Chin-Hsiung Hsu, Yao-Wen Chang, and Sani Rechard Nassif From ICCAD09

Outline INTRODUCTION PROBLEM FORMULATION SIMULTANEOUS LAYOUT MIGRATION AND DECOMPOSITION FLOW Potential DPT-Conflict Graphs and Pattern Splitting DPT-aware Constraint Graphs Basic ILP Formulation ILP Problem-Size Reduction DPT-aware Standard Cells EXPERIMENTAL RESULTS

INTRODUCTION Double 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.

Sub-pattern geometric closeness

Outline INTRODUCTION PROBLEM FORMULATION SIMULTANEOUS LAYOUT MIGRATION AND DECOMPOSITION FLOW Potential DPT-Conflict Graphs and Pattern Splitting DPT-aware Constraint Graphs Basic ILP Formulation ILP Problem-Size Reduction DPT-aware Standard Cells EXPERIMENTAL RESULTS

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.

Outline INTRODUCTION PROBLEM FORMULATION SIMULTANEOUS LAYOUT MIGRATION AND DECOMPOSITION FLOW Potential DPT-Conflict Graphs and Pattern Splitting DPT-aware Constraint Graphs Basic ILP Formulation ILP Problem-Size Reduction DPT-aware Standard Cells EXPERIMENTAL RESULTS

SIMULTANEOUS LAYOUT MIGRATION AND DECOMPOSITION FLOW

Potential DPT-Conflict Graphs and Pattern Splitting In 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

Potential DPT-Conflict Graphs and Pattern Splitting This paper construct an edge between two adjacent tiles even if their spacing is larger than Sd.

DPT-aware Constraint Graphs General 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)

Basic ILP Formulation Boundary constraints DRC constraints DPT constraints Stitch constraints

A C B A B C d1 d2 D D Horizontal Constraint Graph

Stitch

ds Distance(ti,tj)<=ds

Linearization <=0 = 0

Linearization

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.

ILP Problem-Size Reduction reduces the ILP variables by 44.7%, the ILP constraints by 58.2%, and the DPT edges by 79.9% on average

DPT-aware Standard Cells

Outline INTRODUCTION PROBLEM FORMULATION SIMULTANEOUS LAYOUT MIGRATION AND DECOMPOSITION FLOW Potential DPT-Conflict Graphs and Pattern Splitting DPT-aware Constraint Graphs Basic ILP Formulation ILP Problem-Size Reduction DPT-aware Standard Cells EXPERIMENTAL RESULTS

Testcases form UMC 90nm Free library and two artificial cases Testing process is 32nm DPT spacing is 64nm(112nm) for poly(metal)

EXPERIMENTAL RESULTS