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The influences of substrate and metal properties on the magnetic response

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The influences of substrate and metal properties on the magnetic response ofmetamaterials at terahertz region

Xiaoxiang Xia, Yimin Sun, Haifang Yang, Hui Feng, Li Wang, and Changzhi Gu

Citation: Journal of Applied Physics 104, 033505 (2008); doi: 10.1063/1.2961327 View online: http://dx.doi.org/10.1063/1.2961327

View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/104/3?ver=pdfcov Published by the AIP Publishing

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JOURNALOFAPPLIEDPHYSICS104,033505͑2008͒

Theinﬂuencesofsubstrateandmetalpropertiesonthemagneticresponseofmetamaterialsatterahertzregion

XiaoxiangXia,YiminSun,HaifangYang,HuiFeng,LiWang,andChangzhiGua͒

BeijingNationalLaboratoryforCondensedMatterPhysics,InstituteofPhysics,ChineseAcademyofSciences,Beijing100190,China

͑Received20March2008;accepted25May2008;publishedonline1August2008͒

Themetamaterials͑MMs͒withplanarmetalarraysofsplitringresonatorswerefabricatedonquartzandsiliconsubstrates;theinﬂuencesofsubstratepermittivityandmetalconductanceonthemagneticresponsesofintheterahertzregionwereinvestigated.Theelectromagnetic͑EM͒responsesofthemetamaterialswerecharacterizedbyterahertztime-domainspectroscopy.Theexperimentalresultrevealsthatthereisa0.39THzredshiftinthetransmissionspectraforthemagneticresponsewhenthesubstratechangesfromquartztosilicon,whichisinconsistencewiththeﬁnite-differencetime-domain͑FDTD͒simulation.Basedonthesimulationandexperimentalresults,andtakingintoaccounttheEMpropertiesofsubstratematerials,amodiﬁedL-CmodelispresentedtounderstandtheMMsysteminterahertzdomain.©2008AmericanInstituteofPhysics.͓DOI:10.1063/1.2961327͔

I.INTRODUCTION

Themetamaterials͑MMs͒,asartiﬁcialmaterials,exhibitanexoticanduniqueelectromagnetic͑EM͒propertythatisnotavailableintheexistingmaterialsinnature.Veselago1predictedthepossibilityofMMswithnegativeindexofre-fractionin1968.However,theﬁrstMMwasnotdemon-stratedinmicrowave2untiltheoreticalmodels3,4werepro-posedinrecentyears.Sincethen,variousMMshavebeenrealizedinthefrequencybandfromradiotooptical,5–11andtheyhaveshowedgreatpotentialsinapplicationssuchas“perfectlens”12andcloak.13

Generally,MMsareformedbymetalelementarrayssuchassplitringresonators͑SRRs͒orcut-wirepairswithdimensionalscaleinsubwavelength͑␭/5–␭/10͒,andareconsideredastheso-calledmagneticatoms.”10Theycanex-hibitastrongmagneticresponseathighfrequencysuchasterahertz͑1THz=1012Hz͒,6infrared,7andopticalfrequency,11wherethepermeabilityisalwaysconsideredtobe1.Forexample,SRRwasdesignedtoproducenegativepermeabilitywhenthemagneticﬁeldwaspolarizedalongtheringaxis.TheeffectivepermeabilityofaSRRstructure,whichworksinaperpendicularmagneticﬁeldofelectro-magneticradiation,wasintroducedas

f␻2

␮eff=1+2,

␻0−␻2−i⌫␻͑1͒

wherefistheﬁllingfactorofthematerialand␻0istheresonantfrequencyarisingfromtheL-Cresonanceofthesystem.Therefore,theeffectivepermeabilitycanbenegativewithafewhertzshiftfromthe␻0.3

However,athighfrequency,suchasterahertz,themag-neticresponseofSRRisentirelycausedbyapolarizedelec-tricﬁeld,notamagneticﬁeld.Inthiscase,thesplitringcan

a͒

Authortowhomcorrespondenceshouldbeaddressed.Tel.:0086-10-828197.FAX:0086-10-828198.Electronicmail:czgu@aphy.iphy.ac.cn.

beassumedasanL-Coscillator,whereastrongmagneticresponseoftheplanarMMscanbeachievedattheL-Cresonantfrequency.

InthetraditionalL-CmodelofSRRs,metalsaretreatedasperfectconductorsfrommicrowavetomid-IRwave-length,andtheeffectofsubstrateunderneathSRRsontheelectromagneticwavetransmissionpropertiesinthecompos-itematerialsisnormallyignored.Therefore,insuchafre-quencyband,theL-Cresonantfrequencyisconsideredtobeindependentoftheelectromagneticpropertiesofthemetalandthesubstrate.Inotherwords,themagneticresponsefre-quencyofMMsiscompletelydeterminedbythegeometryandsizeofSRRs.14However,theshiftofmicrowavetrans-missionpropertiesoftheMMswithdifferentsubstrateshadbeendemonstratedbycomputersimulationsandexperiments.15Atterahertzfrequency,Padillaetal.16ﬁrstdemonstrateddynamicalcontroloftheelectricalresponseofSRRsthroughphotoexcitationoffreecarriersintheGaAssubstrate,andthentheyfabricatedaMMdevicewithChenetal.,17whereaSchottkydiodeformedbytheMMarraysonGaAssubstrateenablesmodulationofterahertztransmissioneffectively.

Inthispaper,asystematicinvestigationabouttheinﬂu-enceoftheelectromagneticpropertiesofsubstrateandmetalontheMMmagneticresponseinterahertzregionwascarriedout.AseriesofhighqualitySRRMMswerefabricatedusinganimprovedUVphotolithographyandlift-offprocess.ThemagneticresponsesoftheMMswerecharacterizedbytheterahertztime-domainspectroscopy͑TDS͒.Theexperimen-talresultindicatesthatthemagneticresponseinSRRMMsdependsonthepropertiesofbothmetalandsubstratemate-rials.TakingintoaccountthematerialEMproperties,amodiﬁedL-Cmodelispresented,whichprovidesaneffec-tivemethodtodesignandmodulatetheterahertzMMdevicepropertiesutilizingvarioussubstratesandmetallicmaterials.

0021-79/2008/104͑3͒/033505/5/$23.00104,033505-1

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033505-2Xiaetal.J.Appl.Phys.104,033505͑2008͒

FIG.1.͑a͒ThegeometryofSRR.͑b͒AtopviewSEMimageofthegoldenSRRarrayonsiliconsubstrate.

II.EXPERIMENTALDETAILS

FIG.2.ThetransmissionspectrafortheSRRMMswiththedifferentpo-larizationdirectionsofincidentterahertzbeam,theelectricﬁeldpolarizationdirectionofincidentterahertzbeamisparalleltothegap-bearingsidesofSRRincaseI,andperpendicularincaseII.

Inordertoinvestigatethedependenceofmagneticre-sponseofSRRMMsontheEMpropertiesofsubstrateandmetalmaterials,gold,silver,andchromewerechosentofab-ricatemetalsplitringsonquartz͑thicknessof800␮m͒andsilicon͑thicknessof500␮m,resistivityof100⍀cm͒sub-strates.Thegeometries,asshowninFig.1͑a͒,havethefol-lowingdimensionalscale:widthwofmetallinesis3␮m;gapginthesplitringis5␮m;sidelengthais31␮m;periodiclatticeconstantis50␮mandthemetalthicknesshis75–200nm.

ThesamplesofSRRMMs,showninFig.1͑b͒,werefabricatedusinganimprovedUVphotolithographyandlift-offprocessthathasbeendescribedelsewhere.18Brieﬂy,thewaferscoatedwithS1813/LORbilayerresistswereﬁrstex-posedusingaKarlSuessMA6UVphotolithographer.TheS1813/LORbilayerresistsformedaperfectundercutproﬁlethroughcontrollingthedevelopmentconditionscarefully.Thenathinmetalﬁlmwasdepositedonthesamplesbyusingthethermalevaporationmethod.Finally,alift-offpro-cesswasperformedtoformtheSRRMMsamples.

ThetransmissionspectraofSRRMMswereobtainedbytheterahertzTDS.Theterahertz-TDSsystemandthedetailsofcharacterizationprocedureweredescribedinRef.19.BytestingwhethertheabsorptiondipsdisappearornotwhentheplanarSRRsamplesarerotatedorthogonally,onecancon-ﬁrmwhichdipstandsformagneticresponseintransmissionspectra.19,20AsthemeasuredspectraresultsshowninFig.2,fordifferentSRRMMs͑100nmAgSRRonthesiliconandquartzsubstrates͒,absorptiondipsappearedat0.6or1.1THz

whentheelectricﬁeldpolarizationdirectionofincidenttera-hertzbeamwasparalleltothegap-bearingsidesofSRR͑caseI͒,anddisappearedwhenitwasperpendicular͑caseII͒,whichdemonstratedthattheabsorptiondipsareinducedbythemagneticresponse.Inordertostudytheeffectsofelec-tromagneticpropertiesofmetalandsubstratematerialsonthemagneticresponsefrequencyofSRRMMs,onlythemagneticresponsesintheincidentconditionofcaseIwereconsideredinthepresentinvestigation.III.RESULTSANDDISCUSSIONS

Figure3showsthetransmissionspectrafortheSRRMMswithdifferentsubstratesand/ormetals.Usingtheaforementionedmethod,weconﬁrmedthatthedipsinthetransmissionspectrumofthequartzsamplenear1.0THzandthedipsofthesiliconsamplenear0.6THzwereinducedbythemagneticresponse,andthedipsinthetransmissionspec-trumofthesiliconsamplenear1.75THzwereinducedbythehalfwaveresonanceduetothesidelengthoftheSRRMMs.For100nmthicknessgoldandsilverSRRsonthequartz,themagneticresponsefrequenciesareboth1.02THz.However,fortheSRRMMswithsamegeometricsizeonthesiliconsubstrate,themagneticresponsefrequencyshiftedto0.63THz.Thereisa0.39THzredshiftforthemagneticresponseinthetransmissionspectrawhenthesubstratechangesfromthequartztothesilicon,whichdemonstratestheinﬂuenceofsubstratematerialsonthemagneticresponseofSRRMMs.

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033505-3Xiaetal.J.Appl.Phys.104,033505͑2008͒

directlydependentonthesubstratepermittivity␧sub.Ifweassumethatthepermittivityisaconstant,therewillbealargerdisplacementcurrentinthesubstratewithhigher␧subatthesameincidenceconditions.ThuswecanassumeRsub=b/␻␹approximatively,andherebisaconstantandpolar-izability␹=␧sub−1.Withotherfrequencydependenceofcir-cuitelementsignored,resonantfrequency␻0canbeex-pressedas

␻0=

Cb2

LC2b2+L␹2

LC+c␹2

͑3͒

FIG.3.ThetransmissionspectrafortheSRRMMswithdifferentsubstratesand/ormetals.

Generally,unlessthesubstratethicknessisontheorderof͑ormuchthinnerthan͒theresonancewavelength,theef-fectofsubstratethicknessonmagneticresponsecanbeig-nored.Takingthesubstratecontributionintoconsideration,weassumethataleakageresistanceRsubexistsinthesurfaceofdielectricsubstratebetweentheendsofSRRarms.Theleakageresistanceisnotserieswoundwiththecapacitance,butshuntwound,andtheSRRstructureinourworkcanbetreatedasanL-CoscillatorasshowninFig.4.Theresis-tanceRlpresentsthelossesinthemetal,RdielstandsforthelossesinthedielectricbetweentheendsofSRR,ListheinductanceofmetallinesandCisthecapacitancebetweentheendsofSRR.Generally,ifthedielectricmediumbetweenthecapacitanceisair,theresistanceRdielcanbeignoredcompletelyinhighfrequency.Sothecompleximpedancecanbeexpressedas

Z=Rl+iL␻+

+iC␻Rsub

2␻CRsub2

1+C2Rsub␻2

=Rl+

Rsub

1+C2Rsub␻2

+iL␻−

ͩͪ.͑2͒

TheleakageresistanceRsubherestandsfortheresistanceto

thedisplacementcurrentinaninsulatingsubstrate,whichis

FIG.4.AmodiﬁedL-Cresonancemodelconsideringthesubstratecontribution.

wherec=Cb2.

FromEqs.͑2͒and͑3͒,wecanconcludethatthesurfaceconductivityofsubstrateplaysanimportantroleintheSRRmagneticresponse,andthesurfaceresistanceisdependentonthesubstratepermittivity␧sub.Theincreaseinsubstratepermittivitycancausearedshiftinthetransmissionspectra,whichhasbeendemonstratedintheaboveexperimentsandwillbediscussedlaterindetailswiththesimulationresults.

AsseeninFig.3,themagneticresponsefrequenciesarealmostunchangedfortheAuandAgstructuresonthesamesubstrate.However,forthesamethickness,scale,andgeom-etry,theCrSRRMMsshowacompletelydifferenttransmis-sionpropertiescomparedwiththesilverorgoldinthesamecondition.Noabsorptiondipoccursinthetransmissionspec-traofCrSRRMMswithinourmeasurementrange.ItisobviousthatbothAuandAgaregoodconductors,andtheirconductivitiesareaboutanorderofmagnitudehigherthanthatofchromium.Inaddition,chromiumgenerallyexperi-encesstresscracksinthickﬁlmdepositions,whichmayalsodecreaseitsconductivity.Asitisknown,theinductanceLofSRRalsodependsonthepropertiesofmetallicmaterialsapartfromitsgeometryandsize.AccordingtoEq.͑3͒,thechangeininductanceLofmetalwillinﬂuencethemagneticresponseinthetransmissionspectrum.

Theinﬂuenceofmetalthicknessonthemagneticre-sponseofSRRMMswasalsoinvestigated.Figure5showsthetransmissionspectraof75to200nmthicknesssilverSRRMMsonthequartzandsilicon.Apparently,thedepthofdipsvarieswiththedecreaseinﬁlmthickness.Theshiftofmagneticresonancefrequency,however,isnotobviouswhilethethicknessofmetalﬁlmvariesfrom75to200nm.

Inordertochecktheeffectsofdielectricpropertiesofsubstratesonthetransmissionspectra,ﬁnite-differencetime-domain͑FDTD͒simulationsofterahertzEMpropagationinSRRMMsonthequartzandsiliconsubstratesandinvacuumwereperformed.Thepermittivitiesofquartzandsiliconinthesimulationareassumedtobe3.84and12.25interahertzregion,respectively,whichareobtainedfromthemeasuredopticalparametersinterahertz-TDS.AllscaleandgeometricparametersofSRRareconsistentwiththeexperi-mentalcondition.Itwasalsoassumedthatthesurfaceleak-ageresistanceRsubisindependentofthethicknessofsub-stratelayerwhenthethicknessofthesubstratefarlargerthantheresonantwavelength.Forthesimpliﬁcationofsimula-tion,thesubstratewasassumedasa500nmthinlayerforbothquartzandsilicon.Additionally,becauseoftheweakdependenceofthespectralresponseonthethicknessof

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033505-4Xiaetal.J.Appl.Phys.104,033505͑2008͒

FIG.7.Thedependenceofpolarizability␹onmagneticresponsefrequencyfromFDTDsimulation,modiﬁedL-Cresponsemodel,andexperimentaldata.

FIG.5.ThetransmissionspectraforthesilverSRRMMswithdifferentthicknesseson͑a͒quartzand͑b͒siliconsubstrates.

metalstructures,themetalﬁlmthicknesswasassumedas1␮mandthemetalmaterialasaperfectconductor.

Figure6showsthesimulationtransmissionspectraofa1␮mperfectmetalSRRMMson500nmthicknessquartzandsiliconsubstrates͑allpolarizationdirectionsincaseI͒.Themagneticresponsegapisabout0.59THzforsiliconand0.97THzforquartz,respectively.Thevariationofsubstratematerialscausesa0.38THzmagneticresponsefrequencyshiftinthetransmissionspectra.Consideringtherewereprobabledeviationsintheconditionsbetweentheexperi-mentalmeasurementsandthesimulations,thesimulationre-sultsareinarathergoodagreementwiththeexperimentalresultsofthegoodconductors͑AuandAg͒.Furthermore,the

simulationoffreestandingSRRMMsinvacuumwascarriedoutandthemagneticdipwasfoundaround1.46THz,whichishigherthantheresonantfrequenciesofSRRMMswithsubstrate.

TheFDTDsimulationsofSRRMMswerealsocarriedoutonhypotheticsubstratewithpermittivitiesof1,2.25,4,6.25,9,12.25,and16,andcorrespondingmagneticresponsefrequencieswereobtained.AccordingtoEq.͑3͒,wecanob-tainL−C=0.46606fromthesimulationresultoffreestand-ingSRRMMsinvacuum,andassumetheconstantc=0.035bydataﬁtting.Agroupofﬁtteddataaboutthepo-larizabilitydependenceonmagneticresponsefrequencywasobtainedaccordingtothemodiﬁedL-Cresponsemodel.InFig.7,thedependencesofpolarizability␹onmagneticre-sponsefrequency␻0obtainedfromFDTDsimulation,modi-ﬁedL-Cresponsemodel,andexperimentaldata,weredrawntogetherandcompared.OnecanﬁndfromFig.7thatthemodiﬁedL-Cresponsemodelshowsatrendsimilartothesimulationandexperimentalresults.Consideringthatthefre-quencydependenceofothercircuitelementshavebeenig-nored,thedeviationbetweenFDTDsimulationandmodiﬁedL-Cmodelisacceptable,implyingthatthemodiﬁedL-CresponsemodelcansatisfactorilydescribeandexplainthedependenceofthemagneticresponseofSRRMMsonthesubstrates.IV.CONCLUSION

FIG.6.FDTDsimulationtransmissionspectraofSRRMMsonquartz,siliconsubstrates,andwithoutsubstrate.

AseriesofSRRMMsusingdifferentmetals͑Au,Ag,andCr͒onsiliconandquartzsubstrateswerefabricated,theeffectoftheelectromagneticpropertiesofmetalandsub-stratematerialsonthemagneticresponsesofSRRMMsinterahertzregionwereinvestigatedonexperimentandsimu-lation.A0.39THzshiftofmagneticresponsedipsintrans-missionspectrawasobservedwhenthesubstratewaschangedfromquartztosilicon.Themagneticresponsedipsdisappearedinthemeasurementfrequencyrangewhenchro-miumwasusedinplaceofthegoodconductors͑silverorgold͒.TakingintoconsiderationofthepropertiesofthemetalandsubstratematerialsinSRRMMs,amodiﬁedL-C

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033505-5Xiaetal.

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ACKNOWLEDGMENTS

ThisworkwassupportedbytheNationalNaturalSci-enceFoundationofChina͑GrantNos.60501014and10390160͒andtheNationalCenterforNanoscienceandTechnology,China.

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