Source-mask co-optimization (SMO) using level set methods

Abstract

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.

Inverse lithography technology: 30 years from concept to practical, full-chip reality

“…Later, the same mathematical framework has also been applied to source optimization and SMO. [59][60][61][62][63] The enabling technology in this form of ILT is the level-set representation of the design, mask, and wafer patterns. Representing the 2D design pattern, mask pattern, and wafer pattern by level sets is mathematically efficient and gives the mask patterns practically infinite degrees of freedom to change during the optimization.…”

“…Later, ILT was combined with source optimization to gain further lithography improvement. [59][60][61][62][63][64][65][66] As Luminescent was trying to drive ILT into production, it worked with its customers and partners and published numerous papers, many by the author, to demonstrate wafer process window benefits, to address mask-making-related issues, and to explore applications of ILT, such as design rule optimization. 10,18, After the Luminescent ILT business was acquired by Synopsys in 2012, the rest of the decade was a little quiet in terms of new ILT development and publications.…”

Advances in Inverse Lithography

“…For example, the same method has been used for the SMO problem described above where the source map is computed using adjoint and gradient descent optimization methods as shown in Figure 5. 35…”

Evaluation of lithographic benefits of using ILT techniques for 22nm-node

“…The source point optimization algorithm can seek to optimize any one of 2 cost functions for binary sources: Hamiltonian-based SMO or process variation (PV) -based SMO [4]. Luminescent's Level-set SMO also utilizes Hamiltonian cost function to optimize for gray-scale sources [5]. The Hamiltonian cost function is based on the distance of inversion images to the target.…”