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Conference Paper: Alternating phase-shifting mask design for low aberration sensitivity

TitleAlternating phase-shifting mask design for low aberration sensitivity
Authors
KeywordsAberration
Alternating phase-shifting mask
Image placement error
Monte carlo analysis
Phase width
Zernike coefficient
Issue Date2004
PublisherS P I E - International Society for Optical Engineering. The Journal's web site is located at http://spie.org/x1848.xml
Citation
Proceedings Of Spie - The International Society For Optical Engineering, 2004, v. 5377 PART 1, p. 591-601 How to Cite?
AbstractTheories are developed to optimize the mask structure of alternating phase-shifting masks (PSMs) to minimize the average image placement error towards aberration under coherent imaging. The constraint of the optimization is a given mean value of RMS aberration, which corresponds to infinitely many sets of random Zernike coefficients. To begin the analysis, the image placement error is expressed as a function of the mask spectrum and the wave aberration. Monte Carlo analysis on the Zernike coefficients is then performed, which assures us that a global minimum of average image placement error is likely to occur at low phase widths. This result is confirmed by analytically considering the expected value of the square of the image placement error. By Golden Section Search, the optimal phase width is found to be 0.3707(λ/NA) at 0.07λ RMS aberration. This methodology of finding the optimal phase width is applicable to the design of all alternating PSMs.
Persistent Identifierhttp://hdl.handle.net/10722/44718
ISSN
References

 

DC FieldValueLanguage
dc.contributor.authorMak, GYen_HK
dc.contributor.authorWong, AKen_HK
dc.contributor.authorLam, EYen_HK
dc.date.accessioned2007-10-30T06:08:38Z-
dc.date.available2007-10-30T06:08:38Z-
dc.date.issued2004en_HK
dc.identifier.citationProceedings Of Spie - The International Society For Optical Engineering, 2004, v. 5377 PART 1, p. 591-601en_HK
dc.identifier.issn0277-786Xen_HK
dc.identifier.urihttp://hdl.handle.net/10722/44718-
dc.description.abstractTheories are developed to optimize the mask structure of alternating phase-shifting masks (PSMs) to minimize the average image placement error towards aberration under coherent imaging. The constraint of the optimization is a given mean value of RMS aberration, which corresponds to infinitely many sets of random Zernike coefficients. To begin the analysis, the image placement error is expressed as a function of the mask spectrum and the wave aberration. Monte Carlo analysis on the Zernike coefficients is then performed, which assures us that a global minimum of average image placement error is likely to occur at low phase widths. This result is confirmed by analytically considering the expected value of the square of the image placement error. By Golden Section Search, the optimal phase width is found to be 0.3707(λ/NA) at 0.07λ RMS aberration. This methodology of finding the optimal phase width is applicable to the design of all alternating PSMs.en_HK
dc.format.extent245456 bytes-
dc.format.extent41662 bytes-
dc.format.extent4084 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypeimage/tiff-
dc.format.mimetypetext/plain-
dc.languageengen_HK
dc.publisherS P I E - International Society for Optical Engineering. The Journal's web site is located at http://spie.org/x1848.xmlen_HK
dc.relation.ispartofProceedings of SPIE - The International Society for Optical Engineeringen_HK
dc.rightsJournal of Microlithography, Microfabrication, and Microsystems. Copyright © S P I E - International Society for Optical Engineering.en_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.rightsCopyright 2005 Society of Photo-Optical Instrumentation Engineers. This paper was published in Journal of Microlithography, Microfabrication, and Microsystems, 2005, v. 4 n. 1, p. 013008 and is made available as an electronic reprint with permission of SPIE. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.en_HK
dc.subjectAberrationen_HK
dc.subjectAlternating phase-shifting masken_HK
dc.subjectImage placement erroren_HK
dc.subjectMonte carlo analysisen_HK
dc.subjectPhase widthen_HK
dc.subjectZernike coefficienten_HK
dc.titleAlternating phase-shifting mask design for low aberration sensitivityen_HK
dc.typeConference_Paperen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1537-1646&volume=4&issue=1&spage=013008&epage=&date=2005&atitle=Alternating+phase-shifting+mask+design+for+low+aberration+sensitivityen_HK
dc.identifier.emailLam, EY:elam@eee.hku.hken_HK
dc.identifier.authorityLam, EY=rp00131en_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.doi10.1117/12.534686en_HK
dc.identifier.scopuseid_2-s2.0-3843104604en_HK
dc.identifier.hkuros101034-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-3843104604&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume5377en_HK
dc.identifier.issuePART 1en_HK
dc.identifier.spage591en_HK
dc.identifier.epage601en_HK
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridMak, GY=8678365200en_HK
dc.identifier.scopusauthoridWong, AK=7403147663en_HK
dc.identifier.scopusauthoridLam, EY=7102890004en_HK

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