Source-Mask co-Optimization (SMO) using Level Set Methods

Masks computed by use of Inverse Lithography Technology (ILT) are being increasingly used in 32nm and below nodes for their significantly better litho performance outperforming model-based OPC [1,2]. This technique poses the design of photomasks as an inverse problem and then solves for the optimal photomask using rigorous mathematical approach [3,4]. One such approach is the level set based method [5] wherein a level set function φ(x,y) is made to represent the contour of the mask. The zero level set φ(x,y)=0 then represents the actual mask at a given instance. The same level-set technique has now been extended to determine the most optimized source φ(p,q) for a given target or mask. Cooptimization of both the source and mask is a natural extension of optimizing the mask alone in ILT. The same cost function, say maximizing DOF, which is used to compute the ILT mask can be used for the source optimization as well. This approach enables accurate and fast computation of the optimized source and mask for given set of patterns and also utilizes running on a distributed computing environment. In this paper, the level set based SMO approach will be first validated on simple contact array patterns and then extended to the optimization of sample 22nm logic contact design patterns, including array, SRAM and random logic. The effect of using different emphasis in defining the cost function will also be studied.