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Article: 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 Date2005
Citation
Journal Of Microlithography, Microfabrication And Microsystems, 2005, v. 4 n. 1, p. 1-8 How to Cite?
AbstractThe aberration present in the lenses of exposure systems can cause placement errors to the images produced by alternating phase-shifting masks (PSMs). In reality, when the aberration signature varies from one lens to another, the magnitude of placement error also varies. It remains a question of how the alternating PSM should be designed, so that the image placement error, on average, can be minimized. To achieve this goal, we are interested in optimizing the phase width of an alternating PSM with a fixed critical dimension (CD). The constraint of the optimization is the mean of root mean square (rms) aberrations for a set of interest of exposure systems. To begin the analysis, the image placement error is expressed as a function of illumination, mask spectrum, and wave aberration. A Monte Carlo technique is then applied to produce random samples of wave aberration and image placement error. This analysis shows that a global minimum of mean image placement error is likely to occur at phase widths between 0.2[λ/numerical aperture (NA)] and 0.4(λ/NA). This is further confirmed by analytically considering the expected value of the square of the image placement error. The methodology of finding the optimal phase width is applicable to the design of all alternating PSMs. © 2005 Society of Photo-Optical Instrumentation Engineers.
Persistent Identifierhttp://hdl.handle.net/10722/155284
ISSN
2009 Impact Factor: 0.541
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorMak, GYen_US
dc.contributor.authorWong, AKen_US
dc.contributor.authorLam, EYen_US
dc.date.accessioned2012-08-08T08:32:42Z-
dc.date.available2012-08-08T08:32:42Z-
dc.date.issued2005en_US
dc.identifier.citationJournal Of Microlithography, Microfabrication And Microsystems, 2005, v. 4 n. 1, p. 1-8en_US
dc.identifier.issn1537-1646en_US
dc.identifier.urihttp://hdl.handle.net/10722/155284-
dc.description.abstractThe aberration present in the lenses of exposure systems can cause placement errors to the images produced by alternating phase-shifting masks (PSMs). In reality, when the aberration signature varies from one lens to another, the magnitude of placement error also varies. It remains a question of how the alternating PSM should be designed, so that the image placement error, on average, can be minimized. To achieve this goal, we are interested in optimizing the phase width of an alternating PSM with a fixed critical dimension (CD). The constraint of the optimization is the mean of root mean square (rms) aberrations for a set of interest of exposure systems. To begin the analysis, the image placement error is expressed as a function of illumination, mask spectrum, and wave aberration. A Monte Carlo technique is then applied to produce random samples of wave aberration and image placement error. This analysis shows that a global minimum of mean image placement error is likely to occur at phase widths between 0.2[λ/numerical aperture (NA)] and 0.4(λ/NA). This is further confirmed by analytically considering the expected value of the square of the image placement error. The methodology of finding the optimal phase width is applicable to the design of all alternating PSMs. © 2005 Society of Photo-Optical Instrumentation Engineers.en_US
dc.languageengen_US
dc.relation.ispartofJournal of Microlithography, Microfabrication and Microsystemsen_US
dc.subjectAberrationen_US
dc.subjectAlternating Phase-Shifting Masken_US
dc.subjectImage Placement Erroren_US
dc.subjectMonte Carlo Analysisen_US
dc.subjectPhase Widthen_US
dc.subjectZernike Coefficienten_US
dc.titleAlternating phase-shifting mask design for low aberration sensitivityen_US
dc.typeArticleen_US
dc.identifier.emailLam, EY:elam@eee.hku.hken_US
dc.identifier.authorityLam, EY=rp00131en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1117/1.1861732en_US
dc.identifier.scopuseid_2-s2.0-24144494839en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-24144494839&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume4en_US
dc.identifier.issue1en_US
dc.identifier.spage1en_US
dc.identifier.epage8en_US
dc.identifier.isiWOS:000232841700014-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridMak, GY=8678365200en_US
dc.identifier.scopusauthoridWong, AK=7403147663en_US
dc.identifier.scopusauthoridLam, EY=7102890004en_US

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