Fast mask assignment using positive semidefinite relaxation in LELECUT triple patterning lithography

Abstract

One of the most promising techniques in the 14 nm logic node and beyond is triple patterning lithography (TPL). Recently, LELECUT type TPL technology, where the third mask is used to cut the patterns, is discussed to alleviate native conflict and overlay problems in LELELE type TPL. In this paper, we formulate LELECUT mask assignment problem which maximizes the compliance to the lithography and apply a positive semidefinite relaxation. In our proposed method, the positive semidefinite relaxation is defined by extracting cut candidates from the layout, and a mask assignment is obtained from an optimum solution of the relaxation by randomized rounding technique.

Yield-aware mask assignment by positive semidefinite relaxation in triple patterning using cut process

“…The proposed method is based on the method proposed in Ref. 22. In the proposed method, a positive semidefinite relaxation of P1 called SDP-L is formulated and a mask assignment is obtained from an optimum solution of the relaxation by randomized rounding technique with iterative improvement.…”

“…The randomized rounding technique is based on the method proposed in Ref. 22, and the iterative improvement is applied as postprocessing.…”

“…Triple patterning lithography (TPL) is one of the most promising techniques in 14 nm logic node and beyond. In order to realize a target pattern, various types of techniques including design for manufacturability such as LELE type double patterning lithograph, [1][2][3][4][5][6][7] LELELE type TPL, [8][9][10][11][12][13][14][15][16][17][18][19][20] LELECUT type TPL, [21][22][23] and sidewall process [24][25][26][27][28][29] are used in addition to a basic litho-etch process with optimized mask. These techniques are summarized in Refs.…”

“…In Ref. 22, LELECUT mask assignment problem is solved by positive semidefinite relaxation. Although it minimizes the weighted summation of the number of conflicts, stitches, and polygons in the cut mask, the yield of obtained layout is also not discussed.…”

“…The proposed method is an enhancement of the method proposed in Ref. 22 and uses positive semidefinite relaxation and randomized rounding technique. In our method, the cost function that takes the length of boundary of features determined by the cut mask into account is introduced to obtain an overlay tolerant LELECUT assignment.…”