Model-based multiple patterning layout decomposition

Daifeng Guo, Haitong Tian, Yuelin Du, Martin D F Wong

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

As one of the most promising next generation lithography technologies, multiple patterning lithography (MPL) plays an important role in the attempts to keep in pace with 10 nm technology node and beyond. With feature size keeps shrinking, it has become impossible to print dense layouts within one single exposure. As a result, MPL such as double patterning lithography (DPL) and triple patterning lithography (TPL) has been widely adopted. There is a large volume of literature on DPL/TPL layout decomposition, and the current approach is to formulate the problem as a classical graph-coloring problem: Layout features (polygons) are represented by vertices in a graph G and there is an edge between two vertices if and only if the distance between the two corresponding features are less than a minimum distance threshold value dmin. The problem is to color the vertices of G using k colors (k = 2 for DPL, k = 3 for TPL) such that no two vertices connected by an edge are given the same color. This is a rule-based approach, which impose a geometric distance as a minimum constraint to simply decompose polygons within the distance into different masks. It is not desired in practice because this criteria cannot completely capture the behavior of the optics. For example, it lacks of sufficient information such as the optical source characteristics and the effects between the polygons outside the minimum distance. To remedy the deficiency, a model-based layout decomposition approach to make the decomposition criteria base on simulation results was first introduced at SPIE 2013.1 However, the algorithm1 is based on simplified assumption on the optical simulation model and therefore its usage on real layouts is limited. Recently AMSL2 also proposed a model-based approach to layout decomposition by iteratively simulating the layout, which requires excessive computational resource and may lead to sub-optimal solutions. The approach2 also potentially generates too many stiches. In this paper, we propose a model-based MPL layout decomposition method using a pre-simulated library of frequent layout patterns. Instead of using the graph G in the standard graph-coloring formulation, we build an expanded graph H where each vertex represents a group of adjacent features together with a coloring solution. By utilizing the library and running sophisticated graph algorithms on H, our approach can obtain optimal decomposition results efficiently. Our model-based solution can achieve a practical mask design which significantly improves the lithography quality on the wafer compared to the rule based decomposition.

Original languageEnglish (US)
Title of host publicationPhotomask Technology 2015
EditorsNaoya Hayashi, Bryan S. Kasprowicz, Naoya Hayashi, Bryan S. Kasprowicz
PublisherSPIE
ISBN (Electronic)9781628418453, 9781628418453
DOIs
StatePublished - Jan 1 2015
EventPhotomask Technology 2015 - Monterey, United States
Duration: Sep 29 2015Oct 1 2015

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume9635
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X

Other

OtherPhotomask Technology 2015
CountryUnited States
CityMonterey
Period9/29/1510/1/15

Fingerprint

Patterning
Lithography
layouts
Layout
lithography
Model-based
Decomposition
decomposition
Decompose
apexes
Double Patterning
polygons
Coloring
Polygon
Graph Coloring
Minimum Distance
Color
color
Mask
Masks

Keywords

  • Layout decomposition
  • Model-based approach
  • Multiple patterning

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

Cite this

Guo, D., Tian, H., Du, Y., & Wong, M. D. F. (2015). Model-based multiple patterning layout decomposition. In N. Hayashi, B. S. Kasprowicz, N. Hayashi, & B. S. Kasprowicz (Eds.), Photomask Technology 2015 [963522] (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 9635). SPIE. https://doi.org/10.1117/12.2197852

Model-based multiple patterning layout decomposition. / Guo, Daifeng; Tian, Haitong; Du, Yuelin; Wong, Martin D F.

Photomask Technology 2015. ed. / Naoya Hayashi; Bryan S. Kasprowicz; Naoya Hayashi; Bryan S. Kasprowicz. SPIE, 2015. 963522 (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 9635).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Guo, D, Tian, H, Du, Y & Wong, MDF 2015, Model-based multiple patterning layout decomposition. in N Hayashi, BS Kasprowicz, N Hayashi & BS Kasprowicz (eds), Photomask Technology 2015., 963522, Proceedings of SPIE - The International Society for Optical Engineering, vol. 9635, SPIE, Photomask Technology 2015, Monterey, United States, 9/29/15. https://doi.org/10.1117/12.2197852
Guo D, Tian H, Du Y, Wong MDF. Model-based multiple patterning layout decomposition. In Hayashi N, Kasprowicz BS, Hayashi N, Kasprowicz BS, editors, Photomask Technology 2015. SPIE. 2015. 963522. (Proceedings of SPIE - The International Society for Optical Engineering). https://doi.org/10.1117/12.2197852
Guo, Daifeng ; Tian, Haitong ; Du, Yuelin ; Wong, Martin D F. / Model-based multiple patterning layout decomposition. Photomask Technology 2015. editor / Naoya Hayashi ; Bryan S. Kasprowicz ; Naoya Hayashi ; Bryan S. Kasprowicz. SPIE, 2015. (Proceedings of SPIE - The International Society for Optical Engineering).
@inproceedings{db6082aa9ef74f249e8bcf78aee198bc,
title = "Model-based multiple patterning layout decomposition",
abstract = "As one of the most promising next generation lithography technologies, multiple patterning lithography (MPL) plays an important role in the attempts to keep in pace with 10 nm technology node and beyond. With feature size keeps shrinking, it has become impossible to print dense layouts within one single exposure. As a result, MPL such as double patterning lithography (DPL) and triple patterning lithography (TPL) has been widely adopted. There is a large volume of literature on DPL/TPL layout decomposition, and the current approach is to formulate the problem as a classical graph-coloring problem: Layout features (polygons) are represented by vertices in a graph G and there is an edge between two vertices if and only if the distance between the two corresponding features are less than a minimum distance threshold value dmin. The problem is to color the vertices of G using k colors (k = 2 for DPL, k = 3 for TPL) such that no two vertices connected by an edge are given the same color. This is a rule-based approach, which impose a geometric distance as a minimum constraint to simply decompose polygons within the distance into different masks. It is not desired in practice because this criteria cannot completely capture the behavior of the optics. For example, it lacks of sufficient information such as the optical source characteristics and the effects between the polygons outside the minimum distance. To remedy the deficiency, a model-based layout decomposition approach to make the decomposition criteria base on simulation results was first introduced at SPIE 2013.1 However, the algorithm1 is based on simplified assumption on the optical simulation model and therefore its usage on real layouts is limited. Recently AMSL2 also proposed a model-based approach to layout decomposition by iteratively simulating the layout, which requires excessive computational resource and may lead to sub-optimal solutions. The approach2 also potentially generates too many stiches. In this paper, we propose a model-based MPL layout decomposition method using a pre-simulated library of frequent layout patterns. Instead of using the graph G in the standard graph-coloring formulation, we build an expanded graph H where each vertex represents a group of adjacent features together with a coloring solution. By utilizing the library and running sophisticated graph algorithms on H, our approach can obtain optimal decomposition results efficiently. Our model-based solution can achieve a practical mask design which significantly improves the lithography quality on the wafer compared to the rule based decomposition.",
keywords = "Layout decomposition, Model-based approach, Multiple patterning",
author = "Daifeng Guo and Haitong Tian and Yuelin Du and Wong, {Martin D F}",
year = "2015",
month = "1",
day = "1",
doi = "10.1117/12.2197852",
language = "English (US)",
series = "Proceedings of SPIE - The International Society for Optical Engineering",
publisher = "SPIE",
editor = "Naoya Hayashi and Kasprowicz, {Bryan S.} and Naoya Hayashi and Kasprowicz, {Bryan S.}",
booktitle = "Photomask Technology 2015",

}

TY - GEN

T1 - Model-based multiple patterning layout decomposition

AU - Guo, Daifeng

AU - Tian, Haitong

AU - Du, Yuelin

AU - Wong, Martin D F

PY - 2015/1/1

Y1 - 2015/1/1

N2 - As one of the most promising next generation lithography technologies, multiple patterning lithography (MPL) plays an important role in the attempts to keep in pace with 10 nm technology node and beyond. With feature size keeps shrinking, it has become impossible to print dense layouts within one single exposure. As a result, MPL such as double patterning lithography (DPL) and triple patterning lithography (TPL) has been widely adopted. There is a large volume of literature on DPL/TPL layout decomposition, and the current approach is to formulate the problem as a classical graph-coloring problem: Layout features (polygons) are represented by vertices in a graph G and there is an edge between two vertices if and only if the distance between the two corresponding features are less than a minimum distance threshold value dmin. The problem is to color the vertices of G using k colors (k = 2 for DPL, k = 3 for TPL) such that no two vertices connected by an edge are given the same color. This is a rule-based approach, which impose a geometric distance as a minimum constraint to simply decompose polygons within the distance into different masks. It is not desired in practice because this criteria cannot completely capture the behavior of the optics. For example, it lacks of sufficient information such as the optical source characteristics and the effects between the polygons outside the minimum distance. To remedy the deficiency, a model-based layout decomposition approach to make the decomposition criteria base on simulation results was first introduced at SPIE 2013.1 However, the algorithm1 is based on simplified assumption on the optical simulation model and therefore its usage on real layouts is limited. Recently AMSL2 also proposed a model-based approach to layout decomposition by iteratively simulating the layout, which requires excessive computational resource and may lead to sub-optimal solutions. The approach2 also potentially generates too many stiches. In this paper, we propose a model-based MPL layout decomposition method using a pre-simulated library of frequent layout patterns. Instead of using the graph G in the standard graph-coloring formulation, we build an expanded graph H where each vertex represents a group of adjacent features together with a coloring solution. By utilizing the library and running sophisticated graph algorithms on H, our approach can obtain optimal decomposition results efficiently. Our model-based solution can achieve a practical mask design which significantly improves the lithography quality on the wafer compared to the rule based decomposition.

AB - As one of the most promising next generation lithography technologies, multiple patterning lithography (MPL) plays an important role in the attempts to keep in pace with 10 nm technology node and beyond. With feature size keeps shrinking, it has become impossible to print dense layouts within one single exposure. As a result, MPL such as double patterning lithography (DPL) and triple patterning lithography (TPL) has been widely adopted. There is a large volume of literature on DPL/TPL layout decomposition, and the current approach is to formulate the problem as a classical graph-coloring problem: Layout features (polygons) are represented by vertices in a graph G and there is an edge between two vertices if and only if the distance between the two corresponding features are less than a minimum distance threshold value dmin. The problem is to color the vertices of G using k colors (k = 2 for DPL, k = 3 for TPL) such that no two vertices connected by an edge are given the same color. This is a rule-based approach, which impose a geometric distance as a minimum constraint to simply decompose polygons within the distance into different masks. It is not desired in practice because this criteria cannot completely capture the behavior of the optics. For example, it lacks of sufficient information such as the optical source characteristics and the effects between the polygons outside the minimum distance. To remedy the deficiency, a model-based layout decomposition approach to make the decomposition criteria base on simulation results was first introduced at SPIE 2013.1 However, the algorithm1 is based on simplified assumption on the optical simulation model and therefore its usage on real layouts is limited. Recently AMSL2 also proposed a model-based approach to layout decomposition by iteratively simulating the layout, which requires excessive computational resource and may lead to sub-optimal solutions. The approach2 also potentially generates too many stiches. In this paper, we propose a model-based MPL layout decomposition method using a pre-simulated library of frequent layout patterns. Instead of using the graph G in the standard graph-coloring formulation, we build an expanded graph H where each vertex represents a group of adjacent features together with a coloring solution. By utilizing the library and running sophisticated graph algorithms on H, our approach can obtain optimal decomposition results efficiently. Our model-based solution can achieve a practical mask design which significantly improves the lithography quality on the wafer compared to the rule based decomposition.

KW - Layout decomposition

KW - Model-based approach

KW - Multiple patterning

UR - http://www.scopus.com/inward/record.url?scp=84957927748&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84957927748&partnerID=8YFLogxK

U2 - 10.1117/12.2197852

DO - 10.1117/12.2197852

M3 - Conference contribution

AN - SCOPUS:84957927748

T3 - Proceedings of SPIE - The International Society for Optical Engineering

BT - Photomask Technology 2015

A2 - Hayashi, Naoya

A2 - Kasprowicz, Bryan S.

A2 - Hayashi, Naoya

A2 - Kasprowicz, Bryan S.

PB - SPIE

ER -