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NANOEXPRESSOpenAccessThermalconductivityinporoussiliconnanowirearraysJeffreyMWeisse1,AmyMMarconnet1,DongRipKim1,PratapMRao1,MatthewAPanzer2,KennethEGoodson1andXiaolinZheng1*AbstractThenanoscalefeaturesinsiliconnanowires(SiNWs)cansuppressphononpropagationandstronglyreducetheirthermalconductivitiescomparedtothebulkvalue.
ThisworkmeasuresthethermalconductivityalongtheaxialdirectionofSiNWarrayswithvaryingnanowirediameters,dopingconcentrations,surfaceroughness,andinternalporositiesusingnanosecondtransientthermoreflectance.
ForSiNWswithdiameterslargerthanthephononmeanfreepath,porositysubstantiallyreducesthethermalconductivity,yieldingthermalconductivitiesaslowas1W/m/KinhighlyporousSiNWs.
However,whentheSiNWdiameterisbelowthephononmeanfreepath,boththeinternalporosityandthediametersignificantlycontributetophononscatteringandleadtoreducedthermalconductivityoftheSiNWs.
Keywords:Thermalconductivity,Siliconnanowires,Poroussilicon,ThermoreflectanceBackgroundSiliconwithahighdensityofnanoscalefeaturessuchasinterfaces,porosity,andimpuritiescanhavethermalconductivities(κ)uptothreeordersofmagnitudelowerthanthatofbulkSithroughenhancedphononscattering[1-17].
Forexample,thethermalconductivityofnano-porousbulkSigenerallydecreaseswithincreasingpor-osityanddecreasingporesize[1-9]and,withhighporosity,approachestheamorphouslimit(0.
2to0.
5W/m/K)[1-3].
Similarly,siliconnanowires(SiNWs)withdiameterssignificantlysmallerthanthebulkphononmeanfreepath(Λ%100to300nmat300K)werereportedtohavethermalconductivityvaluesaslowas0.
76W/m/KduetostrongphononscatteringattheSiNWboundary[10,11].
IntroducingsurfaceroughnesstotheSiNWsleadstoadditionalphononscatteringatlengthscalesevensmallerthantheNWdiameter[12-16].
However,therehavebeenfewinvestigationsonthecombinedeffectsofexternaldimensionsandinternalporosityonthethermalconductivityvaluesofSiNWs.
Inthiswork,wereporttheeffectsofinternalporosityonthethermalconductivityofSiNWsoftwodifferentdiametersthatallowthephononpropagationtospantherangefromballistictodiffusivethermaltransport(davg%350and130nm)bymeasuringthethermalcon-ductivityofverticallyalignedSiNWarraysusingnano-secondtransientthermoreflectance(TTR).
AsopposedtomeasurementsofindividualSiNWs,measurementsofarraysofSiNWsoffertheadvantageofaveragingouttheinherentthermalconductivityvariationsthatarecausedbydifferencesinSiNWdiameter,surfaceroughness,anddefectswithinthearrays.
MethodsTheverticallyalignedSiNWarraysarefabricatedusingafour-steppreparationprocessillustratedinFigure1.
TwosetsofverticallyalignedSiNWarrayswithdifferentdiametersarefabricated(Figure1a,e)usingtop-downetchingtechniquestoachievearangeofporosities(Table1).
Forthefirstset,thediameter(davg%300to350nm)anddensityoftheSiNWsarecontrolledbynanospherelithography[18].
Specifically,amonolayerofSiO2spheresisdepositedusingtheLangmuir-BlodgettmethodontoSiwafers(p-typewithborondopantatoms,(100))andusedasamaskforthesubsequentetchingsteps.
TheinternalporosityoftheSiNWsisvariedfromnonporoustohighlyporousbychangingtheetchingmethodsandconditions[19-21].
NonporousSiNWsare*Correspondence:xlzheng@stanford.
edu1DepartmentofMechanicalEngineering,StanfordUniversity,Stanford,CA94305,USAFulllistofauthorinformationisavailableattheendofthearticle2012Weisseetal.
;licenseeSpringer.
ThisisanOpenAccessarticledistributedunderthetermsoftheCreativeCommonsAttributionLicense(http://creativecommons.
org/licenses/by/2.
0),whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.
Weisseetal.
NanoscaleResearchLetters2012,7:554http://www.
nanoscalereslett.
com/content/7/1/554formedbydeepreactiveionetching(DRIE),andtheresultingSiNWshaveslightlysmallerdiameters(davg%300nm)thanthespheresusedastheetchmask[22].
PorousSiNWarraysarefabricatedbymetal-assistedchemicaletching(MACE)inasolutionof4.
8MHFand0.
3MH2O2,andtheporosityiscontrolledbyvaryingthemetalcatalystandwaferdopingconcentrations[19-21,23-25].
Forlow-porositynanowires,thecatalystlayerconsistsofa15-nmAgfilmcoveredby5-nmAu,whileforthemoderatetohighlyporousnanowires,a50-nmAgfilmisusedasthecatalystandtheinitialwaferdopingconcentrationisvaried.
ThesecondsetofSiNWs,withgenerallysmallerdiameters,isfabricatedusingatwo-stepMACEprocesswithsilversalts[19,20,23,26,27].
First,theAgfilmisdepositedusingasolutionof0.
005MAgNO3and4.
8MHFfor1min.
Then,theSiNWsareformedbyetchinginasolutionof4.
8MHFwithvariousconcentrationsofH2O2(0.
15,0.
30,0.
60,and1.
20M)toadjusttheSiNWporosity[19,20,23,26,27].
TheresultingSiNWshaveanaveragediameterof130nm,butthereissignificantdiametervariationwithintheSiNWarray(d%20to300nm).
Forallthesamples,theSiNWlengthisapproximately10μm.
FollowingtheformationoftheSiNWarrays,thegapsbetweenSiNWsarecompletelyfilledwithparyleneN(poly-para-xylylene;Figure1b,f),whichhasathermalconductivitysignificantlylowerthantheSiNWs(Kparylene=0.
125W/m/K)andahighmeltingtemperature(Tm%410°C).
Theparylenefillingqualityisinspectedbyexaminingmultiplefreshlycutcrosssec-tionsunderascanningelectronmicroscope(SEM),andnoparylenevoidsareobserved.
TheSiNWtipsaresub-sequentlyexposedviachemicalmechanicalpolishingtoremovetheparylenecoveringtheSiNWs(Figure1c,g)thatfacilitatestheSiNWstoformagoodthermalcon-tactwiththetopmetalfilm.
Finally,a15-nmCrlayer(foradhesion)anda500-nmCulayeraredepositedbyelectronbeamevaporationontopoftheSiNWtipstoformaflat,reflectivetransducerlayerforthethermore-flectancemeasurements(Figure1d,h).
ThethermalconductivityoftheverticalSiNWarraysismeasuredatroomtemperaturebynanosecondTTR;thedetailsofwhichcanbefoundinPanzeretal.
[28].
Briefly,themetaltransducerlayerthatisdepositedontheparylene-filledSiNWarrayisheatedbya3-mmFigure1FabricationoftheverticallyalignedSiNWarraysforthenanosecondthermoreflectancemeasurements.
(a,e)SiNWarraysareformedusingthetop-downetching.
(b,f)ParyleneisconformallydepositedinbetweenNWsandactsasamechanicalscaffoldforthetopmetaltransducerlayer.
(c,g)TheSiNWtipsareexposedbychemicalmechanicalpolishingtoensuregoodthermalcontactbetweentheSiNWsandthemetalfilm,and(d,h)ametalfilmisdepositedovertheSiNWarray.
ThescalebarsontheSEMimagesare5μm.
Table1SummaryofSiNWarrayswithvarieddiametersandporositiesDiametercontrolPorositycontrolSet1NanospherelithographyEtchingmethodanddopingconcentrationdavg%300to350nmNonporous:DRIEVFDRIE=21%to23%Lowporosity:Ag/AuMACEVFMACE=45%to60%Moderateporosity:AgMACE,lightlydopedHighporosity:AgMACE,heavilydopedSet2SilversaltsMACEetchantsolutiondavg%130nmLowporosity,0.
15MH2O2VF=26%to35%Highporosity,1.
2MH2O2Weisseetal.
NanoscaleResearchLetters2012,7:554Page2of5http://www.
nanoscalereslett.
com/content/7/1/554diameter,532-nmwavelength,6-nspulsefromaNd:YAGlaseratafrequencyof10Hz.
Thereflectedinten-sityoftheprobelaser(d%20μm,10mW,658nm,continuouswave)isdirectlycorrelatedtothetemperatureofthemetallayerthatisaffectedbythethermalconductivityoftheSiNW/parylenecomposite.
ThethermalconductivityoftheSiNW/parylenecom-positeanditsinterfacethermalresistanceatthetopmetallayerareextractedusingatwo-parameterfitofthemeasuredtemperaturedecaytrace(normalizedbythemaximumtemperature)tothesolutionofaone-dimensionalheatdiffusionequationforamultilayerstackwithsurfaceheating.
Thevolumetricheatcapacityofthefilm(Cv,composite)isassumedtobethevolumetricaverageoftheheatcapacityofparylene(Cv,parylene)andbulksili-con(Cv,Si):Cv,composite=VFCv,Si+(1VF)Cv,parylene,whereVFisthevolumefractionofSiNWswithinthecomposite.
TheVFofSiNWswithineacharrayismea-sureddirectlyfromtop-viewSEMimagesofthefilmbysettingabrightnessthresholdtodefinetheedgeofSiNWs.
TheaveragethermalconductivityofanindividualSiNWwithinthearrayiscalculatedfromtheextractedfilmthermalconductivity(Kcomposite)usinganeffectivemediummodel:KNW=[Kcomposite(1VF)Kparylene]/VF,whereKNWandKparylenearethethermalconductivitiesoftheSiNWsandparylene,respectively.
Inthismodel,SiNWarraysaretreatedasthermalresistorsinparallelwiththeparylenematrix.
TheuncertaintyoftheextractedkNWiscalculatedthroughanerrorpropagationanalysisgivenbythefollowingequation:ΔkNW@kNW@kfilmΔkfilm2@kNW@VFΔVF2@kNW@kparlyeneΔkparlyene2s1whereΔkparyleneisthethermalconductivityvariationfromtheliterature.
ΔkfilmandΔVFarethemeasuredspot-spotvariationinthesametypeofsamples.
DetailederroranalysisdataforallthedatareportedherecanbefoundinAdditionalfile1.
ResultsanddiscussionThethermalconductivityfortheSiNWswithlargedia-meters(davg%300to350nm)demonstratesaclearde-creasewithincreasingporosity(Figure2).
ThethermalconductivityofnonporousSiNWs,thoughwithroughsurfaces,is142±13W/m/K,whichisveryclosetothatofbulkSi(κ%150W/m/K).
Thissuggeststhatforlarge-diameterSiNWs,surfaceroughnessatthisdepthandperiodicitydoesnotcauseeffectivephonon-externalboundaryscatteringandthereforehaslittleeffectonthethermalconductivity.
Ontheotherhand,theinternalporosityofSiNWssignificantlyreducesthethermalcon-ductivityfrom142W/m/KforthenonporousSiNWsto98W/m/K(Au/Ag-MACE)and51W/m/K(Ag-MACE)fortheincreasinglyporousSiNWs.
Thethermalconductivityoflarge-diameterSiNWarrays(davg%350nm)withthreedifferentp-typeborondopantatomconcentrations(1014,1016,and1018cm3)isfurtherinvestigatedforbothnonporousandporousNWs(Figure3).
Thethermalconductivityofnonpor-ousSiNWsdecreasesslightlywithincreasingdopingconcentrationduetotheincreasedphonon-impurityscattering,similartobulkSi[29,30].
Conversely,thethermalconductivityofporousSiNWsdropstoabout1W/m/Kwhenthedopingconcentrationisincreasedfrom1016to1018cm3.
Itshouldbenotedthatthemainreasonforthedramaticdropinconductivitywithdopingconcentrationisthathigherdopingcon-centrationsleadtoincreasedporosityinSiNWsfabri-catedwithMACE(Figure3b,c,d).
Thedopantatomsitesactaspreferredlocationsforporeformation[19,23,26,27].
IncomparisontotheinternalNWpor-osity,thephonon-impurityscatteringathigherdopingconcentrationhasamuchsmallerimpactonthether-malconductivity[2,12].
ThethermalconductivitiesofSiNWswithsmalldia-meters(davg%130nm)alsodecreasewithincreasingporosity(Figure4),similartothelarge-diameterSiNWs.
However,thethermalconductivityoftheseSiNWsismuchsmallerthanthatoflarge-diameterSiNWsofsimilarporosities(i.
e.
,thesameetchantsolution,0.
3MH2O2).
Specifically,thethermalconductivityisreducedfrom51W/m/Kforthelarge-diameter(davg%350nm)Figure2Thermalconductivityoflarge-diameterSiNWs(approximately350nm;1014cm3p-typedoping).
Thethermalconductivitywiththreelevelsofporosity,correspondingtodifferentetchingconditions,isshown.
Thethermalconductivitydecreasessignificantlywithincreasingporosity.
TheinsetimagesshowthetopviewoftheSiNWs,andthescalebarsare200nm.
Weisseetal.
NanoscaleResearchLetters2012,7:554Page3of5http://www.
nanoscalereslett.
com/content/7/1/554SiNWsto28W/m/Kforthesmaller-diameterSiNWs(davg%130nm).
Thishighlightsthesignificantimpactofphonon-externalboundaryscatteringonthethermalconductivityatlengthscalesthataresmallerthanthephononmeanfreepath.
Theadditionalreductioninthermalconductivity(to17W/m/K)withincreasingH2O2concentrationforthesmaller-diameterSiNWsindicatesthattheincreasinginternalporosityalsohasasignificantimpactonthethermalconductivity.
ConclusionsInsummary,wemeasuredthethermalconductivityofSiNWarrayswithvariousnanowirediameters,dopingconcentrations,surfaceroughnessandinternalporositiesusingananosecondtransientthermoreflectancemethod.
WhentheSiNWdiameter(davg%350nm)islargerthanthephononmeanfreepathinthebulksilicon,thether-malconductivityshowslittledependenceonthedopingFigure3Thermalconductivityoflarge-diameternonporousandporousSiNWarrays.
(a)ThermalconductivityofnonporousandporousSiNWarraysoflargediametersasafunctionofdopingconcentrations.
TEMimagesshowtherelativeporosityforAg-MACESiNWarraysfabricatedwithdopingconcentrationsof(b)1014,(c)1016,and(d)1018cm3.
ThescalebarsontheTEMandinsetTEMimagesare5and200nm,respectively.
TheuncertaintybarfortheMACEnanowireswithadopingconcentrationof1018cm3isontheorderofthedatapointmarkersize.
Figure4Thermalconductivityofsmall-diameter(approximately130nm)SiNWs(1014cm3)asafunctionofporosity.
Forcomparison,thethermalconductivityofthelarge-diameterSiNWetchedatthesameconditionisshownastheredcircle.
IncreasingnanowireporosityisrealizedbyincreasingtheH2O2concentrationduringMACE,asevidencedbytheinsetTEMimages.
ThescalebarsonalltheTEMimagesare100nm.
Weisseetal.
NanoscaleResearchLetters2012,7:554Page4of5http://www.
nanoscalereslett.
com/content/7/1/554concentrationandsurfaceroughnessbutdecreasessig-nificantlywithincreasingporosityduetophononscat-teringattheporeinterfaces.
Incontrast,whentheSiNWdiameter(davg%130nm)issmallerthanthepho-nonmeanfreepath,thethermalconductivitystronglydependsonboththeexternalboundary-phononscatter-ingandtheinternalporeinterface-phononscattering,leadingtoasignificantreductioninthethermalcon-ductivityforsmall-diameterSiNWs.
AdditionalfileAdditionalfile1:ErroranalysisofthethermalconductivityofverticalSiNWarrays.
AnXLSXfileshowingdetailederroranalysisdataforallthedatareported.
CompetinginterestsTheauthorsdeclarethattheyhavenocompetinginterests.
Authors'contributionsJMW,AMM,KEG,andXLZdesignedandinterpretedtheexperiments.
JMWandDRKfabricatedthesamples.
JMWandPMRperformedSEMandTEMcharacterization.
AMMandMAPdesignedandcarriedoutthethermoreflectancesetupandmeasurements.
Allauthorscontributedtoandapprovedthefinalmanuscript.
AcknowledgmentsTheauthorsgratefullyacknowledgethesupportofthePECASEprogram,theLinkFoundationEnergyFellowshipprogram,theNationalScienceFoundationGraduationResearchFellowshipprogram,andtheStanfordGraduateFellowshipprogram.
Authordetails1DepartmentofMechanicalEngineering,StanfordUniversity,Stanford,CA94305,USA.
2KLA-TencorCorporation,Milpitas,CA95035,USA.
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doi:10.
1186/1556-276X-7-554Citethisarticleas:Weisseetal.
:Thermalconductivityinporoussiliconnanowirearrays.
NanoscaleResearchLetters20127:554.
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