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Model Based Double Patterning Lithography and Simulated Annealing

Model Based Double Patterning Lithography and Simulated Annealing. R. Rodrigues and S. Kundu Department of EECS University of Massachusetts at Amherst. ISQED 2011. Outline. Introduction Apply SA to DPL Optimization The Flow of the MDPL Algorithm Experimental Results Conclusions.

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Model Based Double Patterning Lithography and Simulated Annealing

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  1. Model Based Double Patterning Lithography and Simulated Annealing R. Rodrigues and S. Kundu Department of EECS University of Massachusetts at Amherst ISQED 2011

  2. Outline • Introduction • Apply SA to DPL • Optimization • The Flow of the MDPL Algorithm • Experimental Results • Conclusions

  3. Introduction • Double Patterning Lithography(DPL) is currently being used as part of Resolution Enhancement Technique in 45nm and 32nm technologies. • DPL involves partitioning a layout into two masks to reduce inference from neighboring patterns and improve resolution.

  4. Introduction • A simple partitioning of the polygons in a layout may not solve printability. • A single polygon in the mask needs to split into two masks (stitched).

  5. Introduction • DPL may be implemented: • Rules based DPL (RDPL) • The layout partitioning is done based on a minimum distance criterion. • Model based DPL (MDPL) • Lithography simulation is performed while making decisions about moving a polygon from one mask to the other.

  6. Apply SA to DPL Difference in edge placement error

  7. Apply SA to DPL • The newer configuration is accepted with a probability: • T: the temperature. • Z(T): the normalization factor. • kB: the Boltzmann constant.

  8. Cooling Schedule • Linear schedule • Starting with a temperature T0, the temperature is reduced by a constant amount. • Geometric schedule • The cooling schedule results in the multiplication of the current temperature with a factor.

  9. Optimization • Preliminaries • Printability of a polygon is affected if another polygon is within a distance of that polygon, called the optical diameter (OD). • Optical Bound (OB): extending the boundary of the polygon by OD/2 on all sides.

  10. Optimization • Selective simulation • When a polygon is moved to another layer, lithography simulation is run on only those section of other polygons that are within the OB of the polygon being moved.

  11. Optimization • Layout Partitioning into independent sections

  12. Optimization • Layout Partitioning into independent sections

  13. The Flow of the MDPL Algorithm based on SA

  14. The Flow of the MDPL Algorithm based on SA

  15. Experimental Results

  16. Experimental Results • Choice of cooling schedule

  17. Experimental Results • Comparison of possible algorithms

  18. Experimental Results • MDPL with SA and the ISCAS-85 benchmarks

  19. Experimental Results

  20. Conclusions • This paper has explored a novel MDPL solution using the SA algorithm. • Results indicate that the proposed solution produces better quality masks than earlier publications.

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