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 language | English |
|---|---|
| Title of host publication | Proceedings of SPIE - The International Society for Optical Engineering |
| Volume | 7638 |
| DOIs | |
| Publication status | Published - 2010 |
| Externally published | Yes |
| Event | Metrology, Inspection, and Process Control for Microlithography XXIV - San Jose, CA Duration: 2010 Feb 22 → 2010 Feb 25 |
Other
| Other | Metrology, Inspection, and Process Control for Microlithography XXIV |
|---|---|
| City | San Jose, CA |
| Period | 10/2/22 → 10/2/25 |
Fingerprint
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
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 proceeding › Conference contribution
}
TY - GEN
T1 - Statistically accurate analysis of line width roughness based on discrete power spectrum
AU - Hiraiwa, Atsushi
AU - Nishida, Akio
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
KW - correlation length
KW - LER
KW - line edge roughness
KW - line width roughness
KW - LWR
KW - noise
KW - power spectrum
KW - PSD
UR - http://www.scopus.com/inward/record.url?scp=77955870448&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77955870448&partnerID=8YFLogxK
U2 - 10.1117/12.846071
DO - 10.1117/12.846071
M3 - Conference contribution
AN - SCOPUS:77955870448
SN - 9780819480521
VL - 7638
BT - Proceedings of SPIE - The International Society for Optical Engineering
ER -