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Proceedings Paper

Distance-based standard deviation analysis method for line width roughness data
Author(s): Thomas J. Bzik; Madhukar B. Rao; Peng Zhang
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Paper Abstract

Linewidth roughness (LWR) is a major challenge for 90nm node and below. As feature sizes decrease, the reliable measurement, statistical comparison and interpretation of LWR data become increasingly important. The reliability of all LWR statistical analysis methods are strongly impacted by the architecture of LWR data being analyzed. Some of the key structural aspects of the collected data include: measurement box size, distance between neighboring measurements and whether measurement boxes have been "stitched" together for analysis. Additionally, the true nature of underlying line width variation, including both cyclical and non-cyclical trends, impacts how reliable a given interpretation will be. Current statistical methodologies for linewidth data are oriented at estimation of the frequency and scale of cyclical variation in linewidth components. Fourier analysis is traditionally applied for this purpose. Such analyses assume both that there is a cyclical component (e.g., sinusoidal) or components in the data to be modeled, as well as implicitly assuming a Gaussian error distribution for the linewidth variation that remains after modeling. The assumption that Fourier analysis is appropriate for LWR data often not met in practice by the LWR data undergoing analysis. A more model-independent approach, distance-based standard deviations, is proposed for use as part of an LWR statistical analysis methodology. It is based on the calculation of local standard deviations of linewidth for all possible distances between measured points. This methodology permits the statistical comparison of linewidth roughness over any distance of interest and makes efficient use of all data for a given measurement box length. It can determine the minimum measurement box length required to capture all linewidth variation. In addition, the method can confirm the validity of line stitching to increase measurement box size, and locate the sources of variance in the overall LWR value (e.g. line-to-line vs. within line). This new method is an effective alternative to established methods for the statistical evaluation of linewidth data. The new statistical technique will be illustrated on linewidth data (measured in μm) obtained from CDSEM measurements.

Paper Details

Date Published: 10 May 2005
PDF: 8 pages
Proc. SPIE 5752, Metrology, Inspection, and Process Control for Microlithography XIX, (10 May 2005); doi: 10.1117/12.599987
Show Author Affiliations
Thomas J. Bzik, Air Products and Chemicals, Inc. (United States)
Madhukar B. Rao, Air Products and Chemicals, Inc. (United States)
Peng Zhang, Air Products and Chemicals, Inc. (United States)


Published in SPIE Proceedings Vol. 5752:
Metrology, Inspection, and Process Control for Microlithography XIX
Richard M. Silver, Editor(s)

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