Closing the smoothness and uniformity gap in area fill synthesis

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".