Monte-Carlo algorithms for layout density control

Abstract

Abstract| Chemical-mechanical polishing CMP and other manufacturing steps in very deep submicron VLSI have varying e ects on devic e and inter connect features, dep ending on local char acteristics of the layout. T o enhance manufacturability and performance p r edictability, we seek to make the layout uniform with respect to prescribed densit ycriteria, by inserting ll" geometries into the layout. We propose several new Monte-Carlo based lling methods with fast dynamic data structures and report the tradeo between runtime and accuracy for the suggested methods. Compared to existing linear programming based a p p r oaches, our Monte-Carlo methods seem very promising as they produc enearly-optimal solutions within reasonable runtimes.

A simple fast exact density calculation algorithm

“…In industry, most commercial tools use fix-dissection approach [4,5,6]. In this approach, a layout is partitioned into non-overlapping RxR tiles.…”

“…Y [5] rowarea [ 4 ] rowarea [3 ] rowarea [2 ] rowarea [1 ] rowarea [0 ] winarea = winarea + rowarea [3] Finally, since the fix-dissection approach is a special case of DCGW with all grid tiles having the same size, the fix-dissection approach can get the maximum density of all sliding windows in O(M · N).…”

“…The coord field of the two hash tables is initially assigned a value that is lower than Wout.y l . yHash1 [2] yHash1 [3] yHash1 [4] yHash2 [0] yHash2 [1] yHash2 [2] yHash2 [3] yHash2 [4] tile [4,5] .coord is marked as 39. Similarly, the upper edge of the rectangle R1 also corresponds to two horizontal grid lines, and we get yHash2 [3].coord = 40 and yHash1 [3].coord = 29.…”

“…Meanwhile, by checking the left and right edges of R1, we know that the rectangle falls between the 4th and 5th vertical lines. Therefore, we only need to calculate the overlap areas between R1 and tile [4,6] and tile [4,5].…”

Detailed Placement for Enhanced Control of Resist and Etch CDs

“…In addition to the LP approaches, Chen et al [10] introduce the Monte Carlo method for min-variation objective. In the Monte Carlo approach, a tile is chosen randomly and its content is incremented with a predetermined fill amount.…”