NDLI: Lens Heating Induced Aberration Prediction via Nonlinear Kalman Filters

Content Provider	IEEE Xplore Digital Library
Author	Bikcora, C. van Veelen, M. Weiland, S. Coene, W.M.J.
Copyright Year	1988
Abstract	Lens heating induced aberrations rank among the dominant causes of image deteriorations in photolithography. In order to accurately counteract them via the available manipulators within the projection lens, it is crucial to employ a predictive model that is identified with relatively small errors. In this paper, parameters of a phenomenological model are recursively updated with respect to the measurements taken at the end of a wafer and are subsequently utilized in aberration predictions for the dies of the next wafer. To serve this purpose, two suboptimal Bayesian strategies, namely, the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are applied to the nonlinear system at hand. In addition, the classical Kalman filter is tested on an approximate linear model. Filter performances are evaluated using both synthetic and experimental data and compared with respect to the posterior Cramér-Rao lower bound. When synthetic measurements are in use, the UKF moderately outperforms the EKF. Moreover, they both perform significantly better than the classical Kalman filter. However, due to model imperfections, these gains decrease and may even vanish when real measurements are processed. If the computational costs are also considered, then the EKF becomes more preferable over the other options.
Sponsorship	IEEE Electron Devices Society IEEE Components, Packaging, and Manufacturing Technology Society IEEE Reliability Society IEEE Solid-State Circuits Society
Starting Page	384
Ending Page	393
Page Count	10
File Size	4642362
File Format	PDF
ISSN	08946507
Volume Number	25
Issue Number	3
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-08-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Lenses Kalman filters Vectors Heating Mathematical model Predictive models Semiconductor device modeling unscented Kalman filter (UKF) Extended Kalman filter (EKF) lens heating lithography nonlinear dynamical systems
Content Type	Text
Resource Type	Article
Subject	Industrial and Manufacturing Engineering Condensed Matter Physics Electronic, Optical and Magnetic Materials Electrical and Electronic Engineering

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
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9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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