A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Polymer self assembly in semiconductor microelectronics
IBM Journal of Research and Development
Mask cost reduction with circuit performance consideration for self-aligned double patterning
Proceedings of the 16th Asia and South Pacific Design Automation Conference
Layout small-angle rotation and shift for EUV defect mitigation
Proceedings of the International Conference on Computer-Aided Design
A polynomial time triple patterning algorithm for cell based row-structure layout
Proceedings of the International Conference on Computer-Aided Design
Constrained pattern assignment for standard cell based triple patterning lithography
Proceedings of the International Conference on Computer-Aided Design
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At the 10 nm technology node, the contact layers of integrated circuits (IC) designs are too dense to be printed by single exposure using 193 nm immersion (193i) lithography. Among all the emerging patterning approaches, block copolymer directed self-assembly (DSA) is a promising candidate with high throughput and low cost for sub-20 nm features. Traditionally, the study of DSA has focused on achieving periodic regular patterns over large area. Realizing that long range order is not needed for patterning irregularly distributed contact holes, we use topographical guiding templates to alter the natural symmetry of block copolymer and achieve controlled irregular DSA patterns. However, DSA patterning must satisfy the overlay accuracy requirements while the guiding templates also need to be printable by conventional lithography. This presents a unique opportunity of DSA patterning and layout design co-optimization for improving the manufacturability of DSA. This paper discusses the DSA-aware contact layer optimization problem for 10 nm 1D standard cell library. For the first time we propose a cost function for each DSA template based on its overlay accuracy performance. Then given a standard cell library, we simultaneously optimize the layouts of every cell, such that the contact layer of any cell in the library can be fully patterned by a set of guiding templates, and the total cost of the templates is minimal. This optimization problem is first proved to be NP-hard and formulated as a Weighted Partial Maximum Satisfiability (MAX-SAT) problem, which can be optimally solved with a public SAT solver. Then we propose a bounded approximation algorithm that solves the problem much more efficiently. The experimental results demonstrate that our approach is remarkably promising in practice and validate the proposed optimization problem.