chin-hsiung hsu, yao-wen chang, and sani rechard nassif from iccad09
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Simultaneous Layout Migration and Decomposition
for Double Patterning TechnologyChin-Hsiung Hsu, Yao-Wen Chang, and Sani Rechard Nassif
From ICCAD09
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OutlineINTRODUCTIONPROBLEM FORMULATIONSIMULTANEOUS LAYOUT MIGRATION AND
DECOMPOSITION FLOWPotential DPT-Conflict Graphs and Pattern
SplittingDPT-aware Constraint GraphsBasic ILP FormulationILP Problem-Size ReductionDPT-aware Standard Cells
EXPERIMENTAL RESULTS
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INTRODUCTIONDouble patterning
technology (DPT) and layout migration (LM) are crucial technologies for chip manufacturing in the nanometer era.
Due to their interplay, it is necessary to consider the effects of the two technologies simultaneously to obtain a better design flow for manufacturability enhancement.
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Sub-pattern geometric closeness
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OutlineINTRODUCTIONPROBLEM FORMULATIONSIMULTANEOUS LAYOUT MIGRATION AND
DECOMPOSITION FLOWPotential DPT-Conflict Graphs and Pattern
SplittingDPT-aware Constraint GraphsBasic ILP FormulationILP Problem-Size ReductionDPT-aware Standard Cells
EXPERIMENTAL RESULTS
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PROBLEM FORMULATION( SMD problem)Input: original layout L ,double-patterning
spacing Sd minimum overlap length lo for splitting patterns
Output: decomposed and migrated layout L*Objective: minimize # of stitch ,area of
layout and the sub-pattern geometric closeness
Constraint: design rule constraints ,DPT constraints and minimum-overlap-length constraints.
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OutlineINTRODUCTIONPROBLEM FORMULATIONSIMULTANEOUS LAYOUT MIGRATION AND
DECOMPOSITION FLOWPotential DPT-Conflict Graphs and Pattern
SplittingDPT-aware Constraint GraphsBasic ILP FormulationILP Problem-Size ReductionDPT-aware Standard Cells
EXPERIMENTAL RESULTS
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SIMULTANEOUS LAYOUT MIGRATION AND DECOMPOSITION FLOW
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Potential DPT-Conflict Graphs and Pattern SplittingIn traditional DPT-conflict graph, a node is
introduced to represent a tile, and two tiles are connected by an edge if their spacing is smaller than Sd. Not suitable for this SMD problem
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Potential DPT-Conflict Graphs and Pattern SplittingThis paper construct an edge between two
adjacent tiles even if their spacing is larger than Sd.
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DPT-aware Constraint GraphsGeneral edges
Inter-layer constraint (ex: a contact is covered by a metal)
Intra-layer constraint (ex: the minimum width and minimum spacing)
DPT-aware minimum-overlap-length constraints (ex: two tile should overlap with each other for a certain length
at the junction for a stitch)
Optional edges (two tiles can be separated along either the x- or y-
direction and at least one separation constraint is satisfied)
DPT edges(If two tiles are connected by a DPT edge, their spacing
needs be at least Sd only if they are on the same mask)
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Basic ILP Formulation
Boundary constraints
DRC constraints
DPT constraints
Stitch constraints
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A
C
B
A
B
Cd1 d2
D
D
Horizontal Constraint Graph
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Stitch
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ds
Distance(ti,tj)<=ds
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Linearization
<=0
= 0
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Linearization
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Linearization
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ILP Problem-Size Reduction
If a tile is connected and can be pseudo-colored with a different color without inducing a stitch, the tile and the connecting edge are included into the subgraph.
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ILP Problem-Size Reduction
reduces the ILP variables by 44.7%, the ILP constraints by 58.2%, andthe DPT edges by 79.9% on average
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DPT-aware Standard Cells
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DPT-aware Standard Cells
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OutlineINTRODUCTIONPROBLEM FORMULATIONSIMULTANEOUS LAYOUT MIGRATION AND
DECOMPOSITION FLOWPotential DPT-Conflict Graphs and Pattern
SplittingDPT-aware Constraint GraphsBasic ILP FormulationILP Problem-Size ReductionDPT-aware Standard Cells
EXPERIMENTAL RESULTS
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EXPERIMENTAL RESULTS
Testcases form UMC 90nm Free libraryand two artificial casesTesting process is 32nmDPT spacing is 64nm(112nm) for poly(metal)
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EXPERIMENTAL RESULTS