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Closing the Smoothness and Uniformity Gap in Area Fill Synthesis

Supported by Cadence Design Systems, Inc., NSF, the Packard Foundation, and State of Georgia’s Yamacraw Initiative. Closing the Smoothness and Uniformity Gap in Area Fill Synthesis. Y. Chen, A. B. Kahng, G. Robins, A. Zelikovsky (UCLA, UCSD, UVA and GSU) http://vlsicad.ucsd.edu. w. w/r.

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Closing the Smoothness and Uniformity Gap in Area Fill Synthesis

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  1. Supported by Cadence Design Systems, Inc., NSF, the Packard Foundation, and State of Georgia’s Yamacraw Initiative Closing the Smoothness and Uniformity Gap in Area Fill Synthesis Y. Chen,A. B. Kahng, G. Robins, A. Zelikovsky (UCLA, UCSD, UVA and GSU) http://vlsicad.ucsd.edu

  2. w w/r overlapping windows tile Fixed-Dissection Fill Problem • Use dummy features to improve layout uniformity for CMP process • Fixed-Dissection Fill Problem: • given: • rule-correct layout in n  nregion • upper bound U on density • partition layout intonr/w nr/w fixed dissections • monitor only fixed set of windows consisting of r2tiles • fill layout subject to given constraints w.r.t. Min-Var or Min-Fill objective

  3. Gap! floating window with larger density fixed dissection window with maximum density The Smoothness Gap • Fixed-dissection analysis ≠ floating window analysis • Fill result will not satisfy the given bounds • Despite this gap (observed in 1998), all published filling methods fail to consider this smoothness gap

  4. gap between max bloated and max on-grid window accuracy Gap between bloated window and on-grid window Accurate Layout Density Analysis • Optimal extremal-density analysis with complexity inefficient • Multi-level density analysis algorithm: • any arbitrary window contains some shrunk on-grid window • any arbitrary window is contained in some bloated on-grid window

  5. Smoothness Gap in Existing Methods • Window density variation and violation of max window density in fixed-dissection filling are underestimated

  6. Type II: max density variation of every cluster of windows which cover one tile • Type III: max density variation of every cluster of windows which cover tiles Local Density Variations • Type I: max density variation of every r neighboring windows in each row of the fixed-dissection

  7. Linear Programming Formulations • Lipschitz Types: with • Combined Objective: • linear summation of Min-Var, Lip-I and Lip-II objectives with specific coefficients: • add Lip-I and Lip-II constraints as well as:

  8. Computational Experience • Solutions with best Min-Var objective value do not always have the best value in terms of local smoothness • LP with combined objective achieves best comprehensive solutions

  9. Thank you!

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