Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Unbiased Estimation of Linewidth Roughness



John S. Villarrubia, B Bunday


Line width roughness (LWR) is usually estimated simply as three standard deviations of the line width. The effect of image noise upon this metric includes a positive nonrandom component. The metric is therefore subject to a bias or ?systematic error? that we have estimated can be comparable in size to the roughness itself for samples as smooth as required by the industry roadmap. We illustrate the problem using scanning electron microscope images of rough lines. We propose simple changes to the measurement algorithm that, if adopted by metrology instrument suppliers, would permit estimation of LWR without bias caused by image noise. (11 references)
Proceedings Title
Proceedings of SPIE
Conference Dates
February 27-March 4, 2005
Conference Location
San Jose, CA, USA
Conference Title
Metrology, Inspection, and Process Control for Microlithography XIX, Richard M. Silver, Editor, May 2005


line edge roughness (LER), line width roughness (LWR), measurement algorithms, measurement bias, Scanning Electron Microscopy (SEM)


Villarrubia, J. and Bunday, B. (2005), Unbiased Estimation of Linewidth Roughness, Proceedings of SPIE, San Jose, CA, USA, [online], (Accessed July 14, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created April 30, 2005, Updated October 12, 2021