Optimizing measurement configuration for x-ray critical dimension metrology based on condition number

Tianjuan Yang; Xiuguo Chen; Jiahao Zhang; Shuo Liu; Shiyuan Liu

doi:10.1117/12.3008281

24 November 2023 Optimizing measurement configuration for x-ray critical dimension metrology based on condition number

Tianjuan Yang, Xiuguo Chen, Jiahao Zhang, Shuo Liu, Shiyuan Liu

Proceedings Volume 12935, Fourteenth International Conference on Information Optics and Photonics (CIOP 2023); 1293557 (2023) https://doi.org/10.1117/12.3008281
Event: Fourteenth International Conference on Information Optics and Photonics (CIOP 2023), 2023, Xi’an, China

Abstract

In X-ray critical dimension metrology (XCD), it is a common practice to select an appropriate measurement configuration, including incidence angle, azimuth angle, exposure time, etc., to improve measurement results. This is crucial as the quality of the obtained signature is impacted not just by the instrument's precision, but also by the specific chosen measurement configuration. This is known as the measurement configuration optimization (MCO) problem. This paper proposes a general MCO method based on the theory of error propagation and error estimation techniques using condition numbers. Finally, the MCO problem in XCD is framed as optimizing the "max-min" condition number of the coefficient matrix within the context of linear error estimation. The proposed method is showcased on "virtual experiments" conducted via simulations to determine the optimal combinations of rotation angles along two coordinate axes. The method's feasibility is substantiated through a comparison with the distributions of parameter uncertainty. The results suggest that the proposed method holds promise as an alternative approach for comprehensive evaluation in the context of the MCO problem in XCD and various measurement scenarios.

(2023) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Tianjuan Yang, Xiuguo Chen, Jiahao Zhang, Shuo Liu, and Shiyuan Liu "Optimizing measurement configuration for x-ray critical dimension metrology based on condition number", Proc. SPIE 12935, Fourteenth International Conference on Information Optics and Photonics (CIOP 2023), 1293557 (24 November 2023); https://doi.org/10.1117/12.3008281

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $17.00

Non-members: $21.00 ADD TO CART

PROCEEDINGS
7 PAGES

DOWNLOAD PAPER SAVE TO MY LIBRARY

GET CITATION

RIGHTS & PERMISSIONS

Get copyright permission Get copyright permission on Copyright Marketplace

KEYWORDS

Condition numbers

Matrices

Measurement uncertainty

Critical dimension metrology

Metrology

X-rays

Inverse problems

Show All Keywords

Keywords/Phrases

Search In:

Publication Years