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Dual Graph-Based Hot Spot Detection

This paper presents a novel dual graph-based approach for hot spot detection, aiming to enhance manufacturing yield through early identification of critical features. The method effectively reduces the number of falsely detected hot spots while maintaining high accuracy, achieving a runtime improvement of over 287 times compared to traditional optical rule check (ORC) tools. The dual graph methodology utilizes local pattern densities and edge weighting schemes to identify significant variations in critical dimensions (CD). Experimental results validate the efficiency and effectiveness of this approach.

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Dual Graph-Based Hot Spot Detection

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  1. Dual Graph-Based Hot Spot Detection Andrew B. Kahng1 Chul-Hong Park2 Xu Xu1 (1) Blaze DFM, Inc. (2) ECE, University of California at San Diego

  2. Outline • Introduction of Hot Spot Detection • Dual Graph Based Approach • Experimental Results • Conclusions

  3. Why Hot Spot Detection? • Hot spots = features whose CD variation > T • Form under a variety of conditions • Reduce manufacturing yield • Should be detected and solved in the early stage • Commercial tools: ORC (Mentor) and LRC (Synopsys) Hot spot

  4. Previous Methods • Park et al. (SPIE 1999) proposed rule based detection with look-up tables • Number of parameters increase for complex patterns • Speed merit of rule-based approach is reduced • Inaccurate • Simulation-based approach has been a mainstream • Detect hot spots accurately • Hot spots can be changed according to process conditions • Model generations are significant overhead • Key Question Can we detect the hotspots fast and accurately?

  5. How We Think About Hot Spot • Hotspot is a 2-dimensional function of line and space with traditional parameters of DOF and Exposure •  Detect too many hot spots to classify the real hot spots • Our approach: more topological / graph-oriented  Practical methodology: Filter the chip layout down to a small candidate set of hotspots, which can then be checked using the golden ORC/LRC tool

  6. Nominal CD (b) (c) (a) Lithography Simulation Simulation Condition: C-1: NA=0.85, σ=0.96/0.76, C-2: NA=0.75, σ=0.75/0.55, C-3: NA=0.75, σ=0.75/045 DOF=0.2um, Exposure=+10% of nominal exposure • Different complexity leads to different CD variation • CD variation is affected by different process condition • More complex pattern, higher probability of hot spot • Probability: Pattern(c) > Pattern(b) > Pattern(a)

  7. Outline • Introduction of Hot Spot Detection • Dual Graph Based Approach • Experimental Results • Conclusions

  8. Hot Spot Detection Problem Given: Layout L simulation conditions hot spot definition Detect: Hot spots whose CD variation >T To Minimize: Number of un-detected and falsely detected hot spots

  9. “Bad” Patterns Lead to Hotspots Corner effect Proximity effect In general, single effect does not lead to hot spots. Hot spots are accumulative effects. 4 proximity effects, 2 corner effects

  10. Proposed Hot Spot Detection Flow Layout Layout Graph Construction Graph Planarization Three-Level Detection Local Pattern Density Filter Output Hot Spots

  11. Layout Graph Construction Feature  node Proximity effect Two features with corner/proximity effects  edge Corner effect

  12. Edge Weighting Scheme • Closed-form formula based approach • Weights of corner edges: constant • Weights of proximate edges: f(w1, w2, l, d)= (w1’w2’l’) /d Here w1’= w1 when w1 <c0 = c0 otherwise • Lookup table based w1 l w2 d

  13. Graph Planarization • Delete one edge of any pair of crossing edges • Convert the layout graph into its dual graph (face dual node) Planarization Dual graph

  14. Three-Level Hot Spot Detection • Foreach edge • If (its weight > T0) report hot spot • For each face (dual node) • If (the total weight > T1 ) report hot spot • Sort all dual nodes according to weights • Iteratively merge two dual nodes with max merged weight • For each merged face (dual node) • If (the total edge weight > T2 )report hot spot Edge Face Merged Face

  15. Local Pattern Density Filter • Hot spots depend on the local pattern density • A hot spots filtering based local pattern densityto reduce falsely detected hot spots Not Hot spot Hot spot

  16. Outline • Introduction of Hot Spot Detection • Dual Graph Based Approach • Experimental Results • Conclusions

  17. Experimental Setup • Testcase: alu128 core • 8.7K instances • 90nm technology • Chip size is 335 um X 285 um • The netlists from OpenCores. • CalibreOPC , CalibreORC from Mentor Graphics are used for model-based OPC, and optical rule check (ORC) • Our algorithms are implemented in C++

  18. An Example of Hotspot Filtering • 2D function (width, space) finds too many hotspots to classify the real hotspots • Real hotspot can be detected by dual graph based approach with weighted cost function • Detect hotspots which missed by rule-based approach • Result is similar to simulation-based approach (b) Hotspot (a) No Hotspot

  19. Experimental Results • Runtime of our method is more than 287X faster compared to ORC • Achieves 100% hot spot detection with small falsely defected hot spots overhead

  20. Outline • Introduction of Hot Spot Detection • Dual Graph Based Approach • Experimental Results • Conclusions

  21. Conclusion • A novel fast dual graph based hot spot detection algorithm • Our method can detect hot spots with small false detected overhead • Runtime improvement is more than 287X compared with ORC • Future works • Fast hot spot detection engine in detailed router • Cool spot detection: a pattern that is known to be ORC/LRC-clean through the OPC

  22. Thank You!

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