Selective Use of Stitch-Induced Via for V0 Mask Reduction: Standard Cell Design and Placement Optimization

Abstract

Multiple patterning lithography allows fine patterns beyond lithography limit, but it suffers from a large process cost. In this paper, we address a method to reduce the number of V0 masks; it consists of two sub-problems. First, stitch-induced via (SIV) is introduced to reduce the number of V0 masks. It involves the redesign of standard cells to replace some vias in V0 layer with SIVs, such that the remaining vias can be assigned to the reduced masks. Since SIV formation requires metal stitches in different masks, SIV replacement and metal mask assignment should be solved simultaneously. This sub-problem is formulated as integer linear programming (ILP). In the second sub-problem, inter-row via conflict aware detailed placement is addressed. Single row placement optimization is performed for each row to remove metal and inter-row via conflicts, while minimizing cell displacements. Since it is time consuming to consider many cell operations at once, we apply a few operations iteratively, where different operations are applied to each iteration and to each cell depending on whether the cell has a conflict in the previous iteration. Remaining conflicts are then removed by mapping conflict cells to white spaces. To this end, we minimize the number of cells to move and maximize the number of large white spaces before mapping. Experimental results demonstrate that the cell placement with two V0 masks is completed by proposed methods, with 7 times speedup and 21% reduction in total cell displacement, compared to conventional detailed placement.