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A Wafer Pre-Alignment Algorithm Based on Weighted Fourier Series Fitting of Circles and Least Squares Fitting of Circles

The wafer pre-aligner is a crucial component in the lithography process to correct the wafer center and notch orientation. To improve the precision and the efficiency of pre-alignment, a new method to calibrate the center and the orientation of a wafer based on the weighted Fourier series fitting of...

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Detalles Bibliográficos
Autores principales: Chen, Jingsong, Lan, Zhou, Xue, Cheng, Lan, Jun, Liu, Zhenghao, Yang, Yong
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10223695/
https://www.ncbi.nlm.nih.gov/pubmed/37241579
http://dx.doi.org/10.3390/mi14050956
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author Chen, Jingsong
Lan, Zhou
Xue, Cheng
Lan, Jun
Liu, Zhenghao
Yang, Yong
author_facet Chen, Jingsong
Lan, Zhou
Xue, Cheng
Lan, Jun
Liu, Zhenghao
Yang, Yong
author_sort Chen, Jingsong
collection PubMed
description The wafer pre-aligner is a crucial component in the lithography process to correct the wafer center and notch orientation. To improve the precision and the efficiency of pre-alignment, a new method to calibrate the center and the orientation of a wafer based on the weighted Fourier series fitting of circles (WFC) method and the least squares fitting of circles (LSC) method, respectively, is proposed. The WFC method effectively suppressed the influence of the outliers and had high stability compared with the LSC method when fitted to the center of the circle. While the weight matrix degenerated to the identity matrix, the WFC method degenerated into the Fourier series fitting of circles (FC) method. The fitting efficiency of the FC method is 28% higher than that of the LSC method, and the fitting accuracy of the center of the FC method is the same as that of the LSC method. In addition, the WFC method and the FC method perform better than the LSC method in radius fitting. The pre-alignment simulation results showed that the absolute position accuracy of the wafer was ±2 µm, the absolute direction accuracy was 0.01°, and the total calculation time was less than 3.3 s in our platform.
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spelling pubmed-102236952023-05-28 A Wafer Pre-Alignment Algorithm Based on Weighted Fourier Series Fitting of Circles and Least Squares Fitting of Circles Chen, Jingsong Lan, Zhou Xue, Cheng Lan, Jun Liu, Zhenghao Yang, Yong Micromachines (Basel) Article The wafer pre-aligner is a crucial component in the lithography process to correct the wafer center and notch orientation. To improve the precision and the efficiency of pre-alignment, a new method to calibrate the center and the orientation of a wafer based on the weighted Fourier series fitting of circles (WFC) method and the least squares fitting of circles (LSC) method, respectively, is proposed. The WFC method effectively suppressed the influence of the outliers and had high stability compared with the LSC method when fitted to the center of the circle. While the weight matrix degenerated to the identity matrix, the WFC method degenerated into the Fourier series fitting of circles (FC) method. The fitting efficiency of the FC method is 28% higher than that of the LSC method, and the fitting accuracy of the center of the FC method is the same as that of the LSC method. In addition, the WFC method and the FC method perform better than the LSC method in radius fitting. The pre-alignment simulation results showed that the absolute position accuracy of the wafer was ±2 µm, the absolute direction accuracy was 0.01°, and the total calculation time was less than 3.3 s in our platform. MDPI 2023-04-27 /pmc/articles/PMC10223695/ /pubmed/37241579 http://dx.doi.org/10.3390/mi14050956 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Chen, Jingsong
Lan, Zhou
Xue, Cheng
Lan, Jun
Liu, Zhenghao
Yang, Yong
A Wafer Pre-Alignment Algorithm Based on Weighted Fourier Series Fitting of Circles and Least Squares Fitting of Circles
title A Wafer Pre-Alignment Algorithm Based on Weighted Fourier Series Fitting of Circles and Least Squares Fitting of Circles
title_full A Wafer Pre-Alignment Algorithm Based on Weighted Fourier Series Fitting of Circles and Least Squares Fitting of Circles
title_fullStr A Wafer Pre-Alignment Algorithm Based on Weighted Fourier Series Fitting of Circles and Least Squares Fitting of Circles
title_full_unstemmed A Wafer Pre-Alignment Algorithm Based on Weighted Fourier Series Fitting of Circles and Least Squares Fitting of Circles
title_short A Wafer Pre-Alignment Algorithm Based on Weighted Fourier Series Fitting of Circles and Least Squares Fitting of Circles
title_sort wafer pre-alignment algorithm based on weighted fourier series fitting of circles and least squares fitting of circles
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10223695/
https://www.ncbi.nlm.nih.gov/pubmed/37241579
http://dx.doi.org/10.3390/mi14050956
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