# Layout Decomposition for Quadruple Patterning Lithography and Beyond

arXiv: https://arxiv.org/abs/1404.0321 · HTML: https://mlsanity.com/paper/1404.0321/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Mar 2014.

## Built on by (most cited first, 1 of 1)

- [GPU-accelerated Matrix Cover Algorithm for Multiple Patterning Layout Decomposition](https://mlsanity.com/paper/2303.14335/) (2023)

## Abstract (arXiv)

For next-generation technology nodes, multiple patterning lithography (MPL) has emerged as a key solution, e.g., triple patterning lithography (TPL) for 14/11nm, and quadruple patterning lithography (QPL) for sub-10nm. In this paper, we propose a generic and robust layout decomposition framework for QPL, which can be further extended to handle any general K-patterning lithography (K>4). Our framework is based on the semidefinite programming (SDP) formulation with novel coloring encoding. Meanwhile, we propose fast yet effective coloring assignment and achieve significant speedup. To our best knowledge, this is the first work on the general multiple patterning lithography layout decomposition.