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

Atsushi Hiraiwa, Akio Nishida

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

15 Citations (Scopus)

Abstract

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
Volume7638
DOIs
Publication statusPublished - 2010
Externally publishedYes
EventMetrology, Inspection, and Process Control for Microlithography XXIV - San Jose, CA
Duration: 2010 Feb 222010 Feb 25

Other

OtherMetrology, Inspection, and Process Control for Microlithography XXIV
CitySan Jose, CA
Period10/2/2210/2/25

Fingerprint

Discrete Spectrum
Power spectral density
Linewidth
Power spectrum
Power Spectrum
Roughness
Averaging
power spectra
roughness
Power Spectral Density
Surface roughness
Error analysis
Decrease
Fourier transforms
Electron microscopes
Long-range Correlations
Line
Inspection
Pixels
Scanning Electron Microscope

Keywords

  • 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

Cite this

Hiraiwa, A., & Nishida, A. (2010). Statistically accurate analysis of line width roughness based on discrete power spectrum. In Proceedings of SPIE - The International Society for Optical Engineering (Vol. 7638). [76380N] https://doi.org/10.1117/12.846071

Statistically accurate analysis of line width roughness based on discrete power spectrum. / Hiraiwa, Atsushi; Nishida, Akio.

Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7638 2010. 76380N.

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

Hiraiwa, A & Nishida, A 2010, Statistically accurate analysis of line width roughness based on discrete power spectrum. in Proceedings of SPIE - The International Society for Optical Engineering. vol. 7638, 76380N, Metrology, Inspection, and Process Control for Microlithography XXIV, San Jose, CA, 10/2/22. https://doi.org/10.1117/12.846071
Hiraiwa A, Nishida A. Statistically accurate analysis of line width roughness based on discrete power spectrum. In Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7638. 2010. 76380N https://doi.org/10.1117/12.846071
Hiraiwa, Atsushi ; Nishida, Akio. / Statistically accurate analysis of line width roughness based on discrete power spectrum. Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7638 2010.
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