Self-Aligned Double Patterning
Aware Pin Access and
Standard Cell Layout CoOptimization
Xiaoqing Xu1, Brian Cline2, Greg Yeric2,
Bei Yu1, David Z. Pan1
1University
of Texas at Austin
2ARM Inc, Austin
Outline
Introduction & Motivations
 SADP-Aware Pin Access and Optimization
 Experimental Results
 Summary & Future work

Need of Double Patterning

Beyond Single Patterning
› Technology scaling:
» 14nm node - 64nm Metal-2 pitch
» 10nm node - 48nm Metal-2 pitch
› Resolution of litho-tools: CD = 𝑘1 ∗

𝜆
𝑁𝐴
≈ 40𝑛𝑚
Double Patterning - pitch splitting
› Layout decomposition: split one layer into two masks
MinPitch
2*MinPitch
Two Kinds of DPL

Litho-Etch-Litho-Etch (LELE)

Self-Aligned Double Patterning (SADP)
› Better overlay control, but more layout constraints
Main Mandrel
Additional Mandrel
Sub-Metal
Spacer
Trim Mask
SADP Layout Decomposition
Mandrel
Mandrel
Mandrel
Recap: Trim Mask is Single Patterned
(a)
(b)
(c)
(d)
Main Mandrel
Sub-Metal
Additional Mandrel
Spacer
Trim Mask
[G. Luk-Pat+, SPIE’13]
SADP-specific Design Rules

To ensure trim mask printability
𝑙1
𝑙1
OnTrackSpace ≥ 𝑙1
𝑙3
𝑙2
𝑙2
OffTrackOverlap ≥ 𝑙2
𝑙4
Mandrel
Trim Mask
Sub-Metal
𝑙3
OffTrackSpace ≥ 𝑙3
𝑙4
Spacer
OffTrackoffset ≥ 𝑙4 or = 0
[Y. Ma+, SPIE’12], [G. Luk-Pat+, SPIE’13]
Line-end Extension

To fix hot-spots on trim masks
Hot spot
Via-1
(a) OffTrackOverlap ≥ 𝑙2
Mandrel
Trim Mask
Hot spot
Sub-Metal
Spacer
(b) OffTrackoffset ≥ 𝑙4 or = 0
Previous Work on SADP

SADP layout decomposition
› [H. Zhang+, DAC’11], [Y. Ban+, DAC’11]
› [Z. Xiao+, ISPD’12]

SADP-aware routing
› [M. Mirsaeedi+, SPIE’11], [J.-R. Gao+, ISPD’12]
› [C. Kodama+, ASPDAC’13], [Y. Du+, DAC’13]

However, not much on standard cell pin access
which is very challenging (Keynote by Dr. Aitken)
Our Contributions
First work to address standard cell I/O pin access
design/local routing at the cell level
 We propose a MILP-based method to enable
SADP-aware layout design for pin access and
within-cell connections
 Our method can maximize the pin access
flexibility for the entire standard cell library

Outline
Introduction & Motivations
 SADP-Aware Pin Access and Optimization

› Backtracking
› Pin Access Optimization
Experimental Results
 Summary & Future work

Standard Cell Pin access
Metal-2 line-end position vs Via-1 position
 Metal-2 line end extension

(a)
(b)
Metal-1 pin
Via-1
Metal-2 wire
Metal-2 extension
Pin Access and Std-Cell Layout Co-Opt (PICO)

Problem formulation
› Given cell layout, multiple I/O Pins for each cell, and
multiple Hit Points for each I/O Pin
› Design all Valid Hit Point Combinations (Metal2) for
each cell in library
Hit Point
Cell connection
Metal-1 pin
(a)
(b)
Pin access
Routing track
Via-1
Metal-2 extension
Metal-2 wire
(c)
(d)
Proposed Solution
Cell
Layout
PICO
I/O Pins
Hit Points
Hit Point Combination
search tree
Backtracking
reduce search space
PAO
1: Line-end extension minimization
2: Rules to linear constraints
Pin Access Optimization
3: MILP optimization
Backtracking for all Hit Points

Search tree construction
› Level 𝑖: hit points for 𝑖𝑡ℎ I/O pin

Path from root to leaf
› Hit point combination
𝑆
PAO on each path
 Reduce solution space

› Check heuristics
I/O pin 1 𝑝11
I/O pin 2
I/O pin 3
1
I/O pin 𝑚 𝑝𝑚
2
𝑝𝑚
𝑝31
𝑝32
𝑘
𝑝𝑚𝑚
𝑝21
𝑝22
𝑘
𝑝3 3
𝑝12
𝑘
𝑝2 2
𝑘
𝑝1 1
Pin Access Optimization (PAO)

Problem formulation
› Given cell layout and a Hit Point Combination
› Evaluate the validness of the Hit Point Combination
and design the Pin Access optimally
Pin access
(a)
(b)
Metal-1 pin
Metal-2 wire
Via-1
Routing track
Metal-2 extension
Mathematical Formulation

Objective function
› Line-end extension minimization
› Objective function:
𝑥𝑖𝐿
𝑖=𝑛
𝑖=1
0
0
(𝑥𝑖𝐿
− 𝑥𝑖𝐿 ) + (𝑥𝑖𝑅 − 𝑥𝑖𝑅
)
0
𝑥𝑖𝐿
𝑖𝑡ℎ
𝑗𝑡ℎ
𝐶𝐿
0
𝑥𝑗𝑅
𝑥𝑗𝑅
𝐶𝑅
Mathematical Formulation – cont’d

Rules to constraints
› Basic rules
𝑖𝑡ℎ
0
𝑥𝑖𝐿
0
𝑥𝑖𝑅
0
𝐶𝐿 ≤ 𝑥𝑖𝐿 ≤ 𝑥𝑖𝐿
0
𝑥𝑖𝑅
≤ 𝑥𝑖𝑅 ≤ 𝐶𝑅
𝑥𝑖𝑅 − 𝑥𝑖𝐿 ≥ 𝑙𝑚𝑖𝑛
› SADP-specific rules
𝑙1
OnTrackSpace ≥ 𝑙1
𝑙3
OffTrackSpace ≥ 𝑙3
𝑙2
OffTrackOverlap ≥ 𝑙2
𝑙4
OffTrackoffset ≥ 𝑙4 or = 0
Mathematical Formulation – cont’d

SADP-specific rules
› Case 1
𝑖𝑡ℎ
𝑗𝑡ℎ
0
𝑥𝑖𝐿
0
𝑥𝑖𝑅
0
𝑥𝑗𝐿
𝑥𝑗𝐿 − 𝑥𝑖𝑅 ≥ 𝑙1
0
𝑥𝑗𝑅
› Case 2
𝑖𝑡ℎ
0
𝑥𝑖𝐿
0
𝑥𝑖𝑅
𝑗𝑡ℎ
› Case 3
0
𝑥𝑗𝐿
0
𝑥𝑗𝑅
𝑖𝑡ℎ
0
𝑥𝑖𝐿
0
𝑥𝑖𝑅
0
𝑥𝑗𝐿
𝑗𝑡ℎ
0
𝑥𝑗𝑅
𝑥𝑖𝑅 − 𝑥𝑗𝐿 ≥ 𝑙2
𝑥𝑗𝑅 − 𝑥𝑖𝐿 ≥ 𝑙2
𝑥𝑖𝐿 − 𝑥𝑗𝐿 ≥ 𝑙4 𝑜𝑟 𝑥𝑖𝐿 = 𝑥𝑗𝐿
𝑥𝑖𝑅 − 𝑥𝑗𝑅 ≥ 𝑙4 𝑜𝑟 𝑥𝑖𝑅 = 𝑥𝑗𝑅
𝑥𝑗𝐿 − 𝑥𝑖𝑅 ≥ 𝑙3 or 𝑥𝑖𝑅 − 𝑥𝑗𝐿 ≥ 𝑙2
𝑥𝑖𝐿 − 𝑥𝑗𝐿 ≥ 𝑙4 𝑜𝑟 𝑥𝑖𝐿 = 𝑥𝑗𝐿
𝑥𝑖𝑅 − 𝑥𝑗𝑅 ≥ 𝑙4 𝑜𝑟 𝑥𝑖𝑅 = 𝑥𝑗𝑅
MILP Formulation (PAO)
0
0
Objective function: 𝑖=𝑛
(𝑥
−
𝑥
)
+
(𝑥
−
𝑥
𝑖𝐿
𝑖𝑅
𝑖=1
𝑖𝐿
𝑖𝑅 )
 Linearize constraints: big-M transformation

› ∀𝑥𝑖𝐿 , 𝑥𝑗𝑅 ⇒ |𝑥𝑖𝐿 − 𝑥𝑗𝑅 | ≤ 𝑐𝑊 (value for “big-M”)

Remove “or” in constraints
𝑥𝑗𝐿 − 𝑥𝑖𝑅 ≥ 𝑙3 or 𝑥𝑖𝑅 − 𝑥𝑗𝐿 ≥ 𝑙2
𝑥𝑗𝐿 − 𝑥𝑖𝑅 + 𝑐𝑊 + 𝑙3 ∗ 𝑠 ≥ 𝑙3
𝑥𝑖𝑅 − 𝑥𝑗𝐿 + 𝑐𝑊 + 𝑙2 ∗ s ≥ 𝑙2
𝑠 ∈ {0,1}
𝑥𝑖𝐿 − 𝑥𝑗𝐿 ≥ 𝑙4 𝑜𝑟 𝑥𝑖𝐿 = 𝑥𝑗𝐿
𝑥𝑗𝐿 − 𝑥𝑖𝐿 + 𝑐𝑊 + 𝑙4 ∗ 𝑠 ≥ 𝑙4 ∗ 1 − 𝑡
𝑥𝑖𝐿 − 𝑥𝑗𝐿 + 𝑐𝑊 + 𝑙4 ∗ 1 − 𝑠 ≥ 𝑙4 ∗ 1 − 𝑡 + 𝑐𝑊 + 𝑙4 ∗ 𝑡
𝑠 + 𝑡 ≤ 1; 𝑠, 𝑡 ∈ {0,1}
Recap of the Overall Flow
Cell
Layout
PICO
I/O Pins
Hit Points
Hit Point Combination
search tree
Backtracking
reduce search space
PAO
1: Line-end extension minimization
2: Rules to linear constraints
Pin Access Optimization
3: MILP optimization
Experimental Results

Experimental setup
› Linux with 3.33GHz Intel(R) Xeon(R) CPU X5680
› Industrial 14nm library scaled to 10nm-dimensions

An example after PAO
(a)
(b)
Experimental Results
Increase in Valid Hit Point Combinations
› More valid hit point combinations lead to more
flexibility for routing
1200
Number of Hit Point
Combinations

Conventional
PICO
800
400
0
Cell 1
Cell 2
Cell 3
Cell 4
Cell 5
Experimental Results
Increase in ratio on the number of Valid Hit Point
Combinations across the entire library
600
Number of cells

400
200
0
1X
10X
100X
1000X
10000X
The increase in ratio (PICO over conventional)
Experimental Results
Increase in ratio on the number of Valid Hit
Points across the entire library
› Over 25% of cells have 20% or more increase
1000
Number of cells

100
10
1
10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Increase in percentage
Experimental Results – Run Time
Most cells finished within 500 seconds
 Pin access design is one time computation

Number of cells
400
300
200
100
0
1
10
100
500
Run time (s)
1000
5000
Summary & Future Work

Summary
› The impact of SADP has on local routing (Pin Access
Design) is studied
› Pin Access and within-cell connections on Metal-2 are
co-optimized
› Hit Points of different I/O pins are coupled
› Hit Point Combinations are important

Future work
› Pin access information extraction from PICO for
standard cell library
› Handshake between pin access and routing
Thank you!
Q&A
Proposed Solutions

Design rule check and fix
Cell connection
(a)
Hit Point
(b)
Pin access
(c)
(d)
Metal-1 pin
Metal-2 wire
Via-1
Routing track
Metal-2 extension
Proposed solution
SADP-Aware Pin Access
PICO
1: I/O Pins & Hit Points
Cell Layout
2: Hit Point Combination: search tree
3: Backtracking: reduce search space
4: Pin Access Optimization
Pin Access Optimization
SADP design
rules
1: Line-end extension minimization
2: Rules to linear constraints
3: MILP optimization
Pin access design
SADP-Aware Layout Design

SADP-Aware Design Rule (Case I: OnTrackSpace)
𝐿1 ≥ minTrimResistWidth
−2 ∗ trimEtchBias
𝐿1 ≥ minTrimResistWidth
−2 ∗ trimEtchBias
SADP-Aware Layout Design

SADP-Aware Design Rule (Case I, Cont’d)
𝐿1 = SpacerDepositWidth
𝐿1 ≥ minTrimResistWidth
−2 ∗ trimEtchBias
SADP-Aware Layout Design

SADP-Aware Design Rule (Case 2:
OffTrackOverlap)
𝐿2 ≥ minTrimResistSpace
+2 ∗ trimEtchBias
𝐿2 ≥ minTrimResistSpace
+2 ∗ trimEtchBias
SADP-Aware Layout Design

SADP-Aware Design Rule (Case 3: OffTrackSpace)
L3 ≥
minTrimResist𝑊𝑖𝑑𝑡ℎ 2
−2 ∗ trimEtchBias
−SpacerDepositWidth2
L3 ≥
minTrimResis𝑡𝑊𝑖𝑑𝑡ℎ 2
−2 ∗ trimEtchBias
−SpacerDepositWidth2
SADP-Aware Layout Design

SADP-Aware Design Rules (Case 4: OffTrackOffset)
𝐿4 ≥ minTrimResistWidth
or 𝐿4 = 0
𝐿4 ≥ minTrimResistWidth
or 𝐿4 = 0
SADP-Aware Layout Design

SADP-Aware Design Rules – summary
›
›
›
›
OnTrackSpace (L1) >= 32 nm or OnTrackSpace (L1) = 24nm
OffTrackOverlap (L2) >= 58 nm
OffTrackSpace (L3) >= 22 nm
OffTrackOffset (L4) >= 44 nm or OffTrackOffset (L4) = 0 nm
Potential odd-cycle
Not decomposable
Pin Access Optimization

Mathematical formulation
› Line end extension minimization
Notations
𝐶𝐿 , 𝐶𝑅
Left or right boundary of cell
𝐶𝑊
Cell width, 𝐶𝑊 = 𝐶𝑅 − 𝐶𝐿
𝑆𝑚
Set of Metal-2 wires
𝑛
Total number of Metal-2 wires
𝑆𝑘
Set of pairs of wires for rule 𝑘
𝑥𝑖𝐿 , 𝑥𝑖𝑅
The left or right line end of 𝑖𝑡ℎ wire
0
0
𝑥𝑖𝐿
, 𝑥𝑖𝑅
The initial line ends of 𝑖𝑡ℎ
𝑙𝑚𝑖𝑛
Minimum length for Metal-2 wire