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

Atsushi Hiraiwa; Akio Nishida

doi:10.1117/12.846071

1 April 2010 Statistically accurate analysis of line width roughness based on discrete power spectrum

Atsushi Hiraiwa, Akio Nishida

Proceedings Volume 7638, Metrology, Inspection, and Process Control for Microlithography XXIV; 76380N (2010) https://doi.org/10.1117/12.846071
Event: SPIE Advanced Lithography, 2010, San Jose, California, United States

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.

Citation Download Citation

Atsushi Hiraiwa and Akio Nishida "Statistically accurate analysis of line width roughness based on discrete power spectrum", Proc. SPIE 7638, Metrology, Inspection, and Process Control for Microlithography XXIV, 76380N (1 April 2010); https://doi.org/10.1117/12.846071

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