Input: Layout L, ɛ 0, ɛ 1, ɛ 2, d 0Output: A list of hotspots in L1. Construct layout graph G from L, S ←∅2. For all edges e whose weight >ɛ 0 (Edge-level detection)3. S ← S ∪{e}4. Delete e from G5. Perform graph planarization to delete one of the crossing edges6. Construct dual graph G D from G7. For all dual nodes n whose weight >ɛ 1 (Face-level detection)8. S ← S ∪{n}9. Delete n from G D10.While (∃ dual nodes can be merged) (Merged-face-level detection)11. Sort all dual nodes according to weight12. Merge the two connected dual nodes with the max combined weight13. If (the weight of the combined node n c >ɛ 2)14. S ← S ∪{n c}15. Delete n c from G D16. For all hotspots in S17. If (local wiring density
Figure 9. Results of hotspot detection: comparison of (a) hotspot patterns versus (b) no hotspot patternsSimulated # <strong>Hotspot</strong>s Runtime (sec)Condition ORC Detected Falsely Detected ORC <strong>Dual</strong> <strong>Graph</strong>DOF(µm)=0.1, ET=0.36 17 17 13 690 1.37DOF(µm)=0.1, ET=0.37 21 21 22 690 1.52DOF(µm)=0.1, ET=0.38 25 25 46 690 2.32DOF(µm)=0.2, ET=0.38 152 152 1291 690 4.38Total 215 215 1372 2760 9.59Table 1. Comparison of hotspot detection efficiency of ORC and our proposed method.of dual graph-based method is exactly matching to simulation-based method. Thus, dual graph-based methodcan detects a hotspot induced by pattern density which cannot be achieved by rule-based approach.We implemented our proposed iterative dual node merging heuristic in C++. The values of ɛ 0 , ɛ 1 , ɛ 2 and d 0in Figure 7 are chosen according to different conditions. For example, the values are chosen as 0.7, 0.36, 0.67and 0.17 for the first condition. We test our code under four different process conditions. The runtime of ourmethod is more than 287X faster compared with commercial ORC tools. The results are summarized in Table 1.We can see that our proposed hotspot detection method achieves good accuracy (100% of hotspots are detected)with smaller false detection overhead.4. CONCLUSIONSWith the continued shrinkage of minimum feature sizes, hotspots, i.e., printed image with large CD variation,present an important threat for manufacturing yield. Therefore, it becomes more and more important to fastand accurately detect the hotspots in a layout. In this paper, we first describe a novel, fast, dual graph basedlithographic hotspot detection algorithm without significant accuracy degradation. The experimental resultsshow that our method is promising: for the metal layer with 17 hotspots detected by commercial ORC tools,our method can detect all of them while the runtime improvement is more than 287X. In the future, we planto include the fast hotspot detection engine in detailed router to improve the yield. We also want to test ouralgorithm on more large testcases.REFERENCES1. K. Hashimoto, S. Usui, S. Nojima, S. Tanaka, E. Yamanaka and S. Inoue, “Hot Spot Management inUltra-low k1 Lithography”, 2005, Proc. International Society for Optical Engineering (SPIE) Symposiumon Microlithography, vol. 6156, pp. 1207-1219.2. S. Nojima, S. Mimotogi, M. Itoh, O. Ikenaga, S. Hasebe, K. Hashimoto, S. Inoue, M. Goto and I. Mori,“Flexible mask specifications”, 2002, Proc. SPIE 22nd Annual BACUS Symposium on Photomask Technology,Vol.4889, pp. 187-196.3. M. Cote and P. Hurat, “Standard Cell Printability Grading and Hot Spot <strong>Detection</strong>”, 2005, Intl. Symp. onQuality of Electronic Design, pp. 264-269.Proc. of SPIE Vol. 6349 63490H-7
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