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

Abstract

LELECUT type triple patterning lithography is one of the most promising techniques in 14 nm logic node and beyond. To prevent yield loss caused by overlay error, LELECUT mask assignment, which is tolerant to overlay error, is desired. We propose a method that obtains a LELECUT assignment that is tolerant to overlay error. The proposed method 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.

A Routing Method Using Directed Grid-Graph for Self-Aligned Quadruple Patterning

“…The problem of finding a decomposition of features in LELELE type TPL is NP-hard in general [2]. Even though several decomposition methods including an approximation algorithm for LELELE type TPL [2]- [4] and for LELECUT type TPL [5]- [8] were proposed, it is not easy to achieve the target pitch by TPL in practice due to inevitable overlay error.…”