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Distributed force probe bending model of critical dimension atomic force microscopy bias

[+] Author Affiliations
Vladimir A. Ukraintsev

National Institute of Standards and Technology, Gaithersburg, Maryland

University of Maryland, Institute for Research in Electronics and Applied Physics, College Park, Maryland

Nanometrology International, Inc., Allen, Texas

Ndubuisi G. Orji

National Institute of Standards and Technology, Gaithersburg, Maryland

Theodore V. Vorburger

National Institute of Standards and Technology, Gaithersburg, Maryland

Ronald G. Dixson

National Institute of Standards and Technology, Gaithersburg, Maryland

Joseph Fu

National Institute of Standards and Technology, Gaithersburg, Maryland

Rick M. Silver

National Institute of Standards and Technology, Gaithersburg, Maryland

J. Micro/Nanolith. MEMS MOEMS. 12(2), 023009 (Jun 04, 2013). doi:10.1117/1.JMM.12.2.023009
History: Received March 6, 2013; Revised April 24, 2013; Accepted May 10, 2013
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Abstract.  Critical dimension atomic force microscopy (CD-AFM) is a widely used reference metrology technique. To characterize modern semiconductor devices, small and flexible probes, often 15 to 20 nm in diameter, are used. Recent studies have reported uncontrolled and significant probe-to-probe bias variation during linewidth and sidewall angle measurements. To understand the source of these variations, tip-sample interactions between high aspect ratio features and small flexible probes, and their influence on measurement bias, should be carefully studied. Using theoretical and experimental procedures, one-dimensional (1-D) and two-dimensional (2-D) models of cylindrical probe bending relevant to carbon nanotube (CNT) AFM probes were developed and tested. An earlier 1-D bending model was refined, and a new 2-D distributed force (DF) model was developed. Contributions from several factors were considered, including: probe misalignment, CNT tip apex diameter variation, probe bending before snapping, and distributed van der Waals-London force. A method for extracting Hamaker probe-surface interaction energy from experimental probe-bending data was developed. Comparison of the new 2-D model with 1-D single point force (SPF) model revealed a difference of about 28% in probe bending. A simple linear relation between biases predicted by the 1-D SPF and 2-D DF models was found. The results suggest that probe bending can be on the order of several nanometers and can partially explain the observed CD-AFM probe-to-probe variation. New 2-D and three-dimensional CD-AFM data analysis software is needed to take full advantage of the new bias correction modeling capabilities.

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© 2013 Society of Photo-Optical Instrumentation Engineers

Citation

Vladimir A. Ukraintsev ; Ndubuisi G. Orji ; Theodore V. Vorburger ; Ronald G. Dixson ; Joseph Fu, et al.
"Distributed force probe bending model of critical dimension atomic force microscopy bias", J. Micro/Nanolith. MEMS MOEMS. 12(2), 023009 (Jun 04, 2013). ; http://dx.doi.org/10.1117/1.JMM.12.2.023009


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