Filling and slotting: analysis and algorithms
ISPD '98 Proceedings of the 1998 international symposium on Physical design
Model-based dummy feature placement for oxide chemical-mechanical polishing manufacturability
Proceedings of the 37th Annual Design Automation Conference
Practical iterated fill synthesis for CMP uniformity
Proceedings of the 37th Annual Design Automation Conference
Monte-Carlo algorithms for layout density control
ASP-DAC '00 Proceedings of the 2000 Asia and South Pacific Design Automation Conference
Proceedings of the 2001 international symposium on Physical design
Hierarchical dummy fill for process uniformity
Proceedings of the 2001 Asia and South Pacific Design Automation Conference
Filling algorithms and analyses for layout density control
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Research directions for coevolution of rules and routers
Proceedings of the 2003 international symposium on Physical design
Performance-impact limited area fill synthesis
Proceedings of the 40th annual Design Automation Conference
Dummy fill density analysis with coupling constraints
Proceedings of the 2007 international symposium on Physical design
Is your layout density verification exact?: a fast exact algorithm for density calculation
Proceedings of the 2007 international symposium on Physical design
Integrative 3D modelling of complex carving surface
Computer-Aided Design
A novel wire-density-driven full-chip routing system for CMP variation control
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Density gradient minimization with coupling-constrained dummy fill for CMP control
Proceedings of the 19th international symposium on Physical design
Simultaneous flare level and flare variation minimization with dummification in EUVL
Proceedings of the 49th Annual Design Automation Conference
An efficient method for gradient-aware dummy fill synthesis
Integration, the VLSI Journal
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Control of variability in the back end of the line, and hence in interconnect performance as well, has become extremely difficult with the introduction of new materials such as copper and low-k dielectrics. Uniformity of chemical-mechanical planarization (CMP) requires the addition of area fill geometries into the layout, in order to smoothen the variation of feature densities across the die. Our work addresses the following smoothness gap in the recent literature on area fill synthesis. (1)The very first paper on the filling problem (Kahng et al., ISPD98 [7]) noted that there is potentially a large difference between the optimum window densities in fixed dissections vs. when all possible windows in the layout are considered. (2)Despite this observation, all filling methods since 1998 minimize and evaluate density variation only with respect to a fixed dissection. This paper gives the first evaluation of existing filling algorithms with respect to "gridless" ("floating-window") mode, according to both the effective and spatial density models. Our experiments indicate surprising advantages of Monte-Carlo and greedy strategies over "optimal" linear programming (LP) based methods. Second, we suggest new, more relevant methods of measuring a local uniformity based on Lipschitz conditions, and empirically demonstrate that Monte-Carlo methods are inherently better than LP with respect to the new criteria. Finally, we propose new LP-based filling methods that are directly driven by the new criteria, and show that these methods indeed help close the "smoothness gap".