Electromagnetic ray tracing model for line structures and characterization of advanced alignment marks in photolithography

Line structures are an essential part in integrated circuit (IC) fabrication. In photolithography, the electromagnetic scattering of line structures is one of the main factors that determine the advancement of the technology node. From the perspective of modeling, a theoretical model to physically...

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Main Author: Tan, Chin Boon
Other Authors: Yeo Swee Hock
Format: Theses and Dissertations
Language:English
Published: 2009
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Online Access:https://hdl.handle.net/10356/15168
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-151682023-03-11T16:54:33Z Electromagnetic ray tracing model for line structures and characterization of advanced alignment marks in photolithography Tan, Chin Boon Yeo Swee Hock School of Mechanical and Aerospace Engineering Chartered Semiconductor Manufacturing DRNTU::Engineering::Manufacturing DRNTU::Engineering::Electrical and electronic engineering::Semiconductors DRNTU::Science::Mathematics::Applied mathematics::Simulation and modeling Line structures are an essential part in integrated circuit (IC) fabrication. In photolithography, the electromagnetic scattering of line structures is one of the main factors that determine the advancement of the technology node. From the perspective of modeling, a theoretical model to physically understand the scattering phenomenon is necessary for a solid foundation in efficient characterization. When the domain of simulation that needs to be addressed is substantial, an approximate solution is ideal for resource efficient modeling. From the perspective of alignment using line structures, it must meet the stringent overlay budget for new fabrication processes. The robustness of the alignment marks is critical as accurate signal is required to precisely align a masking layer to the previous layer. The key contribution in this research work is the establishment of a new electromagnetic scattering model for line structures based on a ray tracing approach. This electromagnetic ray tracing (ERT) model provides detailed understanding of every physical field that contributes to the scattering solution, which could not be offered by any other photolithography simulators found in the literature. The ERT model is capable of distinguishing all the geometrical optics and diffracted fields. The diffracted field is required to compensate the discontinuities caused by the geometrical optics field. Prior to the establishment of the ERT model for line structures, the diffraction coefficients for both external and internal regions of a wedge were formulated and studied extensively. The external diffraction coefficient was developed by using Maliuzhinets’s impedance approach with the inclusion of higher order in the asymptotic expansion. On the other hand, a heuristic solution was derived for the internal diffraction coefficient by extracting the poles in dual Sommerfeld contour integrals. By exploiting both diffraction coefficients in the ERT model, the electromagnetic field that causes a disturbance in the amplitude profile for the total solution was identified and explained in detail. The accuracy of the ERT model was also verified by comparing with the finite difference time domain (FDTD) solution. For a single polysilicon line structure with width of 1.66 λ (λ is the wavelength) on silicon substrate, the developed ERT model was able to demonstrate amplitude correlation coefficient (ACC) of 0.978 and the maximum amplitude difference, Δ|Ez| of as low as -0.067. The subwavelength line width of 0.4 λ was identified as the limit of the ERT model for the single polysilicon line structure. DOCTOR OF PHILOSOPHY (MAE) 2009-04-08T06:09:57Z 2009-04-08T06:09:57Z 2009 2009 Thesis Tan, C. B. (2009). Electromagnetic ray tracing model for line structures and characterization of advanced alignment marks in photolithography. Doctoral thesis, Nanyang Technological University, Singapore. https://hdl.handle.net/10356/15168 10.32657/10356/15168 en 257 p. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic DRNTU::Engineering::Manufacturing
DRNTU::Engineering::Electrical and electronic engineering::Semiconductors
DRNTU::Science::Mathematics::Applied mathematics::Simulation and modeling
spellingShingle DRNTU::Engineering::Manufacturing
DRNTU::Engineering::Electrical and electronic engineering::Semiconductors
DRNTU::Science::Mathematics::Applied mathematics::Simulation and modeling
Tan, Chin Boon
Electromagnetic ray tracing model for line structures and characterization of advanced alignment marks in photolithography
description Line structures are an essential part in integrated circuit (IC) fabrication. In photolithography, the electromagnetic scattering of line structures is one of the main factors that determine the advancement of the technology node. From the perspective of modeling, a theoretical model to physically understand the scattering phenomenon is necessary for a solid foundation in efficient characterization. When the domain of simulation that needs to be addressed is substantial, an approximate solution is ideal for resource efficient modeling. From the perspective of alignment using line structures, it must meet the stringent overlay budget for new fabrication processes. The robustness of the alignment marks is critical as accurate signal is required to precisely align a masking layer to the previous layer. The key contribution in this research work is the establishment of a new electromagnetic scattering model for line structures based on a ray tracing approach. This electromagnetic ray tracing (ERT) model provides detailed understanding of every physical field that contributes to the scattering solution, which could not be offered by any other photolithography simulators found in the literature. The ERT model is capable of distinguishing all the geometrical optics and diffracted fields. The diffracted field is required to compensate the discontinuities caused by the geometrical optics field. Prior to the establishment of the ERT model for line structures, the diffraction coefficients for both external and internal regions of a wedge were formulated and studied extensively. The external diffraction coefficient was developed by using Maliuzhinets’s impedance approach with the inclusion of higher order in the asymptotic expansion. On the other hand, a heuristic solution was derived for the internal diffraction coefficient by extracting the poles in dual Sommerfeld contour integrals. By exploiting both diffraction coefficients in the ERT model, the electromagnetic field that causes a disturbance in the amplitude profile for the total solution was identified and explained in detail. The accuracy of the ERT model was also verified by comparing with the finite difference time domain (FDTD) solution. For a single polysilicon line structure with width of 1.66 λ (λ is the wavelength) on silicon substrate, the developed ERT model was able to demonstrate amplitude correlation coefficient (ACC) of 0.978 and the maximum amplitude difference, Δ|Ez| of as low as -0.067. The subwavelength line width of 0.4 λ was identified as the limit of the ERT model for the single polysilicon line structure.
author2 Yeo Swee Hock
author_facet Yeo Swee Hock
Tan, Chin Boon
format Theses and Dissertations
author Tan, Chin Boon
author_sort Tan, Chin Boon
title Electromagnetic ray tracing model for line structures and characterization of advanced alignment marks in photolithography
title_short Electromagnetic ray tracing model for line structures and characterization of advanced alignment marks in photolithography
title_full Electromagnetic ray tracing model for line structures and characterization of advanced alignment marks in photolithography
title_fullStr Electromagnetic ray tracing model for line structures and characterization of advanced alignment marks in photolithography
title_full_unstemmed Electromagnetic ray tracing model for line structures and characterization of advanced alignment marks in photolithography
title_sort electromagnetic ray tracing model for line structures and characterization of advanced alignment marks in photolithography
publishDate 2009
url https://hdl.handle.net/10356/15168
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