• Range Patterns and Matching
• Process-Hotspot Detection System
• Experimental Results
• Conclusion

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Experimental Results

• Platform Linux 2.4 system, two 2.2 GHz CPUs, 2
  GB RAM (only a single CPU used)
• Totally 5 layouts D1, D2, D3 metal layers of
  0.6?0.6 mm2 design D4, D5 metal layers of
  1.8?1.8 mm2 design. All are 65 nm designs
• The process-hotspot library

Range Pattern Rects. Overlap Multiple Patterns?
Bird 5 Yes Yes
Bridge 6 Yes Yes
Weave 4 No Yes
Zigzag 3 Yes Yes
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Experimental Results (cont.)
Range Pattern Design Name of Matches of Matches Runtime (s) Runtime (s) Score Range
Range Pattern Design Name Hier. Single-Grid Hier. Single-Grid Score Range
Bird D1 212 212 156.43 3189.94 87.81,97.29
Bird D2 52 52 14.86 2166.80 85.99,96.84
Bird D3 5 5 15.75 2862.74 93.22,96.84
Bird D4 5480 5480 264.07 15933.31 80.11,96.84
Bird D5 36 36 73.24 13397.48 80.56,92.01
Bridge D1 2062 2062 137.98 11517.72 98.32,98.74
Weave D4 14 14 358.59 17694.92 93.40,95.88
Weave D5 2 2 83.46 16036.56 93.40,93.40
Zigzag D2 2474 2474 19.47 2142.57 93.23,98.73
Zigzag D3 1642 1642 13.31 3130.89 97.46,97.46
Zigzag D4 12939 12939 358.59 14888.53 93.23,98.73
Zigzag D5 3038 3038 95.08 12878.50 97.46,97.46
Mountain D4 10 10 157.99 16598.91 91.00,92.50
Staircase D4 349 349 188.11 22865.83 99.15,99.43
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Discussion

• Maximum memory used is about 21MB
• Hierarchical matching runs from a few seconds to
  6 minutes
• Can be embedded in the router to detect
  process-hotspots
• Identified process-hotspots can be eliminated by
  local wire-spreading and/or widening
• Rip up and reroute with new DRC rules based on
  the constraints of the range pattern

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Outline

• Motivation
• Range Patterns and Matching
• Process-Hotspot Detection System
• Experimental Results
• Conclusion

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Conclusion

• Represent process-hotspots as range patterns
• Propose range pattern matching problem and
  algorithm
• Process-hotspot detection system developed to
  find and score process-hotspots in a given layout
• Scalable and fast, can work on large layouts,
  practical for efficiently detecting
  process-hotspots during routing
• Future work
• Handle range patterns with dont care regions
• Algorithmic process-hotspot correction scheme
• Combination with recommended rules to reduce the
  runtime burden on routers
• More thorough comparisons with model-based
  approaches

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Thank You!