Nickel Silicide Growth Modeling Using Level Set Methods

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Nickel Silicide Growth Modeling Using Level Set Methods
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Kumar, Ashish
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Doctorate ( Ph.D.)
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University of Florida
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Electrical and Computer Engineering
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LAW,MARK E
Committee Co-Chair:
NISHIDA,TOSHIKAZU
Committee Members:
GUO,JING
GILA,BRENT P

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diffusion -- silicide -- simulations
Electrical and Computer Engineering -- Dissertations, Academic -- UF
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Electrical and Computer Engineering thesis, Ph.D.
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Abstract:
Nickel silicide is being used as a Local-Interconnect (LI) and source-drain contact material in current CMOS technology. For scaling technologies it has become extremely important to reduce the parasitic resistances from Schottky contacts and LI. Modeling and predicting the silicide shapes has become necessary in order to estimate the transport through device accurately. This paper discuss the NiSi growth models implemented in Florida Object Oriented Process Simulator ( FLOOPS). Level set methods (LSM) coupled with Deal Groves kinetic model has been used for modeling and growth of NiSi. Focus in this work remains on implementing the above numerical techniques and obtaining the solutions by coupling LSM with the diffusion solver of the simulator. Initial dopant segregation capabilities are also demonstrated using chemical potential approach and proposed. Stress profile simulations are also proposed in order to predict the stress generated at the source/drain and channel accurately. These techniques can be easily used for advance technologies and special structures such as FinFETs, Nano-Wires (Silicon), etc.
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by Ashish Kumar.
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Thesis (Ph.D.)--University of Florida, 2013.
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Adviser: LAW,MARK E.
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Co-adviser: NISHIDA,TOSHIKAZU.

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NICKELSILICIDEGROWTHMODELINGUSINGLEVELSETMETHODSByASHISHKUMARADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2013

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c2013AshishKumar 2

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Idedicatethistomyfamily. 3

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ACKNOWLEDGMENTS FirstlyIwouldliketoacknowledgemyadvisorDr.MarkE.Lawforhissupportandencouragementwithouthimthisworkwouldnothavebeenpossible.IalsowanttothankmycommitteemembersDr.BrentGila,Dr.JingGuoandDr.ToshiNishidafortheirvaluablesuggestionsinmywork.Iwouldliketothankallmyfriendsandcolleagueswhohelpedmeduringmygradschool. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 7 LISTOFFIGURES ..................................... 8 ABSTRACT ......................................... 12 CHAPTER 1INTRODUCTIONANDBACKGROUND ...................... 14 1.1CMOSDevicesandInterconnects ...................... 14 1.2SilicideImportanceForLocalInterconnectsandContacts ......... 16 1.3Motivation .................................... 17 2LITERATUREREVIEW ............................... 22 2.1NickelSilicideGrowthKinetics ........................ 22 2.2DopantSegregationDuringSilicidation ................... 29 2.3StressGeneratedDuetoSilicideGrowth .................. 34 3SIMULATIONTECHNIQUES:LEVELSETMETHODSANDDEALGROVE'SMODEL ........................................ 39 3.1SiliconProcessingforSilicideandContacts ................. 39 3.1.1BasicCMOSManufacturingProcess ................. 39 3.1.2SilicidationProcess ........................... 40 3.2LevelSetMethods ............................... 41 3.3DealGrove'sModel .............................. 46 3.4Summary .................................... 49 4IMPLEMENTATIONINFLOOPSANDINITIALRESULTS ............ 50 4.1Introduction ................................... 50 4.2ADualLevelSetMethodImplementation .................. 50 4.3CouplingofDiffusionwithLSM:Model .................... 53 4.3.1NickelConcentrationWithDealGrove'sModel ........... 54 4.3.2LevelSetUpdatesWithDiffusion ................... 56 4.4InitialSimulationResultsandVerication .................. 57 4.5Summary .................................... 61 5DOPANTSEGREGATIONUSINGCHEMICALPOTENTIALAPPROACH ... 64 5.1Introduction ................................... 64 5.2ChemicalPotentialApproach ......................... 64 5

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5.3ModelingofSnowPlowingEffectUsingChemicalPotentialApproach .. 68 5.4SegregationResultsandComparisonwithSIMSdata ........... 73 5.5Summary .................................... 75 6STRESSSIMULATIONSUSINGFINITEELEMENTMETHODS ........ 78 6.1Introduction ................................... 78 6.2StressModelingusingFEM .......................... 78 6.2.1Stress .................................. 79 6.2.2Strain .................................. 81 6.2.3Stress-StrainRelationshipforLinearElasticSolid .......... 83 6.32DStresscontoursandComparison ..................... 84 6.4Summary .................................... 89 7SUMMARYANDFUTUREWORK ......................... 91 7.1OverviewofResults .............................. 91 7.2RecommendationforFutureWork ...................... 93 APPENDIX:ALAGATORSCRIPTFORCOMPLETESIMULATIONINFLOOPS ... 94 REFERENCES ....................................... 99 BIOGRAPHICALSKETCH ................................ 107 6

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LISTOFTABLES Table page 1-1Commonlyusedself-alignedsilicide ........................ 16 2-1ReportedNickelSilicidePhase,CrystalStructureandRangeforTemperatureofFormation ..................................... 24 2-2Reportedreactionrateandactivationenergycomparison ............ 26 2-3Young'smodulus,thermalexpansioncoefcientandresidualbuilt-instressofTiSi2,CoSi2andNiSi .................................. 36 4-1SimulationvsCalculatedResults .......................... 54 7

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LISTOFFIGURES Figure page 1-1Moore'slawshowingtransistorcountdoublingeveryyear. ............ 15 1-2AtypicalMOSFETstructureshowingparasiticresistancesthatplaypartindevicetransportcharctersitics. ........................... 15 1-3TEMimagesofvarioussilicidesshowingTiSi2for180nmnode,CoSi2for130nmnodeandNiSifor90nmandbelow(source:intel). ................. 17 1-4SchottkyBarrierHeightmodulationduetodopantssegregatedattheinterface. ............................................ 18 1-5AntimonysegregationduringNiPtSigrowth.Thissegregationresultsindipolecreationthathelpsinschottkybarrierheightreduction. .............. 20 1-6TEMshowingnickelsilicidegrowthneardummygate .............. 21 2-1ContactResistivitiesofNandPMOSFET. ..................... 23 2-2SheetresistanceofvariousphasesofnickelsilicideshowingNiSibeingthelowest. ......................................... 23 2-3SilicideshapesonSOIsourceanddrainaswellasattheSTIedge ....... 24 2-4SquareofthicknessofNi2Si(Fullcurve)andNiSi(brokencurve)growingonsiliconasafunctionoftime. ............................ 25 2-5Illustrationshowing50nmlmofnickelreactingwith92nmsilicontoform117nmofsilicide. ....................................... 26 2-6Silicidegrowthsequenceshowingnickeldiffusion,reactionandconsumption 27 2-7NickelSilicideformationonnanowireanduxbasedmodel ........... 28 2-8TransfercharacteristicsofaSB-MOSFETwithandwithoutsegregation. .... 30 2-9Current-VoltagecharacteristicsofasilicidediodewithandwithoutArsenicsegregation. ..................................... 30 2-10Comparisonshowtheeffectsofinterfacialdopantsontransmissionandsignicantreductionofbarrierheight. .............................. 31 2-11SIMSdatashowingArsenicsegregationatthesilicide-siliconinterface. .... 32 2-12Datashowingdependenceofimplantdoseandenergyontheslopeofthesegregationproles. ................................. 33 2-13DopantsegregationinSOIMOSFETresultinginreductionofSchottkyBarrierHeight. ........................................ 33 8

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2-14Resultsshowingmobilityenhancementforelectronsandholeswithincreasingtensileandcompressivestress. ........................... 34 2-15Cartoonshowingtensileandcompressivelineronasinglewafercausingdifferentstress. ......................................... 35 2-16TopimageisTEMofNiSistructure.Bottomisthestresscontoursversusdepthfromthesurfacesimulationsshowingstressproleunderthegate. ....... 37 2-17Simulationshowingasymmetricstressgeneratedduetovariationingrainorientations. 38 3-1CMOSprocessingstep ............................... 39 3-2SilicideProcessingaftergateandspacerformation. ............... 40 3-3Markertechniqueshowingdiscretizationofinitialcurve ............. 41 3-4SignedDistancefromtheinitialfrontforlevesetfunction ............. 42 3-5HigherdimensionalLevelSetfunctionwithtimeevolutionwithconstantisotropicvelocity. ........................................ 45 3-6Twodisjointsurfacesevolvingandlevelsetfunctionspropagatingsimultaneously. 45 3-7Dealgrovesmodelshowingallthreeuxes. .................... 47 3-8Oxidationofsiliconindryoxygenshowinglinear-parabolicbehaviorofgrowth. 49 4-1LevelsetinitializationshowingnickelsiliconinitialinterfacewitheachLevelfunctionshowninthedirectionofpropagation. .................. 52 4-2InitialstructureusedforsilicidegrowthsimulationsincomparisontotherealMOStransistorTEMimage. ............................. 53 4-3Simulationsshowingoxygenconcentrationprolefordifferenttimes20min(Green),40min(Pink),60min(Black). ............................. 55 4-4FlowchartshowingstepbystepsimulationsequenceandcouplingofbothLevelSetMethodandDealGrove'sModel. .................... 58 4-5Fourpointuxestimationonarectangulargrid,bluesurfacerepresentsours2Dgridforthelevelsetfunction. .......................... 59 4-6FinalzerolevelsetsshownonFLOOPSgridrepresentingsilicidegrowthonSource/drainandpolygate.. ............................ 59 4-7Simulationresultofduallevelsetgrowthofnickelsilicideonsource/drainandmultiplestepsoflevelsetpropagation. ....................... 60 4-8Simulationofnickelsilicidegrowthonanarrowpolylikestructure. ....... 62 9

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4-9FullProcesssimulationresultsshowinggrowthdifferencesbetweenuniformandnon-uniformgridissues. ............................ 63 5-1Diffusionbehaviorofhomogeneousparticlesinaclosedsystem,particlesowingfromhighchemicalpotentialtolowchemicalpotential. .......... 67 5-2Chemicalpotential,ConductionandValancebandproleoftwosemiconductorsdopedwithdifferentspecies. ............................ 67 5-3Simulationsofdopantsegregationin1-Dimensionalstructure. ......... 70 5-42Dsimulationshowingresultofdopantsegregationperformedaftersilicidegrowth. ........................................ 71 5-5Gaussianimpurityprolesimulationresultswithsnowplowingeffectshownforthreedifferentthicknessesofsilicide. ...................... 72 5-6SIMSdatashowingArsenicdopantprolebeforenickeldeposition. ....... 74 5-7ArsenicsegregationSIMSdataaftersilicidegrowthatvarioustemperatures. 76 5-8ArsenicsegregationSimulationresultsforsilicidegrowthat400and450Ctemperatures. ..................................... 76 5-9Gridsensitivitydatafrom1Dsimulationsforvariousgridsizing. ......... 77 6-1AbarwithforceFactinginnormaldirectionandsheardirectiononitssurfacewithareaA. ...................................... 80 6-2AsmallvolumeelementPwithnormalandsheerstresstensorcomponentsshownalongitssurface. .............................. 81 6-3Innitesimalelementwithnormalstraininx,yandzdirectionisrepresentedbydu,dvanddwrespectively.(du dx<0),dv dx>0,dw dx<0) .............. 82 6-4Stresscontoursimulationshowingupto1GPaofstressonaP-typeMOSFET. 85 6-5Forceperunitwidthfor30nmand100nmofnickeldepositedthicknesses.Stressevolutionwithprocessingtemperature. ................... 86 6-6SimplebendingofawaferorisotropicmaterialwithRbeingtheradiusofcurvature. 86 6-7Stresssimulationswithvaryingsilicidethicknessneartheshallowtrenchisolationstructure. ....................................... 87 6-8Stresssimulationresultsshowingcontoursofcompressivestressgeneratedduetolatticemismatchofnickelsilicide. ...................... 87 6-9Simulationshowingstresscontourduetothinnickelsilicidegrowthonsiliconwithtrenchisolation. ................................. 88 10

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6-10Simulationshowingstresscontourduetothicknickelsilicidegrowthonsiliconwithtrenchisolation. ................................. 89 6-11FEMstresssimulationresultsonaMOSFETlikestructurewithsilicidegrowthonsourceanddrainusinggrowthmodels. ..................... 90 11

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyNICKELSILICIDEGROWTHMODELINGUSINGLEVELSETMETHODSByAshishKumarDecember2013Chair:MarkE.LawMajor:ElectricalandComputerEngineeringNickelsilicideisbeingusedasaLocal-Interconnect(LI)andsource-draincontactmaterialincurrentCMOStechnologies.ForscalingithasbecomeextremelyimportanttoreducetheparasiticresistancesfromSchottkycontactsandLI.Modelingandpredictingthesilicideshapeshasbecomenecessaryinordertoestimatethetransportthroughdeviceaccurately.Inthisdissertation,NickelSilicide(NiSi)growthmodelsusingnumericaltechniqueknowasLevelsetmethodscoupledwithdealgrovesnumericalsolutionusingdiffusionsolverwasimplementedinFLOOPS(FloridaObjectOrientedProcessSimulator).MainfocusinthisworkwastoimplementtheabovetechniquesandobtainaccuratenumericalsolutionsofthephysicsgoverningtheshapeofNiSi.DopantsegregationduringthesilicidegrowthisbeingusedtoreducetheSchottkyBarrierHeightatthesource/draincontact.Oursegregationmodelusingchemicalpotentialapproachisalsopresentedinthiswork.Thesemodelswerealsocoupledwiththegrowthmodelinordertocapturethephysicsofthephenomenonaccurately.Itmeansthatateverydeltatimestepofsimulationsmultipleequations(growth,diffusionandsegregation)aresolvedandupdatedconcurrently.FinallystressgeneratedinsiliconduetosilicidegrowthisalsobeingsimulatedusingtheFiniteElementMethodcapabilitiesofFLOOPS.Stresscontoursimulationresultsarepresentedincomparisontotherealdata.Modelsinthisworkcanbeeasilyextendedfor3-Dstructures.These 12

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techniquescanbetransferredtoacommercialsimulatorsuchasSentaurusprocessandcanbeusedforadvancedtechnologiessuchasFinFETsandNano-Wires. 13

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CHAPTER1INTRODUCTIONANDBACKGROUND 1.1CMOSDevicesandInterconnectsTheComplementaryMetalOxideSemiconductor(CMOS)technologyhasrevolutionizedthewayelectroniccircuitsareintegratedonachip.ContinuouslyshrinkingtechnologydrivenbyMoore'slaw(Fig. 1-1 )[ 1 ]andInternationaltechnologyroadmapforsemiconductors(ITRS)[ 2 ]ispresentingnewchallengesfordevicescalingandintegration.TheMetal-Oxide-SemiconductorFieldEffectTransistor(MOSFET)playsakeyroleinimplementinglogicgatesusingthep-typeandn-typedevicesonasinglesubstrate.Asthetransistorspersquareincharedoubledimplyingdevicesizeisreducedmanyaspectsoftheirperformancearedegradedsubstantiallysuchasoff-stateleakage,gaindecreases,sensitivitytoprocessuctuations.Inordertocompensatetheseeffectsallotherparasiticresistancessuchas,interconnects,contacts,sourceanddrainjunctionmustbescaledaswell.AbasicstructureofMOSFETisshowninFig 1-2 withparasiticresistancesthatplayabigroleingoverningdeviceperformance.Theseresistancesaredependentonvariousfactorssuchasmetallurgicaljunctions,source/drainextensiontogateoverlap,source/drainextensions,silicidation,localinterconnects,contactprocessing,etc.Especiallycontactlengthandsilicide-siliconinterfaceresistancealoneisresponsiblefor4%performancedegradation.Ascontactpitchisscaledcapacitancebetweengateandcontactisalsobecomingamajorconcern.Interconnectdelaystemmingfromthebackendoflineprocessingwithcopperlinesresistanceandcapacitancesisbecominganissuewithscaling.Low-K(dielectricconstant)interlayerdielectricsandthinnercopperbarriersareusedforfurtherscalingtoovercometheseissues.Nevertheless,dielectricreliabilityduetoelectromigrationandtimedependentbreakdownisthenewconcern.Varioussolutionsareunderconsiderationforcurrentandfuturetechnologytoreducetheseparasitics.Overallnewmaterials,betterunderstandingofprocessphysics, 14

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stringentdefectdensityandtightprocesstolerancearethekeytofurtherscalingofdevicetechnologies. Figure1-1. Moore'slawshowingtransistorcountdoublingeveryyear. Figure1-2. AtypicalMOSFETstructureshowingparasiticresistancesthatplaypartindevicetransportcharctersitics. 15

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1.2SilicideImportanceForLocalInterconnectsandContactsMetalsilicideshavebeenakeycomponentofintegrated-circuitsmanufacturingtechnologies.Silicidesarepresentatsource,drain,polygateandlocalinterconnectsandhavebeenusedforohmicandschottkybarriercontacts.Theyareusefulduetotheirlowresistivities,hightemperaturestabilities,easytoformbydiffusionreaction,gooddevicecharacteristics.Silicidechoiceshaschangedwithscalingtechnologiesasshowning 1-3 duetothedeviceperformancerequirements.Someofthedesirablepropertiesarealsogivenintable 1-1 [ 3 ].AftermanyconsiderationscurrenttechnologynodeisusingNickelSilicide(NiSi)asthebestchoiceofsilicidematerial.Oneofthemainreasonforthisisnochangeinresistanceobservedinverynarrowlines(reverselinewidtheffect)ascomparedtotheincreaseinthecasesofcobaltortitaniumsilicidesduetovaryingsilicidethicknessattheedges(mainlyduetonickeldiffusingtoreactwithsiliconascomparedtoreversenatureobservedforothermetalsilicides).AlsoitscompatibilitywithSiGeismuchbetterascomparedtocobaltsilicide.AssiliconconsumedforNiSi(thinnersilicide)ismuchlessercomparedtoothermetalitfacilitatesaneasyintegrationwithSOI(Silicon-On-Insulator)devices.Thesesilicidedlocalinterconnectsprovidegreatexibilityincircuitdesignandreductionindiessize.AgoodsilicidematerialalsohelpsinreductionoftheRCtimedelayofthedevices.Thehighertheresistanceandcapacitanceattheinterconnectlevelsloweristhespeedofthedevice. Table1-1. Commonlyusedself-alignedsilicide PropertiesTiSi2CoSi2NiSi Resistivity()]TJ /F3 11.955 Tf 11.96 0 Td[(cm)13-2014-2014-20Siconsumptionpernmofmetal(nm)2.33.61.8Formationtemperature(C)600-700600-700400-600Schottkybarrierheightonn-typeSi0.60.640.65 16

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Figure1-3. TEMimagesofvarioussilicidesshowingTiSi2for180nmnode,CoSi2for130nmnodeandNiSifor90nmandbelow(source:intel). 1.3MotivationNickelsilicideshasbeenstudiedextensivelyformicroelectronicsuseforseveralyears.TherearemanyaspectsofitsuchasmechanicalandelectricalpropertiesofNisilicidephases,formationandgrowthkineticsanditsdependenceonimpurities.NiSiasthesource/drainandgatecontactmaterialhasalsobeenresearchedingreatdetails.DuetoitslowresistivityandeaseofformationonSiandSiGeitisthebestcandidateforcontactoffuturetechnologysuchasnanowires.SilicidegrowthhasbeenmodeledandstudiedasadiffusioncontrolledprocessquietsimilartosiliconoxidationmodeldevelopedbyDealandGrovein1965[ 4 ].Manyresearchersafterseveralstudieshavecometoaconclusionthatnickelsilicideformationisalsoalinear-parabolicsystemwithnickelbeingthemaindiffusingspecies.Thereareseveralmodelsavailabletopredictthegrowththicknessofsilicide.Asdevicesarecontinuouslyscaledtowardstheatomisticscalefeaturesmorequantumeffectscontrolthesilicide-siliconcontactproperties.Ithasbecomeindispensabletomodelandsimulatethe2D(two-dimensional)and3D(three-dimensional)growthonsilicontoaccuratelypredictthesilicideshape.Duetodiffusion-reactionlimitedcontrolledgrowthsilicideshapecanvarybaseduponthenickeldiffusioncharacteristics.Growthshapesatsource/drainandpolygatecouldbecompletelydifferentduetoseveralfactorssuchasnickeldiffusionrates,dopants,materialboundariesofspacer 17

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oxides,etc.Thiscouldalsohelpinmodelingofthecurrentcrowdingandeldfocusingeffectsintransportoutoftheintrinsicdeviceintocontactinglayers.Predictionofsilicidegrowthorencroachmentunderthespacerisalsousefulinordertodeterminetheadverseeffectssuchasincreasedgateleakage.ModelingsegregationofdopantsduetothesilicidegrowthisalsoextremelyimportantithasbeenshownthataccumulationofarsenicatNiSi-SiinterfacehelpsinmodulatingtheSchottkyBarrierHeight(SBH)(refertog: 1-4 )[ 5 ].LateststudiesalsoshowsthatthedipoleformationattheinterfaceduetosegregationisalsousefulinreducingtheSBH.Althoughinterfacialdopingcanmodulatethebarrierheightatthesametimeitlowersthetransmissionintransportofcarrieracrossthebarrier.SincecontactresistancehasexponentialdependenceonSBHresultinginlowerresistanceoverall,itisusefultohavethecapabilitiestosimulatethesesegregationprolesaccurately.Latestsegregationprolesofantimony(Sb)areshowning 1-5 [ 6 ],atNiPtSi/SiinterfaceincreaseSbconcentrationleadstocreationofdipolesthatultimatelyhelpsinnarrowingofbarrierheight.Usingchemicalpotentialapproachforsegregationcanbebenecialasitdealswithobtainingthediffusionsolutionsnumerically. Figure1-4. SchottkyBarrierHeightmodulationduetodopantssegregatedattheinterface. 18

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AsdeviceperformanceenhancementshasbeenobservedforbothPMOSandNMOSduetotheexternalstressappliedusingcompressiveortensileliners.Stressgeneratedduetonickelsilicideformationhasalsobeenstudiedwidely.ItisalsorequiredforustoincorporatethesimulationmodelswithgrowthmodelstopredicttheinducedstressinMOSdeviceschannelandsource/drain.Nickelsilicidetendstogeneratetensilestressnearthematerialgrowthvicinity(refertog: 1-6 )[ 7 ]resultinginextratensilestresspocketsinthechannel.UsingFLOOPScapabilitiesandFiniteElementMethod(FEM)approachitisconvenienttocomputethestresstensorsandcouplethecontourprolingwiththegrowthmodelsimplementation. 19

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Figure1-5. AntimonysegregationduringNiPtSigrowth.Thissegregationresultsindipolecreationthathelpsinschottkybarrierheightreduction. 20

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Figure1-6. TopimageisaTEMshowingnickelsilicidegrowthneardummygatecausingtensilestressunderandaroundthesource/drain.Bottomimageisasimulatedstressprolealongthechannel. 21

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CHAPTER2LITERATUREREVIEW 2.1NickelSilicideGrowthKineticsNickellayersarefrequentlyusedtoformohmicorrectifyingcontactstosilicon,eitherdirectlyoraftersomeformofheattreatment.Thenickel-siliconsystemisknowntoformcompoundsilicidesbysolid-soliddiffusionatrelativelylowtemperaturesandthusdetailedinformationconcerningboththegrowthkineticsofthesilicidelayersandtheeffecttheselayershaveontheelectricalcharacteristicsoftheresultingSchottkyjunctionsisofconsiderabletechnologicalimportance.NiSialsohassignicanteffectonlessdopantdeactivationinshallowjunctions.Italsohasmuchsmotherinterfaceduetodiffusioncontrolledformationratherthannucleationcontrolled[ 8 ].Asincreaseinmetal-siliconcontactresistanceisamajorproblemforsub-microntechnologiesnickelsilicideascomparedtoothermetalsilicidedisplaysuperiorelectricalperformance.ShowninFig. 2-1 istheelectricalcontactresistivityforvariousmetalsclearlyshowingNiSitobetheleastresistancematerial.MetalsilicidesingeneralhavemanyphasesincaseofnickelsilicidethreemajorphaseNi2Si,NiSiandNiSi2hasbeenobservedbetweenthetemperaturesof200-900C(Pleaserefertotable 2-1 formoredetailedinformationoncomposition,crystalstructureandrangeforthetemperatureofformation.).OurgrowthsimulationsfocusedmainlyonNiSiphase(discussedinChapter4)aredoneatindustrystandardtemperatureof400-450C.AcomparisonofsheetresistanceisshowninFig. 2-2 clearlyindicatingthatNiSiisthedesiredphaseforlowresistivitycontactsinCMOSprocess.BeforethediscussionofsilicideformationkineticsvariousstructureswithnickelsilicidegrowtharealsoshowninFig. 2-3 tocomparetheshapesofnalinterface.InordertobuildthemodelsuccessfullywehavetokeepinmindtheshapepatternsattheedgesofspacerandSTI.[ 9 ]Silicidegrowthisaresultofinterstitialdiffusionofnickelintosilicononthermaltreatment.SinceNiisthedominantdiffusingspeciesthevacanciescreatedarelocated 22

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AContactResistivityonN-typeSilicon BContactResistivityonP-typeSiliconFigure2-1. ContactResistivitiesofNandPMOSFET. Figure2-2. SheetresistanceofvariousphasesofnickelsilicideshowingNiSibeingthelowest. 23

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Table2-1. ReportedNickelSilicidePhase,CrystalStructureandRangeforTemperatureofFormation SilicideCompositionCrystalStructureRangeofTemperature Ni2SiOrthorhombic200-400CNiSiOrthorhombic400-600CNiSi2Cubic600-900C ANickelsilicideonSOIMOSFET BNickelsilicideatSTIedgeFigure2-3. SilicideshapesonSOIsourceanddrainaswellasattheSTIedge.[ 9 ] insidethemetallayer.Diffusioncontrolledformationfollowtherelationthatthicknessisproportionaltosquarerootoftime.Twophasesareformedsequentiallyduringthenickelsilicidationprocess.ItisreportedthatrstlyNi2Siphaseisformedforthetemperaturerangeof(300-400C)withthicknessrelationgivenbyequation 2 .Onlyafternickellayeriscompletelyconsumedsubsequentannealingathighertemperaturesintherangeof400-700CleadstophasetransformationintoalowresistivityphaseNiSi[ 8 10 13 ].Thisfollowsthegrowthrelationshipasperequation 2 thusindicatingreactionratelimitedgrowth.Ploting 2-4 showsthicknessvstimegrowthforboththephasesitcanbeobservedthatNiSiphasestartsappearingonlyaftercompletenickelconversiontoNi2Siphase.Activationenergyforsilicideformationisreportedtobeintherangeof 24

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1.4-1.6eVforNiSiphase[ 8 10 12 14 ].Substrateorientationdoesnothaveastronginuenceonthekineticsofgrowth.Agoodcomparisonbetweenthetwosetsofdatafrom[ 10 12 ]isshowninthetable 2-2 whichareinaccordancewitheachother.Anillustrationofsiliconconsumptionandvolumetricexpansionisalsoshowning 2-5 where50nmofnickelisdepositedontopofsiliconitreactswith92nmofSitoform117nmofnickelsilicide. (WNi2Si)2=RNi2Sitcm2(2) WNiSi=RNiSitcm(2) Figure2-4. SquareofthicknessofNi2Si(Fullcurve)andNiSi(brokencurve)growingonsiliconasafunctionoftime. 25

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Table2-2. Reportedreactionrateandactivationenergycomparison DataReportedRNi2Sicm2s)]TJ /F4 7.97 Tf 6.59 0 Td[(1RNiSicms)]TJ /F4 7.97 Tf 6.59 0 Td[(1 Reference2.90x10)]TJ /F4 7.97 Tf 6.59 0 Td[(134.48x10)]TJ /F4 7.97 Tf 6.59 0 Td[(8Reference7.20x10)]TJ /F4 7.97 Tf 6.59 0 Td[(141.60x10)]TJ /F4 7.97 Tf 6.59 0 Td[(9ActivationEnergy1.3eV1.4eV Figure2-5. Illustrationshowing50nmlmofnickelreactingwith92nmsilicontoform117nmofsilicide. 2DGrowthKineticsofNi-SiSystem ThereisauniedmodelusedbymanyresearcherstogovernthegrowthkineticsofNi-Sisystem.ItisderivedfromtheearlymodelofDealGrove'ssiliconoxidationrelationship[ 15 ].AgeneralizedmodelwasdevelopedbyGoseleandTu[ 16 ]forthinlmandbulkgrowthcases,basedonthediffusionandinterfacialreactions,thismodelwasalsousedtoanalyzethecasesofmetalsilicidegrowth.Gasandd'Heurle[ 17 ]alsodisplayedsimilarmodelonformationofsilicidethinlmsbysolidstatereaction.AnotherX-RayDiffraction(XRD)andDifferentialScanningCalorimetry(DSC)studyfromNemouchietal[ 18 ]conrmstheuseofsimilarmodeltobestdescribetheobservedgrowthresults.EquationdescribingthegrowthmodelisgivenbelowthatisquietsimilartoDealandGroveslawinitsdifferentialform. dL dt=KD KL+D3)]TJ /F7 11.955 Tf 11.96 0 Td[(1 KBT(2)WhereListhegrowingthicknessofsilicide,'srepresentchemicalpotentialthatcanbeeasilytranslatedintoconcentrationvaluesofNiindifferentmaterials.Dbeingthe 26

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interdiffusioncoefcientandKistheinterfacialreactionrateconstant.Lookingcloselythisistheexactsamemodelusedforthermaloxidationofsilicon.AcomparativephaseformationandkineticsstudywasalsodonebyNemouchietal[ 19 ]betweennickelsilicideandnickelgermanides.WhereNickel-Siliconsystemwasobservedtoformthreephasesinthesequence:Ni2Si,NiSiandNiSi2.ObservationsmadebystudyingXRDdatawerealsothatlinear-parabolicgrowthbehavioristhebestsuitedmodelforNiSigrowthkinetics.IncaseofNi-Getwoequationssimilarto 2 wereusedduetotwophasescompetingtogrowsimultaneously.ThislawwasalsomentionedbyJohnsonandMartin[ 20 ]ininuenceofelasticstressonthegrowthkineticsofdiffusioncouples.Toillustratehownickelsilicideformationoccursrefertothecartooning 2-6 showinghownickeldiffusethroughsilicidetoreactwithsiliconandnallyafternickelcompletelytransformedintoNi2Si,phasethentransformationresultsinNiSi. Figure2-6. Silicidegrowthsequencerstnickeldiffusesthroughsilicidetoreactwithsilicon,completeconsumptionofnickellayertoformNi2Silayerfurtherannealingtransformsthephasetonickelmono-silicideNiSi. Kineticsofnickelsilicidegrowthonsiliconnanowiresisalsoobservedtofollowalineartoparabolicgrowth.Againasimplediffusionmodelwiththreeuxes(F1,F2andF3)andnickelconcentrations(Cres,CoandCi)isusedtorepresentthegrowingthicknessofsilicide.Showning 2-7 istheTEMimageofasiliconnanowirewithnickel 27

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silicidegrowthonlateraldirectionandaschematicforNi-silicideintrusionmodel[ 21 ].Insummary,allthestudiespointtoadiffusion-reactionbasedmodeltobethebestcandidateforsilicidegrowthsimulationsasseenonplanar,nanowireskindofstructures.ToincorporatethesemodelsfornoveldevicessuchasFinFET'sshouldnotbeabiggerchallengeasgrowthgoverningphysicsobservedremainsthesameforallcases. Figure2-7. TopimageshowingnickelsilicideformationonaSinanowire.Bottomisaschematicshowingalltheuxesandconcentrationstobeusedinthemodelofsilicidegrowthcalculations. 28

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2.2DopantSegregationDuringSilicidationSegregationorredistributionofdopantsduringthermalprocessingofmaterialinterfacehasbeenobservedforCoSi2duetoveryhightemperatureprocessing(>800C).Butinthecaseofnickelsilicidewithlowergrowthtemperatures(300-600C)doessnowplowingeffectprevails?Severalstudieshavereportedsegregationofdopantsseenduringsilicideprocessing.Dopantslikearsenic(As)duetodifferenceinsolubilitiesanddiffusivitiesinsilicideandsilicontendstosegregateatgrowinginterface.SegregationofdopantsisveryusefulphenomenonandhasbeenexploitedtoenhancethedeviceperformancebyreducingtheSBH.AstudybyKnochetalasshowninFig. 2-8 istheId-VgcharacteristicsofaSOI-MOSFETwith(B)andwithout(A)dopantsegregationclearlyshowingsignicantimprovementindrivecurrentandreductioninoff-stateleakage[ 22 ].InanotherstudybyUrbanetalFig. 2-9 onschottkydiodeusingdopantssegregationduetoNiSigrowthhasresultedinreductionofSBHandultimatelyincreasingforwarddiodecurrentandreversesaturationcurrent.AnotherabinitiotransportsimulationstudybyGaoetalshowhowinterfacialdopantseffecttheelectrontransmissionprobabilityandschottkybarrierheight[ 23 ].Inessencesnow-plowingofdopantisaprominenteffectinscalingtechnologiesandadvantageousfortransportoutofthedevice.Someimportantsegregationprolesarediscussedinfurthersection.Jiangetal[ 25 ]conductedanexperimentwith13nmofnickellmtoformasilicidelayer(at450C)ontopofan+/pjunction.SilicideinducedAsredistributionwasclearlyobservedduringtheSIMS(SecondaryIonMassSpectrometry)analysisofthesamples,resultsareshowning 2-11 .AnaccumulationatthesurfaceisalsoobservedinthesamestudyexplainedbytheKirkendalleffect.TheyalsoconcludethattheSIMSmeasurementconditionsandAs-Niprecipitatecannotbeignoredduringtheanalysisoftheseproles.AdetailedstudywasperformedbyMurarkaandWilliams[ 26 ]toillustratethedopantredistributioninsilicide-siliconandsilicide-polystructures,wheresegregation 29

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AId-VgofMOSFETwithoutdopantsegregation BId-VgofMOSFETwithdopantsegregationFigure2-8. TransfercharacteristicsofaSB-MOSFETwithandwithoutsegregation.[ 22 ] Figure2-9. Current-VoltagecharacteristicsofasilicidediodewithandwithoutArsenicsegregation.[ 24 ] 30

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ATransmissionvsEnergywithoutdopants BTransmissionvsEnergywithdopantsFigure2-10. Comparisonshowtheeffectsofinterfacialdopantsontransmissionandsignicantreductionofbarrierheight.[ 23 ] ofdopantsismodeledusingthefreeenergyconsiderations.Theyalsotalkaboutcompetitionofsegregationcoefcientsofdifferentmetalsilicideandsilicontodetermineamountofdopants.StudieswerealsoperformedbyWhittmerandOhdomarietalondopantredistributionafterNiSiformationexplainedbythephenomenonofsnow-plow[ 27 28 ].Theredistributionofarsenicon(100)SisubstrateisalsoobservedbyHoum-madaetal[ 29 ]atrelativelyhighertemperatures(400-650C).TheyshowthatagglomerationathighertemperatureshasasignicanteffectonAsaccumulationattheinterface.StudyperformedbyFesteetal[ 30 ]impliesthatinitialdopantprolemustbesteepinordertoscalethedevicesfurtherandusethissegregationfavorably.Thereisa 31

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minimumchannellengthdependentontheextentofsegregationlayeratwhichdopanttailcanstartstocontributetothechanneldopingthatcaneventuallyleadtodegradationofcarriermobility.TheyhavealsoshownthedependenceofimplantationenergiesanddopantslopeofAsonthepeakofconcentrationpresentattheinterfaceg 2-12 [ 30 ].Thereforeaccurateinitialdopantprolewhileperformingthesimulationsisabsolutelynecessary.SegregationduetosilicideformationinSOI(Silicon-on-Insulator)MOSFETtechnologyhasturnedouttobearealadvantageinreducingtheschottkybarrierheight.Fig 2-13 AshowaTEMimageofsilicideformationonaSOIMOSFETandgrowthunderthespaceroxideforcingimpuritieslikearsenicintosilicon.ImpurityprolesforvariousdosageisshowninFig 2-13 BwecanseethatthereisaccumulationatthesurfaceandinterfaceverysimilartoabulkMOSFET.ThesemodelsimplementedinFLOOPSshouldbeusefulforawidevarietyofdevices. Figure2-11. SIMSdatashowingArsenicsegregationatthesilicide-siliconinterface.[ 25 ] 32

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Figure2-12. Datashowingdependenceofimplantdoseandenergyontheslopeofthesegregationproles.[ 30 ] ASOIMOSFETwithsilicide BArsenicSegregationProleFigure2-13. DopantsegregationinSOIMOSFETresultinginreductionofSchottkyBarrierHeight.[ 24 ] 33

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2.3StressGeneratedDuetoSilicideGrowthInrecentyearsoftechnologicaladvancementsinduceduniaxialstrainhasemergedasthemostimportanttechniqueatthedevicelevel.Inducingstraintensile(NMOS)andcompressive(PMOS)inthechannelregionofaMOSFETcanimproveelectronandholemobilitiesrespectively(refertoFig. 2-14 )[ 31 ].Thesetechniqueshavebeenincorporatedextensivelyfor90nmandbelowtechnologynodes[ 32 37 ].AduallinertechniquesisusedforNandP-MOSdevicestoarticiallyinducestraininchannel(refertoFig. 2-15 )[ 38 40 ].SilicidesarealsoknowhavesomeeffectonchannelmobilitytounderstandwhatkindofstressnickelsilicidecausesinthechannelweneedtoperformFEMsimulationswiththerightshapes. Figure2-14. Resultsshowingmobilityenhancementforelectronsandholeswithincreasingtensileandcompressivestress.[ 31 ] Metalsilicidesareknowtoinduceasignicantamountofstressinthesource/drainandchannelofadeviceduetolatticemismatch,coefcientofthermalmismatch,etc.Someoftheearlystresscharacterizationofmetalsilicidesrevealedthatthereisavariablestress(compressiveandtensile)inducedinMOSdevicesatseverallocations. 34

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Figure2-15. Cartoonshowingtensileandcompressivelineronasinglewafercausingdifferentstress.[ 36 ] AdetailedstudybySteegenandMaex[ 41 ]showsstressgeneratedduetoTiSi2,CoSi2andNiSi.Theyhaveconsideredthreedifferentsourceofstressintrinsic(duetonon-equilibriumgrowth),thermal(causedbydifferenceincoefcientofthermalexpansion)andepitaxial(duetothinlmsgrownonthickersubstrates).Theyanalyzedthestressusingwafercurvaturemeasurements.ThestressinSi-substrateisgivenbyequation si=E 1)]TJ /F7 11.955 Tf 11.95 0 Td[(z)]TJ /F3 11.955 Tf 11.95 0 Td[(zo R(2)WhereEistheyoung'smodulusandisthepoisson'scoefcientofsilicon,Risthewafercurvatureradius.Duringsilicideformationthermalstressforallthesilicidesiscompressiveduetocoefcientofthermalexpansionofsilicideisgreaterthansilicon.Someofthepropertiesyoung'smodulus,thermalexpansioncoefcientandbuilt-instressvaluesofvarioussilicidesarereportedintable 2-3 .TheyalsoanalyzedthestresseffectsonsubstrateduetosilicidewidthandspacingsusingtheRamanspectroscopydata.CoupleofsimulationswerealsoperformedtoshowthestressnearNisilicideregionsandshallowtrenchisolation(STI),acompressivestressof-150MPatotallyattributedtoSTIinduced.Toquantify 35

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stressinthechannelandsource/drainduetoNiSiisolatedsimulationsneedstobeperformed. Table2-3. Young'smodulus,thermalexpansioncoefcientandresidualbuilt-instressofTiSi2,CoSi2andNiSi SilicideE(GPa)(10)]TJ /F4 7.97 Tf 6.58 0 Td[(6K)]TJ /F4 7.97 Tf 6.59 0 Td[(1)bi(GPa) TiSi226412.52.1CoSi216010.41.1NiSi150160.72Si130-1872.6AnotherstudyperformedbyLiewetal[ 42 ]fornickelsilicidestressevolutionwithtemperature.Whereforceperunitwidthwascalculatedbasedonthecurvaturechangesandstoney'sformulaeq 2 .TheyperformedtwoheatingcycleswherephasetransformationresultingindifferentstressisalsoobserveditcanbeobservedthatstresschangesfromcompressivetotensileduringwhichthelmhascompletelytransformedintoNiSi. F W=ftfE 6(1)]TJ /F7 11.955 Tf 11.95 0 Td[()(ts)2(K)]TJ /F3 11.955 Tf 11.95 0 Td[(Ko)(2)wherefisthestressinthelm,tfisthelmthickness,Fistheforceinthelm,Wisthewidthofthesample,EistheYoungsmodulusofthesubstrate,sisthepoissonratioofthesubstrate,tsisthesubstratethickness,Kisthemeasuredcurvature,andKoistheinitialcurvature.Benedettietal[ 43 ]alsoperformedseveralConvergentBeamElectronDiffraction(CBED)analysisonCoSi2andNiSigrownwithdummygateofvariouslengths.Theyalsoconcludedthattensilestresswasobservedduetonickelsilicideunderthedummygates.AbrightFieldTEMimageandstresscontoursing 2-16 conrmsthataround+100Mpaisobserveddirectlybelowthegate.ImpactofNi-silicidegrainorientationonstressisalsostudiedbyTorregianietal[ 44 ].Wheretheyfoundthatduetodifferenceinorientationofsilicidegrainsat 36

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sourceanddrainregionanasymmetricstrainproleisgeneratedunderthegate.ItwasconrmedbyTEMandCBDanalysisshowning 2-17 .Simulationswerealsoperformedinordertoverifythesameusingcoefcientofexpansiontobe12x10)]TJ /F4 7.97 Tf 6.58 0 Td[(6/CandYoung'smodulusof132GPa. Figure2-16. TopimageisTEMofNiSistructure.Bottomisthestresscontoursversusdepthfromthesurfacesimulationsshowingstressproleunderthegate. 37

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Figure2-17. Simulationshowingasymmetricstressgeneratedduetovariationingrainorientations. 38

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CHAPTER3SIMULATIONTECHNIQUES:LEVELSETMETHODSANDDEALGROVE'SMODEL 3.1SiliconProcessingforSilicideandContacts 3.1.1BasicCMOSManufacturingProcessATypicalCMOSmanufacturingprocessstartswitheitherp-typeorn-typebaresiliconsubstrate.TherearemanyindividualprocessessuchasLithography,Etching,Cleaning,ChemicalMechanicalPolishing(CMP)etc,thatgoesintomakingevenasingleMOSFETdeviceonsiliconsubstrate.Shownincartoon(Fig. 3-1 )issiliconprocessingsequence.Firstislithography,coatingthewaferwiththeresistandthenusingeitheropticalorelectronbeamtocreatepatternsonsilicon.Thenpatternedmaterialisetchedawayusingappropriatechemicaletchantorbybombardingheavyionsonthematerialalsoknowasreactiveionetching.Achemicalcleanisperformedafteretchiscompleteinordertoclean-upanyresidueorpolymerremoval.Thesethreebasicstepsarerepeatedeverytimeanewpatterniscreatedonsiliconoranyotherdepositedmaterial.Coupleofotherimportantstepsareion(dopants)implantationtomodifytheresistivityandjunctiondepths,RapidThermalAnnealing(RTA)tomaintainthematerialintegrityaswellasensuredopantactivation[ 45 47 ]. Figure3-1. CMOSprocessingstep 39

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3.1.2SilicidationProcessSilicidegrowthprocessisathermallyactivatedself-alignedprocess,wheredepositedmetalreactswiththesiliconatanactivationtemperaturetoformmetalsilicidesofvariouscomposition.Thetermselfalignedisusedbecausethisstepdoesnotrequireanylithographysteps.Itisalsocosteffectiveandlesscomplexfortherstcontacttosilicon.Asshownin(Fig. 3-2 )afterallthegate,sourceanddrainprocessingiscompletedametallayerisdepositedontopthestructureusingphysicalvapordepositionbysputtering.Thendeviceisannealedinthefurnaceattherequiredtemperatureformetalandsilicontoreactandformsilicide.Reactionismainlyoftheform xM+ySi!MxSiy(3)whereMxSiyisthedesiredphaseofsilicide.Thennallyunreactedmetaliscleanedfromtopofthespacerandsilicideusingchemicalclean.Contactprocessingisdoneafterthesilicideformationiscomplete.AtypicalcontacttosiliconinsemiconductorindustryislledwithtungstenmetalandnallyCMPisusedtoplanarizetheplug.[ 48 50 ] Figure3-2. SilicideProcessingaftergateandspacerformation. 40

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3.2LevelSetMethodsLevelSetMethods(LSM)[ 51 ]arenumericaltechniquestotrackanyevolvinginterfacein2D/3D.ItwasdevelopedbySethianandOsherforpropagatinginterfacessuchasFlames,Oceanicwaves,MaterialBoundaries,etc.LSMsolvesfortheinitialvaluepartialdifferentialequation.Numericalcomputationsareperformedonaxedcartesiangridundereuleriansettings.TherearemanyadvantagesofLSMoversomeofthehistoricaltechniquessuchasmarkerorstringmethod.ModelingmovingfrontsusingmarkertechniquesreliesondiscretizationoftheLagrangianformofequationintosmallmarkerpointswhosepositionsintimeareusedtopropagatethefront.AsshowninFig. 3-3 [ 51 ]markertechniquefailsinpropagatingasharpcornerwheremarkersarecrossingeachothercalculatingaderivativeatsuchcornersleadstooscillations. Figure3-3. Markertechniqueshowingdiscretizationofinitialcurve Themajorproblemwithmarkertechniqueisthepositivefeedbackonerrorofposition.AsdescribedbySethian Asmallerrorinapproximatepositionofthemarker Leadstolocalvariationincomputedderivatives Causingvariationincomputedparticlevelocitiesandunevenadvancementofmarkers 41

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YieldinglargererrorinpositionoffrontHencewithinafewtimestepsoscillationsbecomesunstableandcomputedsolutionisunbounded.LevelSetMethodtechniquesembedtheinitialpositionofthefrontasthezerolevelsetofahigherdimensionalfunction.Whereisdenedasthesigneddistancefromtheinitialinterfaceasshowinequation( 3 )itispositiveinthedirectionofmovingfrontoroutsideandnegativeintheoppositedirectionorinside. (x,y,z,t)=d(3)ToillustratetheFig. 3-4 showszerolevelsetfunctionbeinginitializedoverthegridbasedonthedistanceofthegridpointsfromtheinitialfront.Soourmovinginterfaceatanygiventimeofevolutioniseasilygivenby=0. Figure3-4. SignedDistancefromtheinitialfrontforlevesetfunction 42

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Levelsetfunctionisatime-dependent,implicitfunctionsolvedoveraxedgrideulerianframework.Itbasicallysolvesanadvectionequation( 3 ) t+Fjrj=0(3)toupdatethehigherorderfunctionthatembedstheinterfaceposition.WhereFisthevelocityofpropagationthatmaybedependentonmanyfactorssuchasnormal,curvature,diffusionofmaterial,concentration,etc.,tisthetimederivativeand5isthespatialderivativeof.Asgettingthenumericalsolutiontothisformofadvectionequationisnoteasy,aweaksolutionsusingthehyperbolicconservationlaws[ 52 53 ]isobtained.Asitisrequiredforustosolvetheaboveequationonadiscretelevelsetgrid,weneedtochooseeitherforward,backwardorcentereddifferenceschemesforcomputingthespatialderivativesolution.Backwarddifferenceisknowasanupwindbecauseitusesthevaluesinthedirectionofpropagation.Tochoosethecorrectschemeaccordingtothenonconstantdirectionofvelocityequation( 3 )isusedtoupdatethevaluesofalloverthegrid.Ittakescareofthetwosituations,ifF>0thenbackwarddifferenceisusedandwhenF<0thenforwarddifferenceisusedtomaintainthesanityofinformationowinthedirectionofmathematicaldomainofdependence. n+1i=ni)-221(4t[max(0,Fi)5++min(0,Fi)5)]TJ /F5 11.955 Tf 7.08 -4.94 Td[()](3)Where5+=[max(0,D)]TJ /F6 7.97 Tf 6.59 0 Td[(xi)2+min(0,D+xi)2]1=2and5)]TJ /F5 11.955 Tf 10.41 -4.94 Td[(=[max(0,D+xi)2+min(0,D)]TJ /F6 7.97 Tf 6.59 0 Td[(xi)2]1=2withD+xirepresentsD+xi=D+xiniandD)]TJ /F6 7.97 Tf 6.59 0 Td[(xi=D)]TJ /F6 7.97 Tf 6.58 0 Td[(xini. 43

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ToillustratehowthelevelsetfunctionisoneorderhigherdimensionthanourproblemimagineacircleonX-Yplaneasourinitialinterface,soourlevelsetfunctionwilllooklikeaconical3Dimensional(3-D)functionasshowninFig. 3-5 .Propagationoftheinterfaceisshownforindividualtimesteps,itclearlyshowshowourinterfaceisalwaysembeddedat=0.LSMuseshyperbolicschemesinconjunctionwithHamilton-Jacobiequationanon-linearpartialdifferentialequation( 3 )[ 54 55 ]togettheaccuratenumericalsolutionstotheinitialorboundaryvalueproblems. H(x1,x2,...,xn,@ @x1,@ @x2...,@ @xN,t)+@(x1,x2,...,xN) @t=0(3)WhereHisthehamiltonianandistheprinciplefunction.Inour3-Dinitialvalueproblemcasehamiltoniantakesasimpleform H=Fq (@ @x)2+(@ @y)2+(@ @z)2(3)oncethehamiltonianandprinciplefunctionisestimatedfromtheinitialinterfacelevelsetfunctionisupdatedandevolvednaturally.AnotherfeatureofLSMisthatnormalsandcurvaturecanbecomputedeasilyandgivenbyasfollows:Normal ~nij=x,y (2x+2y)1=2(3)Wherexisthepartialderivativew.r.txandyisw.r.ty.andCurvature =xx2y)]TJ /F7 11.955 Tf 11.96 0 Td[(xyxy+yy2x (2x+2y)3=2(3)LSMhasbeenusedforsimulationetching,deposition,SPER(SolidPhaseEpitaxialRegrowth),etc[ 56 57 ].Ithasmanyinherentadvantagessuchasevolvingsharpcorners,mergingtwodisjointinterfacesasshowninFig. 3-6 overcomingtheerrorsexplainedinFig. 3-3 .Alsothesetechniquescanbeeasilyextendedtothreedimensionalstructures. 44

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Figure3-5. Levelsetfunctionofoneorderhigherdimensionwithembeddedinitialinterface.Timeevolutionofthelevelsetfunctionatdifferenttimestepsmovingwithaconstantisotropicvelocity. Figure3-6. Twodisjointsurfacesevolvingandlevelsetfunctionspropagatingsimultaneously(a)Surfacesevolvingandmergingintime.(b)3Dviewoflevelsetfunctions. 45

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3.3DealGrove'sModelThethermal-oxidationofsiliconisaveryimportantprocessstepforsemiconductorindustry.Understandingofthebasicoxidationmechanismaswellascontrolledandrepeatablegrowthisreallyimportant.SiliconoxidationhasbeenstudiedoverseveralyearswithgrowthmodelingcontributioncomingfromDealandGrovein1965[ 4 ].Thismodeldescribesthekineticsofsiliconoxidationwithvaryingtemperatureandpressure.Thechemicalreactionsdescribingthethermaloxidationofsiliconinoxygenandwatervaporaregivenineq( 3 )and( 3 )respectively. Si+O2!SiO2(3) Si+H2O!SiO2+2H2(3)Thismodelshowsthatwhentherearereactionstakingplaceatthetwoboundariesoftheoxidelayer,ageneralrelationshipcanbeobtainedusingonlythephysico-chemicalconstantstodescribetheoxidationsystem.ThismodelisbasedonthefactthatoxygenisbeingtransportedintothesiliconandreactingwithSitoformSiO2.Therearethreedifferentstagesthattheoxygenmoleculeshouldgothrough: 1. Movingspeciesistransportedformthebulkofthegastotheoutersurfacewhereitreactsorisadsorbed. 2. Itisthentransportedthroughtheexistingoxidethicknesstowardsthesilicon. 3. ItnallyreactswiththesilicontoformanewlayerofSiO2.Sothemodelusestheux(Theuxisdenedbythenumberofoxidantsmoleculescrossingaunitsurfaceareainaunittime.)oftheoxidantineachoftheabovestepstopresentthenalmodelingequationofgrowth.Itisalsoassumedthattheuxforallthethreestepsisidenticalatalltimes.ToillustrateFigure 3-7 showstheuxfromthebulkofthegastothevicinityoftheoutersurfacegivenbyeq( 3 ) F1=h(C)]TJ /F3 11.955 Tf 11.95 0 Td[(Co)(3) 46

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wherehisthegas-phasetransportcoefcient,Coistheconcentrationoftheoxidantattheoutersurfaceofoxide,andCistheequilibriumconcentrationoftheoxidantintheoxide.AlsoCisrelatedtothepartialpressurepoftheoxidantbyHenry'slawC=Kp.Theuxoftheoxidantacrosstheoxidelayerisgivenbytheeq( 3 )thatisalsotheFick'slawofdiffusiongivenbyF=)]TJ /F3 11.955 Tf 9.3 0 Td[(D@C @x F2=De(Co)]TJ /F3 11.955 Tf 11.96 0 Td[(Ci)=xo(3)WhereDeistheeffectivediffusioncoefcientthatisdependentontheactivationenergyandtemperature,Ciistheoxidantconcentrationneartheoxide-siliconinterface.Finallythethirduxisrelatedtotheoxidationreactionattheinterfacerepresentedbytherst-orderreactionrelationeq( 3 ) F3=kCi(3)withkbeingthereactionratecoefcientbetweenoxygenandsiliconmolecules. Figure3-7. Dealgrovesmodelshowingallthreeuxes. 47

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AtequilibriumF1=F2andF2=F3duetothesteady-statecondition.Therearetwolimitingcasesthatarisediffusion-controlledgrowth(whendiffusivityisverysmall)orreaction-limitedgrowth(whendiffusivityishighbuttheoxidationiscontrolledbythereactionrateconstantk).SolvingforCiandCoequationsobtainedare: Ci C=1 1+k h+kxo De(3) Co C=1+kxo De 1+k h+kxo De(3)FinallyifN1isthenumberofoxidantsmoleculesincorporatedintoaunitvolumeofoxide,therateofgrowthisdescribedbythedifferentialequation dxo dt=kC N1 1+k h+kxo De(3)Solutiontothisdifferentialequationbystraightforwardintegrationisgivenby x2o+Axo=Bt+x2i+Axiorx2o+Axo=B(t+)(3)whereA=2De(1 k+1 h)B=2DeC N1and=(x2i+Axi) BThissystemofsiliconoxidationisalinear-parabolicsystemasshowninFig. 3-8 ,whereoxidethicknessisestimatedbasedontheoxidantsconcentrationatthetwointerfaces.AlsotheparabolicrateconstantsBhasalineardependenceonpressureandanexponentialdependenceontemperaturedependentontheactivationenergy.This 48

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phenomenaofdiffusion-controlledgrowthisexhibitedbysilicideformationonsiliconaswell. Figure3-8. Oxidationofsiliconindryoxygenshowinglinear-parabolicbehaviorofgrowth. 3.4SummaryInsummary,thischapterpresentsthreebasicmathematicaltechniquesimplementedinFLOOPStomodelthenickelsilicidegrowth.LevelSetMethodstoaccuratelymodeltheinterfacepropagationofsilicide,maintainingerrorandoscillationsfreesimulationsascomparedtothetraditionaltechniques.ExplanationoftheDealGrove'smethodforsiliconoxidation,numericaluxmethodtobecoupledwiththelevelsettechniquetoprovidetheaccuratevelocityofgrowthineachdirection.Finally,thechemicalpotentialformulationformodelingthesegregationofdopantsduringsilicideformationandhowthisapproachisthermodynamicallysuitable. 49

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CHAPTER4IMPLEMENTATIONINFLOOPSANDINITIALRESULTS 4.1IntroductionAsexplainedintheLiteraturereview:chapter 2 andSimulationtechniques:chapter 3 ,LevelSetTechniqueisapowerfulandhighlyaccuratemethodtobeusedforsilicidegrowthmodelingandboundarytracking.Toimplementthesetechniquesweneedavelocityfunctiontopropagatethesilicide-siliconinterface.Thisvelocity,asmentioninsection 2.1 isdependentonthegrowingphaseofnickelsilicide,Ni2SiphasehasaparabolicgrowthrateordiffusioncontrolledandourdesiredphaseNiSihasalineartimedependenceorreactionratelimitedgrowth.Itisalsoknowfromtheliteraturethatthesilicide-siliconisalinear-parabolicsystemquietsimilartotheDeal-Grove'smodelforsiliconoxidation.ThischapterfocusesonimplementationofLevelSetfunctionandcouplingofdiffusionwithLSMinFLOOPS.Tofacilitateournumericalsolutionstoupdatethetwointerfacesnickel-silicideandsilicide-siliconsimultaneouslywehaveimplementedDual-LevelSetfunctionstotracktheboundariesindividually.ItalsoincludestheinitialsimulationresultsandvericationwithTransmissionElectronMicroscopy(TEM)data.Theseresultsandtechniquesaregoingtobecoupledwithdopantsegregationandstressprolinginlaterchapters. 4.2ADualLevelSetMethodImplementationInordertoimplementtheLevelSetMethodsaxedrectangulargridissetuprstintheFloridaObjectOrientedProcessSimulator(FLOOPS)asitgivesustheeaseofcalculatingnitedifferenceapproximationsandhigherdegreeofaccuracy.Alsothisworksbestforthelevelsetdiscretizationscheme.LevelSetmethodbasicallysolvesfortheadvectionequationasmentionedinchapter 3.2 .isahigherdimensionalfunctionof(x,y,z,t)thatembedstheinterfacelocation=0atalltimes.LevelsetissolvedusingtheEulerianmethodfortimeintegrationoftheequationtoobtainthefuturelevelset 50

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functions. @Level1,2 @t+FjrLevel1,2j=0(4)InthiscaseofnickelsilicidegrowthmodelingwehaveusedtwolevelsetfunctionsLevel1andLevel2totracktheNickel-SilicideandSilicide-SiliconBoundariesrespectively.Thetwolevelsetequationssimilartoeq( 4 )or( 3 )aresolvedtoupdatethelevelsetfunctions,alsoeachlevelusesseparatevelocityfunctions(F)dependentonthevolumetricexpansionofNiSiandthereactionatNiSi-Siinterface.InterfacevelocityFintheadvectionequation( 4 )isalsoembeddedintoahigherdimensionalfunctionknownastheextensionvelocity.WhatthismeansisthatnotonlyFisdenedattheinterfaceorzerolevelsetbutisalsodenedforallthelevel'sateverynodeoftherectangularFLOOPSmesh.Theduallevelsetsareinitializedbasedinthenickelandsiliconinterface,tovisualizehowtwolevel'spropagaterefertoFig. 3-6 asthesetwofunctionswillmoveintheoppositedirectionlevelsareinitializedaccordinglyasshowninFig. 4-1 Level1ispositiveinthedirectionofpropagation(innickel),negativeontheotherside(insilicon)andsamegoesforLevel2,positiveinsiliconandnegativeinnickel.Asmentionedintheliteraturereviewchapter 2.1 silicideformationisasequentialprocesswithNi2SiphaseformsrstandthenfurtherannealingcausingthelinearphasetransformationtoNiSi.Botharethermallyactivatedprocessforthetemperaturerangeof300-700Cwithactivationenergyof1.5eVforNi2Siand1.4eVforNiSiphase[ 10 19 50 58 61 ].ThegrowingthicknessofrstphaseNi2Sifollowsaparabolicrelationwithtimegivenbyequation: W2Ni2Si=RNi2Sitcm2(4)WhereWNi2SiisthethicknessandRNi2Si=0.02e)]TJ /F15 5.978 Tf 5.75 0 Td[(Ea KTcm2s)]TJ /F4 7.97 Tf 6.59 0 Td[(1istherateofgrowthforNi2Si.ForNiSiphasegrowththicknesshaslineardependenceontime[ 10 12 ]. WNiSi=RNiSitcm(4) 51

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WhereRNiSi=104e)]TJ /F15 5.978 Tf 5.76 0 Td[(Ea KTcms)]TJ /F4 7.97 Tf 6.59 0 Td[(1istherateofgrowthforNiSi[ 10 12 ]. Figure4-1. LevelsetinitializationshowingnickelsiliconinitialinterfacewitheachLevelfunctionshowninthedirectionofpropagation. TheinitialstructureiscreatedontheFLOOPSmesh,foroursimulationpurposesitisverysimilartoarealMOSFETdeviceasshowninFig. 4-2 rectangulargridusedforthelevelsetmeshis0.0020.002m.Thestructureisasilicon(100)substratewithpolysiliconasthegatematerialandoxideasspacer,ontopofthewholestructurenickelisdepositedtomatchtheinitialconditionofsilicideformation.ComparedtotheTEMimagefrom[ 62 ].Levelsetequationsaresolvedfromthestartinginterfaceofsiliconandnickel.Tocontrolthegridsensitivityissuesspacingnearthenickel-oxide-siliconedgeboundariesismaintainedat0.002m,aswellasreducethesimulationtimesneartheoutsideedgesitisrelaxedto0.01m.AlsothisensuresthatinterpolationerrorfromFLOOPSgridovertothelevelsetgridisminimized.Theboundaryconditionsforthesimulationsarethatnickelsupplyfromthebulkisunlimitedandtheleftandrightgridboundariesarereectingforcomputationofnormalsattheedgesthatcandeveloposcillations. 52

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Figure4-2. InitialstructureusedforsilicidegrowthsimulationsincomparisontotherealMOStransistorTEMimage[ 62 ]. 4.3CouplingofDiffusionwithLSM:ModelCouplingofdealgrove'smodelwiththelevelsetisthebasisofournumericalformulationtomodelandsimulatethesilicidegrowth.ToadvancethelevelsetfunctionsweneedtoevaluatetheHamiltonianupdatesateachtimestep(refertosection 3.2 ).Nowtheseupdatesarebasedonthevelocityofgrowthfunctionthataccordingtoourmodelisobtainedusingthedealgrove'sequations(explainedinsection 3.3 ).Nickelconcentrationsalloverthegridisdeterminedusingthethreeuxessimilartoequations( 3 ),( 3 )and( 3 ).FirstlyitisimplementedasanAlagatorscriptandtestedin1-Dimensiontopredictthecorrectconcentrationofoxygenandmatchtothereferencedata[ref].EquationbelowisusedinFLOOPSforconstantdiffusivityofoxygeninoxideatatempof1000C.setdi(3.0e)]TJ /F5 11.955 Tf 11.96 0 Td[(10(x<$gas)(x>$sil)+1.0e)]TJ /F5 11.955 Tf 11.96 0 Td[(21)Thenanordinarydifferentialequation( 4 )(implementedinAlagator)summingupalltheuxesissolvedtogettheoxygenconcentrationprolesasshowninFig. 4-3 Firstandsecondtermintheequationtakescareofthespeciesdiffusion,thirdtermistheux 53

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attheoxygen-oxideboundaryandfourthtermaccountsforthereactionbetweenoxygenandsilicon.Valueofh(Gasphasetransportcoefcient)is1.0e8=hrandk(oxidationreactionrate)is1.0e3=hraretakenfromtheDealGrove'sdata[ 15 ].Simulationresultsareshownintable 4-1 theymatchwellwiththecalculateddatausingdealgrovesequations( 3 )and( 3 ).Figure. 4-3 showsthesimulateddiffusionprolesinoxideforvaioustimesofsimulation. setstr"ddt(C))]TJ /F5 11.955 Tf 9.3 0 Td[(($di)Cgrad(log(C)+1.0e8(x<$gas)(C)]TJ /F5 11.955 Tf 9.3 0 Td[(1.0e22)+1.0e3(x>$sil)(C)]TJ /F5 11.955 Tf 9.29 0 Td[(1)"(4) Table4-1. SimulationvsCalculatedResults PositionLocation(m)SimulatedConc.(cm)]TJ /F4 7.97 Tf 6.58 0 Td[(3)DiffusionTime(min)CalculatedConc.(cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3) Co-0.0339.92e2120-Ci0.0334.77e21204.76e21Co-0.0669.92e2140-Ci0.0663.08e21403.14e21Co-0.19.96e2160-Ci0.12.30e21602.33e21 4.3.1NickelConcentrationWithDealGrove'sModelWeknowthatnickelisthemaindiffusingspeciesforNiSiformationandbehaveslikeanoxidationsystem.Tocouplethelinearparabolicgrowthmodel(asexplainedintheliteraturereviewchapter 2 )ofnickelsilicidewithlevelsetmethod,nickelconcentrationvalueswereobtainedbynumericalsolutionofthedealgrove'sequationsonseparategridofsilicon,nickelandtheinterfaces.Thusprovidingacontinuoussolutionoftheconcentrationvalueseverywhereinthegrid.EquationsimplementedinFLOOPSaregivenbelow.Diffusioncoefcientpreexponentialof6*exp(-Ea/kT)cm2/sischosenfromtheliteraturebyCelvengeretall[ 61 ].Diffusivityissetusingthetermbelow.setdi(1.0e)]TJ /F5 11.955 Tf 11.96 0 Td[(10(xLevel2)+1.0e)]TJ /F5 11.955 Tf 11.95 0 Td[(21) 54

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Figure4-3. Simulationsshowingoxygenconcentrationprolefordifferenttimes20min(Green),40min(Pink),60min(Black). VariableTestrepresentingnickelconcentrationisdeclaredtohavenon-negativeandcontinuoussolutions.Firstequation( 4 )issolvedinLevel1nickelgridforthetransportofnickelatomsfrombulktothesurfaceofsilicide.Transportcoefcientischosentobehighenoughforacontinuoussupply. setNistr"ddt(Test))]TJ /F5 11.955 Tf 9.3 0 Td[(($di)Testgrad(log(Test)+1.0e10(Level1<0)(Test)]TJ /F5 11.955 Tf 9.29 0 Td[(1.0e22)"(4)Thenequation( 4 )issolvedinLevel2siliconwithreactionrateconstantoftheorder104s)]TJ /F4 7.97 Tf 6.58 0 Td[(1fornickel-siliconrstorderreactionasreportedbyAckeretall[ 63 ]. setSistr"ddt(Test))]TJ /F5 11.955 Tf 10.35 0 Td[(($di)Testgrad(log(Test)+1.0e3(Level2>0)(Test)]TJ /F5 11.955 Tf 10.34 0 Td[(10)"(4)Continuityofthesolutioninnickelandsiliconismaintainedusingahighuxequation( 4 )forTestvariable. setux"(Test Silicon)]TJ /F3 11.955 Tf 19.15 0 Td[(Test Nickel)1e10"(4) 55

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pdbSetStringNickel SiliconTestEquation Silicon")]TJ /F5 11.955 Tf 11.96 0 Td[($ux"pdbSetStringNickel SiliconTestEquation Nickel"$ux"Abovedeclarationistomaintaintheequalityofuxacrossnickelandsilicon.ThesethreeequationsaresolvedusingtheFLOOPSembeddeddiffusionsolverandcontrollerateachtimestepofsimulation.Alsonickeldiffusionintooxideisrestrictedinordertopreventanyerroneouscalculationsduringlevelsetupdates. 4.3.2LevelSetUpdatesWithDiffusionTosimulatethegrowthofsilicidenallylevelsetupdatesarecalculatedbasedonthenickelconcentrationvaluesasobtainedinprevioussection.Hamiltoniansforeachlevelisestimatedbaseduponthenitedifferenceapproximations(ForwardScheme).ValuesofnickelconcentrationandNiSiunitcellvolumeareusedtoestimatethevelocityfunctionforhamiltonianupdates.ToillustratethecompletecouplingoflevelsetwithdiffusionrefertotheowchartinFig. 4-4 .Thesequenceisexplainedbelow 1. InitializationofLevelsetfunctionbasedoninitialinterface. 2. CalculationandupdatesforLevelset'sbasedoninitialvelocity. 3. SolveDealGrove'sequationsfornickelconcentrationprole. 4. EstimateLSMupdatesbasedonnickelvalues. 5. CheckforLSMandDiffusioncouplingisintact(meaningdiffusionneveroutrunslevelsetmovement).Levelsetsareadvancedbasedontheinitialsilicidegrowthvelocityforaverysmalltimestept.Subsequentlevelupdatesarebasedonournumericalsolutionofthediffusion-reactionsequationsofNickelbasedonDealGrove'sbehavior.BottomlevelsetLevel1(silicidegrowth)isupdatedbasedonthenickelconcentration(Test)atthesilicide-siliconinterface,NiSiunitcellvolume(97.23e)]TJ /F4 7.97 Tf 6.59 0 Td[(21cm)]TJ /F4 7.97 Tf 6.59 0 Td[(3)[ 50 ]andgridspacing(0.002m).ToplevelsetLevel2(volumetricexpansion)isupdatedbasedontheamountofnickelleavingandthedifferencebetweentheunitcellvolumeofnickel 56

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(4.376e)]TJ /F4 7.97 Tf 6.59 0 Td[(23cm)]TJ /F4 7.97 Tf 6.58 0 Td[(3)[ 64 ]andsilicide.AmountofnickelleavingthesurfaceisestimatedbasedonthefourpointuxasshownintheFig. 4-5 .Valueofnickelconcentrationsatfourimmediateneighboringpointswereobtainedtocalculatetheincominguxatnickelsilicideboundary.Basedonthisuxhamiltonianfortoplevelsetisupdated.Tomaintaintheintegrityofourmodelitisnecessarythatthelevelsetneveroutrunsdiffusion.Inordertocontrolthatdiffusiontimestepsarekeptmuchsmallerthanlevelsetupdatetimesteps,sothattherearemultipleoratleastonediffusionstepoccurringbeforelevelsetmovestominimizetheerrors. 4.4InitialSimulationResultsandVericationToverifytheabovedescribedmodelwehaveperformedsimulationsonseveralstructuresandveriedtheresultscomparingittotheTEMdataavailable.Wehavealsodoneacompleteprocesssimulationincludingdepositionandetchingofsilicontoderiveamorerealisticstructureforsilicidegrowth.Inthisrststudyinitial2D-simulationsareperformedonaMOSFETkindofstructureasexplainedinsection4.2.FinalsimulationprolesarecomparedtotheTEMdatafromseveralreferences[ 62 65 68 ].AsshowninFig. 4-6 arethenalprolesofdualzero-levelset'sontheFLOOPSgrid,growthprolesatthesource-drainandpolygateregionareshown.Forsimulationpurposestemperatureof400Cwasusedforthegrowthofsilicidefor30min.Figure 4-7 Aisthecloseuplookintothespacer-source/drainregionwherelimitedsupplyofnickelduetodiffusionprolesarecapturedusingourmodels.Thiscomesdirectlyfromoursolutionofnickelbasedondealgrove'sbehavior.Multiplesolutionsofthelevelsetequation(eachbluelineisasolutionofmultipleorsinglediffusionstepandlevelset)atvarioustimestepduringthesimulationarealsoshowninFig. 4-7 B.Siliconconsumptionratioisalsomaintained1Aofnickelreactswith1.83Aofsilicontoform2.3Aofnickelsilicide[ 50 ].ComparisonofsimulationresultswiththeTEMdatafromLuetal[ 62 ]displaysgoodagreementbetweensilicideshapesunderthespacer. 57

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Figure4-4. FlowchartshowingstepbystepsimulationsequenceandcouplingofbothLevelSetMethodandDealGrove'sModel. 58

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Figure4-5. Fourpointuxestimationonarectangulargrid,bluesurfacerepresentsours2Dgridforthelevelsetfunction. Figure4-6. FinalzerolevelsetsshownonFLOOPSgridrepresentingsilicidegrowthonSource/drainandpolygate.. 59

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AZeroLevelSetatSource/Drain BMultipleLevelSetSolutionsFigure4-7. Simulationresultofduallevelsetgrowthofnickelsilicideonsource/drainandmultiplestepsoflevelsetpropagation. ThesecondstructuresimulatedisanarrowpolygatestructureshowninFig. 4-8 .Nickelisdepositedontopofthepolygateandiswrappedaroundwithoxidetoactasaspaceronthelateralsides.ResultsshowamushroomdomekindofgrowththatmatchquietwellwiththepresentedTEMdatafromAsayamaetal[ 67 ].Wecanclearlyobservethatduetothelargenickelsupplyatthetwoedgesamountofnickeldiffusingthroughpoly-oxideedgeismuchmorethanthebulkresultingingreatergrowthanddesireddomeshape.InsetinFig. 4-8 Aisthelevelsetprogresscoupledwithdiffusion.FullprocesssimulationisshowninFig. 4-9 wheresiliconisrstlydepositedwithpolyselectivelyatthedesiredregionthenoxidespacerisdepositedconformallyontopofthewholestructurefollowedbyanisotropicetchtogiveustheL-shapespacer,nallynickelisdepositedtoproceedwiththelevelsetNiSigrowthsimulations.Interestingresultsrelatedtogriduniformitywereseenduringthesesimulations.WecanclearlyobserveinFig. 4-9 C&Dthatsilicidegrowththesource/drainedgeandatpolyisnotuniformgrowthisfasterneartheoxideedgesatbothlocations.Ithappenedduetovaryinggridsizeresultingfromdepositionandetchingprocessatthesecorners.Grid 60

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sensitivityisanissuesometimeswhendiffusionandlevelsetarebeingsolvedondifferentsizegrids.Tocheckourassumptionofgridrelatedissueswereducedthedepositionandetchratestomakethegriddenserandcloserthelevelsetgrid.ResultsareshowninFig. 4-9 E&FuniformlygrowingsilicideisseenatboththelocationsaswellassilicidegrowthisobservedattheoveretchedoxidespacernearpolyedgethatistypicallythecasewitharealCMOSprocess.Tohandletheseissuesinfuturediffusionsolverisbeingimplementedforthelevelsetgrid.Sothatwhenwesolvethediffusionfornickelconcentrationsandlevelsetforgrowthcoupledtogethertheyworkatthesameminimumgridspacing. 4.5SummaryInSummary,levelsetmethodcoupledtogetherwithDealGrove'smodelswasimplementedinFLOOPStosimulatethegrowthofnickelsilicide.SimulationsshowagoodmatchwiththeTEMdataavailablefromthestudies[ 62 65 68 ].Howeversimulatingafullprocessstartingwithbaresiliconandusingthesimulatorscapabilitytoetch,depositandregeneratethegridsgaveusaninsightongriddependencybetweendiffusionandlevelset.Thus,totackletheseissuesimplementationofdiffusionsolverforthelevelsetgridisnecessary.Tokeepthesemodelcoherentwithothercapabilitiesofthesimulatorgridsensitivityneedstoberesolved. 61

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AZeroLevelSetatPolyGate BTEMimageofasilicidedpolygateFigure4-8. Simulationofnickelsilicidegrowthonanarrowpolylikestructure,insetshowszerolevelsetforthecompletesimulation.TEMdatashowingsilicidegrowthontopofthepolygate. 62

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AFullProcessSimulationstructure BSpacer-Poly-Source/DrainEdge CNon-UniformGrowthatS/D DNon-UniformGrowthatpolygate EUniformGrowthatS/D FUniformGrowthatpolygateFigure4-9. FullProcesssimulationresultsshowinggrowthdifferencesbetweenuniformandnon-uniformgridissues. 63

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CHAPTER5DOPANTSEGREGATIONUSINGCHEMICALPOTENTIALAPPROACH 5.1IntroductionInthischapterwepresentourworkofdopantsegregation(snowplowing)duringsilicidegrowth.Itisknowthatdopantspresentinsiliconatsource,drainorpolygatesegregateduetosilicidegrowth(refertoChapter 2.2 ).Modelforsegregationisproposedbasedonthechemicalpotentialapproach(explainedinchapter 5.2 )forthedopantslikearsenic.BasedonthesilicidegrowthinterfacethesemodelsarealsoincorporatedasanAlagatorscript.InordertosolveforsegregationinparallelwiththeNiSigrowthusinglevelsetandDealGrove'smodelitrequiresustocoupleallthreemethodsdirectlyusingthesametimestepsequence.ThismeansthatLSM,DealGroveandchemicalpotentialapproachshouldbeupdatedsimultaneously.Itdemandsahugecomputationaleffortforeachtimestepofgrowthandsnowplowing. 5.2ChemicalPotentialApproachWhatischemicalpotential?[ 69 70 ]Anintuitiveconceptofchemicalpotentialstartswitheverysubstancehasatendencytochange.Asafunctionofpositionthechemicalpotentialmeasuresthetendencyofparticlestodiffuse.Itmeasurestherateofchangeofathermodynamicfunctionperparticleandforindividualspecies.Insimplewordschemicalpotentialofaspeciesinthemixturecanbedenedasthepartialderivativeofthefreeenergywithrespecttochangeinconcentrationofthatspecies.InsemiconductorphysicsitisawidespreadpracticetorefertothechemicalpotentialastheFermilevel.ToillustrateconsiderasimplesystemshowninFig. 5-1 ofhomogeneousparticleseparatedbyabarrierandwhenthebarrierisremovedparticlestendtodiffusefromhighconcentrationtolowconcentration,untilconcentrationisthesameeverywhere.Herechemicalpotentialdenotedbythesymbolisrelatedanddirectlyproportionalto 64

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thelogarithmicoftheconcentrationofparticle. /1 2kBTlnC(5)WherekBistheBoltzmannconstant,TisthetemperatureandCistheconcentrationofparticles.Inanintrinsicsemiconductorchemicalpotentialliesinbetweentheconductionandthevalanceband,ifwehavetwooppositelydopedsemiconductorsjoinedtogethertheirchemicalpotentialsalignafterasteady-stateconditionisreachedthroughdiffusionasshowninFig. 5-2 andtheuxoftheparticle(orcurrentdensityJ)ineachsemiconductorinrelationtoitschemicalpotential(orthequasi-fermilevel)isgivenbytheequation( 5 )[ 71 ]. J=Dnr(5)Inordertotacklethesegregationofdopantsduringsilicidegrowth.Wehaveusedthechemicalpotentialapproachforthedopantspresentinthesiliconsubstrate.Assilicideisgrownontopofthesilicondopantssuchasarsenicsegregatebetweentwomaterialsdependinguponthesegregationcoefcientandtransportcoefcientsofeachmaterial.Atypicaluxequationtosolveforthesegregationisgivenbyeq( 5 ) FAB=h(CA)]TJ /F3 11.955 Tf 16.85 8.09 Td[(CB mAB)(5)WhereuxFABismeasuredbytheconcentrationofparticlesonindividualsidesAandBofthematerialinterface,histhetransportcoefcientandmABbeingthesegregationcoefcient.Asweknowthechemicalpotentialofaspeciesofparticlesisdirectlyproportionaltoitsconcentrationinthatmaterial,theaboveequationcanbesummarizedintermsofchemicalpotentialsAandB. IfA>BthenparticlesmovefrommaterialAtomaterialB. IfA=Bnotransportwilloccur. 65

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IfA
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Figure5-1. Diffusionbehaviorofhomogeneousparticlesinaclosedsystem,particlesowingfromhighchemicalpotentialtolowchemicalpotential. Figure5-2. Chemicalpotential,ConductionandValancebandproleoftwosemiconductorsdopedwithdifferentspecies(a)Chemicalpotentialsnotalignedseparately(b)Singlechemicalpotentiallevelaftertheyarejoinedtogetherduetodiffusionofparticles. 67

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5.3ModelingofSnowPlowingEffectUsingChemicalPotentialApproachChemicalpotentialisathermodynamicallysuitableapproachtomodelthesegregationofdopantsduringsilicideformation.Inordertopredictthesegregationproleswearegoingtoimplementtheuxequationbasedonchemicalpotential()ofthespeciesinthiscasearsenic.Asexplainedinchapter 5.2 chemicalpotentialofaspeciesisproportionaltoitsconcentrationinthematerial.Thematerialoffsetresultsfromadifferentineachmaterial.Usingthisconceptwehaveformulatedanequation 5 forsegregation.Thisequationisequivalenttothetraditionaluxequationusedformodelingsegregation. J=DCgrad()(5)WhereDisthediffusivitygivenbyequation 5 withthreedifferentdiffusivitiesrepresentingintwodifferentmaterials(D1,D2)andaninterfacecrossingdiffusivity(D3).Cbeingtheconcentrationofdopantsperunitvolume.gradisthegradientoperatorin2Dandisgivenbytheequation 5 .TheZerocrossoperatorisdenedtoassignthecrossingdiffusivityatthesilicide-siliconinterface. D=D1(Level1<0.0)+D2(Level2>0.0)+D3Zerocross(Level1)(5) =log(C)+K(Level1<0)(5)WhereKisrelatedtothesegregationcoefcientbetweensiliconandNiSi.Firstlytheseequationsareimplementedandtestedasa1-Dimensionaltomakesuretheformulationiscorrect.FLOOPSimplementationispresentedbelow.Initialconcentrationisdenedtobeaconstantvaluefortesting,alsoconstantdiffusivityisusedforpreliminarysimulations.selz=1.0e20name=Test 68

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Thenisequationgoverningsegregationwasimplementedasshownbelow. setstr"ddt(Test))]TJ /F5 11.955 Tf 11.96 0 Td[(9.9e)]TJ /F5 11.955 Tf 11.96 0 Td[(16Testgrad(log(Test)+5.0(x<0.05))"(5)Finallydiffusionforthetimeof60swasperformedusingthedefaultcodeavailableinFLOOPS.ResultasshowninFig. 5-3 showsanaccumulationproleoftheTestvariableataninterfacedenedat0.05mwithconstantdiffusivityandthesegregationcoefcientK=5.0.Thisistheexpecteddopantproletobepresentinamovingboundaryorinterfaceproblem.Asinthiscaseofsilicidegrowthheavydopantslikearsenictendstogetpushedfromsilicideintosiliconduetodifferentdiffusivitiesineachmaterial.A2-DimensionalimplementationtestofthismethodwasperformedwiththesilicidegrowthusingLSMandDealGrove.Afterthesilicidegrowthwascompleteequationsimilarto 5 wassolvedbasedontheLevel1dataandresultswerecapturedasshowninFig. 5-4 segregationatdifferentlocationsisobservedtobeconsistent.Afterobservingthatconstantprole1Dand2Dresultsareinaccordancewiththenatureofsegregationnextstepofcouplingthemodelsandvaryingimpurityprolewasintroduced.InordertolinkallthreemethodsLSM,DealGrove'smodelandchemicalpotentialforsegregationthetimestepof(LSM+diffusion)andchemicalpotentialequationwasloopedandsolvedsimultaneously.Tofacilitatethiscongruencewesolvedfornickeldiffusionrstasdescribedinsection 4.3 ,thenlevelsetupdatesbasedonthenickelconcentrationvaluesandnallysolvingthedifferentialequationgoverningsegregationateachtimestepofsimulations.Allthetimestepsarelimitedbytheslowestprocessforthestabilityofsolutions.LevelsetitselffollowsitsCFLstabilitycriterionthatlevelshouldnotmovemorethanonegridspacingatatime.Theninitialimpurityprolewasassumedtobeofgaussianextendingonbothsides(nickelandsilicon)oftheinterfaceandwasdeclaredbytheequation 5 .Itspeakwasplaced10nmbelowsiliconsurfaceamatchingthesilicidegrowththickness. 69

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selz=1.0e20exp(()]TJ /F5 11.955 Tf 9.3 0 Td[((x)]TJ /F5 11.955 Tf 11.95 0 Td[(0.36)(x)]TJ /F5 11.955 Tf 11.96 0 Td[(0.36)=0.01))name=Test1(5) setstr"ddt(Test1))]TJ /F5 11.955 Tf 11.19 0 Td[(9.9e)]TJ /F5 11.955 Tf 11.19 0 Td[(16Test1grad(log(Test1)+5.0(Level<0.0))"(5)Dopantredistributionwasperformedbyimplementingequation 5 asanAlagatorscript.PreliminaryresultsareshowninFig. 5-5 andaccumulationisobservedatthesilicideinterface,alsothedopantprolesaftersilicidegrowthatthreedifferentlocationsareshownbluecurverepresentsthesegregationathighestthickness,greenatthelesserthickpartandredfortheleastthicknessofsilicide.Althoughsegregationdepthisoverexaggeratedinthesesimulationsduetoconstantdiffusivityof9.9e-16,thisisimprovedbyusingourdiffusionequation 5 withvariablediffusivityandtransportcoefcient.Allthesimulationresultsareshowingagoodbehaviorascomparedtotherealdata.Nowweneedtomakemodelworkwiththerealinputdataandpostsilicideimpurityproleinbothmaterial(siliconandsilicide). Figure5-3. Simulationsofdopantsegregationin1-Dimensionalstructure. 70

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Figure5-4. 2Dsimulationshowingresultofdopantsegregationperformedaftersilicidegrowthiscomplete,accumulationattwodifferentsilicidethicknessareshown(blueandred). 71

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Figure5-5. Gaussianimpurityprolesimulationresultswithsnowplowingeffectshownforthreedifferentthicknessesofsilicide.ThisistheresultfromcouplingofLSM,DealGrove'smodelandchemicalpotentialapproach. 72

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5.4SegregationResultsandComparisonwithSIMSdataFinalimplementationuseappropriatediffusionandsegregationcoefcienttomakeourmodelaccurateinpredictingtheimpurityproleandmatchingitwiththerealSIMSdata.DiffusioncoefcientDdeclaredinequation 5 wasusedwithrightdiffusionandtransportcoefcientfornickeleq 5 .Alagatorequation 5 wasalsomodiedto 5 withconcentrationdependentdiffusivityandsolvedforinboththematerialssiliconandnickel.Wealsousedthepre-silicidearsenicimplantproledatafrom[ 29 ]anddigitizedtheplottouseitasaninputforoursegregationmodel.ShowninFig. 5-6 istheSIMSdepthproleofArsenic(As)beforenickeldepositionandafteractivationanneal(Initialproleisnotexactlygaussian). setdico"(2.5e)]TJ /F5 11.955 Tf 9.3 0 Td[(16(Level>0)+2.5e)]TJ /F5 11.955 Tf 9.3 0 Td[(16(Level<0)+2.5e)]TJ /F5 11.955 Tf 9.29 0 Td[(14(zerocross(Level))+1e)]TJ /F5 11.955 Tf 9.3 0 Td[(21)"(5) setstr"ddt(Test1))]TJ /F5 11.955 Tf 9.3 0 Td[(($dico+2.5e)]TJ /F5 11.955 Tf 9.3 0 Td[(16Test1=1.0e20)Test1grad(log(Test1)+5.0(Level<0.0))"(5)proleinf=As)]TJ /F3 11.955 Tf 11.95 0 Td[(Implanted.txtname=Test1selz=Test1+5.0e17name=Test1Simulationswereperformedfor20nmofsilicidegrowthatvarioustemperaturesandgridspacingof0.002m.Resultsforcoupleoftemperatures400and450CareshowninFig. 5-8 alongwiththedigitizeddatafromSIMSanalysis.Boththeshapesshowaclosematchwiththerealdata[ 29 ].Figure 5-7 isthedepthproleofAsaftersilicidegrowthasafunctionofdepthatvariousRTP(RapidThermalProcessing)temperature.Wecanclearlyobservethatredistributionofarsenicin20nmNiSilayeris 73

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Figure5-6. SIMSdatashowingArsenicdopantprolebeforenickeldeposition.[ 29 ]. nonhomogeneousbuttowardstheaccumulationatthesurfaceandattheinterfaceandincreaseofarsenicconcentrationisobservedaftersilicidation.Ithasalsobeenobservedthatatahighertemperaturestheaccumulationpeakisreducedwhichisclearlycapturedinoursimulationproleaswell(bluecurvefor450C).Atfurtherhighertemperatures500-700CarsenicpeakgoesdownsubstantiallythatcanbeexplainedbyagglomerationofNiSi.SimulationdataatthesurfaceshowalowerpeakascomparedtoSIMSdata,itcanbeaccountedforduetothelimitationofaccuratemeasurementofdosagepresentatafewnanometerdepthbeneaththesurface.Alsoanotherfactoristhatourstructureshasbeendeclaredtoletimpuritiesdiffuseonbothsideofthesurface. 74

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Gridsensitivityisalsoaconcernwhensolvingdiffusionlikeequationonvaryinggridsizes.Segregationequationimplementedasanalagatorscriptweretestedin1Dinordertoestimatetheerror.ResultsareshowninFig. 5-9 forvaryinggridsizewecanclearlyseethatbiggergridsizeleadstomoreerror.Nevertheless,computationerrorisnoworsethansolvingdiffusionerrorsolvedonFLOOPSgrid.Overallthismodelseemstobereliableforpredictingtheprolesandhasbeenimplementedinsuccessfully. 5.5SummaryTosummarizea2DmodelingofdopantsegregationusingchemicalpotentialapproachwasdevelopedinaddendumtothenickelsilicidegrowthbycouplingLevelSetMethodandDealGrove'smodelimplementedinchapter 4 .StandardsegregationwasimplementedusingaFick'slawtypediffusionequationbasedonthechemicalpotentialofspeciesaccommodatingthesegregationandtransportcoefcient.Initial1Dand2DsimulationresultsdisplayedagoodbehaviorascomparedtotheSIMSdata.Accurateinitialprolewasusedasainputtosimulatethesnowplowingeffectively.Gridsensitivitystudiesalsovalidatetheintegrityofthismodel. 75

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Figure5-7. ArsenicsegregationSIMSdataaftersilicidegrowthatvarioustemperatures.[ 29 ]. Figure5-8. ArsenicsegregationSimulationresultsforsilicidegrowthat400and450Ctemperatures. 76

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Figure5-9. Gridsensitivitydatafrom1Dsimulationsforvariousgridsizing. 77

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CHAPTER6STRESSSIMULATIONSUSINGFINITEELEMENTMETHODS 6.1IntroductionInthischapterwediscussandpresenttheresultsofstresssimulationsaftersilicidegrowthespeciallyonsource/drainregion.AssilicideisgrownontopofsiliconitinducesstressinsourceanddrainaswellasinthechannelregionofaMOSFET.StressprolesaresimulatedusingtheFLOOPScapabilities.Intrinsicandextrinsicstressinducedatseverallocationscanbeclassiedbaseduponlatticemismatch,volumetricexpansionduetogrowth,coefcientofthermalexpansion,etc.Itisnecessarytoperformafront-endprocesssimulationtosimulatethestressandstraincontoursinalldirections. 6.2StressModelingusingFEMStressgeneratedduetosiliconprocessingisveryimportantfortheICindustry.Itisknownthatinducedstresscanaffectthedeviceperformancedrastically.InducedstresscaneffectvariousparameterofadevicesuchasPiezoresistivity,energybandofsemiconductorcrystals,carriermobilityetc.Piezoresistanceisthemeasureofchangeinresistivityduetomechanicalstress.Piezoresistivecoefcientsrelateinduced-stresstoresistivityusinga36componenttensormatrix.Carriermobilitycanbeexpressedasarelationbetweenvelocityandelectriceld=E.Alsomobilityisdependentuponthescatteringrateandeffectivemassbyarelation=q mwhere1 isthescatteringrateandmiseffectivemass.Nowapplyingstresstosiliconchangesthebandstructuresuchthatthe6-degeneratevalleyssplitbetweenhighandlowenergystatesresultingincarrierrepopulationandreductionofeffectivemassultimatelyleadingtoincreasemobility.Scatteringrateofelectronisalsoreducedduetothisbandsplittingthatalsocontributestowardthedevicespeedimprovement.Althoughholesdonotseesignicantscatteringrateimprovementneverthelessholemobilityisalsoincreasedwhenthedegeneracybetweenlightandheavyholebandsisliftedresultinginreductionofeffectivemass.Mechanicalstress 78

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alsoinuencegeneration-recombinationcurrentcomponentsinp-ndiodes.Stressedsilicontechniquesisofutmostimportanceincurrentscalingtechnologiesandrequiresdeepunderstanding.FLOOPSusesFiniteElementMethod(FEM)tocomputethestressinducedbyseveralprocessessuchassiliconoxidation,impuritydopants,volumetricexpansion,depositionofvariouslms,etching,etc[ 73 75 ].AbriefoverviewofcontinuummechanicsandFEMmethodisprovidedhereinordertomodelandsimulatethestressprolesduetosilicidegrowth. 6.2.1StressStressisasumofinternalforcesactingonabodyperunitareawithunitsofdynespercm2,itisaresultantofreactiontotheexternalforces.Stresshastwocomponentsnormalandshear.Stressthatactstostretchtheobjectisknownastensilestress(Positive)andstressthatshrinkstheobjectisknownascompressivestress(Negative).AsstressisnotuniformlydistributedoveradeformablebodyitisimplementedinthesimulatorasasecondorderCauchystresstensor.ForasimplecaseofnormalstressconsiderabarwithforceFn(TensionorCompression)actingonitinanormaldirection(OutwardorInward)(Fig. 6-1 )itsaveragenormalstressisgivenby=Fn=A.Shearforcescauseashearstressrepresentedby=Fs=A.Incaseofanarbitraryhomogeneousbody(gure 6-2 )variousforcesactonitsinnitesimalsmallsurface.Thestressvectoronax-planeofthecuberepresentedbyanequation 6 Tx=xx^x+xy^y+xz^z(6)Whereisnormalstress,isshearstressand^x,^y,^zareunitvectorsinx,y,zdirections.StresstensoratanysmallvolumeP(forsimplicityitisconsideredtobeacube)isgivenbythreeorthogonalnormalstressesandsixorthogonalsheerstresses 79

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Figure6-1. AbarwithforceFactinginnormaldirectionandsheardirectiononitssurfacewithareaA. representedbythetensormatrix 6 ij=266664xxxyxzyxyyyzzxzyzz377775(6)Whereiirepresentthenormalcomponentofstress,ijaretheshearstresscomponents.Instaticequilibrium,theshearcomponentsareequal(xy=yx)andthestressmatrixcanbereducedtomatrix 6 .Thinlmsgrowthusuallyexhibitplanestressonthesubstratesandisdenedasstateofstressinwhichnormalandshearstressperpendiculartothesurfaceisassumedtobezero.Inthiscasestraincomponentsonlyexistinx-yplaneandcomponent(z=xz=yz=0). 80

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ij=2666666666666664xxyyzzxyyzxz3777777777777775(6) Figure6-2. AsmallvolumeelementPwithnormalandsheerstresstensorcomponentsshownalongitssurface. 6.2.2StrainStrainisdenedasachangeinlengthperunitofitsoriginallengthanditisadimensionlessquantity.Whenforcesactonabodyitdeformsinalldirections.ConsiderasmallelementasshowninFig. 6-3 withdimensionsdx,dyanddzwithdisplacementsrepresentedbyu,vandzrespectively.Changeinlengthisgivenbydu dx,dv dyanddw dzaccordingtothestressappliedpositiveistensileandnegativeifcompressive.Poisson'sratioofanymaterialisdenedbytheratiooftransversetolongitudinalstrain.Shear 81

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strainisdenedasthesumofchangeinlengthinonedirectionwithrespecttotheotherandvice-versagivenbytheequation 6 forx-direction.Strainisalsodenedasamatrixofnineelements(eq 6 )andisreducedtosixelements(eq 6 )inthecaseofstaticequilibrium(xy=yx). xy=(ux y+uy x)(6) Figure6-3. Innitesimalelementwithnormalstraininx,yandzdirectionisrepresentedbydu,dvanddwrespectively.(du dx<0),dv dx>0,dw dx<0) "ij=266664"xxxyxzyx"yyyzzxzy"zz377775(6) "ij=2666666666666664"xx"yy"zzxyyzxz3777777777777775(6) 82

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6.2.3Stress-StrainRelationshipforLinearElasticSolidStress-StrainrelationshipisdenedbyHooke'slaw.Theratioofstresstostrainisknowasyoung'smodulusofelasticityE.Normalstressisproportionaltothenormalstrainby:=E".Thestresstensor(ij)foranlinearelasticbodyislinearlyproportionaltothestraintensor("ij)givenby:ij=cijkl"ijWherecijklisafourthorderstiffnesstensorofelasticconstantswith81materialconstants.Itisreducedto36componentmatrix( 6 )forsymmetriccrystalstructuresuchassiliconwiththreeelasticconstantsc11=166GPa,c12=64GPa,andc44=80GPa. cijkl=2666666666666664c11c12c12000c12c11c12000c12c12c11000000c44000000c44000000c443777777777777775(6)Withtheassumptionofsiliconasanisotropicmaterialelasticconstantsreducetotheformbelow:c11=E(1)]TJ /F7 11.955 Tf 11.95 0 Td[() (1)]TJ /F7 11.955 Tf 11.95 0 Td[()(1)]TJ /F5 11.955 Tf 11.95 0 Td[(2)c12=E (1)]TJ /F7 11.955 Tf 11.95 0 Td[()(1)]TJ /F5 11.955 Tf 11.95 0 Td[(2)c44=E (1)]TJ /F7 11.955 Tf 11.96 0 Td[() 83

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WhereEisyoung'smodulusandispoisson'sratio.InFLOOPSstiffnesstensormatxiiscalculatedusingtwomatrices:B-Matrix(functionofgeometryofelementandnodalcoordinate)andD-Matrix(dependsonmaterialconstantsEand).Inequilibriumconditionofandelementstiffnesstensoriscalculatedbytheequationbelow.Amoredetailexplanationcanbereadfromreferences[ 73 74 76 ]ce=Areae.BT.D.B 6.32DStresscontoursandComparisonDuringsilicidegrowththerearemanysourcesofstresssuchasintrinsicstress,thermalstress,epitaxialstress,etc.Intrinsicstressisproducedduetotheformationofthermodynamicallyunstableandhighlynon-equilibriummicrostructuresonsiliconcausingvolumetricexpansionorshrinkageofthematerialgrowth.Thermalstressisattributedtothedifferencesbetweenthecoefcientofthermalexpansionofsilicideandsilicon.Aftersilicidegrowthiscompleteatahighertemperatureduringthecoolingdownphaseofthesampleanelasticthermaltensilestressisgeneratedinthelm.Epitaxialstressisaresultofdifferentlatticeparametersaswellasduetothethinlmisgrownonarigidthickersubstrateandhastoaccommodatealloftheelasticstrain.Sobasedontheyoung'smodulus,poisson'sratio,silicideshapeanddopantproleofnickelsilicideandsiliconwecaneasilysimulatethestressgeneratedduetothegrowth.AsanexamplestresssimulationonaP-typeMOSFETisshowninFig. 6-4 .Stressupto1GpaisshownbelowthegateduetoSiGe.SeveralsimulationswereperformedusingtheLevelsetboundaryinformationfromourgrowthmodels.Usingsimilarstructureasdeclaredinchapter 4 growthandsegregationwasperformedthenusingLevelboundarydataweassigntheyoung'smodulusandpoisson'sratiofordifferentmaterial.Alsousingthelatticemismatchasthebodystrainparameter.Figure 6-5 showsstressevolutionduringNiSigrowthatincreasingtemperatureswithdifferentsilicidethickness[ 77 ].Stresscharacterizationis 84

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Figure6-4. Stresscontoursimulationshowingupto1GPaofstressonaP-typeMOSFET. usuallydoneusingthecurvaturemeasurementsonawaferasshownintheschematic(Fig. 6-6 )[ 78 ].Basedonradiusofcurvature,angle,young'smodulusandpoisson'sratiostresscanbecalculatedanalytically.SomeexperimentaldatacollectedbySteegenetalwasnotastrongindicatorofamountofstressgeneratedbyNiSithereforetheyperformedsimulationsasshowninFig. 6-7 toestimatethestresscontributionfromsilicide.WecanseethatthereisacompressivestressgeneratedjustbelowsilicideandtensilebelowSTIduetooxide.WeperformedoursimulationsonasimilarstructureasshowninFigure 6-7 .Thissimulationwasperformedonthestructuredeclaredwithoutanylevelsetgrowth,insteadjustdeclaringmaterialswithpropertiesofnickelsilicide,oxideandsilicon.Observedresultsslightlydifferascomparedtotheliteraturedataduetodifferentedgeshapes. 85

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Figure6-5. Forceperunitwidthfor30nmand100nmofnickeldepositedthicknesses.Stressevolutionwithprocessingtemperature. Figure6-6. SimplebendingofawaferorisotropicmaterialwithRbeingtheradiusofcurvature.[ 78 ]. 86

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Figure6-7. Stresssimulationswithvaryingsilicidethicknessneartheshallowtrenchisolationstructure. Figure6-8. Stresssimulationresultsshowingcontoursofcompressivestressgeneratedduetolatticemismatchofnickelsilicide. 87

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Inordertosimulatethestresswithrightshapesofsilicidewecoupledoursimulationwithourgrowthmodels.WerstperformedsilicidegrowthonthesimilarstructureasFig. 6-8 thenusesilicideboundaryinformationtosimulatestress.Athinlayerofaround10-15nmofsilicidewasgrownthatcausescompressivestressbelowsilicideonthesubstrateresultisshowninFig. 6-9 andtensilestressbelowtheoxide.Anothersimulationwasperformedwiththickersilicideofaround30nm.AsshowninFig. 6-10 isthecontoursonthesamestructure.Comparingresultswithdifferentsilicidethicknesseswecanseethatcontoursmoveclosertothexedboundaryandmorecompressive.AsimilarpatterncanbeseenfromthestudyinFig. 6-7 Figure6-9. Simulationshowingstresscontourduetothinnickelsilicidegrowthonsiliconwithtrenchisolation. AnalstructuresimulatedwithsilicidegrowthmodelissimilartoaMOSFETwithdummygateandsilicidegrowthonsource/drain.ImageinFig. 6-11 shows 88

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Figure6-10. Simulationshowingstresscontourduetothicknickelsilicidegrowthonsiliconwithtrenchisolation. contoursbelowthegateandsilicideregions.Againsimilarbehaviorisobservedcompressivestressbelowthesilicidedregionsandtensilebelowthedummygate.AllthesimulationresultslookconsistentandFEMbasedmodelisabletopredictthecontourssuccessfully.Theseresultscouldbeusefulinestimatingthedeviceperformanceinuencedbytheinducedstress. 6.4SummaryInsummary,FiniteElementMethodbasedsimulationswereperformedtoestimatethestressgeneratedduetonickelsilicidegrowthonsilicon.Variousstructureswithdifferentsilicidethicknesswereused.Alsomodelusinglevelsetmethodsfrom 4 was 89

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Figure6-11. FEMstresssimulationresultsonaMOSFETlikestructurewithsilicidegrowthonsourceanddrainusinggrowthmodels. usedforgrowthalongwiththechemicalpotentialmodelofsegregationinchapter 5 toestimatetheshapesofsilicide.ThenFEMcapabilitiesofFLOOPSwereintegratedtopredictthestresscontoursinsilicon. 90

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CHAPTER7SUMMARYANDFUTUREWORK 7.1OverviewofResultsInsummary,workpresentedinthisdissertationhasbeenfocusedonstudyingthematerialgrowthaspectsofNickelSilicide.NumericalmodelsusingtheLevelSetMethods(LSM)weredevelopedandimplementedinFLOOPSforNiSigrowth.Dopantsegregationduetosilicidegrowthisalsostudiedandachemicalpotentialbasedmodelwasdevelopedandimplemented.Thesemodelsweretimecoupledtogethertorunsimultaneouslyforaccurateresults.Finallystressinducedduetosilicidewasalsoincludedaspartofsimulations.SimulationswereperformedusingtheFiniteElementMethodimplementedinFLOOPS.Maindevelopmentandaccomplishmentsarediscussedbelow.InChapter2and3,weintroducedthenumericaltechniqueknownasLevelsetmethodsandsomebackgroundon2-dimensionalsilicidegrowthkinetics.AlsodiscussedhowgrowthisadiffusioncontrolledprocessaswellasreactionratecontrolledmakingthewholecaseaDealGrove'skindofmodelforoxidation.Thenwediscussedthedopantsegregation(snowplowing)effectobservedbymanyresearcher,specieslikearsenicpileupatthesilicon-silicideinterfaceduringsilicidegrowth.Finallystresshasbeenstudiedanditisknowthatsilicideinherentlycausescompressivestressinthesilicon.Althoughthestressisnotveryhighascomparedtothecurrenttechnologyneverthelessitisstillimportanttoaccountforitasdevicesizeisshrinkingrapidly.InChapter4afterdiscussingLSMandDealGrove'smodelbrieyweshowpreliminaryresultsfromoursilicidegrowthmodel.Weusedduallevelsetstotracktopandbottominterfacesofgrowingsilicide.WealsocoupleddiffusionwiththeLSMtomakethemodeldiffusioncontrolledratherthanusingsimplegrowthequations.Implementeddealgrove'smodeltoverifyresultthencombineditwiththe2Dgrowthastimestepsolutioncoupling.Resultsobtainedfromthesesimulationswerevery 91

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promising.MOSFETlikestructurewassimulatedandcomparedtheTEMdatafromliterature.Alsoperformedsimulationsonanarrowpolystructuretocomparediffusioncontrolledandmushroomdomekindofgrowth.Alltheresultsobtainedfromourmodelswereveryaccuratealsothesemodelscanbetransferredtoacommercialsoftwarelikesentaurusprocessfromsynopsyseasily.InChapter5dopantsegregationwasthemainfocus.Asobserveddatashowssnowplowingofarsenicduringsilicidegrowthcanbeveryusefulinreducingtheschottkybarrierheightaswellasparasiticresistance.Oursegregationmodelisbasedonthechemicalpotentialofsegregatingspecies.ThiskindofapproachhasalsobeendemonstratedbyTanetalGaAsinterdiffusionofvacancies.Wetestedourmodelsforaconstantandgaussianimpurityproles,resultsshowedustherightbehaviorofdopantredistribution.InordertosimulatetherightprolesweusedSIMSdatafromseveralstudiesanddigitizedthedatatobeusedasaninputtoourmodels.Resultswereverypromisingandwellmatchedwiththerealdatafromseveralstructures.Thesemodelswerealsocoupledwiththegrowthmodeltomakethismodelhighlyaccurate.CouplingrequiredustosolveLSM,DealGrove'sandChemicalPotentialofdopantssimultaneously.Thisincreasesthecomplexityofthenumericalcomputationsgivingusabetteroverallmodelforthewholeprocess.FinallyinChapter6wepresentourresultsofstresssimulationsperformedusingFiniteElementMethodsinFLOOPS.Firstlywesimulatedaplanarstructurebydeclaringindividualmaterials.ResultswerecomparabletothestudyfromSteegenetalbutnotastrongindicationofhowshapeanddopantproleinuencethestressduetosilicide.Usingtheresultsfromgrowthmodelsanddopantsegregationstudyweperformedanothersetofsimulations.WeusedLevelboundarydatatodeclaretheyoung'smodulusandpoisson'sratioforthematerials.Weobservedthattheedgeproleofsilicidedoescausesignicantdifferencesinstresscontours.Coupleofsimulationswereperformedwiththinandthicksilicideshowingthatstressishigherandcontoursmove 92

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towardstheedgeasthesilicidethicknessisincreased.Valuesofstressobservedarealsocomparabletothestressreportedinmanystudies.Overallthismodelbenetsfromthegrowthandsegregationmodels. 7.2RecommendationforFutureWorkAscomplexityofthesemiconductorprocessesisincreasingeverytwoyearswehavetoworktowardsmakingthesemodelsworkforthespecialstructureandatascalemuchsmallerthanfewnanometers.Silicidegrowthcouldbeinuencedbythestressgeneratedduringthegrowth.Stresseffectsbecomeimportantingoverningtheoverallnalshape.Alsodopantspresentinthesiliconduringsilicidationcanincreaseordecreasetherateofgrowthandhavevitaleffectondiffusionofnickelitbecomesimportanttoincludethoseeffectsintogrowthmodels.Dopantsegregationmodelsareveryusefulindeterminingthenalimpurityproles.HoweverduetosomegridsensitivityobservedinourworkitisrecommendedtoimplementthenumericaldiffusionsolverontheLevelSetgridratherthanonFLOOPSgridthiscouldfurtherimprovetheaccuracyofourgrowthmodels.Finallystresssimulationscanbeimprovedbyimplementingtheyy-componentofstressaccuratelythatdependsuponourboundaryconditions.Additionallytofurtheraccommodatethenanostructuresimulationsandgetabetterunderstandingofconned3-dimensionalstructuresitisalsorecommendedtoextendthesemodelsinto3-Dsimulations. 93

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APPENDIX:ALAGATORSCRIPTFORCOMPLETESIMULATIONINFLOOPS AcompleteAlagatorscriptisprovidedheretorunthesilicidegrowth,dopantsegregationandstresscontourssimultaneously.linexloc=0.0spac=0.01tag=nickellinexloc=0.2spac=0.002tag=toplinexloc=0.35spac=0.01tag=waferlinexloc=0.48spac=0.01linexloc=1.0spac=.01tag=botlineyloc=0.0spac=0.01tag=leftlineyloc=0.20spac=0.01tag=spacerlineyloc=0.35spac=0.002tag=polylineyloc=0.5spac=0.01tag=rightmateraddname=Nickelregionsiliconxlo=waferxhi=botylo=leftyhi=rightregionNickelxlo=nickelxhi=topylo=leftyhi=polyregionNickelxlo=nickelxhi=topylo=polyyhi=rightregionoxidexlo=topxhi=waferylo=leftyhi=polyregionsiliconxlo=topxhi=waferylo=polyyhi=rightinitpdbSetStringSiliconYoungsModulus1.6e12pdbSetStringSiliconPoissonRatio0.22pdbSetStringNickelYoungsModulus(1+1.32e12*(Level1>0))pdbSetStringNickelPoissonRatio0.31pdbSetStringOxideYoungsModulus0.77e12 94

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pdbSetStringOxidePoissonRatio0.17pdbSetStringGasYoungsModulus1e1pdbSetStringGasPoissonRatio0.22pdbSetStringNickel SiliconYoungsModulus1.6e12pdbSetStringNickel SiliconPoissonRatio0.22pdbSetStringNickel OxideYoungsModulus1.6e12pdbSetStringNickel OxidePoissonRatio0.22pdbSetStringOxide SiliconYoungsModulus1.6e12pdbSetStringOxide SiliconPoissonRatio0.22pdbSetStringGas NickelYoungsModulus1.6e12pdbSetStringGas NickelPoissonRatio0.22pdbSetStringGas OxideYoungsModulus1.6e12pdbSetStringGas OxidePoissonRatio0.22solutionname=displacementaddsolvedimcontinuousnegativepdbSetStringSilicondisplacementEquationelastic(displacement)+BodyStrain(-5.0e-3*(Level<0)*(Level1>0))pdbSetBooleanSilicondisplacementNegative1pdbSetDoubleSilicondisplacementAbs.Error1.0e-3pdbSetStringNickeldisplacementEquationelastic(displacement)+BodyStrain(-5.0e-3*(Level<0)*(Level1>0))pdbSetBooleanNickeldisplacementNegative1pdbSetDoubleNickeldisplacementAbs.Error1.0e-3pdbSetStringOxidedisplacementEquationelastic(displacement)+BodyStrain(5.0e-4)pdbSetBooleanOxidedisplacementNegative1 95

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pdbSetDoubleOxidedisplacementAbs.Error1.0e-3pdbSetBooleanReectLeftdisplacementFixed.y1pdbSetStringReectLeftdisplacementEquationdisplacementpdbSetBooleanReectRightdisplacementFixed.y1pdbSetStringReectRightdisplacementEquationdisplacementpdbSetBooleanReectBottomdisplacementFixed1pdbSetStringReectBottomdisplacementEquationdisplacementselz=CompStrain(xx,displacement)selz=CompStress(xx,displacement)+CompStress(yy,displacement)selz=CompStress(yy,displacement)mathdiffusedim=1umfnonecol!scalesolutionaddname=Testsolve!negativesolutionaddname=Test1solve!negativecontinuouspdbSetDoubleSiliconTestAbs.Error1.0e-8pdbSetDoubleSiliconTestRel.Error1.0e-2pdbSetDoubleNickelTestAbs.Error1.0e-8pdbSetDoubleNickelTestRel.Error1.0e-2pdbSetDoubleoxideTestAbs.Error1.0e-8pdbSetDoubleoxideTestRel.Error1.0e-2selz=1.0e1name=Testsetdiff(1.0e-10*(Level<0)*(Level1>0)+1.0e-21)setSistrddt(Test)-($diff)*Test*grad(log(Test))+1.0e3*(Level0)*(Test-10)setNistrddt(Test)-($diff)*Test*grad(log(Test))+1.0e10*(Level1)*(Test-1.0e22) 96

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pdbSetStringNickel SiliconTestEquatione10*Transport12(Test,Test)pdbSetStringNickelTestEquation$NistrpdbSetStringSiliconTestEquation$Sistrproleinf=As-Implanted.txtname=Test1selz=Test1+5.0e17name=Test1proleinf=As-Implanted.txtname=Test1selz=log10(Test1)plot.1dy.v=0.2label=As-Implantedsetdiffco(2.5e-16*(Level)+2.5e-16*(Level)+2.5e-14*(zerocross(Level))+1e-21)setstrddt(Test1)-($diffco+2.5e-16*Test1/1e20)*Test1*grad(log(Test1)+5.0*(Level))pdbSetStringSiliconTest1Equation$strpdbSetStringNickelTest1Equation$strSilicidesilicontemp=400time=1200spac=0.005conc=0level mat=Levelplot.surfaceormovie=fselz=Levelcontourval=0selz=Level1contourval=0gselz=log10(Test1)plot.1dy.v=0.1label=@0.1umplot.1dy.v=0.195!clelabel=@0.195um 97

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selz=0name=Postproleinf=As Post Prole.txtname=Postselz=log10(Post)plot.1dy.v=0.0label=As-Post!cleselz=0name=Preproleinf=As-Implanted.txtname=Preselz=log10(Pre)plot.1dy.v=0.0label=As-Pre!cle 98

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BIOGRAPHICALSKETCH AshishKumarwasborninDelhi,India.HecompletedhisBachelorofTechnologyfromIndianInstituteofTechnology,Madras,Indiainelectricalengineeringin2004.ThenhejoinedGlobalFoundriesSingaporeasProcessIntegrationengineerfor130nm.Heworkedon130nm,110nmand90nmuntil2005.HethenjoinedUniversityofFloridatostudydeviceandprocesssimulationsofMOSdevicesundertheguidanceofDrMarkLaw.ThegraduateresearchinvolvedNickelSilicidegrowthmodeling,dopantredistributionandstressproling.HecurrentlyworksforIntel'sPortlandTechnologyDevelopmentgroupinHillsboro,OR 107