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

Atsushi Hiraiwa*, Akio Nishida


研究成果: Conference contribution

16 被引用数 (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.

ホスト出版物のタイトルProceedings of SPIE - The International Society for Optical Engineering
出版ステータスPublished - 2010
イベントMetrology, Inspection, and Process Control for Microlithography XXIV - San Jose, CA
継続期間: 2010 2月 222010 2月 25


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

ASJC Scopus subject areas

  • 応用数学
  • コンピュータ サイエンスの応用
  • 電子工学および電気工学
  • 電子材料、光学材料、および磁性材料
  • 凝縮系物理学


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