Practical iterated fill synthesis for CMP uniformity

ABSTRACT

We propose practical iterated methods for layout density control for CMP uniformity, based on linear programming, Monte-Carlo and greedy algorithms. We experimentally study the tradeoffs between two main filling objectives: minimizing density variation, and minimizing the total amount of inserted fill. Comparisons with previous filling methods show the advantages of our new iterated Monte-Carlo and iterated greedy methods. We achieve near-optimal filling with respect to each of the objectives and for both density models (spatial density [3] and effective density [8]). Our new methods are more efficient in practice than linear programming [3] and more accurate than non-iterated Monte-Carlo approaches [1].

REFERENCES

• 1: Yu Chen , Andrew B. Kahng , Gabriel Robins , Alex Zelikovsky, Monte-Carlo algorithms for layout density control, Proceedings of the 2000 conference on Asia South Pacific design automation, p.523-528, January 2000, Yokohama, Japan [doi>10.1145/368434.368778]
• 2: R.R. Divecha, B. E. Stine, D. O. Ouma, J. U. Yoon, D. S. Boning, et al., "Effect of Fine-line Density and Pitch on Interconnect ILD Thickness Variation in Oxide CMP Process", Proc. CMP-MIC, 1998.
• 3: A.B. Kahng, G. Robins, A. Singh, H. Wang and A. Zelikovsky, "Filling Algorithms and Analyses for Layout Density Control", IEEE Trans. Computer-Aided Design 18(4) (1999), pp. 445-462.
• 4: H. landis, P. Burke, W. Cote, W. Hill, C. Hoffman, et al., "Integration of Chemical-Mechanical Polishing into CMOS Integrated Circuit Manufacturing", Thin Solid Films 220(20) (1992), pp. 1-7.
• 5: W. Maly, Moore's law and physical design of ICs, Proceedings of the 1998 international symposium on Physical design, p.36, April 06-08, 1998, Monterey, California, United States [doi>10.1145/274535.274540]
• 6: G. Nanz and L. E. Camilletti, "Modeling of Chemical-Mechanical Polishing: A Review", IEEE Trans. on Semiconductor Manufacturing 8(4) (1995), pp. 382- 389.
• 7: B. Stine, "A Closed-Form Analytical Model for ILD Thickness Variation in CMP Processes", Proc. CMP-MIC, 1997.
• 8: Ruiqi Tian , D. F. Wong , Robert Boone , Alfred Reich, Dummy Feature Placement for Oxide Chemical-mechanical PolishingManufacturability, University of Texas at Austin, Austin, TX, 1999
• 9: M. Tomozawa, "Oxide CMP Mechanisms", Solid State Technology 40(7) (1997), pp. 169-175.

INDEX TERMS

Primary Classification:
  J. Computer Applications

Additional Classification:
  B. Hardware
  B.7 INTEGRATED CIRCUITS
  B.8 Performance and Reliability

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.6 Optimization
          Subjects: Linear programming

  J. Computer Applications
  J.2 PHYSICAL SCIENCES AND ENGINEERING
      Subjects: Electronics

General Terms:
Algorithms, Design, Experimentation, Measurement, Performance, Theory