Statistically accurate analysis of line width roughness based on discrete power spectrum

Atsushi Hiraiwa*, Akio Nishida

*Corresponding author for this work

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

16 Citations (Scopus)


We established guidelines for accurately analyzing line-edge and line-width roughness (LER and LWR) basing on the recent discrete power-spectral-density (PSD) method. Extraction of correlation length ζ requires a plateau of PSD in a small-wave-number region. This requirement is met by letting a ratio of inspection length L to ζ be larger than 4π. Analysis errors caused by scanning-electron-microscope image noise are determined by ratios of measurement interval Δy to ζ and of noise-induced variance var(φ) to LWR variance var(w). The ratios need to be at most 20/35 and 1, respectively. var(φ) is reduced by averaging image pixels perpendicularly to lines. This averaging does not smooth LWR, unlike parallel averaging. Statistical noise, i.e. jaggy of PSDs, is another noise source that is caused by a finiteness of the number NFT of Fourier transforms averaged to obtain PSDs. The jaggy level decreases with NFT and with a decrease in Δy. Under the above Δy, NFT should preferably be 50 or larger. The total variance of this study was larger than the sum of var(w) and var(φ). The additional roughness results from a long-range correlation that exceeds the limit of this study. It will be analyzed in our forthcoming report.

Original languageEnglish
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
Publication statusPublished - 2010
Externally publishedYes
EventMetrology, Inspection, and Process Control for Microlithography XXIV - San Jose, CA
Duration: 2010 Feb 222010 Feb 25


OtherMetrology, Inspection, and Process Control for Microlithography XXIV
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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