Statistical-noise effect on power spectrum of line-edge and line-width roughness with long-range correlation

Atsushi Hiraiwa*, Akio Nishida

*Corresponding author for this work

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

1 Citation (Scopus)


We formerly developed the "assembly method" for analyzing the line-edge and line-width roughness (LER/LWR) that has a long-range correlation beyond the conventional analysis limit. In the method, we repeatedly assembled virtual long lines by gathering line segments, which were arbitrarily disposed on actual long lines and by randomly changing their combination and order, permitting the assembled lines to share the same line segments. Then, we obtained the PSD of the LER/LWR of the assembled lines considering the lines as seamless. We also derived an analytic formula of the assembled-line PSDs. This formula excellently agreed with experimental PSDs. In this report, we propose guidelines for suppressing the statistical-noise effect on the assembly method for the purpose of accurately analyzing the long-range- correlated LER/LWR. The guidelines will greatly help shed light on the long-range correlation, which causes the variability even in large devices but has long been veiled due to the lack of metrology.

Original languageEnglish
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
Publication statusPublished - 2011
Externally publishedYes
EventMetrology, Inspection, and Process Control for Microlithography XXV - San Jose, CA
Duration: 2011 Feb 282011 Mar 3


OtherMetrology, Inspection, and Process Control for Microlithography XXV
CitySan Jose, CA


  • correlation length
  • LER
  • line edge roughness
  • line width roughness
  • LWR
  • noise
  • power spectrum
  • PSD

ASJC Scopus subject areas

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


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