DSA-aware multiple patterning for the manufacturing of vias: Connections to graph coloring problems, IP formulations, and numerical experiments

In this paper, we investigate the manufacturing of vias in integrated circuits with a new technology combining lithography and Directed Self Assembly (DSA). Optimizing the production time and costs in this new process entails minimizing the number of lithography steps, which constitutes a generalization of graph coloring. We develop integer programming formulations for several variants of interest in the industry, and then study the computational performance of our formulations on true industrial instances. We show that the best integer programming formulation achieves good computational performance, and indicate potential directions to further speed-up computational time and develop exact approaches feasible for production

The kk-path coloring problem in graphs with bounded treewidth: an application in integrated circuit manufacturing

In this paper, we investigate the $k$-path coloring problem, a variant of vertex coloring arising in the context of integrated circuit manufacturing. In this setting, typical industrial instances exhibit a `tree-like' structure. We exploit this property to design an efficient algorithm for our industrial problem: (i) on the methodological side, we show that the $k$-path coloring problem can be solved in polynomial time on graphs with bounded treewidth and we devise a simple polytime dynamic programming algorithm in this case (not relying on Courcelle's celebrated theorem); and (ii) on the empirical side, we provide computational evidences that the corresponding algorithm could be suitable for practice, by testing our algorithm on true instances obtained from an on-going collaboration with Mentor Graphics. We finally compare this approach with integer programming on some pseudo-industrial instances. It suggests that dynamic programming cannot compete with integer programming when the tree-width is greater than three. While all our industrial instances exhibit such a small tree-width, this is not for granted that all future instances will also do, and this tend to advocate for integer programming approaches

Integer programming for DSA grouping and multiple lithography

International audienc

DSA-aware multiple patterning for the manufacturing of vias: Connections to graph coloring problems, IP formulations, and numerical experiments

In this paper, we investigate the manufacturing of vias in integrated circuits with a new technology combining lithography and Directed Self Assembly (DSA). Optimizing the production time and costs in this new process entails minimizing the number of lithography steps, which constitutes a generalization of graph coloring. We develop integer programming formulations for several variants of interest in the industry, and then study the computational performance of our formulations on true industrial instances. We show that the best integer programming formulation achieves good computational performance, and indicate potential directions to further speed-up computational time and develop exact approaches feasible for production

The kk-path coloring problem in graphs with bounded treewidth: an application in integrated circuit manufacturing

In this paper, we investigate the $k$-path coloring problem, a variant of vertex coloring arising in the context of integrated circuit manufacturing. In this setting, typical industrial instances exhibit a `tree-like' structure. We exploit this property to design an efficient algorithm for our industrial problem: (i) on the methodological side, we show that the $k$-path coloring problem can be solved in polynomial time on graphs with bounded treewidth and we devise a simple polytime dynamic programming algorithm in this case (not relying on Courcelle's celebrated theorem); and (ii) on the empirical side, we provide computational evidences that the corresponding algorithm could be suitable for practice, by testing our algorithm on true instances obtained from an on-going collaboration with Mentor Graphics. We finally compare this approach with integer programming on some pseudo-industrial instances. It suggests that dynamic programming cannot compete with integer programming when the tree-width is greater than three. While all our industrial instances exhibit such a small tree-width, this is not for granted that all future instances will also do, and this tend to advocate for integer programming approaches

Efficient solutions for the manufacturing of vias/contacts using DSA technology

International audienc

Dynamic programming for generalized coloring problems arising in the manufacturing of integrated circuits

International audienc

Toward an Optimal Scan Insertion at the Register Transfer Level

Les Cahiers Leibni

Efficient solutions for the manufacturing of vias/contacts using DSA technology

International audienc