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Revisiting the Layout Decomposition Problem for Double Patterning LithographyPowerPoint Presentation

Revisiting the Layout Decomposition Problem for Double Patterning Lithography

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### Revisiting the Layout Decomposition Problem for Double Patterning Lithography

Outline Patterning Lithography

Outline Patterning Lithography

Outline Patterning Lithography

Andrew B. Kahng, Chul-Hong Park,

Xu Xu, Hailong Yao

http://vlsicad.ucsd.edu/

University of California, San Diego

UCSD VLSI CAD Laboratory BACUS-2008

Outline Patterning Lithography

- Background
- Contributions
- DPL Layout Decomposition Flow
- DPL Color Assignment Problem Formulation
- Experimental Results
- Summary

UCSD VLSI CAD Laboratory BACUS-2008

Background: DPL Patterning Lithography

DPL is a primary lithography candidate for 32nm node

Partitions dense circuit patterns into two separate exposures

Improves resolution and depth of focus (DOF)

Two primary approaches

LELE (litho-etch-litho-etch)

Self-aligned

Major concern is overlay control

Requires more accurate overlay metrology, more representative sampling, reduced model residuals, and improved overlay correction

ITRS DPL overlay control requirement is 6-9nm challenging for production deployment

UCSD VLSI CAD Laboratory BACUS-2008

Background: Layout Decomposition Patterning Lithography

Two features are assigned opposite colors if their spacing is less than the minimum coloring spacing

IF two features within minimum coloring spacing cannot be assigned different colors

THEN at least one feature is split into two or more parts

Pattern split increases manufacturing cost, complexity

Line ends corner rounding

Overlay error and interference mismatch line edge errors tight overlay control

Optimization : minimize cost of layout decomposition

UCSD VLSI CAD Laboratory BACUS-2008

Outline Patterning Lithography

- Background
- Contributions
- DPL Layout Decomposition Flow
- DPL Color Assignment Problem Formulation
- Experimental Results
- Summary

UCSD VLSI CAD Laboratory BACUS-2008

Contributions Patterning Lithography

Reference [1] (our group, Proc. ICCAD-2008)

Integer linear programming (ILP)

Conflict cycle detection and removal

Report unresolvable conflict cycles

This work

Consider all feasible splitting points for layout features

Different ILP formulation

minimize design changes, line-ends; maximize overlap length

Phase conflict detection (PCD) method [2]

good solution quality, much less runtime

Node-deletion bipartization (NDB) method [3]

also fast, worse solution quality

Report deleted conflict edges more direct metric of design changes

[1] A. B. Kahng, C.-H. Park, X. Xu and H. Yao, “Layout Decomposition for Double Patterning Lithography”, Proc. IEEE Intl. Conf. on Computer-Aided Design, 2008.

[2] C. Chiang, A. B. Kahng, S. Sinha, X. Xu, and A. Zelikovsky, "Fast and Efficient Bright-Field AAPSM Conflict Detection and Correction", IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems, 26(1) (2007), pp. 115-126.

[3] A. B. Kahng, S. Vaya and A. Zelikovsky, "New graph bipartizations for double-exposure, bright fieldalternating phase-shift mask layout", Proc. Asia and South Pacific Design Automation Conference, 2001, pp. 133-138.

UCSD VLSI CAD Laboratory BACUS-2008

Outline Patterning Lithography

- Background
- Contributions
- DPL Layout Decomposition Flow
- DPL Color Assignment Problem Formulation
- Experimental Results
- Summary

UCSD VLSI CAD Laboratory BACUS-2008

DPL Layout Decomposition Flow Patterning Lithography

Layout fracturing

Polygons rectangles

Conflict graph construction

Projection computation

Adjacent nodes connected with conflict edges

Node splitting and graph updating

Split at all feasible dividing points

Update the conflict graph

Compute overlap lengths

For each pair of touch rectangles, based on projections

Color assignment

ILP, PCD or NDB based graph bipartization and color assignment

Layout fracturing

Graph construction

Projection computation

Node splitting

and graph updating

Compute overlap lengths

ILP/PCD/NDB based

color assignment

UCSD VLSI CAD Laboratory BACUS-2008

e Patterning Lithography1

e2

Example: DPL Layout Decomposition- Polygonal layout features rectangles
- Conflict graph construction
- Compute projections and feasible dividing points
- Node splitting and graph updating
- ILP, PCD, or NDB method obtains final coloring solution

(b)

(a)

(d)

(c)

UCSD VLSI CAD Laboratory BACUS-2008

- Background
- Contributions
- DPL Layout Decomposition Flow
- DPL Color Assignment Problem Formulation
- Experimental Results
- Summary

UCSD VLSI CAD Laboratory BACUS-2008

Min-Cost Color Assignment Problem Patterning Lithography

Given: A list of rectangles R which is color assignable, and maximum distance between two features, t, at which the color assignment is constrained

Find: color assignment of rectangles to minimize the total cost

Subject to:

For any two adjacent non-touching rectangles with 0<d(i,j)≤ t, assign different colors

For any two touching rectangles (i.e., d(i,j) = 0), if they are assigned different colors, there is a corresponding cost cij

where,d(i,j) = distance between features of i and j

t = minimum color spacing between features of i and j

UCSD VLSI CAD Laboratory BACUS-2008

Fracturing and Conflict Graph Construction Patterning Lithography

Given a layout, a rectangular layout is obtained by fracturing polygons into rectangles

Minimum-sliver fracturing [1]

Easier feature operations

Avoids design rule violation

Given a rectangular layout, construct the conflict graph G =(V, EC ET)

Node n represents a feature

Conflict edge eci,j:non-touching features ni and nj within distance t

Touching edge eti,j: touching features ni and nj

n4

n5

n6

n3

n1

n2

et1,2

et3,4

et4,5

et2,3

ec1,3

ec3,5

ec5,6

horizontal

vertical

min-sliver

[1] A. B. Kahng, X. Xu and A. Zelikovsky, “Fast Yield-Driven Fracture for Variable Shaped-Beam Mask Writing", Proc. SPIE Conf. on Photomask and Next-Generation Lithography Mask Technology, 2006, pp. 62832R-1 - 62832R-9.

UCSD VLSI CAD Laboratory BACUS-2008

Node Splitting and Graph Updating Patterning Lithography

d < t

nl

nj

d < t

nk

no dividing

point

ni

nl

nj

np

oq,p

op,q

nq

dividing

point

nk

ni

Case (1)

Case (2)

- Split all nodes with feasible dividing points
- Update conflict graph
- Conflict graph may not be two-colorable after node splitting
- Two cases
- Overlap length less than overlap margin
- No dividing point with nonzero overlap length

- Minimized conflict edges are deleted
- Design change: preferentially between features of different cell instances

- ILP/PCD/NDB based method for graph bipartization

- Two cases

UCSD VLSI CAD Laboratory BACUS-2008

Method 1: ILP Based Min-Cost Color Assignment Patterning Lithography

- xi: binary variable (0/1) for the color of rectangle ri
- yij: binary variable for touching edge etij ET
- yij = 0 when xi = xj
- yij = 1 when xi xj

- zij: binary variable for conflict edge ecij EC
- zij = 0 when xi xj
- zij = 1 when xi = xj

- Minimize:
- Subject to:

- lij: length of rectangle edge of ri opposite to the touching edge between ri and rj
- FSmin: minimum feature size
- Lij: overlap length between touching rectangles ri and rj
- OM: required overlap margin

UCSD VLSI CAD Laboratory BACUS-2008

Method 2: Phase Conflict Detection Based Graph Coloring Patterning Lithography

conflict

edge

e1

e2

touching

edge

Conflict graph

feature

edge

e1

e2

conflict

edge

Conflict cycle graph

- Gadget based approach: optimal edge-deletion bipartization for planar graph [1]
- Two main steps
- Heuristic planar graph embedding
- Optimal conflict removal for planar graph

- Conflict graph conflict cycle graph
- Conflict (green) edge feature (red) edge
- Touching (blue) edge conflict (black) edge

- Edge cost
- Conflict edge: design change
- Touching edge cut and overlap length
- /2: design rule or OL violation
- +/OLij: no design rule or OL violation

- Output: deleted edges with two-colorable graph

[1] C. Chiang, A. B. Kahng, S. Sinha, X. Xu, and A. Zelikovsky, "Fast and Efficient Bright-Field AAPSM Conflict Detection and Correction", IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems, 26(1) (2007), pp. 115-126.

UCSD VLSI CAD Laboratory BACUS-2008

Method 3: Node-Deletion Bipartization Based Graph Coloring Patterning Lithography

conflict

edge

e1

e2

touching

edge

Conflict graph

feature

edge

n1

n2

new node

conflict

edge

Conflict cycle graph

- Node-deletion graph bipartization [1]
- Conflict cycle graph construction
- Conflict (green) edge new node, feature (red) and conflict (black) edge
- Touching (blue) edge new node and two feature (red) edges

- Only newly inserted nodes are deletable
- Cost of new nodes: same as in PCD
- Output: deleted nodes
- Map back to conflict and touching edges

- After PCD or NDB step, color with breadth first search (BFS) based process

[1] A. B. Kahng, S. Vaya, A. Zelikovsky, "New Graph Bipartizations for Double-Exposure, Bright Field Alternating Phase-Shift Mask Layout", Proc. Asia and South Pacific Design Automation Conference, 2001, pp. 133-138.

UCSD VLSI CAD Laboratory BACUS-2008

Layout Partitioning Patterning Lithography

Conflict graph is sparse: due to poly-to-cell boundary and whitespace

Many islands found in the conflict graph

Layout partitioning

Partitions conflict graph into connected components

Each component has separate conflict graph

No edges or nodes of a polygon occur in multiple components

Color each component separately

Final solution: union of solutions for all components

Improves runtime and memory efficiency

UCSD VLSI CAD Laboratory BACUS-2008

- Background
- Contributions
- DPL Layout Decomposition Flow
- DPL Color Assignment Problem Formulation
- Experimental Results
- Summary

UCSD VLSI CAD Laboratory BACUS-2008

Testcases Patterning Lithography

- AES: real-world design
- Top-B, Top-C, Top-D
- Artificial designs
- >600 types of cell masters

- Artisan 90nm libraries
- Placement: 70% and 90% utilization
- Minimum design rule: GDS scaled down by 0.4x
- Minimum spacing:140nm 56nm
- Minimum width: 100nm 40nm

UCSD VLSI CAD Laboratory BACUS-2008

ILP Results Patterning Lithography

- Sweep t and placement utilization
- Various metrics: deleted conflict edges, overlap length and number of cuts
- Minimum overlap length overlap margin 8nm
- No design rule violation

UCSD VLSI CAD Laboratory BACUS-2008

PCD Results Patterning Lithography

- Sweep t and placement utilization
- Various metrics: deleted conflict edges, overlap length and number of cuts
- Minimum overlap length overlap margin 8nm
- No design rule violation

UCSD VLSI CAD Laboratory BACUS-2008

NDB Results Patterning Lithography

- Sweep t and placement utilization
- Various metrics: deleted conflict edges, overlap length and number of cuts
- Minimum overlap length overlap margin 8nm
- No design rule violation

UCSD VLSI CAD Laboratory BACUS-2008

Comparison (1) Patterning Lithography

- Higher priority on deleted edges design changes
- Deleted edges: ILP < PCD < NDB
- Same deleted edges: ILP obtains minimal cuts with maximal overlap length

UCSD VLSI CAD Laboratory BACUS-2008

Comparison (2) Patterning Lithography

- Same deleted edges: ILP obtains larger mean overlap length
- Solution quality: ILP > PCD > NDB
- Runtime: ILP > NDB > PCD

UCSD VLSI CAD Laboratory BACUS-2008

- Background
- Contributions
- DPL Layout Decomposition Flow
- DPL Color Assignment Problem Formulation
- Experimental Results
- Summary

UCSD VLSI CAD Laboratory BACUS-2008

Summary Patterning Lithography

Three approaches: ILP, PCD and NDB methods

Address DPL layout decomposition at 45nm and below

Improve overlap length and lithography yield

Experimental results are promising

Overlap lengths overlap margin

Report all necessary design changes

Ongoing work

Optimal timing/power model guardbanding under bimodal CD distribution in DPL

Variability-aware DPL layout decomposition cost function

Minimize difference between pitch distributions of two masks

Minimize number of distinct DPL layout solutions across all instances of same master cell

Balanced mask layout density

Integration of forbidden pitch intervals

UCSD VLSI CAD Laboratory BACUS-2008

Thank you! Patterning Lithography

UCSD VLSI CAD Laboratory BACUS-2008

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