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Layout Decomposition for Triple Patterning

Years and Authors of Summarized Original Work

2011; Yu, Yuan, Zhang, Ding, Pan

Problem Definition

Layout decomposition is a key stage in triple patterning lithography manufacturing process, where the original designed layout is divided into three masks. There will be three exposure/etching steps, through which the circuit layout can be produced. When the distance between two input features is less than certain minimum distance min s , they need to be assigned to different masks (colors) to avoid coloring conflict. Sometimes coloring conflict can be resolved by splitting a pattern into two different masks. However, this introduces stitches, which lead to yield loss because of overlay error. Therefore, two of the main objectives in layout decomposition are conflict minimization and stitch minimization. An example of triple patterning layout decomposition is shown in Fig. 1, where all features are divided into three masks without any conflict and one stitch is introduced.

Fig. 1
figure 1

Layout...

Keywords

  • Layout decomposition
  • Lithography
  • Graph coloring
  • Mathematical programming

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Fig. 1
Fig. 2

Recommended Reading

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  3. Tian H, Zhang H, Ma Q, Xiao Z, Wong M (2012) A polynomial time triple patterning algorithm for cell based row-structure layout. In: IEEE/ACM international conference on computer-aided design (ICCAD), San Jose, pp 57–64

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  4. Yu B, Pan DZ (2014) Layout decomposition for quadruple patterning lithography and beyond. In: IEEE/ACM design automation conference (DAC), San Francisco

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  5. Yu B, Yuan K, Zhang B, Ding D, Pan DZ (2011) Layout decomposition for triple patterning lithography. In: IEEE/ACM international conference on computer-aided design (ICCAD), San Jose, pp 1–8

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  6. Yu B, Lin YH, Luk-Pat G, Ding D, Lucas K, Pan DZ (2013) A high-performance triple patterning layout decomposer with balanced density. In: IEEE/ACM International conference on computer-aided design (ICCAD), San Jose, pp 163–169

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  7. Yu B, Xu X, Gao JR, Pan DZ (2013) Methodology for standard cell compliance and detailed placement for triple patterning lithography. In: IEEE/ACM international conference on computer-aided design (ICCAD), San Jose, pp 349–356

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  8. Zhang Y, Luk WS, Zhou H, Yan C, Zeng X (2013) Layout decomposition with pairwise coloring for multiple patterning lithography. In: IEEE/ACM international conference on computer-aided design (ICCAD), San Jose, pp 170–177

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Yu, B., Pan, D.Z. (2014). Layout Decomposition for Triple Patterning. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27848-8_744-1

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  • DOI: https://doi.org/10.1007/978-3-642-27848-8_744-1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Online ISBN: 978-3-642-27848-8

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