Fast and Area-Efficient Phase Conflict Detection and Correction in Standard-Cell Layouts Charles Chiang, Synopsys Andrew B. Kahng, UC San Diego Subarna Sinha, Synopsys Xu Xu, UC San Diego

Outline Introduction of AAPSM AAPSM Conflict Detection AAPSM Conflict Correction Conclusions

AAPSM: Enabling Technology Alternating Aperture Phase Shift Mask (AAPSM): Phase-modulation at the mask level to increase resolution capabilities of optical lithography. Mask Wafer

AAPSM: Enabling Technology Alternating Aperture Phase Shift Mask (AAPSM): Phase-modulation at the mask level to increase resolution capabilities of optical lithography Mask 180 o phase-shifter Wafer

AAPSM: Enabling Technology Alternating Aperture Phase Shift Mask (AAPSM): Phase-modulation at the mask level to increase resolution capabilities of optical lithography. Mask 180 o phase-shifter Shifters Mask Wafer Feature 0.11  m Printed using a 0.35 um nominal process

AAPSM: Enabling Technology Benefits: - Smaller feature sizes. - Better optical resolution - Extend equipment life Alternating Aperture Phase Shift Mask (AAPSM): Phase-modulation at the mask level to increase resolution capabilities of optical lithography.

Outline Introduction AAPSM Conflict Detection AAPSM Conflict Correction Conclusions

Additional Layout Rules Feature Rule: Shifters of the same feature must have different phases Overlapping Rule: Overlapping shifters must have the same phase 0180 Feature Shifters Overlapping Shifters Conflict: A pair of shifters violate the rules after phase assignment Legal Layout: No conflicts

Conflict Detection Problem Formulation Conflict correction lead to increased area Given: A layout (a set of shifters) Conflict weights = area increase for correcting the conflict Assign: phases to shifters To minimize the total area increase of all conflicts ConflictArea increase after correction

AAPSM Conflict Detection Flow Layout Conflict Cycle Graph Construction

AAPSM Conflict Detection Flow Layout Conflict Cycle Graph Construction Graph Planarization

AAPSM Conflict Detection Flow Layout Conflict Cycle Graph Construction Graph Planarization Graph Legalization / Phase Assignment

AAPSM Conflict Detection Flow Layout Conflict Cycle Graph Construction Graph Planarization Graph Legalization / Phase Assignment Check Removed Edge During Planarization

AAPSM Conflict Detection Flow Layout Conflict Cycle Graph Construction Graph Planarization Graph Legalization / Phase Assignment Check Removed Edge During Planarization Set of AAPSM conflicts for correction

Review of Work in Conflict Detection Conflict Graph Construction  Feature Graph (Kahng et al. ASPDAC 2003)  Phase Conflict Graph (Chiang et al. DATE 2005)  Conflict Cycle Graph (Non-bipartite Formulation) Graph Legalization  Iterative Voronoi Graph (Kahng et al. BACUS 98)  T-join based bipartization for planar graph (Berman et al. TCAD 2000)  Spanning Tree-Based Algorithm (Kahng et al. ASPDAC 2003)  Modified T-join algorithm for non-bipartite graph

Conflict Cycle Graph Node represents a shifter Feature edge connects two nodes of the same feature  Nodes of the feature edge have different phases Overlap edge connects overlapping nodes  Nodes of the overlap edge have the same phase Edge weight = conflict weight Remove one edge = correct the corresponding conflict Overlap edge Feature edge

Conflict Cycle and Conflict Face Conflict cycle = cycle with odd # feature edges Legal cycle = cycle with even # feature edges Conflict Fact: Legal Layout No conflict cycles

Phase Conflict Graph (DATE 2005) 9 edges Conflict Cycle Graph (Proposed) 5 edges Comparison with Previous Graph After removing uncorrectable edges 2 edges Uncorrectable edges can be removed with non-bipartite formulation

Min-Weight Edge-Deletion Fact: A planar graph has no conflict cycle if  Remove even number of edges for legal faces  Remove odd number of edges for conflict faces Legal Face Conflict Face

Min-Weight Edge-Deletion Problem Formulation Given: A planar conflict cycle graph G(V,E) Find: a set of edges E’ to be deleted such that  For each legal face, the number of edges in E’ is even  For each conflict face, the number of edges in E’ is odd To minimize the total weight of edges in E’ Flow to optimally solve the problem Conflict cycle graph  Dual graph (T-join problem) Dual graph  Gadget graph (Perfect matching problem) From optimal matching solution  edges to be deleted

Conflict Cycle Graph  Dual Graph face node dual edge edge Conflict Graph Dual Graph Conflict face  Conflict node Legal face  Legal node 4

T-join Problem Formulation Given: A graph G D (V, E, T) (T is the set of all conflict nodes) Find: a set of edges E’ to be deleted such that  For each node v, the edge number in E’ is odd iff To minimize the total weight of edges in E’ Conflict Graph Dual Graph facenode dual edge edge

Dual Graph  Gadget Graph node gadget Dual Graph true node edge T-join problem  min-weight perfect matching Gadget Graph

Perfect Matching Delete edges 1 and 2 + Phase assignment

Experiments Setup Implement proposed algorithms in C Use 4X400M Ultra-Sparc II with 4G RAM Ten large industry testcases  90 nm designs  # features from 10,274 to 159,070

Conflict Detection Results 5.9x Faster Speedup Ten Test Cases

Conflict Detection Results # Conflicts Ten Test Cases 3.88% Reduction

Outline Introduction AAPSM Conflict Detection AAPSM Conflict Correction Conclusions

Mask-level Conflict Correction Modify shifters on mask.  Split shifter region whenever two shifters of opposite phase overlap. Pros: no design modification Cons:  Increases mask complexity, correction not always possible  Can negatively affect process latitude Split

Widen Feature Increase width of certain features to make them non-critical No shifters needed for widened feature Widen Pros: small change in layout Cons: performance degradation

Add Spacing Insert vertical or horizontal gaps between overlapping shifters of different phases. Spacing Pros: small performance penalty as width of gate features remains unchanged Cons: larger area increase  Our focus

Insert gap locally Introduce new conflict Local versus Global Spacing Insert gap across the whole layout Large area increase

PSM Conflict Correction Divide layout into rows Divide each row into cells Original Layout

PSM Conflict Correction Insert gap across the cell to remove conflicts Divide layout into rows Divide each row into cells Original Layout

PSM Conflict Correction Insert gap across the cell to remove conflicts Adjust cell distance to avoid new conflicts Divide layout into rows Divide each row into cells Adjust row distance Original Layout

PSM Conflict Correction Insert gap across the cell to remove conflicts Adjust cell distance to avoid new conflicts Divide layout into rows Divide each row into cells Adjust row distance Original Layout Modified Layout

Generalized Correction Scheme H VVV HHH H H Solve conflicts within each region From the bottom of the tree  Insert spacing along the slicing line to avoid the conflicts between features of different regions

Conflict Correction Results DesignAreaConflict%Area Increase newold >100

Outline Introduction AAPSM Conflict Detection AAPSM Conflict Correction Conclusions

Conclusion AAPSM Conflict Detection:  First non-bipartite graph based approach  5.9x runtime improvement  3.88% conflict reduction AAPSM Conflict Correction:  Hierarchical layout modification  Small area increase on the average ( 6.1% ) for large testcases Future Work:  Incorporate feature widening as an option  Timing-driven PSM conflict correction

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