Filling and slotting: Analysis and algorithms

In very deep-submicron VLSI, certain manufacturing steps – notably optical exposure, resist development and etch, chemical vapor deposi-tion and chemical-mechanical polishing (CMP) – have varying effects on device and interconnect features depending on local characteristics of the layout. To make these effects uniform and predictable, the layout itself must be made uniform with respect to certain density parame-ters. Traditionally, only foundries have performed the post-processing needed to achieve this uniformity, via insertion (“filling”) or partial deletion (“slotting”) of features in the layout. Today, however, physical design and verification tools cannot remain oblivious to such foundry post-processing. Without an accurate estimate of the filling and slot-ting, RC extraction, delay calculation, and timing and noise analysis flows will all suffer from wild inaccuracies. Therefore, future place-and-route tools must efficiently perform filling and slotting prior to performance analysis within the layout optimization loop. We give the first formulations of the filling and slotting problems that arise in lay-out post-processing or layout optimization for manufacturability. Such formulations seek to add or remove features to a given process layer, so that the local area or perimeter density of features satisfies prescribed upper and lower bounds in all windows of a given size. We also present efficient algorithms for density analysis as well as for filling/slotting synthesis. Our work provides a new unification between manufactur-ing and physical design, and captures a number of general requirements imposed on layout by the manufacturing process.