BOSTON UNIVERSITY

COLLEGEOFENGINEERING

Dissertation

PHYSICS AND MODELING OF ION IMPLANT ATION INDUCED TRANSIENT

DEACTIVATION AND DIFFUSION PROCESSESIN BORON DOPED SILICON

by

SRINIVASAN CHAKRAVARTHI

B.Tech.,BanarasHinduUniversity, 1995

Submittedin partialfulfillment of the

requirementsfor thedegreeof

Doctorof Philosophy

2001

Approvedby

First Reader

ScottT. Dunham,Ph.D.

AssociateProfessorof ElectricalandComputerEngineering

SecondReader

DanielCole,Ph.D.

AssociateProfessorof ManufacturingEngineering

Third Reader

MichaelYeung,Ph.D.

AssistantProfessorof ManufacturingEngineering

FourthReader

SoumendraN. Basu,Ph.D.

AssociateProfessorof ManufacturingEngineering

ACKNOWLEDGEMENTS

I would like to first thank my researchadviser, ProfessorScott T. Dunhamfor hisguidanceandsupportthatgreatlyenhancedmy graduateschooleducationat BostonUni-versity. His expertizein thefield of processmodelingandhiscuriosityto learnmoremademy experienceextremelyenjoyableandrewarding.

I wouldliketo thankcommitteemembersProfessorsDanCole,MichaelYeung,Soumen-draBasufor theirconstructivecommentsrelatedto my researchanddissertation.I amalsodeeplyindebtedto ProfessorTheodoreMoustakasfor agreeingto serve asmy oral com-mitteechairman.

I would like to thankProfessorSoumendraN. Basufor his guidanceasmy academicadviserduring thecourseof my doctoralwork. I would like to thankProfessorMichaelYeungfor introducingmeto processmodeling.

I would liketo acknowledgetheSemiconductorResearchCorporationwhosefinancialsupportmadethis researchprojectpossible.

My many thanksalsogo to Dr. Alp Gencerfor providing with theDOPDEESframe-work which wasalmostusedexclusively in this work. My colleagues(presentandpast)andfriendsfrom the electronicmaterialscommunityin the bostonarea(in no particularorder): BrendonMurphy, Pavel Fastenko, Dr. Marius Bunea,Dr. Alp Gencer, Dr. MitraNavi, Dr. Iuval Clejan,Dr. Anu Agarwal, AimeeSmith,andDr. DharanipalDoppalapudihavebeengoodfriendsandprovidedwith invaluablesuggestions,discussionsandsupport.

I would like to thankthe following peoplefor discussionsandproviding their exper-imentaldata: Dr. Nick Cowern,Dr. Aditya Agarwal, Dr. Iuval Clejan,Dr. DanDowney,Dr. Martin Giles,Dr. HansGossmann,Dr. SandroSolmi, Dr. Silva Theiss. I would alsolike to thankDr. Martin Giles andtheprocessmodelinggroupat Intel TCAD for givingmeachanceto work with them,aspartof asummerinternshipin 1997.

Lastly, I would like to expressmy love andgratitudeto my parentswho keptme fo-cusedandencouragedmeto do my best,to my sistersfor their constantsupport.I wouldalsolike to acknowledgeall my friendswho mademy graduateschoolexperiencememo-rable.

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PHYSICS AND MODELING OF ION IMPLANT ATION INDUCED TRANSIENTDEACTIVATION AND DIFFUSION PROCESSESIN BORON DOPED SILICON

(OrderNo. )SRINIVASAN CHAKRA VARTHI

BostonUniversity, CollegeOf Engineering,2001Major Professor:ScottT. Dunham,

AssociateProfessorof ElectricalandComputerEngineering

ABSTRACT

Theeconomicsof silicon processingrequirespredictive modelingcapabilitiesfor thecontinuedrapidadvancementof semiconductortechnology. This is becauseit hasbecomeprohibitively expensive to develop a new processby running a large seriesof test lotsthroughmulti-billion dollar fabricationfacilities. Effective processmodelingrequiresanaccuratephysicalunderstandingof the variousinteractingprocesses.The complexity ofthisproblemiscompoundedbyhighlynon-equilibriumphenomenaassociatedwith IC fab-ricationprocessessuchasimplantationannealing.Pointdefectsupersaturationsof manyordersof magnitudeareintroducedfollowing ion implantation,which is usedto introducethedopantsinto silicon. Suchsupersaturationsdramaticallyalter thediffusionof dopantsandreducetheelectricalactivationduringtheinitial phaseof theanneal.

Boron is theprimary p-typedopantusedin silicon andthusunderstandingandmod-eling its deactivation/activationanddiffusion is critical to predictive processsimulation.Sinceboronis smallerthansilicon, boronagglomerateswith interstitialsbecomingelec-trically inactive. Modeling of boronclustersis complicated,as thereis a hugearrayofpotentialboron-interstitialclustercompositions.A physicalmodelfor boronclusteringisderivedby identifying dominantclustersandratelimiting stepsvia atomisticcalculationsperformedat LawrenceLivermoreNationalLabs.Themodelis thenusedsuccessfullytomatcha wide varietyof chemicalandelectricaldata.We furtherapply this modelto un-derstandandsuccessfullypredictultra shallow junction formation. We find it is possibleto explain someintriguing phenomenonobserved during the formationof ultra shallowjunctions,likesaturationin junctiondepthdespiteincreasingramp-uprates.

Researchersareexploringnovel experimentalprocessingstepslikehighenergy Si pre-implantsto producehighly active andshallow B junctions.To understandandmodelthisphenomenonit is essentialto beableto modeltheevolution of theexcessvacancy regionformedaftertheimplant. Hencewe have developeda detailedmodelfor vacancy cluster-ing built basedonatomisticcalculationsandverifiedthemodelby comparisonto datafromgold labelingexperiments.However this modelis computationallyintractablefor routineusein TCAD (TechnologyComputerAided Design). Hence,a computationallyefficient

iv

physicalmodelhasbeenderivedfrom this full modelthatcanbereadilyincorporatedintoprocesssimulators.

This researchleadsto an understandingof a broadrangeof dataapplicableto bothcurrentandfuturegenerationof devicesandpresenta self-consistentmodelwhich canbeincorporatedinto TCAD diffusionequationsolvers.

v

Contents

1 Intr oduction 1

2 Dopant Diffusion in Silicon 5

2.1 Atomistic perspectiveof dopantdiffusion . . . . . . . . . . . . . . . . . 5

2.1.1 Vacancy mechanism . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.2 Interstitialmechanism . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Coupleddiffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Pointdefectproperties . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4 Metaldiffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4.1 Zinc diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4.2 Platinumdiffusion . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.5 Boronindiffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3 Ion Implant DamageEvolution 33

3.1 Initial damage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.2 Earlywork onborondeactivationandTED . . . . . . . . . . . . . . . . 35

3.3 Interstitialclusters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.4 Boroninterstitialclusters . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.5 Vacancy clusters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.6 Simulationof initial damage . . . . . . . . . . . . . . . . . . . . . . . . 42

3.6.1 Effectof surface . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.6.2 Effectof clusteringduringrecombination . . . . . . . . . . . . . 43

3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

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4 Boron Cluster Models 49

4.1 Kinetic precipitationmodel . . . . . . . . . . . . . . . . . . . . . . . . 49

4.2 Multi clustermodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.2.1 Analysisof model . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.3 Simpleclustermodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.4 Extensionto chargestates. . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.5 Comparisonto chemicaldata . . . . . . . . . . . . . . . . . . . . . . . . 64

4.6 SolidSolubility Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.7 Comparisonto marker layerexperiments. . . . . . . . . . . . . . . . . . 69

4.7.1 Experimentalbackground . . . . . . . . . . . . . . . . . . . . . 69

4.7.2 Model results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.8 Comparisonto electricalactivationdata . . . . . . . . . . . . . . . . . . 78

4.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

5 Ultra Shallow Boron Junctions 84

5.1 Rapidthermalsoakanneals. . . . . . . . . . . . . . . . . . . . . . . . . 84

5.2 Spikeanneals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

6 High Energy Implants and VacancyClustering 99

6.1 Vacancy clustermodel . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

6.2 Comparisonto Au-labelingexperiments . . . . . . . . . . . . . . . . . . 102

6.3 Momentbasedmodels . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

7 Conclusionsand Future Work 121

7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

7.2 FutureDirections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

8 Bibliography 124

9 Vita 133

vii

List of Tables

4.1 Clusterenergeticsbasedon atomisticcalculations[60] usedfor the fullsystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

6.1 Parametersfrom Bongiornoet al � [11] usedfor the simulations.Ef�n� is

theformationenergy andEb�n� is thebindingenergy in eV. We useSPC

formationenergiesfor n � 24 andHRC for theclusterssmallerthan25. . 103

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List of Figures

1.1 Costper lot of 25 wafersof packagedDRAM with time, for eachDRAMgenerationlabeledasbitsperchip. . . . . . . . . . . . . . . . . . . . . . 3

1.2 A MOS transistorshowing how a source/drainimplant affectsthe chan-nel dopantdistributionsduring annealing. The interstitial flux not onlyleadsto anenhanceddopantdiffusion in thesource/drainbut alsothat inthe channelregion. Furthersuchinteractionsbecomemorecritical withdecreasein lateralchannellength. . . . . . . . . . . . . . . . . . . . . . 4

2.1 Thedopant(D) vacancy (V) pairmigrationin asilicon lattice.Thedopantandvacancy startthediffusionstepasfirst nearestneighbors.Thehoppingratesaresuchthat thedopantcanhop into theemptysiteandbackmanytimeswithout any effect on diffusion. Thehostatoms,though,couldalsohop into the emptysite suchthat at somepoint the vacancy movesto athird nearestneighborsite with respectto the dopant. The vacancy cango aroundthe six memberring of atomsandapproachthe dopantfroma differentdirection. After the dopanthopsinto the now emptysite thedopantvacancy pair completesonediffusionstep. . . . . . . . . . . . . . 6

2.2 Schematicof kick-outmechanismshowing interstitialassistedmechanismof diffusion. In (a) the dark atomis the substitutionaldopantatomto bekicked out by the silicon self interstitial (unfilled atom). (b) shows thedopantatomthatis now kickedinto aninterstitialsiteandcannow diffusein thelattice.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Diffusionpathfor boroninterstitial for thekick-out mechanismascalcu-latedby Zhuet al. [103]. . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4 Comparisonof thediffusionpathfor boronvia thekick-outmechanismascalculatedby Windl et al. [98] for (a)neutral(b) negativechargestates. . 10

2.5 Normalizedzinc diffusion profilesat 870� C into defect-freesilicon andcomparisonto simulationsusingpointdefectparametersfrom Brachtetal.[12]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

ix

2.6 Normalizedzinc diffusionprofilesat 1208� C into defect-freesilicon andcomparisonto simulationsusingpointdefectparametersfrom Brachtetal.[12]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.7 Normalizedzinc diffusion profilesat 870� C into defect-freesilicon andcomparisonto simulationsusingpoint defectparametersobtainedin thiswork. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.8 Normalizedzinc diffusionprofilesat 1208� C into defect-freesilicon andcomparisonto simulationsusingpoint defectparametersobtainedin thiswork. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.9 Measuredandsimulatedplatinumprofilesat 770� C [105]. . . . . . . . . 24

2.10 Measuredandsimulatedplatinumprofilesat 700� C [106]. Note theuni-form Pt concentrationin bulk which is unchangedwith time, andthe in-verseU profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.11 Effect of carbonon zinc diffusion at 870� C. Carbonhasonly a minoreffectevenat thelowestavailablediffusiontemperature. . . . . . . . . . 26

2.12 Extractedvaluesof DVC �V � Cs, DIC �I � Cs (Cs is the silicon lattice density)from fitting Zn diffusiondataof Brachtet al. [12] andcomparisonto pre-viousanalysisbasedon metaldiffusion[49]. . . . . . . . . . . . . . . . . 27

2.13 Extractedvaluesof C �V andC �I fromfitting Zndiffusiondataof Brachtetal.[12] andcomparisonto previous analysisbasedon both metaldiffusionandatomisticcalculations[94]. . . . . . . . . . . . . . . . . . . . . . . . 28

2.14 Effect of variationin a singlepoint defectparameterandreoptimizingalltheprofiles.It canbeseenthatDIC �I is themostreliably extractedparam-eterandC �V is theleast. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.15 Boron diffusion from implantedpolysilicon from Garbenet al. [39] andcomparisonto predictionof coupleddiffusionmodel. Also shown is pre-dictionby Fermimodelnot consideringpoint-defectmediateddiffusion. 30

2.16 Boron indiffusion for the highestsurfaceconcentration,also plotted isCI � C �I . Notethatthetail diffusionis enhancedby a factorof about3. . . . 31

3.1 Totalandnetdamagecreatedbya40keV, 5 � 1013cm� 2 Si implant.MonteCarlosimulationswith TRIM [10]. . . . . . . . . . . . . . . . . . . . . . 34

3.2 MonteCarlosimulationshowing netinitial distributionsof interstitialsandvacanciesfollowing a2 MeV, 1 � 1016cm� 2 Si implant.Thevacancy richlayerextendswell overaµm. . . . . . . . . . . . . . . . . . . . . . . . . 35

x

3.3 Boronchemical(SIMS) andactivation(SRP)profilesafterannealingof a2 � 1015cm� 2 doseimplantat 850� C for 2 h. Thepeakof the implantedboronprofile is immobileandinactive to concentrationswell below equi-librium solubility (from Solmi et al. [90]). Equilibrium boronsolid solu-bility at 850� C 5 � 1019cm� 3. . . . . . . . . . . . . . . . . . . . . . . 37

3.4 Deltadopedboronmarker layerafterTED drivenby a 5 � 1013cm� 2, 40keV Si implantandannealedat790� C for 10mins. . . . . . . . . . . . . 38

3.5 Area densityof interstitialscontainedin 311� defectsas a function ofbackgroundboronconcentrationfollowing annealat 740� C for 15 mins.The solid line is a fit to the dataassuminga quadraticdependenceon Bconcentration.Thiswouldbethedependenceof aclusterof typeB2mIm. . 39

3.6 Clusteringdrivenby a 2 � 1013cm� 2, 40 keV Si implant for a B markerlayerof doses2 � 1013cm� 2, annealedat 800� C for 35 mins. . . . . . . 40

3.7 Clusteringdriven by a 2 � 1013cm� 2, 40keV Si implant for a B markerlayerof doses9 � 1013cm� 2, annealedat 800� C for 35 mins. Notethatalow interstitialdosecandeactivateamuchlargerfractionof boron. . . . . 41

3.8 Net interstitial doseremainingafter the recombinationprocessstartingfrom thetotal initial defectdistributions.Eb is thebarrierto I/V recombi-nation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.9 Dosedependenceof TED measuredfor a boronmarker layer following200keV Si implants.A “+n” modelbasedon thefull initial defectprofileis ableto predictdiffusionbehaviour. . . . . . . . . . . . . . . . . . . . . 44

3.10 Predictionof B TED for 40 keV 1013cm� 2 B implant. A “+1” modelpredictslessdiffusion thanseenexperimentally. A “+n” modelbasedonthefull initial defectprofile is ableto predictdiffusionbehaviour. Dataisfrom Intel Corp. [44]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.11 Interstitialsuper-saturationsat 600� C and800� C obtainedusingfull dam-age(bold lines) andusinga “+1” model (dashes).Note that the super-saturationsobtainedarealmostindependentof theinitial conditions. . . . 46

3.12 Figureshows evolution of interstitialandvacancy clustersduringanneal-ing of a2 � 1013cm� 2 Si implantat600� C. Thevacanciesexist till around600sec,afterwhich theinterstitialstrappedin interstitialclustersis closeto a “+1”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.1 Array of possibleBICs. Also indicatedschematicallyare the rangeofcompositionsconsideredby clusterandKPM approaches.. . . . . . . . . 50

4.2 Simulationsresultsfor a 2 � 1014 cm� 2, 40 keV B implant annealedat700� C usingKPM modelcomparedto datafrom Intel Corp. [44]. . . . . 52

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4.3 Simulationsresultsfor a 2 � 1014 cm� 2, 40 keV B implant annealedat800� C usingKPM modelcomparedto datafrom Intel Corp. [44]. . . . . 53

4.4 Simulationsresultsfor a 2 � 1014cm� 2, 80 keV B implant annealedat800� C usingKPM model,comparedto datafrom Intel Corp. . . . . . . . 54

4.5 Clusterreactionsconsideredin the full model as given by fundamentalphysicalcalculations[102]. . . . . . . . . . . . . . . . . . . . . . . . . 55

4.6 Simulationsusingthe full clustermodelof normalizedclusterconcentra-tions(relative to theirequilibriumvalue)versustime for an800� C anneal. 58

4.7 Equilibriumclusterconcentrationsversusfreeboronconcentrationat800� Cfor free interstitial concentrationsof 109C �I characteristicof very earlystagesof TED. Initially, BI2 is the primary clusterandhelpsimmobilizetheboronasnotedby Pelazet al. [83] . . . . . . . . . . . . . . . . . . . 59

4.8 Equilibriumclusterconcentrationsversusfreeboronconcentrationat800� Cfor free interstitial concentrationsof 103C �I typical of TED conditionsinthepresenceof 311� defects.B3I is theprimary clusterduring mostoftheanneal.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.9 Comparisonof full modelwith thesimplifiedmodelfor a40keV2 � 1014cm� 2

B implantsannealedat 800� C for varioustimes.Also shown for compar-ison areSIMS datafrom Intel [44]. Note that the full modelandsimplemodelshow indistinguishablefinal profiles. The B3I concentrationsforthetwo models(shown aftera 1 h anneal)arealsonearlyidentical. . . . 61

4.10 Comparisonof simulationto experimentaldata[44] for 2 � 1014cm� 2 (a)20keV (b) 80 keV boronimplantsafter1 hr annealsat800� C. . . . . . . 65

4.11 Comparisonof simplemodelto datafromSolmietal. [90] for a5 � 1014cm� 2

20keV B implantannealedat 800� C for (a)30 min (b) 2 hr. . . . . . . . 66

4.12 Comparisonof modelto experimentaldata[44] for a2 � 1015cm� 2 40keVboronimplantaftera60min annealat 800� C. . . . . . . . . . . . . . . . 67

4.13 Comparisonof modelto experimentaldatafor a2 � 1015cm� 2, 20 keV Bimplantannealedat 800� C for 2 hrs.SIMS datais from Solmi etal. [90] 68

4.14 SIMS profilesof boronbeforeandafterannealingfor a rangeof timesat600� C. Datafrom Manninoet al. [68]. Also plottedis the total damagefrom theSi implantascalculatedby UTMARLOWE [62]. . . . . . . . . 70

4.15 Supersaturationsobserved by the deepermarker layersfor Wafer A (NoB layer) and Wafer B (B layer) shown with time at 600� C. Data fromManninoet al. [68]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.16 Thefiguresketchesthedepthandtimevariationof S�x � t � in wafersA and

B aftertheinitial BIC nucleationphase(afterManninoet al. [68]). . . . . 72

xii

4.17 SIMSprofilesof boronbeforeandafterannealingat600� C for 1 seccom-paredto experimentalSIMS data.Experimentaldatafrom Manninoet al.[68]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.18 SIMS profilesof boronbeforeandafter annealingat 600� C for 15 mincomparedto experimentalSIMS data. Experimentaldatafrom Manninoetal. [68]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.19 SIMS profilesof boronbeforeandafterannealingat 600� C for 2 h com-paredto experimentalSIMS data.Experimentaldatafrom Manninoet al.[68]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.20 Simulatedsupersaturationscomparedto experimentallyobservedvaluesat600� C. Experimentaldatafrom Manninoetal. [68]. . . . . . . . . . . . . 77

4.21 Comparisonof experimentally-measuredactive fraction[87] to modelfor150 keV, 2 � 1014cm� 2 and2 � 1015cm� 2 boron implantsannealedfor30 min. at varioustemperatures.Lines representmodelpredictions,andsymbolsrepresentdata. . . . . . . . . . . . . . . . . . . . . . . . . . . 79

4.22 Comparisonof simulatedandexperimentallymeasuredactive fractionfora 2 � 1014cm� 2 boronimplantannealedat 800� C. Datafrom Pelazet al.[84]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.23 Comparisonof simulationwith SIMS andSRPdatafrom Pelazet al. [84]for a2 � 1014 cm� 2 implantannealedat800� C for 1 s. Notethatmostoftheboronis alreadyin clusters.. . . . . . . . . . . . . . . . . . . . . . . 81

4.24 Comparisonof simulationwith SIMS andSRPdatafrom Pelazet al. [84]for a2 � 1014cm� 2 implantannealedat 800� C for 1000s. . . . . . . . . 82

5.1 Simulatedand measuredboron profiles following 1015cm� 3 boron im-plantsat 0.5 to 5 keV. Datafrom Agarwal et al. [3]. . . . . . . . . . . . . 85

5.2 Comparisonbetweensimulatedandmeasuredbroadeningof borondelta-dopedsuper-latticesin thepresenceof anMBE-depositedboronlayerandannealingat 950� C for 10 sec.Datafrom Agarwal etal. [3]. . . . . . . . 86

5.3 Comparisonbetweensimulatedandmeasuredbroadeningof borondelta-dopedsuper-latticesin thepresenceof anMBE-depositedboronlayerandannealingat 1050� C for 10sec.Datafrom Agarwal et al. [3]. . . . . . . . 87

5.4 Predictedandmeasureddiffusivity enhancementof boronmarker layersfor various0.5 keV boron implant dosesand annealingat 1050� C for10sec.Datafrom Agarwal et al. [2]. . . . . . . . . . . . . . . . . . . . . 88

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5.5 Temperaturedependenceof MBE marker layersasreportedby Agarwalet al. [6] andcomparedto simulations.As observedat 800� C thereis noenhancement,howevera preannealat 1050� C maintainsanenhancement.Theenhancementsat highertemperatureareplottedfor 10 s. . . . . . . . 89

5.6 Temperatureversustime profiles usedfor the simulations. Ramp-upismodeledaslinearwhereascooldown is radiative. . . . . . . . . . . . . . 91

5.7 Boron profilesversusoxygenpartial pressurefor 1keV, 1015cm� 2 boronimplantsannealed10sat1050� C (Lerchetal. [65]) areshown alongwithsimulationsmatchedto theseprofiles by varying the surfaceinterstitialconcentration.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.8 The effect of ramprateon reductionin junction depthfor 1 � 1015cm� 2

B implantsfollowing 1050� C spike anneals.The differencein junctiondepth(x j@5� 1018 cm� 3) relative to a ramp-uprateof 2000� C/s is shownfor variousimplantenergies. . . . . . . . . . . . . . . . . . . . . . . . . 93

5.9 The effect of ramprateon reductionin junction depthfor 1 � 1015cm� 2

B implantsfollowing 1050� C spike anneals.The effect of changingthecooling rate is shown. Note that increasingthe ramp-down rategivesagreaterjunction depthreductionfor higherramp-uprates,sincemoreoftheTED thenoccursduringramp-down. . . . . . . . . . . . . . . . . . . 94

5.10 Comparisonof simulationandexperimentfor a1 � 1015cm� 2 250eV B implantfor a1050� C spikeannealin 33 ppmO2 in N2 ambient.Ramp-upratesare50� C/sand425� C/s, andinitial ramp-down rateis 87� C/s. Datafrom Downey etal. [30]. . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.11 Comparisonof simulationandexperimentfor a1 � 1015cm� 2 500eV B implantfor a1050� C spikeannealin 33 ppmO2 in N2 ambient.Ramp-upratesare50� C/sand425� C/s, andinitial ramp-down rateis 87� C/s. Datafrom Downey etal. [30]. . . . . . . . . . . . . . . . . . . . . . . . . . . 96

5.12 Comparisonof simulationandexperimentfor a 1 � 1015cm� 2 1 keV andimplantfor a1050� C spikeannealin 33 ppmO2 in N2 ambient.Ramp-upratesare50� C/sand425� C/s, andinitial ramp-down rateis 87� C/s. Datafrom Downey etal. [30]. . . . . . . . . . . . . . . . . . . . . . . . . . . 97

6.1 Boronprofilesformedfrom a2 � 1014 cm� 2, 5 keV B implantaftera two-stepannealat 800� C/60secandthen1000� C/15sec.A shallower junctionis formedif a100keV Si pre-implantis usedprior to theboronimplantation.100

6.2 Clusterenergeticscalculationsfrom Bongiornoet al. [11]. It canbenotedthat for small clusters(n � 24), HexagonalRing Clustersaremoreener-geticallyfavorablewith respectto SpheroidalClusters. . . . . . . . . . . 101

xiv

6.3 Simulatedsizedistribution of clustersafter a short time annealat 750� Cand950� C. Clustersareripeninginto largerclustersmorepredominantlyat the highertemperature.This alsoshows the moststablesmall clustersizesto bearound6, 10,14,18 and24 dueto thenon-monotonicbindingenergy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

6.4 Simulatedclusteredvacancy concentrationscomparedto Au RBSdatafor750� C annealsof 10 min and1 h. Simulationshow that thereis very litlechangein the clusteredvacancy concentrationbetween10 min and1 h.This is in agreementwith resultsfrom Veneziaet al � [96] who alsoreportthatAu concentrationsarenearlyconstantfor longerannealsup to 8 h at750� C. Notethatthesurfacepeakin thedatais becauseof theAu implantusedfor thein-diffusion. . . . . . . . . . . . . . . . . . . . . . . . . . . 105

6.5 Simulatedandclusteredvacancy concentrationscomparedto Au RBSdataafter 950� C annealof 10 s and10 min. At 950� C, vacancy clustersareannihilatedby anincreaseddissolutionof interstitialdefectsfrom thebulkandlossto thesurface.Notethatthesimulationsagreewell with thetimedependenceof thedata. . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

6.6 Simulationand clusteredvacancy concentrationscomparedto Au RBSdataafter a 1000� C annealof 10 min. At 1000� C, the vacancy clustersareincreasinglyannihilatedfrom thesurfaceandthedissolutionof inter-stitial defectsfrom thebulk. TheclustersaroundRp/2 arethe largestandthereforethe moststable. Hencethereis a peakin clusterconcentrationat Rp/2 (0.9 µm) in thesimulationssimilar to thatobservedin theexperi-mentaldata[96]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

6.7 At 750� C, a considerablefraction of the vacanciesare in smallersizedclusters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

6.8 Theabovefigureshowsthesignificanceof theadditionof largersizedclus-ters. At 950� C mostof the clustersespeciallyaroundRp/2 have ripenedinto largerclusters(n � 35). . . . . . . . . . . . . . . . . . . . . . . . . 109

6.9 Time dependenceof vacanciesin system(depthof 1000µm). Usingonlya 311� modelwithout any loop formationleadsto dissolutionof all theclustersby about60s,contraryto experiments.It shouldbenotedthattheexperimentalvalue reportedby Veneziaet al � [96] is measuredbetween0.2 – 1 µm to avoid including the Au implant profile. This methodalsoleavesout the doseof vacanciesbelow 0.2 µm. Hencethe experimentalresultsareexpectedto be lower than the simulationresultsdespitehav-ing a goodagreementin the depthdistributions. Also, without loopsthevacancy concentrationdropsbelow theequilibriumvaluedueto theinter-stitial supersaturationfrom thedissolving 311� defects. . . . . . . . . . 110

xv

6.10 γ0 valuesextractedfrom simulationsof the full systemof rateequationsfor threedifferenttemperatures(400, 800, 1000� C) . Also shown in thesameplot is γ0 valuefor a1000� C annealafterapreannealat400� C. Notethattheγ0 is almostindependentof its thermalhistory. . . . . . . . . . . 114

6.11 γ1 valuesextractedfrom simulationsof the full systemof rateequationsfor threedifferenttemperatures(400, 800, 1000� C) . Also shown in thesameplot is γ1 valuefor a1000� C annealafterapreannealat400� C. Notethattheγ1 is almostindependentof its thermalhistory. . . . . . . . . . . 115

6.12 Analytic fit to γ0 neglectingsmallsizeeffects.This wasdoneto avoid theexponentialchangein γi values. . . . . . . . . . . . . . . . . . . . . . . 116

6.13 Analytic fit to γ1 neglectingthenearexponentialchangenearsmallsizes. 117

6.14 Comparisonof AKPM andfull discreteclustermodelat 950� C . . . . . . 118

6.15 Comparisonof AKPM andfull discreteclustermodelat 1000� C . . . . . 119

xvi

Chapter 1

Intr oduction

Oneof the mostimportantchallengesin developingVLSI technologytodayis to shrinkdevicesizesto their limits, sinceboththespeedandthenumberof transistorsperunit areaincreaseasdevicesgetsmaller. Eachnew generationrequiresalargedevelopmentaleffort,traditionallyexecutedby scalingtheexisting technologygenerationto therequirementsofthe new generationandaddressingemerging problemswith a seriesof matrix-typeex-periments.Wafer lots areprocessedandin eachlot selectedparametersarevaried. Anexisting technologyis similarly fine-tunedwhile commercialproductis shippedto cus-tomers. Fig. 1.1 illustratesthat this approachbecomesprohibitively expensive, with thecurrentcostper DRAM lot, or oneexperimentat abouta million dollarstoday, andpro-jectedto exceed10 million dollarsin 2012. For thefigure it wasassumedthat50%of awafer areayieldsusabledies;andpackagingis includedin the cost[1, 52]. This makescomputer-aidedtechnologydevelopmentimperative, requiringaccurate,truly predictivesimulationtools. The goal, therefore,consistsof replacingreal experimentswith virtualones,i.e. a new processis placedin manufacturingonly after it hasbeenascertained,incomputersimulationsof theproposedsequence,thattheresultingdeviceswill meetall thespecifications.Currentprocesssimulatorscontainempiricalmodelsandoften lack phys-ical elementsneededfor accuratesimulation. However, the ever-progressingshrinkageof device dimensionsandtolerancesleadsto new non-equilibriumprocessesthatcannotbemodeledusingempiricalmodelscommonlyusedin the industry. Thusphysics-basedmodelsarenecessaryfor usein theseprocesssimulators.

Ion implantationis the most powerful and widely usedtool for the introductionofdopantsin silicondevicetechnology. However, implantationalsointroducesalargeamountof crystaldamageto thesemiconductor. Thisdamageconsistsof highconcentrationsof in-terstitialsandvacanciesandis muchhigherthantheimplantdose.Hence,any subsequentannealingstepis a highly non-equilibriumprocessandinvolvestheformation/dissolutionof extendeddefects,metastablephasesand precipitates. Unfortunately, the introduceddopantsthemselvesdo not all lie on substitutionalsites. Therefore,a high temperaturepostimplantannealis necessaryto activatethedopantatomsandremove damagewhich

1

compromisesdevice performance.As a resultof this high temperatureanneal,bothpointdefectsanddopantatomsexperiencea periodof high mobility. This activationprocessischaracterizedby anomalousdiffusionin thatduringpost-implantannealingdopantatomsmayactuallydiffusemuchlargerdistancesfor low temperatureannealscomparedto highertemperatureanneals.This anomalousdopantdiffusionduringtheannealof an implant isknow astransientenhanceddiffusion(TED). Dueto thehighly non-equilibriumpoint de-fect concentrationsinvolved,dopantatomsmayalsoform inactive immobileclustersanddeactivatemuchbelow their solid solubility. This is acharacteristicexhibitedduringTEDby smalleratomslike boronwhoseagglomerationis enhancedby excessinterstitials. Indeviceswith large critical dimensions,this diffusion of dopantsduring post-implantan-nealingmaynotsignificantlyaffectdeviceperformance.However, with continuedshrink-ageof devices,evenminor changesin dopantdistributionsmay leadto large changesinelectricalbehavior of thedevices.For example,in a MOS device asshown schematicallyin Fig 1.2, thesource/drainimplantandassociatedinterstitialexcessleadsto a changeinthe dopantdistribution in the channelregion aswell as in the sourceanddrain regions.The final dopantdistribution is thus a net sum of a wide rangeof atomic interactions.In orderto predict the final thresholdvoltageof this device, it is necessaryto modelallthesecomplex interactionssimultaneously. The simulationof sucha systeminvolvesalargenumberof parametersto describeeachmechanism.Speciallydesignedandtailoredexperimentshave beenusedsuccessfullyto identify key mechanisms.Thoughtheseex-perimentshave beenvery helpful to betterunderstandimportantprocessesthey arestilllimited in their ability to separatemechanismsat anatomiclevel. For example,while ex-perimentsareableto find thetotal diffusioncoefficient, they generallycannot determinethe microscopicdiffusion mechanism.Recentadvancesin atomistictechniquessuchasab-initio andmoleculardynamicsprovide further informationto probemoredeeplyintothe variousatomisticmechanismsof diffusion anddefectinteractions,thusbridging theknowledgegap.

This researchhasthefollowing uniquefeatures:� Knowledgefrom atomisticcalculationsis used(whenavailable),coupledwith ex-perimentalknowledgein developingphysicalmodels.� Our work relieson a physicalmodelof diffusion andinteractionof dopantatomsandpointdefects,ratherthanon anempiricalapproach.� The work is basedon the evolution of the size distributions of extendeddefectsduringTED.� It includesdeactivationof boronandincorporationof point defectsinto boronclus-tersor precipitates.� Simple computationallyefficient modelsare derived from complex but physicalmodelsdevelopedduringthework, for incorporationinto processsimulators.

2

|�1985

|�1995� |�

2005� |�2015

|� |� |� |� |� |�|� |� |� |� |�

|� |� |� |� |�

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|� ||� |� |� |� |� |�

Year�

D

RA

M c

ost p

er lo

t ($

)

1M

4M� 16M

256M

1G4G 16G

64G� 256G

105

106

� � � � � � � � � �

Figure 1.1: Cost per lot of 25 wafersof packagedDRAM with time, for eachDRAMgenerationlabeledasbits perchip.

We begin Chapter2 by discussingthemechanismof borondiffusionin silicon anditsinteractionwith point-defects.We gainvaluableinsightsinto thepoint-defectparametersusedin thesimulationsby comparisonto anextensivedatasetfrom metaldiffusionexper-iments.In Chapter3, variousexperimentsby differentresearchersareanalyzedto identifythe primary physicalmechanismsoccurringduring TED andlay the framework for ourmodelingefforts. We alsolook at theassumptionsmadefor theinitial cascadeevolution.In Chapter4, weconsiderdifferentapproachesto modelingboronclusteringeffectsin sili-con.A physicalmodelfor boronclusteringis derivedbasedonatomisticcalculations.Themodelis thensuccessfullyusedto matcha wide varietyof chemicalandelectricalactiva-tion data. In Chapter5, we apply this modelto understandandsuccessfullypredictultrashallow junction formation. We demonstratethatwe cansuccessfullypredictbothquali-tatively andquantitatively junctionformation,includingsomeintriguingphenomenonlikesaturationin junctiondepthdespiteincreasingramp-uprates.In Chapter6, we modeltheformationof vacancy clustersduringannealingof highenergy implants.This is developedfrom atomisticenergeticscalculationsof vacancy clusters.Wethenderiveanefficientmo-mentbasedmodelfor incorporationinto processsimulationsoftware. Finally, Chapter7summarizestheconclusionsandfuturedirections.

3

Source Drain

Gate

Dopant Flux

Interstitial Flux

Channel

Figure 1.2: A MOS transistorshowing how a source/drainimplant affects the channeldopantdistributionsduringannealing.The interstitial flux not only leadsto anenhanceddopantdiffusionin thesource/drainbut alsothatin thechannelregion. Furthersuchinter-actionsbecomemorecritical with decreasein lateralchannellength.

4

Chapter 2

Dopant Diffusion in Silicon

Dopantdiffusion in silicon occursthroughthe interactionof dopantswith native pointdefects. This chapteris devotedto modelsandparametersassociatedwith this process.We first review dopantdiffusionin silicon, followedby a discussionof coupleddiffusionmodelsusedin all our simulations. We thenconsiderthe propertiesof point defectsinsilicon. Finally, in Section2.4wepresentour analysisof metaldiffusionexperimentsasaway to re-evaluatepointdefectproperties.

2.1 Atomistic perspectiveof dopant diffusion

Historically, thediffusivity of dopantsin silicon hasbeenmodeledmacroscopicallyusingtheArrheniusexpression

D�T ��� D0exp

� �Ea

kT ! (2.1)

where,D0 is thepre-exponentialconstantandEa is theactivationenergy of thediffusionconstant.However, beginning with experimentsperformedin 1970’s and1980’s, it wasfound that this simplediffusion modelwas inadequate.In theseexperiments,the diffu-sivity of dopantswasseento be differentundervaryingenvironments,especiallyduringoxidationof thesilicon surfaceor after ion implantation[29, 38, 57, 63,69,76,78]. Thisis becauseEq.2.1considersonly a temperaturedependenceof thediffusivity. In ordertoexplaintheseresults,amorecomplicatedmodelfor dopantdiffusionbasedonpointdefectmediateddiffusionis needed.In silicon, asin othersemiconductormaterials,dopantdif-fusionoccursvia interactionswith pointdefects,suchasinterstitialsandvacancies.Theseinteractionsdeterminethedopantdiffusivities.

5

D

V

1

2

3

2 2

3

2

1

Figure2.1: The dopant(D) vacancy (V) pair migration in a silicon lattice. The dopantandvacancy startthediffusionstepasfirst nearestneighbors.Thehoppingratesaresuchthat the dopantcanhop into the emptysite andbackmany timeswithout any effect ondiffusion. The hostatoms,though,could alsohop into the emptysite suchthat at somepoint the vacancy movesto a third nearestneighborsite with respectto thedopant.Thevacancy can go aroundthe six memberring of atomsand approachthe dopantfrom adifferentdirection.After thedopanthopsinto thenow emptysitethedopantvacancy paircompletesonediffusionstep.

2.1.1 Vacancymechanism

In thevacancy diffusionmechanism,asubstitutionaldopantatomexchangespositionwithan empty lattice site. This diffusion mechanismwasproposedfor silicon basedon theexperimentalobservationthatthevacancy is themainpoint defectin metals[89].

A schematicof the pair diffusion is shown in Fig. 2.1. At an atomisticscale,thismechanismpresentssomeparticularitiesgiven thedifferentdopantvacancy interactions.The vacancy mechanismdoesnot occurthrougha simplevacancy dopantexchange,butthroughwhatis calleda “ring mechanism.” Thevacancy notonly mustexchangeits posi-tion with thedopantbut alsohasto moveawayto athird nearestneighborsitewith respectto the dopantandreturnvia a new directionfor a long rangemigrationof the dopanttotakeplace.

6

Note that in the pair diffusion mechanismthe resultingdopantflux is in the samedirectionasthevacancy flux. This is contradictoryto thesimpleexchangemechanisminwhichthevacancy flux is oppositeto thedopantflux. Onamacroscopicscale,thisprocesscanbedescribedby thereaction:

Bs " V # BV (2.2)

For this reaction,thenetrateof formationof BV from Bs andV is givenas:

RBV � 4πσDV�CBCV

� CBV

KB $ V � (2.3)

where,DV is thevacancy diffusivity, KB $ V is theequilibriumconstantgivenas,

KB $ V � 1CSi

exp

�EB

kT ! � (2.4)

CSi is thenumberof availablelatticesitesin silicon 5 � 1022 cm� 3, andEB is thebindingenergy of BV relativeto freeboronandvacancy. σ is thecaptureradiusof thereactionandis definedas:

σ � Acap

4πahop� (2.5)

ahop is thehopdistanceof a vacancy andis takento beequalto ao, thelatticeconstantofsilicon. Acap is thecapturecross-sectionof Bs andis givenby,

Acap � π�rcap � 2 � (2.6)

If rcap � 2a0, thenσ � a0. This is theassumptionwe will generallymake in this work.

2.1.2 Interstitial mechanism

Experimentsinvolving theinjectionof point defectsinto borondopedsampleshasshownthat borondiffusion in silicon is dominated( � 98%) by an interstitial mechanism[37,53]. Most early workersassumedthat the interstitial mediateddiffusion occursthroughan interstitialcy mechanism,i.e. thediffusingdefectis a complex formedby animpurityatomandaSi atomsharingthesamesite[50]. For heavier atomslikeAl andAu akick-outmechanismwasproposed[97, 48]. In this mechanism,a silicon self interstitialmigratesthroughthe latticeandapproachesa substitutionalatom. If theenergy barrieris low, thesubstitutionalatom is kicked into an interstitial position andcould migratethroughthesilicon lattice. Fig. 2.2shows anexampleof thekick-out mechanism.Cowernet al. [25]experimentallymeasuredanomalousdiffusionin thetailsof aB concentrationdistributionasa resultof shorttime annealsat low temperatures.Theone-dimensionalprofile of thedopantafterdiffusionshowsexponentialtailsnotexpectedfrom Gaussiandiffusion.Thus,they suggestedtheformationof a fastmigratingintermediatespecies(Bi) thatcandiffuse

7

% % %% % %% % %% % %% % %& & && & && & && & && & & ' ' '' ' '' ' '' ' '' ' '( ( (( ( (( ( (( ( (( ( (Figure2.2: Schematicof kick-out mechanismshowing interstitialassistedmechanismofdiffusion. In (a) the dark atomis the substitutionaldopantatomto be kicked out by thesilicon self interstitial (unfilled atom). (b) shows thedopantatomthat is now kickedintoaninterstitialsiteandcannow diffusein thelattice.

long distancesbeforegettingkicked backinto a substitutionalsite. This processcanbedescribedby thereaction:

Bs " I # Bi � (2.7)

To accuratelymodelborondiffusion, it is necessaryto know the atomicparametersgoverningthepoint defectenergetics.First principlescalculationshaveemergedasa toolto provide informationon theenergeticsanddifferentdiffusionpathwaysin Si. Themostacceptedmodeluntil recentlyfor B diffusion in Si assumedthat a Bs

�SiT2n

i (a tetrahe-dral (T) interstitial in 2nd neighborpositionwith respectto Bs) pair is first formed[77].Subsequently, the Bs becomesinterstitial (Bi) by beingkicked out into a [110] channelconnectinghexagonal(H) andT interstitial sites. This modelfurther suggestthat in thenetwork of [110] channels,theBi diffusesrapidlyby performinga largenumberof jumpsbeforegetting kicked back into a substitutionalsite releasinga interstitial (which mayremainboundto the Bs). This mechanism(barriersfrom Zhu et al. [103]) is shown inFig. 2.3.Macroscopically, this mechanisminvolves:

B " I # BI � (2.8)

BI # Bi (2.9)

8

More recently, Windl et al. [98, 86] have founda new borondiffusionmechanism.Asshown in Fig 2.4(a) thelowestenergy configurationfor theneutralcasewasfoundto beaBs�

SiT1n0i ( a tetrahedral(T) interstitial in 1stneighborpositionwith respectto Bs) with

abindingenergy of 0.8eV relative to neutralI andB �s . Unlike thepreviousmechanism,Windl etal. foundtheBs atomto migratevia theBS0

i (aboroninterstitialcy) to ahexagonalBH0

i interstitialsitewith amigrationbarrierof 0.2eV. Thusthediffusionpathway is

Bs�

SiT1n0i ) BH0

i ) Bs�

SiT1n0i (2.10)

For negatively charged systems,a BX �i (anotherinterstitialcy configuration)was foundto be the moststableconfigurationwith a binding energy of 0.5 eV with respectto freeB � and I0. As shown in Fig. 2.4 (b), they found a BX �i ) BS�i ) BX �i path with anintermediatemetastableBS�i configurationanda migrationbarrierof 0.6 eV. For the +1chargedsystem,Bs

�SiT1n i wasfoundto bethemoststableconfigurationwith a binding

energy of 1 eV with respectto B � andI * . However the migrationpathway of a Bs�

SiT1n i wasfoundto beaone-stepprocessBs

�SiT1n

i ) Bs�

SiT1n i with no intermediate

metastableinterstitialpositionanda migrationbarrierof 0.8 eV. Thus,thesecalculationspredictthatalthoughthedominantpair is positivelychargedin p-typematerial,B diffusionis dominatedby neutralpairs,consistentwith the approximatelylinear dependenceof Bdiffusivity oncarrierconcentration(p� ni) asseenexperimentally[99]. Thus,for all chargestatesthediffusionmechanismcanberepresentedby thereactionof thetype:

B " I # BI (2.11)

where,BI is the lowestenergy configurationfor that charge state(e.g. Bs�

SiT0i for the

neutralcase),with subsequentdiffusionof thiscomplex. Themigrationbarrieris givenbythehighestbarrierenergy in thepathway. Notethat,a moreaccuraterepresentationcouldinvolveall thereactionse.g.,Bs

�SiT1n0

i # BS0i # BH0

i . However, undermostconditions,it is sufficient to usethesimplifiedsinglereactionstep.

9

1.0

1.0

0.6

(BI)

Bi(H)

Bi(T)0.3

0.4

++B_

I

0

0

0

Figure2.3: Dif fusionpathfor boroninterstitial for thekick-out mechanismascalculatedby Zhuet al. [103].

_+ I+B

HS S

T T T

H0

0

0

0 00

0

X_ X

_

B_

+ I

S_

0

Figure2.4: Comparisonof the diffusion path for boronvia the kick-out mechanismascalculatedby Windl et al. [98] for (a) neutral(b) negativechargestates.

10

2.2 Coupleddiffusion

Thecurrentstandardmodelfor coupleddopant/defectdiffusionis thepairdiffusionmodel[33, 71, 72, 100,101, 37]. For a systemcontaininga singledonorspecies,we first writedown all thepossibleinteractions.Thepairingreactionsaregivenas:

Bi " I j # �BI � i j � (2.12)

Bi " V j # �BV � i j � (2.13)

Theparametersi and j representthechargestatesof thedefector pair. Therecombinationandgenerationof Frenkel pairscanbedescribedas:

I i " V j # � �i�

j � e� � (2.14)

In addition,thepairscaninteractdirectly with oppositetypedefectsto producea reactionwhich is equivalentto apair dissociationfollowedby defectrecombination.�

BI � i " V j # B � � � 1 " i " j � e� � (2.15)�BV � i " I j # B � � � 1 " i " j � e� � (2.16)

Weneedto alsoconsiderionizationreactionsor chargeexchangereactionsfor eachof thechargedspecies.

Becauseelectronicreactionsaremuchfasterthantheatomicdiffusionprocesses,weassumethatall of theionizationreactionsarenearequilibrium. For example,theconcen-trationof negatively chargedinterstitialsis:

CI + � θI +θI0

exp

� � EI + � Ef

kT ! CI0 � θI +θI0

exp , Eif

�EI +

kT - CI0

�nni ! (2.17)

where,Ef is theFermi level with Eif beingtheintrinsic Fermi level andEI + is theenergy

level in thebandgap.Thetermsn andni arethelocal andintrinsiccarrierconcentrations.Theratioof thenumberof configurations(θ) accountsfor thefactthatwith unpairedelec-tronsthereis aspindegeneracy of 2 ( " or

�spin).Thus,theconcentrationsof interstitials

andBI pairsin variouschargestatesaregivenby:

CI i � KI iCI0�ni � n� i � (2.18)

C. BI / i � K . BI / iC. BI / + � ni � n� i 1 (2.19)

where,KX representsequilibriumcoefficients.

It is necessaryto determinetheFermilevel in orderto considerthebehavior of chargedspecies.It is possibleto solvePoisson’sequationin conjunctionwith continuityequations,but it hasgenerallyprovensufficient to simply assumelocal chargeneutrality[37, 58], so

11

that the electronconcentrationcanbe calculatedalgebraicallyfrom the dopantdistribu-tion. In addition,we assumethat chargeddefectsandpairswhendilute canbe ignoredin determiningtheFermi level. Sincebothdefectsandpairscanexist in multiple chargestates(e.g.,V � , I * ), CI, CV, CBI andCBV haveto besummedoverall chargestates.Thus,for example,thetotal interstitialconcentrationis

CI � ∑i

CI i � χICI0 � ∑i 0 KI i 1 ni

n 2 iCI0 3 � (2.20)

whereCI0 is theconcentrationof neutralinterstitials.Similarly, for pairsatequilibrium,

CBI � ∑i

C. BI / i � πICBCI0 � (2.21)

C. BI /4+ � KB + $ I0CBCI0 � KB + $ I0CBI

πI�

whereKB + $ I0 is the equilibrium constantfor the pairing of a neutral interstitial with aB substitutionalatom. Sinceelectronicexchangecanoccurbeforeor after pairing andequilibriumconcentrationareindependentof path,wecanwrite,

KB + $ I0K . BI / i � KI i KB + $ I i � (2.22)

Thuswecanwrite,

πI � KB + $ I0 0 1 " K . BI / 0 � pni ! " K . BI / +5+ � n

ni ! 3 (2.23)� KB +6$ I0 " KB + $ I 7 KI 7 � pni ! " KB + $ I + KI + � n

ni !Notethat for simplicity, we have left off interactionwith doublychargeddefectsin theseequations.Boron beingan accepter, KB +6$ I + is expectedto be small. This resultsin thefollowing diffusion/reactionequations[43]:

∂CB

∂t� �

RB I�

RB V " RBI V " RBV I " 2RBI BV

∂CBI

∂t� �98

∇8JBI " RB I

�RBI V

�RBI BV

∂CBV

∂t� � 8

∇8JBV " RB V

�RBV I

�RBI BV (2.24)

∂CI

∂t� � 8

∇8JI�

RB I�

RI V

∂CV

∂t� � 8

∇8JV�

RB I�

RI V

12

JX representsthe flux of speciesX andRX Y representsthe net rateper unit volumeofthereactionof speciesX andY (e.g.,RB I representsthenetforwardrateof thekick-outreactiongivenby Eq. 2.7). This modelis commonlyreferredto asa “fi ve streammodel”basedon thenumberof continuityequationsfor a singledopant.Eachadditionaldopantaddsthreeadditionalequationswith correspondingflux andreactiontermsaddedto thepoint defectequations.

Note that dueto the charge of ions, the continuity equationwill not only have a dif-fusioncomponent(

8Jdiff), but alsoa drift component(

8Jdrift). Thedrift termsarisebecause

the chargedspeciescanalsomove becauseof forcesof the electricfield, createdby thegradientof electronconcentrationin thesubstrate.Thetotalflux of pointdefectsandpairswill beequalto thesumof fluxesof eachchargestatei:8

J. BI / i � 8Jdiff. BI / i " 8

Jdrift. BI / i (2.25)

Boronbeinganacceptor, we will expandin termsof thenegativedefectpair (BI) � . Thusthediffusiontermis:8

Jdiff. BI / i � �D . BI / i 8∇C. BI / i (2.26)� �D . BI / i 8∇ : K . BI / iC. BI / + � p� ni � i 1 ;� �D . BI / i K . BI / i 8∇ <C. BI /4+ � p� ni � i 1 =� �D . BI / i K . BI / i : � p� ni � i 1 8∇C. BI /4+ " � i " 1� C. BI /4+ � p� ni � i 8∇ � p� ni � ; �

Thedrift termbecomes: 8Jdrift. BI / i � µ. BI / i iq 8> C. BI / i� D . BI / i � q� kT � i 8> C. BI / i � (2.27)

whereµ � D � kT is themobility accordingto theEinsteinrelationshipand8>

is theelectricfield vector. Theelectricfield canbecalculatedfrom thegradientof thepotential,whichinturn canbefoundfrom thelocal carrierconcentration,givenby a Boltzmanndistribution(Ψ denotestheintrinsic potential):

n � ni exp

�Ψ

kT � q ! � (2.28)

or FermiDiracdistribution. 8> � � 8∇Ψ� � 8∇ ? kT � qln

�n� ni �A@� 8

∇ ? kT � qln�p� ni �A@ (2.29)

13

8Jdrift. BI / i � iD . BI / iC. BI / i 8∇ ln

�p� ni �� iD . BI / i : K . BI / iC. BI / + � p� ni � i 1 ; � ni � p� 8∇ � p� ni �� iD . BI / i K . BI / iC. BI / + � p� ni � i 8∇ � p� ni � � (2.30)

Adding thediffusionanddrift termsweget:8JBI i � �

D . BI / i K . BI / i � p� ni � i 1 : 8∇C. BI / + " C. BI / + 8∇ ln�p� ni � ; (2.31)� �

D . BI / i K . BI / i KB + $ I0 � p� ni � i 1 0 8∇ �CBI

πI ! " CBI

πI

8∇ ln

�pni ! 3 �

Summingoverall thechargestates,weget:8JBI � 1

∑i B � 1

8JBI i (2.32)� � � DI0B " DI 7

B�p� ni � " DI +

B�n� ni �C�

C �I0 0 8∇ �CBI

πI ! " CBI

πI

8∇ ln

�pni ! 3 �

Theseparatecomponentsof diffusivitiessuchasDI 7B standfor diffusivity of borondue

to pairingwith interstitialsin agivenchargestate(I or�BI � 0 in thiscase). Fromoxidation

andnitridationexperiments,it is known thatborondiffusesprimarily by interstitials[54](i.e f intr

I 1). It is alsonecessaryto make anassumptionon thevariationof fI for eachchargestate.Assuming,f intr

I is independentof Fermilevel,

f intrI � DI0

B " DI 7B

D0B " D B (2.33)

It is alsonecessaryto make assumptionon the ratio f 0I � f I or DI0

B � DI 7B andwe assume

they areequal.Hence,

f intrI � DI0

B

DI0B " DV0

B

� DI 7B

DI 7B " DV 7

B

� (2.34)

wecannow calculateDI 7B from experimentalborondiffusivity data.However, to calculate

πI it is necessaryto assumethatthediffusivity of boroninterstitialpairsis independentoftheir chargestate,sinceexperimentsyield theratio:

D BD0

B

� D . BI / 0D . BI /D+ KI 7 KB +6$ I 7

KI0KB + $ I0 � (2.35)

14

Thedopantvacancy pair flux is calculatedsimilarly,8JBV � � DV

B

C �V0 0 8∇ �CBV

πV ! " CBV

πV

8∇ ln

�pni ! 3 � (2.36)

DVB � DV0

B " DV 7B

�pni ! " DV +

B

�nni !

πV � KB + $ V0 " KB + $ V 7 KV 7 � pni ! " KB + $ V + KV + � n

ni ! �The total flux of interstitialsin eachof the charge statescanbe written in termsof thegradientin theneutralconcentrationandtheelectronconcentration:8

JI i � � DI i , 8∇CI i� iq

8>kT

CI i - � � DI i KI i 1 ni

n 2 i 8∇CI0 � (2.37)

whereDI i representsthediffusivity of interstitialsof chargestatei. Thusthetotal intersti-tial flux is: 8

JI � ∑i

8JI i � � DI0χI

8∇CI0 (2.38)

where,

χI � 1 " KI 7 � pni ! " KI + � n

ni ! (2.39)

Noteagainthat,dueto lack of betterexperimentalevidenceit is assumedthatDI i = DI0 .Thisassumptionis madethroughoutthis work. Similarly wecanwrite for vacancies,8

JV � �DV0χV

8∇CV0

χV � 1 " KV 7 � pni ! " KV + � n

ni ! (2.40)

Theexpressionsfor thenetrateof pairingandrecombinationreactionsarealsosummedover all the charge states.Noting the definitionsof χI � χV andπI � πV from Eq. 2.20and2.21,we canwrite down thenetreactionratesof thepairingandrecombinationreactionsas:

RB I � kB $ I ?CBCI� χI

πICBI @

RB V � kB $ V ?CBCV� χI

πICBV @ (2.41)

RBI V � kBI $ V � CBICV�

C �I0C �V0πI χVCB �RBV I � kBV $ I � CBVCI

�C �I0C �V0πVχICB �

RBV BI � kBV $ BI�CBVCBI

�C �I0C �V0πI πVC2

B �15

Notethatthekinetic forwardreactionratekX $ Y for thereactantswith diffusivitiesDX andDY is assumedto bediffusionlimited andthusequivalentto thatderivedin Eq.2.5:

kX $ Y � 4πa0�DX " DY � (2.42)

Whenotherspeciessuchasclustersor extendeddefectsarealsopresentadditionalcon-tinuity equationsmustbeaddedandadditionaltermsrepresentingtheformation/dissolutionof thesespeciesmustbe includedon the right handsidesof Eqs.2.24. Undermostcon-ditions(althoughnotduringtheearlystagesof ion implantannealingwhentheconcentra-tion of pairsis not dilute), thedopant/defectpairing reactions(e.g.,B " I # BI) arefastenoughto maintainthepair concentrationnearlocal equilibriumwith theconcentrationsof isolateddopantsanddefects(e.g.,C. BI / i � KB + $ I i KI iCB + CI0

�p� ni � i 1).

Undertheseconditions,thefivestreammodelcanbereducedto threecontinuityequa-tions (oftenreferredto asthe“fully-coupled” model)[33]. Thoughthis modelis usedinmostProcessSimulators,it is not alwayscorrectto usethis approach.To understandthiscasebetter, we cancalculatethetime it takesfor thepair to reachequilibriumor thedis-tanceit movesasa pair beforedissociatingto a substitutionalsiteandanself-interstitial.This is equivalentto lookingattimescalessmallerthantheaveragelife time(τBI) of apair.In otherwords,mostof theatomshave undergoneonly onemigrationevent in timeslessthanτBI . The life time of a pair is the reciprocalof the reversereactionrateτBI � 1� kr .Thedistancewhich thepair travelsin this time is onaverage

λ �FE DBIτBI � DB

4πaDIC �I (2.43)

Interestingly, the pair diffusion lengthcanbe estimatedin termsof macroscopicquanti-ties. Thecalculatedvalueat 800� C is 3.7nm andcomparesfavorablyto theexperimentalvalueof 5 nm [25]. However at 600� C the calculatedvalueis 20 nm which is twice theexperimentalvalue. It shouldbenotedthat theexperimentaldeterminationwasobtainedmonitoringthe movementof a marker layer in a structuregrown MBE which generallyleadsto higher levels of carbon. This could result in a lower valueof λ. The valueofλ thuscalculatedis alsocomparableto the junction depthsof ultra low energy implantsmodeledin Chap.5. Hencethe“fully coupled”modelis not usedfor any of thesimula-tions in this thesisandinsteadthemorephysical“fi ve-stream”(Eq. 2.24)modelis used.Someinstanceswhenthefive-streammodelmaynot give reliableanswerswould involvevery low dopantconcentrations(e.g.,a few atoms)whereit would bequestionableto usea continuumapproach.Similarly, it may be inappropriateto usea continuumapproachto modelthe initial recombinationof point defectswherethe initial correlationbetweeninterstitialandvacancy cascadesis expectedto beimportant[15].

Under intrinsic conditionsnearequilibrium with no spatialvariation in point defectconcentrations,the effective diffusivity of a dopantcanbe shown to be (calculatefrom

16

Eq.2.32and2.36)[37]:DB

D �B � f intrI

CI

C �I " � 1 � f intrI � CV

C �V (2.44)

where,the ’*’ denotesequilibriumvalues.FromEq. 2.44it is clearthatdopantdiffusiv-ities canbe alteredby changesin point defectconcentrations.Therefore,to understanddopantdiffusionin silicon, it is necessaryto understandandmodelhow differentprocessinteractandthusgovernpoint defectsupersaturations.Henceoneof the key parametersfor modelingthesesystemsaretheparametersof theintrinsic pointdefects.

17

‘

2.3 Point defectproperties

Thepropertiesof pointdefectsclearlyplayacentralrolein controllingdiffusionprocesses,especiallyduringTED. Becausethediffusionof metalatoms(aswell asdopants)dependsquite directly on total point defectfluxes,valuesfor the DIC �I andDVC �V productshavebecomebroadlyaccepted[12, 37, 49, 51, 74, 95, 109]. However, therecontinueto existsubstantialdisagreementsover themagnitudeof thediffusivitiesandequilibriumconcen-trationswhichgo to makeup theseproducts.

Mainly two typesof experimentsgiveusinformationaboutpoint defects.Analysisofdiffusionprofilesfor metalssuchasAu, Pt andZn, andstudyof dopantdiffusion underpoint defectinjection conditionssuchasoxidation andnitridation. However, the lattermethodhasprovidedawealthof dataaboutdopantdiffusionmechanismsandmuchlessontheintrinsicpointdefectsinvolved.Themostwidely usedestimatesof vacancy parameterscomefrommetaldiffusionexperiments,but evenheretheissueof vacancy diffusivity isnotclear. Most of themetaldiffusionexperimentspredicta relatively low vacancy diffusivity[12, 109]. In contrast,ab-initio [77, 103] andtight-bindingMD calculations[94] find thatformationenergiesfor vacanciesareonthesameorderor largerthanthatof interstitialsandthat themigrationenergy for vacanciesis smallerthanthatof interstitials.This issuehasbeenrecentlybeencomplicatedfurtherascarbonhasbeenshown to actasan interstitialtrapandhencereducestheeffective interstitialdiffusivity if presentin largeamounts[91].Until recently, theacceptedview within theTCAD communityhadbeenthatvacanciesarerelatively slow diffuserscomparedto interstitials,but arepresentin muchlargernumbers.Thisconclusionwaslargelybasedonanalysisof metaldiffusionexperiments[12,75, 107].

2.4 Metal diffusion

Upon reexaminingtheanalysisof metaldiffusionexperimentswhich gave largeequilib-rium concentrationsandlow diffusivities for vacancies,it canbeobservedthatin ordertosimplify theanalysis,theoriginal work [12, 107] generallyneglectedbulk recombinationandmadea numberof assumptionsaboutthedominantmechanismscontrollingbehaviorat differenttemperaturesandtime scales.Hence,to resolve this issue,it wasnecessarytomodelmetaldiffusionexperimentsmorerigorously.

ThemetalsAu, Pt andZn diffusemainly via thekick-out andFrank-Turnbull (or dis-sociativemechanism)[12, 70, 108]. This leadsto thereactions,

Ms " I # M i � (2.45)

18

Ms # M i " V � (2.46)

whereM i andMs representinterstitial andsubstitutionalmetalaswell as their concen-trations. A third reactionthat needsto be consideredis the bimolecularrecombinationbetweeninterstitialsandvacancies,

I " V # φ � (2.47)

Assumingthatsubstitutionalmetalis immobilewe cannow write thefull setof equationsthatneedto besolvedsimilar to thatdiscussedin Section2.2.

It is alsonecessaryto specify the initial boundaryconditions. For point defects,weassumethattheSi/metalsurfaceis aninfinite sourceandsink for pointdefects.Hence,theconcentrationsof interstitialsandvacanciesarefixedat their equilibrium values(C �I andC �V) at all timesduringthediffusionprocess.Theinitial interstitialconcentrationis takento be equalto C �I . However, thereis somedebateover the initial vacancy concentrationsincepreviouswork on metaldiffusionhasuseddifferentinitial concentrationsof vacan-cies[12, 109]. We discussthis issuefurther in the subsequentsections.For the metals,the initial concentrationin thesilicon is considerednegligible ( � 108cm� 3). Thesurfaceconcentrationof interstitialmetalis setto its solubility.

2.4.1 Zinc diffusion

Sinceextensivezinc diffusiondatais availablefor bothheavily dislocatedanddefect-freematerial[12, 13], we focuson this metal for muchof our analysis. In the experiments,Bracht et al. [12] first equilibratedthe samplesat diffusion temperaturesrangingfrom870� C to 1208� C andthenintroducedzinc, which diffusedin from bothsurfaces.Dislo-cationsact assourcesandsinksfor point defects.Hence,in heavily dislocatedmaterial,point defectconcentrationsremainnearequilibrium(CI � C �I , CV � C �V) anddiffusion isindependentof theintrinsic point defectproperties.

We usethe metal propertiesfound by Bracht et al. [13] for diffusion in dislocatedsilicon in our modelingof the defect-freematerial. For consistency, insteadof fittingsingle temperatures,all the curves were simultaneouslyfit using temperatureactivatedparameters.Brachtet al. [12] extracteda high valuefor C �V from this data,but requiredan initial vacancy concentrationmuchlessthanequilibrium(CV

�t � 0�HG 10� 4C �V). The

simulatedandmeasuredprofilesusingthe parametersextractedby Brachtet al. [12] areshown in Figs.2.5and2.6.alsounableto fit thedata.Howeverusingthemodeldescribedabove andavoiding someof the assumptionsmadeby Bracht,we wereableto obtainasimilarfit to theobserveddatausingCV

�t � 0�I� C �V (asexpectedgivenequilibrium) and

a muchlower valueof C �V (Figs.2.7and2.8). TheextractedC �V hasthefurtheradvantageof beingmuchcloserto theoreticalpredictions[49].

19

|�0.0J |�

0.2J |�0.4J |�

0.6J |�0.8J |�

1.0J|� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� ||� |� ||� |� |� |� |� |� |� |� |� |� |� |� |

� |� |� |� |� |� |� |� |||� |� |� |� |� |� |� |� |� |� |� |� |� |� |� ||� |� |� |� |� ||� |� |� |� |� |� |� |� |

� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� ||� |� |�

Normalised Depth (x/D)

C

once

ntra

tion

(Zn(

x)/Z

n(0)

)

10-4

10-2

100

K K K K K KK K K K K KK K K K K K K K K K K K K KK KK K K K K K K K K K K K K KKK K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K KK K K KK KK KK K K KK K K KK K K K K K KK K K K K K KK K K K K K K K K K K K K KKK K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K KK KK K K K K KK K K K KK KK K KK K K K K K K K KK KK KK K K K KK K KK K K K K K K K K K K K K K K K K KK K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K

K K K K K K K

Figure2.5: Normalizedzinc diffusionprofilesat 870� C into defect-freesilicon andcom-parisonto simulationsusingpoint defectparametersfrom Brachtet al. [12].

2.4.2 Platinum diffusion

Low temperaturediffusiondataexist for Pt asit diffusesfasterthanZn or Au [66]. Plat-inum profiles are characterizedby uniform bulk concentrationsof the substitutionalPtwhich do not changewith time, and at the lowest temperaturean inverseU profile isseenin non-equilibratedsamples[106]. Theflat profileshavebeenattributedto theinitialconcentrationof point defectsandassumingthe dominanceof the dissociative reaction,Zimmermannet al. calculatedaC �V valuesimilar to thatof Brachtet al. [12]. TheinverseU profileswereexplainedby an initial super-saturationof vacancies,leadingto a metalconcentrationin the bulk greaterthanits solid solubility. However, we find this behav-ior canalsobeexplainedby a carbonclusteringmodelasdiscussedbelow andshown inFigs.2.9and2.10.

It hasbeenreportedbasedonMBE grown sampleswith elevatedcarbonconcentrationsthat carbonactsasan interstitial trap [91]. Carbonin silicon canbemodeled[49] basedon diffusionasaninterstitial,

Cs " I # Ci � (2.48)

plusreactionof interstitialcarbonwith substitutionalcarbonto form animmobilecomplex

20

|�0.0J |�

0.2J |�0.4J |�

0.6J |�0.8J |�

1.0J|� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� ||� |� ||� |� |� |� |� |� |� |� |� |� |� |� |

� |� |� |� |� |� |� |� |||� |� |� |� |� |� |� |� |� |� |� |� |� |� |� ||� |� |� |� |� ||� |� |� |� |� |� |� |� |

� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� ||� |� |�

Normalised Depth(x/D)L

C

once

ntra

tion

(Zn(

x)/Z

n(0)

)

10-4

10-2

100 M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M

M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M MM M M M M M M M M M M M M

M M M M M M M M M M M M M M M M M M M M MM M M MM M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M MM M M M M M M M M M M M

M MM M M M M M M M M M M M M M M M M M MM M M M M MM M MM M

M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M MM M M M M M M M M M M M M M M M M M M M M M M M M M M M MM M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M MM M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M MM M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M MM M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M

M M M M M M M M M M M M M M M M M M MM M M M M M M M M MM M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M

M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M

M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M

M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M MM M M M M M M M M M M

Figure2.6: Normalizedzincdiffusionprofilesat1208� C into defect-freesiliconandcom-parisonto simulationsusingpoint defectparametersfrom Brachtet al. [12].

C2I,Ci " Cs # C2I � (2.49)

Sincecarbonclusterswith aninterstitial,eachclusterformationannihilatesaninterstitialor generatesavacancy. If theinitial carbonclusterconcentrationis lessthanitsequilibriumvalue, the formationof carbonclustersleadsto an under-saturationof interstitials(or acorrespondingsuper-saturationof vacancies)which leadsto the inverseU profile. Thisis possibleduring FZ crystal growth, if we assumethat the material is quenchedfroma high temperatureat which the clustersare unstable. It shouldbe notedthat the flatprofile of platinumin the bulk is expectedeven if the sampleswereequilibratedbeforethe in-diffusion [104], althoughthebulk Pt concentrationis lower in this case.To checkour analysis,the samecarbonmodelandparameterswere usedfor simulationsof zincdiffusion. As seenin Fig. 2.11, we find that at the higher temperaturesusedfor zinc,moderatecarbonlevelscarbondonot producea significantchangein theprofiles.

Shown in Fig. 2.12 [16] is comparisonof extractedvaluesof DVC �V, DIC �I . Fromthis analysis,we obtainC �V C �I asshown in Fig. 2.13 [16], four ordersof magnitudesmallerthanoriginally calculatedandmuchcloserto theresultsof atomisticcalculations.Fig. 2.14shows the changein meansquarederror aseachof the parametersis changed

21

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0.2J |�0.4J |�

0.6J |�0.8J |�

1.0J|� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� ||� |� ||� |� |� |� |� |� |� |� |� |� |� |� |

� |� |� |� |� |� |� |� |||� |� |� |� |� |� |� |� |� |� |� |� |� |� |� ||� |� |� |� |� ||� |� |� |� |� |� |� |� |

� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� ||� |� |�

Normalised Depth (x/D)

C

once

ntra

tion

(Zn(

x)/Z

n(0)

)

10-4

10-2

100

N N N N N NN N N N N NN N N N N N N N N N N N N NN NN N N N N N N N N N N N N NNN N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N NN N N NN NN NN N N NN N N NN N N N N N NN N N N N N NN N N N N N N N N N N N N NNN N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N NN N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N NN N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N NN N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N NN NN N N N N NN N N N NN NN N NN N N N N N N N NN NN NN N N N NN N NN N N N N N N N N N N N N N N N N NN N N N N N N N N NN N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N

N N N N N N N

Figure2.7: Normalizedzinc diffusionprofilesat 870� C into defect-freesilicon andcom-parisonto simulationsusingpoint defectparametersobtainedin this work.

from its optimumvalue.ThuswecanconcludethattheDIC �I productis well characterizedby thedataandthatit is possibleto establishsolid upperlimits for DVC �V andC �I , but thatC �V is not accuratelydeterminedby theseexperimentsandonly a relatively looseupperboundcouldbeobtained.

22

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1.0J|� |� |� |� |� |� |� |� |� |�|� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |�|� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |

|� |� ||� |� |� |� |� |� |� |� |� |� |� |� |� |� |� ||� |� |� |� |� |� |� ||||� |� |� |� |� |� |� |� |� |�

Normalised Depth (x/D)

C

once

ntra

tion

(Zn(

x)/Z

n(0)

)

10-4

10-2

100 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O OO O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O OO O O OO O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O OO O O O O O O O O O O O

O OO O O O O O O O O O O O O O O O O O OO O O O O OO O OO O

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O OO O O O O O O O O O O O O O O O O O O O O O O O O O O O OO O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O OO O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O OO O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O OO O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O OO O O O O O O O O OO O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O OO O O O O O O O O O O

Figure2.8: Normalizedzincdiffusionprofilesat1208� C into defect-freesiliconandcom-parisonto simulationsusingpoint defectparametersobtainedin this work.

23

P 0.5 hrQ 4 hr

|� |R |R |R |R |R |R |R |R |� |R |R |R |R |R |R |R |R |� |R |R |R | |R |R |R |R |� |R |R|� |� |�|� |� |� |� |� |� |�

|� |� |� |� |�|� |� |� |� |� |S |S |S |S |S |S |S |S |� |S |S |S |S |S |S |S |S |� |S |S |S |S |S |S |S |S |� |S |S

|� |� |� |� |� |�|� |� |� |� |� ||� ||�

|� ||� |�

Depth (um)10� -1 10� 0 10� 1 10� 2

1013

1014

1015

C

once

ntra

tion

(ato

ms/

cm-3) T T T T T T T T T T T T T T T T T T T T T T TU U U U U U U U U U U U U U U U U U U U U U U U

Figure2.9: Measuredandsimulatedplatinumprofilesat 770� C [105].

24

V 4 hrW 142 hr

|� |R |R |R |R |R |R |R |R |� |R |R |R |R |R |R |R |R |� |R |R |R |R |R |R |R |R |� |R |R|� |� |�|� |� |� |� |� |� |�

|� |� |� |� |�|� |� |� |� |� |S |S |S |S |S |S |S |S |� |S |S |S |S |S |S |S |S |� |S |S |S |S |S |S |S |S |� |S |S

|� |� |� |� |� |�|� |� |� |� |� |� |� |� |�

||� |� |�

Depth (um)10� -1 10� 0 10� 1 10� 2

1013

1014

1015

C

once

ntra

tion

(ato

ms/

cm-3) X X X X X X X X X X

Y Y Y Y Y Y Y Y Y

Figure2.10: Measuredandsimulatedplatinumprofilesat 700� C [106]. NotetheuniformPt concentrationin bulk which is unchangedwith time,andtheinverseU profile.

25

|�0.0J |�

0.2J |�0.4J |�

0.6J |�0.8J |�

1.0J|� |� |� |� |� |� |� |� |� |�|� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |�|� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |

|� |� ||� |� |� |� |� |� |� |� |� |� |� |� |� |� |� ||� |� |� |� |� |� |� ||||� |� |� |� |� |� |� |� |� |�

Normalised Depth (x/D)

C

once

ntra

tion

(Zn(

x)/Z

n(0)

)

10-4

10-2

100

Z Z Z Z Z ZZ Z Z Z Z ZZ Z Z Z Z Z Z Z Z Z Z Z Z ZZ ZZ Z Z Z Z Z Z Z Z Z Z Z Z ZZZ Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z ZZ Z Z ZZ ZZ ZZ Z Z ZZ Z Z ZZ Z Z Z Z Z ZZ Z Z Z Z Z ZZ Z Z Z Z Z Z Z Z Z Z Z Z ZZZ Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z ZZ Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z ZZ Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z ZZ Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z ZZ ZZ Z Z Z Z ZZ Z Z Z ZZ ZZ Z ZZ Z Z Z Z Z Z Z ZZ ZZ ZZ Z Z Z ZZ Z ZZ Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z ZZ Z Z Z Z Z Z Z Z ZZ Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z

Z Z Z Z Z Z Z

Figure2.11: Effect of carbonon zinc diffusionat 870� C. Carbonhasonly a minor effectevenat thelowestavailablediffusiontemperature.

26

[[\\

|]6

|]7_ |]

8|]9a |]

10

|b |c |c |c |c |c |c |c |c |b |c |c |c |c |c |c |c |c |b |c|c |c |c |c |c |c |c |b |c |c |c |c |c |c |c |c |b |c |c |c |c |c |c

|c |c |b |c |c |c |c |c |c |c |c |b |c |c |c |c |c |c |c |c |b |c|c |c |c |c |c |c |c |b |c |c |c |c |c |c |c |c |b |c |c |c |c |c |c

|c |c |b |d |d |d |d |d

|e |f |f |f |f |f |f |f |f |e |f |f |f |f |f |f |f |f |e |f |f |f |f |f |f |f |f |e |f |f |f |f |f |f |f |f |e |f |f |f |f |f |f |f |f |e |f |f |f |f |f |f |f |f |e |f |f |f |f |f |f |f |f |e |f |f |f |f |f |f |f |f |e |f |f |f |f |f |f |f |f |e |f |f |f |f |f |f |f |f |e Chakravarthi DvV*

Gosele DVV*

Chakravarthi DII*

Gosele DII*

10-22

10-21

10-20

10-19

10-18

10-17

10-16

10-15

10-14

10-13

10-12

10g 4/T (K-1)

D

iffus

ivity

(cm

2 /s) h h h h h h h h h h h

h h h h h h h h h h h

i i i i i i i i i i i

i i i i i i i i i i iFigure2.12:Extractedvaluesof DVC �V � Cs, DIC �I � Cs (Cs is thesilicon latticedensity)fromfitting Zn diffusiondataof Brachtetal. [12] andcomparisonto previousanalysisbasedonmetaldiffusion[49].

27

jklmno|]5p |]

6|]7_ |]

8|]9a |]

10

|b |c |c |c |c |c |c |c |c |b |c |c |c |c |c |c |c |c |b|c |c |c |c |c |c |c |c |b |c |c |c |c |c |c |c |c |b |c

|c |c |c |c |c |c |c |b |c |c |c |c |c |c |c |c |b |c |c |c|c |c |c |c |c |b |c |c |c |c |c |c |c |c |b |c |c |c |c |c |c

|c |c |b |d |d |d |d |d |d

|e |f |f |f |f |f |f |f |f |e |f |f |f |f |f |f |f |f |e |f |f |f |f |f |f |f |f |e |f |f |f |f |f |f |f |f |e |f |f |f |f |f |f |f |f |e |f |f |f |f |f |f |f |f |e |f |f |f |f |f |f |f |f |e |f |f |f |f |f |f |f |f |e |f |f |f |f |f |f |f |f |e Chakravarthi V*

Bracht V*

Tang V*

Chakravarthi I*

Bracht I*

Tang I*108

109

1010

1011

1012

1013

1014

1015

1016

1017

10g 4/T (K-1)

C

once

ntra

tion

(cm-3

)

q q q q q q q q q q q

r r r r r r r r r r rs s s s s s s s s s s s st t t t t t t t t t tu u u u u u u u u u u

v v v v v v v v v v v v v vFigure2.13: Extractedvaluesof C �V andC �I from fitting Zn diffusiondataof Brachtet al.[12] and comparisonto previous analysisbasedon both metal diffusion and atomisticcalculations[94].

28

|w |x |x |x |x |x |x |x |x |w |x |x |x |x |x |x |x |x |w |x |x |x |x |x |x |x |x |w |x |x |x |x |x |x |x |x |w|y |z |z|z |z |z |z |z |z |y

|z ||z |z |z

|z |z |z |y |{ || || || || || || || || |{ || || || || || || || || |{ || || || || || || || || |{ || || || || || || || || |{

|} |~ |~ |~ |~ |~|~ |~ |~ |} |~ |~ |~ |~ |~

|~ |~ |~ |}

Change in parameter�

Nor

mal

ised

Err

or� DVV*

DII*

I*

V*

10� -2 10� -1 10� 0 101 102100

101

102

Figure2.14:Effectof variationin a singlepoint defectparameterandreoptimizingall theprofiles. It canbe seenthat DIC �I is the mostreliably extractedparameterandC �V is theleast.

29

� Data Garben et al. Five-Stream Model Fermi Model

|�0.0J |�

0.3J |�0.6J |�

0.9J |�1.2J |�

1.5J|� |� |� |� |� |�|� |� |� |� |� |� |�

|� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |�

|� |� |� ||� |� |� |� |�

|� |� ||� |||� ||�

|�

Boron Diffusion

1017

1018

1019

1020

Depth in Silicon (� µm)

B C

once

ntra

tion

(cm� -3

)

from Poly�950� oC, 8h

� � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �Figure2.15:Borondiffusionfrom implantedpolysiliconfrom Garbenetal. [39] andcom-parisonto predictionof coupleddiffusionmodel.Also shown is predictionbyFermimodelnot consideringpoint-defectmediateddiffusion.

2.5 Boron indiffusion

Combiningtheknowledgegainedfrom theprevioussections,we cannow simulateborondiffusion in silicon successfully. To demonstrateandverify our modelsandparameterswe focuson the in-diffusionof boron. In theseexperiments,a boronsourceis depositedon the surfaceof silicon andthe sampleis annealedfor varioustimesandtemperatures.Henceborondiffusesinto silicon from a constantsurfacesource.Fig. 2.15shows suchasimulationfor a 950� C boronin-diffusionannealfrom Garbenet al. [39]. It is interestingto notethatan increasein boronsurfaceconcentrationsleadsto larger fluxesof BI pairsinto thesubstrateleadingto larger tail enhancements(asshown in Fig. 2.16). This is thesamecoupleddiffusionphenemenonwhich leadsto phosphoruskink anstail profiles[33].

30

� Five-Stream

|�0.0J |�

0.3J |�0.6J |�

0.9J |�1.2J |�

1.5J|� |� |� |� |� |�|� |� |� |� |� |� |�

|� |� |� |� |� |� |� |�|� |� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |�|� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |�

|� 950oC, 8h

(CI/CI*)x1018

1017

1018

1019

1020

Depth in Silicon (µm)

B C

once

ntra

tion

(cm� -3

) � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �Figure2.16:Boronindiffusionfor thehighestsurfaceconcentration,alsoplottedisCI � C �I .Notethatthetail diffusionis enhancedby a factorof about3.

31

2.6 Summary

Thus,in thischapterwereviewedthediffusionof dopantsparticularlyboronin silicon. Wefollowedit by reviewing coupleddiffusionmodelsfor dopantdiffusionin silicon. Finally,in Section2.4wepresentedouranalysisof metaldiffusionexperimentsto re-evaluatepointdefectpropertiesin silicon.

32

Chapter 3

Ion Implant DamageEvolution

In thischapter, wefirst review thedifferentaspectsof transientenhanceddiffusion(TED).It is necessaryto understandthe differentphenomenaanddecouplethem to be able tosuccessfullymodelTED. Later, in Section3.6,wediscussour work on modelingtheevo-lution of theinitial implantcascade.Mainly weverify thevalidity of someof thecommonassumptionsmadefor theinitial conditions.Theseassumptionsareusedasabasisfor oursimulationsin therestof this work.

3.1 Initial damage

At first glance,the predictionof defectevolution after implantationmight appearverydifficult. Large numbersof point defectsarecreated,andthey cancoalesceinto variousformsof extendeddefects.However, it is possibleto makesomesimplifying assumptions.Lookingatthedamagecreatedby theion implantationprocess,wecanseethatthenumberof Frenkel pairsgeneratedis muchhigherthanthenumberof implantedions(Fig. 3.1). Infact, the interstitial andvacancy curvesarealmostindistinguishablefrom eachother, butthereis a vacancy-rich region nearthesurfaceandaninterstitial-richregion deeperin thesubstrate.This stemsfrom thefactthattheimplantationdrivessomesilicon atomsdeeperinto the substrate.Recombinationof this cascade,however, would leave us with a net“ " 1” damage,whereeachincomingion displacesonesiliconatom,suchthatthenetI

�V

doseis equalto the implantdose.For light atomssuchasboron,this separationbetweenthe net interstitial andvacancy profiles is minimal. Hencea “plus-one” model [46] hasbeenverysuccessfulin predictingTED.

This picturemaysoundvery simplifiedbut hasreceivedstrongexperimentalsupport.For sub-amorphizingimplants,Chenet al. [22] showedthattheamountof transientdiffu-sioncausedby aSi implantwasindependentof bothdoseandimplanttemperature.Sincebothfactorsaffect thenumberof Frenkel pairsremainingaftertheimplant,it supportsthenotionthat thenumberof pairscreatedby implantationis not a primaryvariablein TED.

33

Total Interstitials Total Vacancies Net Interstitials Net Vacancies

|�0.00� |�

0.02� |�0.04� |�

0.06� |�0.08� |�

0.10� |�0.12�|� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� ||� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� ||� |� ||� |� |� |� |� |� |� |� |� |� |� |� ||� |� |� |� |� |� |� |� |� |� |� |� |� |� ||� |� |� |�

1016

1017

1018

1019

1020

1021

1022

Depth (� µm)

Con

cent

ratio

n (c

m� -3 )

Figure3.1: Total andnetdamagecreatedby a 40keV, 5 � 1013cm� 2 Si implant. MonteCarlosimulationswith TRIM [10].

Similarly Gileset al. [47] implantedphosphorusat normalincidenceanda high tilt anglewith theenergy adjustedto have similar projectedrange.Again thetotal amountof TEDwasthesamedespitethehigherenergy tilted implantcreatingmoreFrenkel pairs.

Hence,the conclusionfrom presentexperimentaldataseemsto indicatethat the to-tal net damagecreatedis insensitive to the detailsof the Frenkel pair generationduringimplantationand mainly sensitive to the distribution of implantedions. However, thisconvenientscenarioneedsrevision whenconsideringvery low dose,high massor veryhigh energy implantswhenthedetailsof theinitial damagedistribution leadto deviationsfrom the“plus-one”model.Henceit is necessaryto carefullyselecttheinitial conditionsdependingon a particularimplant. This will bediscussedfurther in Section3.6. For ex-ample,thesituationis muchdifferentfor ahigh energy implant,wheretheinterstitialsarekicked in deeperinto the silicon leaving behinda vacancy rich region nearthe surface.Fig. 3.2shows simulationsfrom TRIM [10] a MonteCarlo ion implantationsimulatorofa 2 MeV Si implant. Notethatthereis a distinctnetvacancy rich region nearthesurface.The vacancy rich region extendswell over 1µm and hasnet vacancy concentrationsof 1018 cm� 3.

34

|�0.0J |�

0.5J |�1.0J |�

1.5J |�2.0J |�

2.5J |�3.0J|� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� ||� |� |� |� |� |� |� |� |� |� |� ||� |� ||� |� |� |� |� |� |� |� |� ||� |� |�TRIM Simulation

Net I-V�

Net V-I�

1016

1017

1018

1019

1020

1021

Depth (� µm)

Con

cent

ratio

n (c

m� -3 )Si Implant�2 MeV, 1x10� 16 cm-2

Figure3.2: Monte Carlo simulationshowing net initial distributionsof interstitialsandvacanciesfollowing a 2 MeV, 1 � 1016cm� 2 Si implant. Thevacancy rich layer extendswell overa µm.

3.2 Early work on boron deactivation and TED

Early work on BoronTED concentratedon experimentalobservations,measuringtheex-tent of TED. After the inventionof rapid thermalannealing(RTA), first observationsofTED werereported:evenfor very shortannealingtimestherewasa considerableamountof dopantdiffusion.

Most of the early papers[8, 73, 88] dealwith dopantimplantsinto silicon. A (high)doseof boron,phosphorusor arsenicwasimplantedinto silicon, andafter an RTA stepthefinal profile wasmeasuredto determinetheextentof TED. Angelucciet al. observedthatboronandphosphorusshow TED to a largeextent,but arsenicshows little TED, andantimony showsalmostno TED [8, 9]. To show this,Angelucciformeduniform layersofthe dopants,patternedthe sample,createddamageby silicon implantationandannealedat varioustimesandtemperatures.For B andP, theSi-implantedregionsshoweda largeincreasein junctiondepth,whereasfor As andSb,thedifferencewasminimal.

Combiningthe knowledgeprimary diffusion mechanismsof individual dopantswiththe observationson TED for differentdopants,we may concludethat TED is relatedto

35

interstitial assisteddiffusion. Indeed,after an ion implantation,there is a high super-saturationof interstitialsdueto the damageof the implant, andthus,this result is quitelogical.

If we look at thetimebehavior of TED, wecanobservethattheenhancementis nearlyindependentof the ion-implantdamagefor initial timesandafter someperiod(durationof TED) theenhancementgoesaway [8, 79], suchthatwe areleft with normaldiffusionwhich is many ordersof magnitudesmaller. This meansthat for earlystagesof TED theexcessinterstitialconcentrationis approximatelyfixed,andaftersometime it dropsto itsequilibriumvalue.

Anotherseeminglyanomalousobservationis thattheamountof TED is largerat lowertemperatures[73, 79]. This canbeexplainedin the following fashion:Although thedif-fusionof dopantsis fasterat highertemperatures,thedurationof TED is muchshorterathighertemperatures,sothattheoverall junctionmovementgetssmallerasthetemperatureis increased.

Hence,thefollowing conclusionscanbemade:� TED iscausedbyexcessinterstitialconcentrationthatpersistsafterion implantation.� Theexcessinterstitial concentrationremainsapproximatelyfixedduringTED, andthendropsto its equilibriumvalue.� At highertemperaturestheexcessinterstitialconcentrationdisappearsmorerapidly,i.e. thedurationof TED is shorter.

3.3 Interstitial clusters

As mentionedin Section3.2, theexcessinterstitial concentrationremainsapproximatelyfixedduringTED, andthendropsto its equilibriumvalue.This tells usthattheremustbea mechanismthatstoresthe interstitialscreatedby the implantdamageandthenreleasesthemduringTED, actingasa “source”of interstitials. In fact, if sucha meta-stablestatefor interstitialsdidn’t exist, they would rapidly diffuseto the surfaceandTED would beover in a veryshorttime.

Experimentsby Eagleshamet al. revealedtheactualsourceof the interstitialsduringTED[28,35]. They createddamageby implantingSi into Siandthenannealedthesamplesat varioustemperatures.They thenperformedplan-view andcrosssectionalTransmissionElectronMicroscopy (TEM) onthesamples.They clearlysaw thedefectsthatstoreexcessinterstitials.Thesedefectsaretheso-called“rod-like” or “ 311� ” defects.

The atomicstructureof 311� defectshasbeenonly recentlyresolved [93]. It is be-lievedthatinterstitialsform chainsalong � 110� directionandthesechainscometogether

36

Implant Chemical� Active

|�0.0J |�

0.1J |�0.2J |�

0.3J |�0.4J |�

0.5J|� |� |� |� |� |� |� |� |� |�|� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� |� ||� |� |� |� |� |� |� |� |� |� |� ||� |� ||� |� |� |� |� |� |� |� |� ||� |� |�

Data from Solmi

1016

1017

1018

1019

1020

1021

Depth (� µm)

Con

cent

ratio

n (c

m� -3 )

2 x 10� 15 cm-2, 20 keV850� oC, 2h

� � � � � � � � � � � � � � � � � � � � � � � � � � � � �

Figure 3.3: Boron chemical(SIMS) and activation (SRP)profiles after annealingof a2 � 1015cm� 2 doseimplant at 850� C for 2 h. The peakof the implantedboronprofileis immobileandinactive to concentrationswell below equilibriumsolubility (from Solmiet al. [90]). Equilibrium boronsolid solubility at 850� C 5 � 1019 cm� 3.

to form a 311� plane. This defectcan get very long (about1µm) in the � 110� di-rection, henceis given the name“rod-like” defects. The fact that the time neededfordissolutionof 311� defectsis equalto thedurationof TED [35] is anexcellentindicatorthat 311� defectsare the sourceof the interstitialsduring TED. More recently, Cow-ernet al. haveshown thatat low temperaturessmall interstitialclustersarealsoimportant[27]. Thesesmallinterstitialclusters(ICs)beinglessstablethan 311� defects,maintainamuchhighersupersaturationclearlyevidentat lower temperatures.On furtherannealing,theseICsappearto transforminto themorestable 311� defectsby a ripeningtransition.

3.4 Boron interstitial clusters

A strikingfeatureof profilesfollowing implantationis thatpreviouslysubstitutionaldopantmaybecomenon-substitutional,asevidencedby lossof electricalactivity andinability todiffuse. Fig. 3.3 shows a typical implant profile after an anneal. It is clearthat mostofboronat thepeakis inactiveandimmobilewhereastheboronat thetail hasundergonean

37

Final Initial

|�0� |�

200� |�400� |�

600� |�800�|� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� |� |� |� |� |� |� |� |� |�

|� |� |� |� |� |� ||� |�

||

|� |� |� |� |� |� |�

Depth (nm)�

Data from Lucent,�

1017

1018

1019

1020

Con

cent

ratio

n (

cm� -3 )5 x 10� 13 cm-2 Si, 790� oC/10 min

Figure3.4: Deltadopedboronmarker layerafterTED drivenby a 5 � 1013cm� 2, 40 keVSi implantandannealedat 790� C for 10 mins.

enhanceddiffusion.Earlywork by Solmietal. showedapparentsolubility almostconstantwith dosebut muchlower thansolidsolubility.

Observationsby Cowern et al. [26, 28] suggestthat in systemswhereB is presentin largedoses,excessinterstitialshelpboronatomsto form boronclustersandarethem-selvesincorporatedinto theseclusters(so-calledBoronInterstitialClusters,BICs),therebyreducingthe numberof mobile boron atoms. Although the BICs are not visible evenwith high resolutionTEM, the diffusion profilesindicatethat boronis becomingimmo-bile whereit is presentat high doses. Boron marker layer experimentsof Stolk et al.[91] show this effect very clearly. In theseexperimentsmarker layersweregrown usingmolecular-beamepitaxy(MBE) andthenimplantedwith Si. Thus,thedamagedoseis con-trolled independentlyfrom thedopantdose.Fig. 3.4shows resdistribution aftera 40 keV5 � 1013cm� 2 Si implantannealedat 790� C for 10 mins. Theprojectedrange(Rp) of theSi implantis closeto thefirst boronspike. However, interstitialsfrom theSi implanthaveto diffuseinto thesampleto reachthedeeperspikes. It wasobservedthata considerablepartof thenearsurfaceboronspikeremainimmobileduringannealingwhereasthedeeperspikesexhibit regularbroadeningwithout any immobileB. They alsofoundthatsampleswith lowerdopingonly exhibit anenhanceddiffusionandnot animmobilepeak.Further,they observedtheboronpeaksexist evenafter thedissolutionof all 311� defects.In the

38

� Data Quadratic fit

|�0� |�

2� |�4� |�

6� |�8� |�

10|�

12

|�0.0

|�1.0

|�2.0

|�3.0 |� |� |� |� |� |� |�

| 

| 

| 

| 

Data from Haynes et al.,¡

B concentration (cm¢ -3)

In

ters

titia

l den

sity

(101

3 cm

-2)

60 keV 1 x 10£

14 cm-2 Si, 740oC/15 min

¤ ¤ ¤¤ ¤

¤Figure3.5: Areadensityof interstitialscontainedin ¥ 311¦ defectsasa functionof back-groundboronconcentrationfollowing annealat 740§ C for 15 mins. The solid line is afit to the dataassuminga quadraticdependenceon B concentration.This would be thedependenceof aclusterof typeB2mIm.

absenceof enoughinterstitials,theborononly showsenhanceddiffusionasseenin thelastpeak. It canbenotedthata higherdosemarker layershows considerableclusteringevenfor the low doseSi implant. This suggestsa high interstitial supersaturationis necessaryfor nucleationof theboronclusterprecursor. Boronclustersmustgrow by absorbingin-terstitials.This would alsoexplain thedecreasein effective solid solubility with increasein interstitialsuper-saturations.Onceformed,theseclustersarefairly stableandcanexistin theabsenceof any I super-saturations.

Hayneset al. [55] measuredthe total numberof interstitialsassociatedwith ¥ 311¦defectsformedafterSi implantationfor differentbackgroundborondoping. They foundthefractionof excessinterstitialstrappedin ¥ 311¦ defectsdecreasedasa functionof theboron concentration,up to nearlycompletedisappearanceof the ¥ 311¦ defectsat highborondoping.Again, this clearlyindicatestheformationof boroninterstitialclustersthatcompetewith ¥ 311¦ defectsfor interstitials.Fromtheir results,it is possibleto establishupperandlowerboundsfor theaveragenumberof B atomsthatarerequiredto effectively

39

as grown anneal

|

0© |

100© |

200© |

300©|ª |ª |ª |ª |ª |« |ª |ª

|ª |ª |ª |ª |ª |ª |« |ª

|ª |ª |ª |ª |ª |ª |ª |« |ª

|ª |ª |ª |ª |ª |ª |ª |« |¬ |¬ |¬ |¬

|­ |­ |­ |­ |­ |® |­ |­ |­ |­ |­ |­ |­ |­ |®

|­ |­ |­ |­ |­ |­ ||­ |®

||

|­ |­ |­ |­ |­ |­ |®

Depth (nm)¯

Data from Pelaz et al., °

1017

1018

1019

1020

Con

cent

ratio

n (

cm± -3 )2 x 1013 Si, 2 x 1013 B, 800² oC/35 min

Figure3.6: Clusteringdrivenby a 2 ³ 1013cm 2, 40 keV Si implantfor a B marker layerof doses2 ³ 1013cm 2, annealedat 800§ C for 35 mins.

removeoneexcessinterstitialfrom thefreeinterstitialpopulationin Si. Thiswasestimatedto bemorethan2 but lessthanabout25.

Pelazet al. [83] performedsimilar experimentsto Stolket al. on deltadopedsuperlat-ticesbut variedthemarker layerborondoseandSi implantdose.Figs.3.6 and3.7 showtheannealedprofilesfor two differentB marker layerdosesfor a2 ³ 1013cm 2, 40keV Siimplantandannealedat 800§ C for 35 mins. It is apparentfrom Fig. 3.7asmallinterstitialdosecanimmobilizeseveraltimesits own doseof boron.

Hence,thefollowing conclusionsarein order:µ Boronapparentsolubility is loweredbelow solidsolubility becauseof agglomerationwith interstitials.µ Formationof boroninterstitialclustersalsodecreaseinterstitialsboundto ¥ 311¦ .µ A smallinterstitialdoseis enoughto immobilizeamuchlargerborondosesuggest-ing anaverageB/I sizeof around3 – 5.µ Boronclusteringoccursonly underhigh I super-saturations.

40

as grown anneal

|

0© |

100© |

200© |

300©|« |ª |ª |ª |ª |ª |ª |ª

|ª |« |ª |ª |ª |ª |ª |ª

|ª |ª |« |ª |ª |ª |ª |ª

|ª |ª |ª |« |ª |ª |ª |ª |¬ |¬ |¬ |¬

|® ||­ |­ |­ |­ |­ ||­ |® |­ |­ |­ |­ |­ |­ |­ |­ |®

|­ |­ |­ |­ |­ |­ |­ |­ |®

|­ |­ |­ |­

Depth (nm)¯

Data from Pelaz et al., °

1017

1018

1019

1020

C

once

ntra

tion

(cm± -3 )

2 x 1013 Si, 9 x 1013 B, 800² oC/35 min

Figure3.7: Clusteringdrivenby a 2 ³ 1013cm 2, 40keV Si implant for a B marker layerof doses9 ³ 1013cm 2, annealedat 800§ C for 35 mins. Note thata low interstitial dosecandeactivateamuchlargerfractionof boron.µ Boronclustersaremorestablethan ¥ 311¦ defects.

3.5 Vacancyclusters

It hasbeenarguedin Section3.1 that most of the vacanciesfrom the implant damagequickly recombineduring the early stagesof annealing.However, it wasshown in Sec-tion 3.1 that during annealingof higherenergy or larger massimplantsit is possibleva-canciesmayexist evenafterrecombination.

Severalexperimentshaveindicatedthepresenceof thisvacancy rich region. Enhanceddiffusion of Sb marker layershave beenobserved after MeV Si implants[36]. Metallicimpuritiesgetternotonly atRp theprojectedrangeof theimplantbut alsoatRp/2 for highenergy implants[14]. Thegetteringat Rp is attributedto interstitial typedefects,whereasthegetteringatRp/2 is explainedby thepresenceof theexcessvacanciesfrom theimplant.It is alsopossibleto createa vacancy rich region by highermassimplants. Pb implantshave beenfound to decreaseboronclusteringin shallow boronmarker layers[56]. This

41

vacancy rich layercanbeusedasatool to reducethedepthandincreaseactivationof boronor phosphorusjunctions.For instance,useof MeV Si implantshavebeenfoundto reducethe interstitialsin endof rangeloops from high doseimplants[85]. Sincethe vacancyinducedeffectsseemto last over a periodof annealingtime [36], vacanciesmost likelygrow into largervacancy clustersor voids.Modelsfor vacancy clusteringarediscussedinChapter6.

3.6 Simulation of initial damage

It hasbeenpointedoutin Section3.1thatmostof therecombinationoccursquickly leavinga netdamageverysimilar to a “plus one” modelfor light atomslikeboron.However, I/Vrecombinationis not theonly processoccurringduringthepostimplantphase.Interstitialsandvacanciescanalsodiffuseandrecombineat thesurface. They canalsoagglomerateinto extendeddefects.Herewediscusseachof theseeffectsseparately.

3.6.1 Effect of surface

It is possiblefor a considerablefractionof the fastermoving speciesto recombineat thesurfaceandleavebehindanetexcessof theoppositetypedefect.This is becausewhenthedefectdensityis relatively small, the fasterdiffusingspeciescanreachthesurfacebeforeencounteringthe oppositetype defect. As discussedin Section2.4, calculationssuggestthat the diffusivity of vacanciesis higherthanthe diffusivity of interstitials,particularlyat lower temperatures.Thuswe would expecta significantnumberof the vacanciesinthe vacancy-rich region nearthe surfaceto recombineat the surface. Thus,we will endup with muchhigher“plus” valuesfor low doseor high atomicmassimplants. Fig. 3.8shows a simulationconsideringthedamageannealing.TRIM simulationresultsareusedasinitial damage.It maybenotedthat for moderateor high implantdosesI/V recombi-nationquickly leadsto a approximately“+1” distribution (particularly for lighter atomsandlowerenergies),thusvalidatingtheeffectivenessof the“+1” approach.A morerigor-oustreatmentof this “+n” factorinvolvestheinclusionof correlationfactorsbetweentheinterstitialandvacancy cascades[15] andis beyondthescopeof thepresentstudy.

Experimentshave shown thatTED scalesnon-linearlywith doseandseemsto almostsaturateat low doses.Thisbehavior cannotbesatisfactorilyexplainedusinga“+1” model.We foundthatusingthe“+n” factorobtainedfrom simulationsof thefull I andV profilesalong with fast vacancy diffusion satisfactorily explains the dosedependenceof boronmarker layer experimentsfor silicon implants[80] as shown in Fig. 3.9. As shown inFig. 3.10,usingthis samemethodologyfor boronTED, we cansuccessfullypredictlowdoseTED, while usinga “+1” modelunder-estimatesthetotal amountof diffusion. Notethatfor low dosesimulations,clusteringis minimalandthemodelusedfor BICshaslittleor no impact.

42

|¶ |· |· |· |· |· |· |· |· |¶ |· |· |· |· |· |· |· |· |¶ |· |· |· |· |· |· |· |· |¶ |·|¸0.0

|¸5.0

|¸10.0

|¸15.0

|¸20.0 |¹ |º |º |º |º |º |º |º |º |¹ |º |º |º |º |º |º |º |º |¹ |º |º |º |º |º |º |º |º |¹ |º

|»

|»

|»

|»

|» ’+

N’ f

acto

r ¼40keV B implant½

1012 1013 1014 1015

Implant Dose (cm¾ -2)

E¿

b = 0.2 eV

E¿

b = 0

700À oC,time = 1Á µs

Figure3.8: Net interstitial doseremainingafter the recombinationprocessstartingfromthetotal initial defectdistributions.Eb is thebarrierto I/V recombination.

3.6.2 Effect of clustering during recombination

For a accuratetreatmentof the damageannealingprocessit is necessaryto alsoincludeclusteringof both interstitialsandvacanciesasthesemay decreasethe efficiency of therecombinationprocess.Recentexperimentsof Cowernet al. [27] have shown thatat lowtemperaturessmallinterstitialclustersarethemainsourceof interstitials.However, theva-lidity of usinga “+1” modelfor parameterextractionatsuchlow temperaturesis not clear[27]. For modelinginterstitial clusters,we usethe interstitial modelderived by Cowernet al. [27]. Usingparametersfrom Cowernet al. [27] gave goodmatchto theexperimen-tal resultsusinga “+1” approach.Themodelderivedin Sec.6 [19] is usedfor modelingthe evolution of vacancy clusters.As seenin Fig. 3.11usingthe full damageleadsto agoodmatchto theexperimentaldataof Cowernet al. It canbenotedthattheinitial super-saturationis dominatedby small interstitial clustersthat ripen into larger ¥ 311¦ defects.Also shown in Fig. 3.11 is comparisonof super-saturationsusingthe full initial cascadeto usinga “+1” approximation.Both modelswerefound to yield almostidenticalsuper-saturations.However looking at thetotal numberof vacanciesandinterstitialsin clusters,

43

 Data (Packan) +1 Model Full I/V Model

|· |· |· |· |· |¶ |· |· |· |· |· |· |· |· |¶ |· |· |· |· |· |· |· |· |¶ |·|¸0

|¸40

|¸80

|¸120 |º |º |º |º |º |¹ |º |º |º |º |º |º |º |º |¹ |º |º |º |º |º |º |º |º |¹ |º

|»

|»

|»

|»

1012 1013 1014

Implant Dose (cm-2)

(D

t)0.

5 (

nm) Ã Ã Ã

Ã

Figure3.9: Dosedependenceof TED measuredfor a boronmarker layer following 200keV Si implants. A “+n” modelbasedon the full initial defectprofile is ableto predictdiffusionbehaviour.

it canbenoted(Fig. 3.12)that therecombinationprocessis not completeandsignificantvacancy clustersarepresenttill around600sec.This doesnot affect thesuper-saturationasit is governedby thesmall interstitialclusters.This alsoconfirmsthevalidity of usinga “+1” modelfor lower temperatureswhererecombinationmaynot havebeencompleted.

44

As implÄ Data +4.2 Model +1 Model

|

0.0Å |

0.2Å |

0.4Å |

0.6Å |

0.8Å|ª |ª |ª |ª |ª |« |ª|ª |ª |ª |ª |ª |ª |ª |«

|ª |ª |ª |ª |ª |ª |ª |ª |«|ª |ª |ª |ª |¬ |¬ |¬ |¬ |¬

|­ |­ |­ |­ |­ |® |­ |­ |­ |­ |­ |­ |­ |­ |®|

|­ |­ |­ |­ |­ |­ |­ |®

|­ |­ |­ |­

1016

1017

1018

Depth (Æ µm)

B

Con

cent

ratio

n (

cmÇ -3 )

40 keV, 1 x 10È 13 cm-2 B800² oC anneal 1 hÉ É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É ÉÉ É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É É

Figure3.10:Predictionof B TED for 40keV 1013cm 2 B implant.A “+1” modelpredictslessdiffusion than seenexperimentally. A “+n” model basedon the full initial defectprofile is ableto predictdiffusionbehaviour. Datais from Intel Corp. [44].

45

+1 full I/V

| | | |

|« |«|« |«

|¬ |¬ |¬ |¬

|® |® |® |®

Time (s)10© 0 10

© 2 10© 4 10

© 6

102

104

106

108

sup

er s

atur

atio

n (CÊ I/C

I* )

600Ë oC

800oC

Ì Ì Ì Ì ÌÍ Í Í Í Í Í Í Í Í Í Í

Figure3.11: Interstitialsuper-saturationsat 600§ C and800§ C obtainedusingfull damage(bold lines)andusinga “+1” model(dashes).Notethatthesuper-saturationsobtainedarealmostindependentof theinitial conditions.

46

V in clusters I in clusters Net I

| | | | ||«|«

|«|« |¬ |¬ |¬ |¬ |¬

|®|®

|®

|®

Time (s)10© -6 10

© -3 10© 0 10

© 3 10© 6

1010

1012

1014

1016

Con

cent

ratio

n (c

m± -3 )

Figure3.12: Figureshows evolution of interstitialandvacancy clustersduringannealingof a 2 ³ 1013cm 2 Si implant at 600§ C. The vacanciesexist till around600 sec,afterwhich theinterstitialstrappedin interstitialclustersis closeto a “+1”.

47

3.7 Summary

In this chapter, we have reviewed the experimentsandmodelsneededfor simulationofthe evolution of a ion implantedsilicon during annealing.Particularly, we reviewed ex-perimentsthat highlight the needfor modelinginterstial, vacancy andboron/interstitialclustersfor successfulprocesssimulation. In Section3.6 we showed our simulationstojustify theuseof a “+1” approachfor the initial recombinationprocess.In particular, wefoundin Section3.6deviationsto the“+1” modelfor low doseimplantswherethesurfaceplaysa importantrole.

48

Chapter 4

Boron Cluster Models

In this chapter, we will describeour work on differentapproachesfor modelingof boroninterstitial clusters. As illustratedin Fig. 4.1, thereis a hugearray of potentialclustercompositions.It is possibleto model this systemwith a variety of approaches.Exam-plesincludeeithercluster-basedor moment-basedapproaches.Clustermodelsconsiderasubsetof discretesmallersizedclusters,whereasmoment-basedmodelslike Kinetic Pre-cipitationModel (KPM) [23] considera wide rangeof clustersizesbut make assumptionaboutsmoothchangesin propertieswith size,andlimits thesystemto anarrowerrangeofcompositions.

4.1 Kinetic precipitation model

Theaggregationprocessis drivenby theminimizationof thechangein freeenergy withclustering. Herewe arerestatingthe approachof Clejanet al. [24, 32] usingmomentsto describethe evolution of the sizedistribution. This energy canbe written asthe sumof a volumeterm which representsthe changein energy uponaddingeithera boronorinterstitialto theBnIm cluster, plustheexcesssurfaceenergy andstrainenergiesassociatedwith finite sizeprecipitates:

∆Gn Îm ÏÑÐ nkT ln Ò CB

CBss Ó Ð mkT ln Ò CI

CI Ô ÓÖÕ ∆Gsurfn Îm Õ ∆Gstress

n Îm × (4.1)

Weassumethattheexcesssurfaceenergy is asmoothfunctionof sizegivenby

∆Gsurfn Îm Ï c1na1 Õ c2na2 Ø (4.2)

where1 Ù a1 Ù a2 ÙÛÚCÚCÚ . The first term correspondsto theasymptoticbehavior at largesizes,which is generallyassociatedwith thedependenceof theactivesurfaceareaonsize(BICsareassumedto besphericalandhencea1 Ï 2Ü 3), andtheothertermsarecorrections

49

BI

B

Bi

BI 2

I

B I

Bi

I

B I2

B I3B I2

Bi Bi

B2

I

B I23 B I24

Bi BiI I

B I3 B I4

B I B I

B

I

B IB I

B

I

B I B I

Bi BiI

B I B I

B I B I

B

I

3 3 33

3

44

4

4

4 4B I3 4 6

5

5

5

5

5

6

6

7

2

3

Bi

2 2

Bi I Bi BiI I Bi BiI I

2

Bi Bi BiI I Bi BiI II

B I 4

Bi I Bi BiI I Bi I I

Bi

I

4

2

Bi

Bi

I

Bi

Bi

I

Cluster

KPM

Figure4.1: Array of possibleBICs. Also indicatedschematicallyaretherangeof compo-sitionsconsideredby clusterandKPM approaches.

for thedeviationof thefreeenergy from thisasymptoticbehavior atsmallsizes.Thestressenergy canbefoundfrom elasticitytheoryto beof theform,

∆Gstressn Îm Ï Hn Õ α

n Ý m Ð γnÞ 2 × (4.3)

If therewere no point defectsupersaturation,the optimum numberof incorporatedinterstitialswould be mÔ Ï γn. However, whenCI Ù C ÔI , the optimumnumberof pointdefectsincorporatedcanbefoundby minimizing thefreeenergy to be:

mÔ Ï n Ò γ Õ kT2α

log Ý CI Ü C ÔI Þ Ó Ø (4.4)

which leadsto aneffectivesolid solubility of:

Ceffss Ï Css Ò CI

C ÔI Ó ´ γexp ß Ð kT

4α Ý log Ý CI Ü C ÔI ÞCÞ 2 à × (4.5)

It is evident from theabove equationthat theeffective solubility decreaseswith increasein interstitialsuper-saturationasobservedexperimentally. Thetypicalcompositionrangesdescribedby this approachis shown in Fig. 4.1.

Thesizedistributionfor sizeslargerthank Ð 1 is representedin termsof asmallnumber

50

of momentsasdiscussedby Clejanet al. [23]. Themomentsaredefinedas:

mi Ï ∞

∑ná k

ni fn Ø (4.6)

wherei Ï 0 Ø 1 Ø 2 Ø ×C×C× . Thezerothordermomentof thedistribution is simply theprecipitatedensity, while the first momentcorrespondsto the densityof precipitatedsoluteatoms.Higherordermomentsfurtherdescribetheshapeof thesizedistribution. This transformsthesystemof equationsto thefollowing set[23]:

∂mi

∂t Ï kiRk Õ ∞

∑ná k â Ý n Õ 1Þ i Ð ni ã Rn (4.7)

NotethatthesumsovertheRn canall bewritten in termsof sumsover fn, nfn, etc.Hence,they canbecalculatedfrom themomentsif momentsareusedto describethedistribution.Sincenofinite numberof momentscanfully describeafull distribution,weneedaclosureassumption,which is an assumptionaboutthe form of the distribution. Sincenothingisknown aboutthe distribution over sizespace,it is logical to usean energy minimizingclosureassumption[23]. The energy minimizing closureassumptionassumesthat thedistribution is the onethat minimizesthe free energy, given the moments.The resultingsystemis a threemomentsystemin which the first threemoments(m0

Ø m1 andm2) aresolved[23, 43].

Settingk Ï 2 in Eq.4.7andoptimizingfor theenergy parameterswefind wecanmatchalargeamountof availabledata.Figs.4.2,4.3and4.4show representativefits of this threemomentmodel[17] to boronimplantannealdatafrom Intel [44].

51

As implant Data 1 hr 4 hr

|

0.0Å |

0.2Å |

0.4Å |

0.6Å |

0.8Å|ª |ª |ª |ª |ª |« |ª |ª |ª|ª |ª |ª |ª |ª |« |ª |ª |ª

|ª |ª |ª |ª |ª |« |ª |ª |ª|ª |ª |ª |ª |ª |« |ª |ª |¬ |¬ |¬ |¬ |¬

|­ |­ |­ |­ |­ |® |­ |­ |­ |­ |­ |­ |­ |­ |®|­ |­ |­ |­ |­ |­ |­ |­ |®

|­ |­ |­ |­ |­ |­ |­ |­ |®

||­

1016

1017

1018

1019

Depth (Æ µm)

Con

cent

ratio

n (c

m± -3 )

40 keV, 2 x 10È 14cm-2 B 700ä oC anneal

Figure4.2: Simulationsresultsfor a 2 ³ 1014 cm 2, 40 keV B implantannealedat 700§ CusingKPM modelcomparedto datafrom Intel Corp. [44].

52

As impl Data 15 mins 1 hr

|

0.0Å |

0.2Å |

0.4Å |

0.6Å |

0.8Å|ª |ª |ª |ª |ª |« |ª |ª |ª|ª |ª |ª |ª |ª |« |ª |ª |ª

|ª |ª |ª |ª |ª |« |ª |ª |ª|ª |ª |ª |ª |ª |« |ª |ª |¬ |¬ |¬ |¬ |¬

|­ |­ |­ |­ |­ |® |­ |­ |­ |­ |­ |­ |­ |­ |®|­ |­ |­ |­ |­ |­ |­ |­ |®

|­ |­ |­ |­ |­ |­ |­ |­ |®

||­

1016

1017

1018

1019

Depth (Æ µm)

B

Con

cent

ratio

n (

cmÇ -3 )

40 keV, 2 x 10È 14 cm-2 B800² oC anneal

Figure4.3: Simulationsresultsfor a 2 ³ 1014 cm 2, 40 keV B implantannealedat 800§ CusingKPM modelcomparedto datafrom Intel Corp. [44].

53

As impl Data 5 min 1 hr

|

0.0Å |

0.4Å |

0.8Å|ª |ª |ª |ª |ª |« |ª |ª |ª|ª |ª |ª |ª |ª |« |ª |ª |ª

|ª |ª |ª |ª |ª |« |ª |ª |ª|ª |ª |ª |ª |ª |« |ª |ª |¬ |¬ |¬

|­ |­ |­ |­ |­ |® |­ |­ |­ |­ |­ |­ |­ |­ |®|­ |­ |­ |­ |­ |­ |­ |­ |®

|­ |­ |­ |­ |­ |­ |­ |­ |®

||­

1016

1017

1018

1019

Depth (Æ µm)

B

Con

cent

ratio

n (

cmÇ -3 )

80 keV, 2 x 10² 14 cm-2 B800² oC anneal

Figure4.4: Simulationsresultsfor a 2 ³ 1014cm 2, 80 keV B implantannealedat 800§ CusingKPM model,comparedto datafrom Intel Corp.

54

BI

B

Bi

B I23 B I24B I2 2

B I3B I2

B2

BI 2

Bi

Bi

Bi

Bi

Bi

I

I I I

I

Figure4.5: Clusterreactionsconsideredin thefull modelasgivenby fundamentalphysicalcalculations[102].

4.2 Multi cluster models

Anotherapproachto modelBICsis to considerafinite setof discreteclustersasshown forexample(dottedlines) in Fig. 4.1. Pelazet al. [83] derivedsucha modelwith theclusterenergeticsoptimizedto fit data.For a morephysicalbasis,we useclusterenergiescalcu-latedby ab-initio methodsatLawrenceLivermoreNationalLabs[102]. In previouswork,Caturlaet al. [60] andLilak et al. [67] presentedboronclusteringmodelsbasedon thesamecalculationswhich we usein this work. In eachcase,they considereda largerangeof clusterssuchasshown in Fig. 4.5,with anassociatedlargesetof continuityequationsandparameters.A problemwith theseapproachesis thatthey leadto complicatedmodelswith associatedlongsimulationtimesandlargesetsof non-uniqueparameters.Henceit isnecessaryto derivesimplermodelsfor effectiveusein ProcessSimulators.

As shown in Fig. 4.5eachclustercangrow/dissolveby theaddition/releaseof asiliconself-interstialor boron interstitial. For example,a substitutionalboroncanreactwith aboroninterstitial to form animmobileB2I whichcanfurtherreactwith anotherinterstitialto form a B2I2 clusteror with a mobile interstitialboron(Bi) to give B3I2. Therearethustwo possiblesetof reactions:

BnIm Õ I å BnImæ 1Ø (4.8)

BnIm Õ Bi å Bnæ 1Imæ 1 × (4.9)

with associatedratesgivenby theequations:

RBnIm ç I Ï 4πaDI è CBnImCI Ð CBnImé 1

KBnIm ç I ê Ø (4.10)

55

Table4.1: Clusterenergeticsbasedonatomisticcalculations[60] usedfor thefull system.

Reaction BindingEnergy (eV)B + I å BI 1.0B + I å Bi 0.7

Bi + B å B2I 1.3B2 + I å B2I 1.6

B2I + I å B2I2 1.2BI + Bi å B2I2 1.5BI + I å BI2 1.4B3 + I å B3I 3.3

B2 + Bi å B3I 2.8B2I + Bi å B3I2 Ð 0.1B3I + I å B3I2 Ð 1.3

B3I + Bi å B4I2 1.5

RBnIm ç Bi Ï 4πaDBi è CBnImCBi Ð CBné 1Imé 1

KBnIm ç Bi ê × (4.11)

Clusterenergeticscalculationsfrom Caturlaet al. [60] wereusedasthebasisfor thesimulations,with 10 differentclustersconsidered:BI, BI2, B2I, B2I2, B3I, B3I2, B4I2,B2, B3. The clusterenergiesusedin the simulationaretabulatedin Table4.1. It shouldbenotedthatusingdissociationenergiesfrom Caturlaet al. [60] andfollowing differentpathwaysfor the formationof B2I andB2I2 from B andI yields differentbinding ener-gies.Hence,anintermediateenergy waschosen.Thischoicedoesnot changetherelativestabilityof clusters.

4.2.1 Analysisof model

We now try to derive a simplemodel from this multi clustermodel. The large bindingenergiesfor the formationof B3I suggeststhe importanceof B3I clusters.However, it isnecessaryto look atthekineticsandenergeticsof all theseprocessesto identify thenumberof equationsandclusterconcentrationsthatneedto be solved to modelthis system.Forexample, interstitial rich clustersmay be more important in the presenceof the higherinterstitialsupersaturationstypicalof theveryearlystagesof annealing.

We first look at thekineticsof thedifferentprocesses.Concentrationsof clustersthatarein dynamicequilibriumwith the free interstitial andboronconcentrationscanbe ex-pressedassimpleanalyticexpressions(e.g.CBnIm Ï KBnImCn

BCmI ). Fig. 4.6shows thetime

evolutionof clusterconcentrationsnormalizedby theirequilibriumvalue(CBnIm Ü KBnImCnBCm

I )

56

for eachclusterspecies.A valueof ’1’ indicatesthatthesystemis in dynamicequilibriumwith the free B andI. Thesenormalizedvaluesarecalculatedat the peakof the implantprofile. Our analysisof this systemfind thatmostof theclustersrapidly achievedynamicequilibrium with the freeboronandinterstitial concentrations,suggestingthepossibilityof reducingthe numberof equationsandparametersneededto describethe system.Asshown in Fig. 4.6, except for B3I andB4I2, all the clustersreachdynamicequilibriumwith the B andI concentrationswithin 0.1 sec. B3I andB4I2 arealso in local dynamicequilibriumwith eachotherasdemonstratedby their overlappingcurvesin Fig. 4.6.

We next identify themoststableclustersfor interstitialsupersaturationscharacteristicof differentannealingtimes.Fig. 4.7shows theequilibriumconcentrationsof theclustersunderconditionstypical of theperiodbefore ¥ 311¦ defectsform. For high interstitialsu-persaturationsrepresentativeof veryshorttimes( ë 1 sec),BI2 canbepresentin significantnumbers.This helpsto immobilizeboronatomsinitially. Note that thestrongclusteringkeepsthefreeB andthustheB2I2 concentrationlow, andat suchshorttimestheB3I andB4I2 concentrationsarefarbelow theirequilibriumvaluesdueto theslowerformationrateof B3I (Fig.4.6).Once ¥ 311¦ defectsform, theinterstitialconcentrationdrops.For typicalTED supersaturations(CI Ü C ÔI ì 103), thedominantspeciesis B3I, asshown in Fig. 4.8.

At the sametime, only a small subsetof the clustersare ever presentin significantnumbers. Fig. 4.7 shows the equilibrium concentrationsof the clustersbeforethe for-mationof ¥ 311¦ defects.Underhigh interstitial super-saturationsrepresentative of veryshort times ( ì 1 sec),BI2 canbe presentin significantnumbers. This helpsto immo-bilize boronatomsinitially. At suchshort timesthe B3I andB4I2 concentrationsarefarbelow their equilibrium valuesdueto the slower formationof B3I. Once ¥ 311¦ defectsform, the interstitial concentrationdrops.Fromtheequilibriumdiagramfor typical TEDsuper-saturations(CI Ü C ÔI ì 103) asshown in Fig. 4.8,thedominantspeciesis B3I.

4.3 Simplecluster model

Thefollowing conclusionscanbemadefrom theaboveanalysis:(i) The concentrationof all the small clustersrapidly equilibratewith the free B and Iconcentrations.(ii) At shorttimes,BI2 is thedominantcluster.(iii) At longertimes,B3I is thedominantclusterandneedsto besolvednumericallysinceit is presentin non-equilibriumquantities.

Basedontheaboveobservations,wecansimplify thesystemof immobileclustersfromtento thatof just B3I. SinceB3I formsvia theunstableclusterB3I2 [60] thereactions,

B2I Õ Bi

k f1íî

kr1

B3I2 (4.12)

57

ï ðñ

| | | ||«|«

|« |¬ |¬ |¬ |¬

|®

|®

|®

Time (s)òBI ó

B2 B2I B2I2 B3I B4I2

10© -8 10

© -4 10© 0 10

© 410-4

100

104

B

n I m

/(K

eq (

CB)n

(C

I)m

)

Bi

BIô

2

õõ õ õ õ õ õ õ õö ö ö ö ö ö ö ö

÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷÷ ÷

Figure4.6: Simulationsusingthefull clustermodelof normalizedclusterconcentrations(relative to their equilibriumvalue)versustime for an800§ C anneal.

B3I2

k f2íî

kr2

B3I Õ I (4.13)

canbecombinedto giveanetformationratefor B3I:

RB3I Ï keffB3I Ò CB2ICBi Ð CB3ICI

KB3IÓ × (4.14)

KB3I Ï k f1k f

2

kr1kr

2Ï exp Ò Ð 0 × 1 eV Õ 1 × 3 eV

kT Ó Ø (4.15)

usingvaluesfrom Table1.

keffB3I Ï k f

1 è k f2

kr1 Õ k f

2 ê Ïùø k f1

1 Õ k f1 Ü Ý kr

2KB3I Þûú Ø (4.16)

wherek f2 Ü Ý kr

1 Õ k f2 Þ representstheprobability thatB3I2 will dissociateinto B3I Õ I rather

58

|ü |ü |ü |ü |ü|ý|ý

|ý|ý

|ý |þ |þ |þ |þ |þ

|ÿ|ÿ

|ÿ|ÿ

|ÿ

BI�

Bi

10� 12 10� 14 10� 16 10� 18 10� 20

1012

1016

1020

1024

1028

Free Boron (cm� -3)

C

lust

er C

once

ntra

tion

(cm

�

-3)

CI/CI* = 109

B3I2

B2I

BI2

B2I2

B3I

B4I2

B2

Figure4.7: Equilibrium clusterconcentrationsversusfree boronconcentrationat 800§ Cfor free interstitial concentrationsof 109C ÔI characteristicof very early stagesof TED.Initially, BI2 is theprimaryclusterandhelpsimmobilizetheboronasnotedby Pelazetal.[83]

59

| | | | ||« |«

|« |«

|« |¬ |¬ |¬ |¬ |¬

|® |® |® |® |®

B

10© 12 10

© 14 10© 16 10

© 18 10© 20

1012

1014

1016

1018

1020

Free Boron (cm� -3)

C

lust

er C

once

ntra

tion

(cm

�

-3)

C�

I/CI* = 103

Bó

2I

Bó

3I

B4I2

Figure4.8: Equilibrium clusterconcentrationsversusfree boronconcentrationat 800§ Cfor free interstitial concentrationsof 103C ÔI typical of TED conditionsin thepresenceof¥ 311¦ defects.B3I is theprimaryclusterduringmostof theanneal.

thanB2I Õ Bi . Sincethesmallclustersarein dynamicequilibrium,

CB2I Ï KB2ICBCBi × (4.17)

k f1 andkr

2 areassumedto bediffusionlimited andarehence,

k f1 Ï 4πa0DBi

Ø (4.18)

kr2 Ï 4πa0DI × (4.19)

As BI2 is thedominantclusterat shorttimes(seeFig. 4.7 ), we canneglect theothersmall clusters. Sincethe BI2 reacheslocal equilibrium quickly (seeFig. 4.6), we canapproximatetheBI2 concentrationby solvingtheequations:

CtotB Ï CB Õ KBI2CBC2

IØ (4.20)

CtotI Ï CI Õ KBI2CBC2

I × (4.21)

We canthususean analytic function for BI2 asa function of the total B andI concen-

60

Full Model Simple Model SIMS Data

|

0.0Å |

0.2Å |

0.4Å |

0.6Å |

0.8Å |

1.0Å|« |ª |ª |ª |ª |ª |ª |ª |ª |«|ª |ª |ª |ª |ª |ª |ª |ª |« |ª |ª

|ª |ª |ª |ª |ª |ª |« |ª |ª |ª |ª |ª |ª

|ª |ª |« |ª |ª |ª |ª |ª |ª |ª |ª |« |¬ |¬ |¬ |¬ |¬ |¬

|® |­ |­ |­ |­ |­ |­ |­ |­ |® |­ |­ |­ |­ |­ |­ |­ ||® |­ |­ |­ |­ |­ |­ |­ |­ |® |­ ||­ |­ ||­ |­ |­ |® |­ |­ |­ |­ |­ ||­ |­ |®40 keV B impl,È

1015

1016

1017

1018

1019

1020

Depth (Æ µm)

B

Con

cent

ratio

n (

cmÇ -3 )

Bó

3I

15 & 60 min/800oC

Figure 4.9: Comparisonof full model with the simplified model for a 40 keV2 ³ 1014cm 2 B implantsannealedat 800§ C for varioustimes. Also shown for com-parisonareSIMS datafrom Intel [44]. Note that the full modelandsimplemodelshowindistinguishablefinal profiles.TheB3I concentrationsfor thetwo models(shown aftera1 h anneal)arealsonearlyidentical.

trations.However, the rateequationfor BI2 is actuallyeasierto incorporateandrequiresminimal computationaloverhead.

We comparedour simplified model to the full systemandfound that the resultsarevirtually indistinguishable.A moment-basedmodelcharacterizedbasedon TEM resultswasusedfor interstitialdefects( ¥ 311¦ defectsanddislocationloops)[41,42,43]. Fig. 4.9show anexampleof this comparisonaswell asto datafrom Intel [44] for TED at 800§ C.Similaragreementwasobtainedathigherandlowertemperatures(700and900§ C) aswellasfor otherimplantdoses.

4.4 Extensionto chargestates

Theclustermodelsconsideredin earliersectionsdid not includechargestatesfor thevar-iousclusters.However, sinceclusteringinvolvesdeactivationandformationof clustersof

61

differentcharges,it is necessaryto includeclusterchargestatesto bephysicallyconsistent.Wehaveextendedourmodelbasedonchargeddefectcalculationsfrom Lenosky etal. [64]whichconcludethatthedominantchargestatesof theclusterswehaveidentifiedascriticalto modelingare Ý BI2 Þ æ , Ý B2I Þ 0 and Ý B3I Þ ´ . Clusteringproceedsas:Ý Bi Þ ´ Õ B ´ å Ý B2I Þ 0 Õ 2e Ø (4.22)Ý Bi Þ 0 Õ B ´ å Ý B2I Þ 0 Õ e Ø (4.23)

Since Ý B2I Þ 0 quickly reachesdynamicequilibriumwith B andBi ,

C� B2I � 0 Ï Keq� B2I � 0CB C� Bi � Ò pniÓ 2 × (4.24)Ý B3I Þ ´ formationcanproceedby a reactionwith Bi which haseithera netnegative Ý Bi Þ ´

or neutral Ý Bi Þ 0 charge.Hencewecanwrite:Ý Bi Þ ´ Õ Ý B2I Þ 0 å Ý B3I Þ ´ Õ I0 Ø (4.25)Ý Bi Þ 0 Õ Ý B2I Þ 0 å Ý B3I Þ ´ Õ I æ × (4.26)

It shouldbe notedthat underextrinsic conditions,diffusion via Ý Bi Þ 0 dominates(DB ∝pÜ ni), soEq.4.26is thedominantpathway. Thereactionratesgivenby Eqs.4.25and4.26are:

R� Bi � ç B2I Ï kB i ç B2I ø C� Bi � C� B2I � 0 Ð C� B3I � CI0

K � Bi � ç B2I ú Ø (4.27)

R� Bi � 0 ç B2I Ï kB0i ç B2I ø C� Bi � 0C� B2I � 0 Ð C� B3I � CI é

K � Bi � 0 ç B2I ú × (4.28)

Assumingionizationreactionsarefastandthatdiffusivitiesareindependentof chargestate(D � Bi � Ï D � Bi � 0 andDI0 Ï DI é ), wecanwrite theequilibriumconstantsfor Eqs.4.27and4.28in termsof theFermi level dependentborondiffusivities availablefrom equilib-rium experiments[99] (D æB andD0

B):

K � Bi � ç B2I

K � Bi � 0 ç B2IÏ C� Bi � 0

C� Bi � CI0

CI é Ï D æBD0

BKI é × (4.29)

KI é accountsfor theFermilevel dependenceof interstitialconcentration[45]. It is definedasdiscussedin Sec.2.2(Eq.2.18)to be:

C æI Ï KI é C0I Ò p

niÓ × (4.30)

62

Thetotal rateof formationof (B3I) ´ is then

R� Bi � ç B2I Ï Ý keffB i ç B2I Õ keff

B0i ç B2I

Þ ³ ø C� Bi � C� B2I � 0 Ð C� B3I �� CI0

K � Bi � ç B2I ú Ø (4.31)

where,K � Bi � ç B2I is theequilibriumconstantdefinedfor Eq.4.27with,

keffB i ç B2I Ï �

4πrcapDB0

KB i ç B2IC ÔI0 � 1 Õ γeffB i ç B2I �

�� Ø (4.32)

keffB0

i ç B2I Ï �� 4πrcapDB é Ý pÜ ni Þ

KB i ç B2IC ÔI0 � 1 Õ γeffB0

i ç B2I ����� Ø (4.33)

γeffB i ç B2I Ï DB0 Ü Ý DI0C ÔI0KI0 ç � Bi � KB i ç B2I Þ Ø (4.34)

γeffB0

i ç B2I Ï DB é Ü Ý DI0C ÔI0KI é KI0 ç � Bi � KB i ç B2I Þ × (4.35)

Theformationof Ý BI2 Þ æ canproceedby thesereactions,Ý Bi Þ 0 Õ I æ å Ý BI2 Þ æ Ø (4.36)Ý Bi Þ 0 Õ I0 å Ý BI2 Þ æ Õ e Ø (4.37)Ý Bi Þ ´ Õ I æ å Ý BI2 Þ æ Õ e Ø (4.38)Ý Bi Þ 0 Õ I0 å Ý BI2 Þ æ Õ 2e × (4.39)

Theoverallnetreactionrateis thus:

RBI2 Ï kBI2 ø C� Bi � 0CI é Ð CBI2

K � Bi � 0 ç I é ú Ø (4.40)

kBI2 Ï 4πa0 Ý DBi Õ DI Þ ³ Ò 1 Õ 1KI é n

niÓ Ò 1 Õ D0

B

D æB nniÓ × (4.41)

63

4.5 Comparison to chemicaldata

Theextendedboronclustermodelwasfoundto give goodmatchto theTED datashownin theprevioussection.Themodelparameterswerefurtheroptimizedto fit a wide rangeof data. Shown in Fig. 4.10 is comparisonto datafrom Intel [44]. Similarly Fig. 4.11showscomparisonto datafrom Solmietal. [90]. Wefind theboronclustermodelalsocanpredicttheTED profilesfor higherborondosesby includinga loopmodelfor interstitials.Shown in Figs.4.12and4.13is comparisonto data[44, 90] for a 2 ³ 1015cm 2, 40 and20 keV B implant annealedat 800§ C. However, it shouldbe notedthat this modeldoesnot predicthigh dose,high temperatureanneals.For thesecases,experimentsshow sharpboronpeakssuggestive of larger sizedclusters.Henceit would be necessaryto includelargersizeclustersto modelsuchdata.

4.6 Solid Solubility Model

Thesimplestmodelto includetheeffect of largersizedclustersis to usea solid solubilitymodel.Therateequationsfor thesolidsolubility modelcanbeformulatedasfollows[43]:

∂m1

∂t Ï DBλm1 Ý CB Ð CssÞ Õ�� DBλ Ý CB Ð CssÞ 2 for CB Ù Css

0 for CB � Css(4.42)

∂CB

∂t Ï Ð ∂m1

∂t

whereCss is theboronequilibriumsolidsolubility, λ is aneffectivecapturedistanceandm1

tracksthetotalnumberof boronatomsin precipitates.Thefirst termin theaboveequationis for growth/dissolutionof theprecipitates,whereasthesecondtermis for nucleationofprecipitateswhenCB Ù Css. Thismodelis usedfor modelingannealingof ultra low energyimplantsasdiscussedin Chapter5.

64

As impl

Model

|

0.0Å |

0.1Å |

0.2Å |

0.3Å |

0.4Å |

0.5Å|« |«|« |«

|« |¬ |¬ |¬ |¬ |¬ |¬

|® |® |® |® |® 800 oC/1h

1016

1017

1018

1019

1020

Depth (Æ µm)

B

Con

cent

ratio

n (

cmÇ -3 )

20 keV, 2 x 10� 14 cm-2 B Intel SIMS data

B3I

As impl

Model

|

0.0Å |

0.2Å |

0.4Å |

0.6Å |

0.8Å |

1.0Å|« |«

|« |«|« |¬ |¬ |¬ |¬ |¬ |¬

|® |® |® |® |® 800 oC/1h

1016

1017

1018

1019

1020

Depth (Æ µm)

B C

once

ntra

tion

(cm

�

-3)

80 keV, 2 x 10² 14 cm-2 BIntel SIMS Data

B3I

Figure4.10:Comparisonof simulationto experimentaldata[44] for 2 ³ 1014cm 2 (a)20keV (b) 80keV boronimplantsafter1 hr annealsat800§ C.

65

As impl

Model

|

0.0Å |

0.1Å |

0.2Å |

0.3Å |

0.4Å |

0.5Å|« |«|« |«

|« |« |¬ |¬ |¬ |¬ |¬ |¬

|® |® |® |® |® |® 800 oC/30m

1016

1017

1018

1019

1020

1021

Depth (Æ µm)

B C

once

ntra

tion

(cm

�

-3)

20 keV, 5 x 1014 cm-2 BData from Solmi et al.°

Bó

3I

As impl

Model

|

0.0Å |

0.1Å |

0.2Å |

0.3Å |

0.4Å |

0.5Å|« |«

|« |«|« |« |¬ |¬ |¬ |¬ |¬ |¬

|® |® |® |® |® |® 800 oC/2h

1016

1017

1018

1019

1020

1021

Depth (Æ µm)

B C

once

ntra

tion

(cm

�

-3)

20 keV, 5 x 1014 cm-2 BData from Solmi et al.°B3I

Figure 4.11: Comparisonof simple model to data from Solmi et al. [90] for a5 ³ 1014cm 2 20 keV B implantannealedat 800§ C for (a)30 min (b) 2 hr.

66

As impl

Model

|

0.0Å |

0.2Å |

0.4Å |

0.6Å |

0.8Å|« |«|« |«

|« |«

|¬ |¬ |¬ |¬ |¬

|® |® |® |® |® |® 800oC/1h

1016

1017

1018

1019

1020

1021

Depth (Æ µm)

B C

once

ntra

tion

(cm

�

-3)

40 keV, 2 x 1015 cm-2 B SIMS data from Intel�

B3I

Figure4.12: Comparisonof modelto experimentaldata[44] for a 2 ³ 1015cm 2 40 keVboronimplantaftera60 min annealat800§ C.

67

As impl

Model

|

0.0Å |

0.1Å |

0.2Å |

0.3Å |

0.4Å |

0.5Å|« |«|« |«

|« |«

|¬ |¬ |¬ |¬ |¬ |¬

|® |® |® |® |® |® 800 oC/2h

1016

1017

1018

1019

1020

1021

Depth (Æ µm)

B C

once

ntra

tion

(cm

�

-3)

20 keV, 2 x 1015 cm-2 B Data from Solmi et al.

B3I

Figure4.13: Comparisonof model to experimentaldatafor a 2 ³ 1015cm 2, 20 keV Bimplantannealedat 800§ C for 2 hrs.SIMSdatais from Solmi et al. [90]

68

4.7 Comparison to marker layer experiments

Dopantmarker layer experimentshave emergedasa very powerful methodto probetheunderlyingmechanismsof dopant/defectinteractions.Recently, a uniqueexperimentwasperformedby Mannino et al. [27, 68] to understandthe formation of boron interstitialclusters.We first describetheir experimentandresultsin detail. In the next sub-section(4.7.2),wepresentmodelingof this data.

4.7.1 Experimental background

Manninoet al. [68] comparepost-implantmarker layerdiffusiondatain waferswith andwithoutanadditionalboronlayercloserto thesurface.WaferA containstwo borondopedmarker layers,locatedat depthsof 900 and1300nm, well beyond the implant damagedistribution. WaferB containsin additiona boronbox profile locatedin thedepthrange200–500nm. Bothwaferswereimplantedwith 40keV Si ionsto adoseof 2 ³ 1013cm 2.Thedamagefrom thisimplantevolvesinto abandof intrinsicinterstitialdefects-interstitialclusters(ICs) and ¥ 311¦ defectscloseto the projectedrangeof the Si implant, duringsubsequentannealingasdiscussedin Sec.3.3 [27]. For conveniencewe will refer to thisdefectbandasthe“IC band”.Theboronlayerin waferB wasfabricatedsuchthatthedeeptail of theSi implantdamageoverlapswith theborondopedbox profile (seefor exampleFig. 4.14). Manninoet al. [68] suggestthat this overlapcausesnucleationof a bandofboroninterstitial clusters(BICs) at the left-handbox edge,locatedbetweenthe IC bandandthediffusionmarkers.A comparisonof marker-layerdiffusionin wafersA andB thenprovidesinformationon therelativestabilityof BICsandICs.

Fig.4.14showsSIMSprofilesobtainedby annealingat600§ C for varioustimes.Threemajorphasesof annealingareobserved[68]:µ After 1 s anneal,fastdiffusion of the left sideof the box profile wasobserved in

wafer B. According to Manninoet al. [68], “This diffusion evidently takesplaceat a very early stageof annealing,beforethe interstitialshave hadtime to diffusethroughthedopingstructure.” They suggestit is associatedwith thedisplacementofB atomsat low temperaturedueto captureof freeinterstitialsfrom theion collisioncascade.“This diffusionphaseis accompaniedby immobilization(clustering)of asignificantfractionof B atomsnearthetopleft sideof theboxprofile.” This is notedbecauseof the low boronsolubility on the left side(Css

B ì 2 ³ 1017cm 3). “Notethat BIC nucleationseemsto occurchiefly on the left sideof the region (comparewith thesignificantdiffusionat thetop right cornerof thebox profile). Thenarrowbandof BICs is stableenoughto persistfor at least2 h of furtherannealing.”µ “Rapid marker-layer diffusion occursin the period 1 s – 15 min, indicating thatinterstitialsdiffusethroughtheentiredopingprofile within 1 s,andthata veryhigh

69

Total I Initial B Data (1 sec) Data (15 min) Data (2 h)

|

0.0Å |

300.0© |

600.0© |

900.0© |

1200.0© |

1500.0©|« |ª |ª |ª |ª |ª |ª |ª |ª |« |ª

|ª |ª |ª |ª |ª |ª |ª |« |ª |ª |ª |ª |ª |ª |ª

|ª |« |ª |ª |ª |ª |ª |ª |ª |ª |« |ª

|ª |ª |ª |ª |ª |ª |ª |« |ª |ª |ª |ª |¬ |¬ |¬ |¬ |¬ |¬

|® |­ |­ |­ |­ |­ |­ |­ ||® |­ |­ |­ |­ |­ |­ ||­ |® |­ |­ |­ |­ |­ |­ |­ |­ |® |­ |­ |­ |­ |­ |­ ||­ |® |­ |­ |­ |­ |­ |­ |­ |­ |® |­ |­ |­ |­

Depth (nm)¯

Data from Mannino et al.°

1015

1016

1017

1018

1019

1020

B C

once

ntra

tion

(cm

�

-3)

600� oC anneal

Figure4.14: SIMS profilesof boronbeforeandafter annealingfor a rangeof timesat600§ C. Data from Mannino et al. [68]. Also plotted is the total damagefrom the Siimplantascalculatedby UTMARLOWE [62].

interstitialsupersaturationis presentduringthis period.After 1 s thebroadeningoftheshallow anddeepmarker layersis essentiallythesame,indicatingthat thereisno longera significantgradient(andthusno significantflux) of interstitialsinto thebulk of thewafer. Thisconfirmedthatthedensityof interstitialtrapsin thematerialwasnegligible. The measuredmarker-layer diffusion in wafer A thereforereflectstheinterstitialsupersaturation,SIC Ý t Þ , in theregionof theIC band.During this timeperiod,theTED measuredin waferB is clearlymuchlower thanin waferA, but isstill extremelyhigh.”µ “During theperiod15 min – 2 hr theratesof diffusionin wafersA andB aremuchreducedandappearto haveconvergedto approximatelythesamevalue.”

Fig. 4.15shows the supersaturationsSÝ t Þ for wafersA andB for annealingat 600§ Casreportedby Manninoet al. [68]. “The supersaturationdecreasesasa functionof timein bothwafers,but thereareobviousdifferencesat shorttimesandlow temperatures.Forexample,at 600§ C, thesupersaturationin waferA falls graduallyduring theperiodup to15 min, thendropsrapidly. This dropis causedby a ripeningtransitionin theIC band,at

70

� Data (No B Layer)� Data (B Layer)

| | ||«|«

|«

|« |¬ |¬ |¬

|®

|®

|®

|®

Time (s)òData from Mannino et al.°

10© 0 10

© 2 10© 4

102

104

106

108

sup

er s

atur

atio

n (CÊ I/C

I* )

600� oC anneal

�� � � �

�� � � �

Figure4.15: Supersaturationsobserved by the deepermarker layersfor Wafer A (No Blayer)andWaferB (B layer)shown with time at600§ C. Datafrom Manninoet al. [68].

a characteristictime τ ( ì 15 min at 600§ C), from small ICs to morestable ¥ 311¦ defects[27]. In waferB, SB Ý t Þ startsat lowervalues,theIC- ¥ 311¦ transitionappearsto beblurred,andat long timesSB Ý t Þ convergestowardsthevaluein waferA.”

This behavior wasexplainedasfollows by Manninoet al. [68]. “After IC nucleationandinitial growth, SIC rapidly reachesa local equilibriumwithin theIC bandasdescribedin Ref. [27]. Becausethe interclusterdistancewithin theIC bandis ordersof magnitudesmallerthanthedistanceto theBIC band,this localequilibriumvalueis unaffectedby theexistenceof theBIC band.Consequentlythevaluesof SIC in wafersA andB arethesame,andthedifferenceSA Ð SB asobservedin Fig. 4.15canbetakenasadirectmeasureof thedecreasein the supersaturationSÝ x Ø t Þ with depthin waferB. Since,during the diffusionphases,the B-dopedregionsaretransparentto interstitials,the spatialdecreasein SÝ x Ø t Þcanonly arisefrom trappingof interstitialsin theBIC band.” Basedon thesearguments,they identify S Ï SIC and S Ï SBIC whereSBIC is the supersaturationat the BIC band.After time t Ï τ, thevalueof SIC falls by 1-2 ordersof magnitude,to a valuelower thanthat previously existing in the BIC band. The BIC bandno longeractsasan interstitialsink, andmayevenbecomea weaksource.Thebehavior of SÝ x Ø t Þ beforethe IC- ¥ 311¦defecttransitionis summarizedin Fig. 4.16. The changein BIC behavior asa functionof SIC shows thatonceformedtheBICs aremorestablethantheICs which controlTED

71

S B

SA

Depth

Sup

ersa

tura

tion

ICs

BICs

Figure4.16:Thefiguresketchesthedepthandtime variationof SÝ x Ø t Þ in wafersA andBaftertheinitial BIC nucleationphase(afterManninoet al. [68]).

at shorttimes,andarein factof comparablestability to ¥ 311¦ defectsdespitetheir muchsmallersize.

Sincethereis noevidenceof aformationof ashoulderontheright sideof theboronboxprofile,Manninoet al. [68] suggestthatthenumberof clusteredB atomsremainsroughlyconstantandtheBICssimplybecomeenrichedin interstitials.Hence,they supportPelaz’sideathatBIC evolution followsanI-rich pathwayduringTED [82].

4.7.2 Model results

Although, Manninoet al. [68] suggestthat the interstitialsaddedto the BIC layer maybejust gettingattachedto alreadynucleatedboronclusters,a carefulanalysisof thephe-nomenonindicatesthatthis is not theonly possibility. Theseexperimentscanbeexplainedbasedoneitheroneor acombinationof thefollowing mechanisms:

(i) Thedecreasein interstitialsupersaturationmaybecausedby theadditionof intersti-tials to existing clustersto form largeinterstitialrich clusters(e.g.BI Õ Ý n Ð 1Þ I å BIn). Henceduringthecourseof TED theseinterstitialrich clusterswill dissolveandreleasethe trappedinterstitials. Thedissolutionof theseinterstitial rich boronclusterswill con-trol thesupersaturationSB andthusmeasuringthesupersaturationSB anddurationof the

72

enhancementwill yield thestabilityof theseclusters.

(ii) Anotherpossibleexplanationmaybedueto theformationlargeboronclusterslikeB4I4. Theseareformedby attachingmobileBi to theexistingBI clusterformedduringtheinitial stagesof annealingof theimplant. This mechanismcanbeconsideredasgetteringof Bi atomsby theexisting BI clusters.If thestability of B4I4 is similar to ¥ 311¦ defects,thenonceagainthetrappedinterstitialswouldbereleasedduringthedissolutionof ¥ 311¦defects(dueto formationof B4I from B4I4).

(iii) It is alsopossiblethat new boronclustersarenucleateddueto the high intersti-tial supersaturationsprevalentundertheseconditions.Underthis mechanism,boronrichclusters(e.g.B3I) areformedto trapinterstitials.Theseboronclusterscanexist evenafterthe ¥ 311¦ defectsdissolve,andhencethetrappedinterstitialsmaytakemuchlongerto bereleasedbackinto system.

The modelby Pelazet al. [82] seemsto suggestpathway (ii) as the possiblemech-anism. However, both (i) and (ii) appearto contradictboron clusteringdata(seeSec-tion. 3.4),which indicatedthat theratio of B to I in clusters(at leastat 800§ C) is greaterthan2 to 1. Thesimplerexplanationis to allow nucleationof new boronclusters(pathway(iii)) ratherthanadditionof interstitialsto existing clusters.Theonly limiting criterionisthatthenumberof boronclustersnucleatedduringtheannealingprocessberelatively lowandhencecannotbe observed by SIMS on the right sideof the box profile. If we nowapplyourexistingmodelfor nucleationof boronclustersvia theboronrich pathsuggestedby ab-initio calculationsanddescribedin Section4.2,we observe it is possibleto obtainsimilar results.For thesesimulations,thefull implantcascadefrom UTMARLOWE [62]is usedasinitial conditions.Comparisonto SIMS is shown in Figs.4.17– 4.19.It maybenotedthatalthoughnew boronclustersarenucleatedthereis noobservableshoulderontheright sideof theB boxprofile,whereasthereis substantialnucleationontheleft sideof theboxprofile. Fig. 4.20showscomparisonto simulatedandobservedsupersaturations.Withthe exceptionof underestimatingdiffusion for the very short times(1s), the modeldoesa goodjob of predictingtheobserved behavior, thusestablishingit asa plausiblemech-anismfor formationof boroninterstitial clusters.Of course,in theabsenceof long timeexperimentaldataprobingthe stability of the nucleatedboronclusters,any combinationof thelistedpathwayscanleadto adecreasein theobservedexperimentalsupersaturationSA Ð SB.

73

Initial B total B3I Data (1 sec)

|

0.0Å |

300.0© |

600.0© |

900.0© |

1200.0© |

1500.0©|« |ª |ª |ª |ª |ª |ª |ª |ª |«

|ª |ª |ª |ª |ª |ª |ª |ª |« |ª |ª|ª |ª |ª |ª |ª |ª |« |ª |ª |ª |ª |ª

|ª |ª |ª |« |ª |ª |ª |ª |¬ |¬ |¬ |¬ |¬ |¬

|® |­ |­ |­ |­ |­ |­ |­ |­ |® |­ |­ |­ |­ |­ |­ |­ |­ |® |­ |­ |­ |­ |­ |­ |­ |­ |® |­ |­ |­ |­ |­ |­ ||­ |® |­ |­ |­ |­

Depth (nm)

1015

1016

1017

1018

1019

B C

once

ntra

tion

(cm

�

-3)

Figure4.17: SIMS profilesof boronbeforeandafter annealingat 600§ C for 1 seccom-paredto experimentalSIMS data.Experimentaldatafrom Manninoet al. [68].

74

Initial B total B3I Data (15 min)

|

0.0Å |

300.0© |

600.0© |

900.0© |

1200.0©|« |ª |ª |ª |ª |ª |ª |ª |ª |«

|ª |ª |ª |ª |ª |ª |ª |ª |« |ª |ª|ª |ª |ª |ª |ª |ª |« |ª |ª |ª |ª |ª

|ª |ª |ª |« |ª |ª |ª |ª |¬ |¬ |¬ |¬ |¬

|® |­ |­ |­ |­ |­ |­ |­ |­ |® |­ |­ |­ |­ |­ |­ |­ |­ |® |­ |­ |­ |­ |­ |­ |­ |­ |® |­ |­ |­ |­ |­ |­ ||­ |® |­ |­ |­ |­

Depth (nm)

1015

1016

1017

1018

1019

B C

once

ntra

tion

(cm

�

-3)

Figure4.18:SIMS profilesof boronbeforeandafterannealingat 600§ C for 15 min com-paredto experimentalSIMS data.Experimentaldatafrom Manninoet al. [68].

75

Initial B total B3I Data (2 hr)

|

0.0Å |

300.0© |

600.0© |

900.0© |

1200.0©|« |ª |ª |ª |ª |ª |ª |ª |ª |«

|ª |ª |ª |ª |ª |ª |ª |ª |« |ª |ª|ª |ª |ª |ª |ª |ª |« |ª |ª |ª |ª |ª

|ª |ª |ª |« |ª |ª |ª |ª |¬ |¬ |¬ |¬ |¬

|® |­ |­ |­ |­ |­ |­ |­ |­ |® |­ |­ |­ |­ |­ |­ |­ |­ |® |­ |­ |­ |­ |­ |­ |­ |­ |® |­ |­ |­ |­ |­ |­ ||­ |® |­ |­ |­ |­

Depth (nm)

1015

1016

1017

1018

1019

B C

once

ntra

tion

(cm

�

-3)

Figure4.19:SIMSprofilesof boronbeforeandafterannealingat600§ C for 2 h comparedto experimentalSIMSdata.Experimentaldatafrom Manninoet al. [68].

76

Data (No B Layer)! Data (B Layer) Simulation (No B Layer) Simulation (B Layer)

| | ||«|«

|«|« |¬ |¬ |¬

|®|®

|®|®

Time (s)

Data from Mannino et al.°

10© 0 10

© 2 10© 4

102

104

106

108

sup

er s

atur

atio

n (CÊ I/C

I* )

600� oC anneal

"" " " "

## # # #

Figure4.20: Simulatedsupersaturationscomparedto experimentallyobserved valuesat600§ C. Experimentaldatafrom Manninoet al. [68].

77

4.8 Comparison to electrical activation data

In previous sections,we wereconcernedmostly with matchingthe chemicalconcentra-tion profiles. However, predictingelectricalactivationis essentialfor theeffectivenessofprocessmodeling.Thus,wenow look at modelingof boronelectricalactivation.

For modelingborondeactivation,weconsidertheclustersBI2, B2I2, B2I, B3I [18, 20].As discussedin Section4.4, basedon charged defectcalculations,Lenosky et al. [64]concludethatthedominantchargestatesfor theseclustersare Ý BI2 Þ æ Ø Ý B2I2 Þ 0 Ø Ý B2I Þ 0 andÝ B3I Þ ´ . However, sinceelectricalactivationdataindicatesdominantclustersareneutralatroomtemperature,weassumethedominantclusterB3I to beneutral(B3I)0.

A temperatureramp-upof 50§ C/s for theRTA and1§ C/s for the furnaceannealswasusedfor the simulations. We compareour model to isochronalannealingresultsfromSeidelet al. [87]. In theseexperiments,the active fraction of boron is measuredas afunction of temperaturefor a fixed annealingtime. Shown in Fig. 4.21 is a matchtoreverseannealingprofilesfrom Seidelet al. [87] for two differentimplantdoses.In theseexperiments,boronwasimplantedat 150keV andfurnaceannealedfor 30 mins. At lowtemperatures(500 – 700§ C, as shown in Fig. 4.21), boron clustersare stableand thusmostof theboronis inactive. Theactivationinitially decreaseswith temperaturesastheseclustersform. At highertemperatures( Ù 750§ C), theseboronclustersdissolve, andthustheactivefractionincreasesasafunctionof temperature.As shown in Fig.4.21,ourmodelcapturesthemainfeaturesof thedeactivation/activationprocessfor differentdoses.Thisisalsoexhibitedfor higherdoses,wheretheclusteringbehavior is stronger, leadingto loweractivation.

We further compareour model to SRPand SIMS data from Pelazet al. Fig. 4.22shows the evolution of the active fraction comparedto experimentaldata[84]. Clustersform during the ramp-upto 800§ C, reducingthe active fraction quickly. During furtherannealing,interstitialsupersaturationdropsrapidlysubsequentto dissolutionof interstitialdefects.This reducesthestability of boroninterstitialclustersandleadsto anincreaseinactive boronfraction with time asshown in Fig. 4.22. Note that the dissolutionprocessneedsfreeinterstitialsfor theformationof theintermediatespeciesB3I2, while dissolvingfrom B3I to B2I. Thus activation of boron as seenin Fig. 4.22 is a slow processoncetheseclustersareformed.Shown in Fig. 4.23is comparisonto a2 ³ 1014cm 2 B implantdatafrom Pelazet al. [84] spike annealedat 800§ C. Similarly we find good matchtoexperimentaldatafor longerannealtimesasshown in Fig. 4.24.

78

$%

|¶450& |¶

650& |¶850& |¶

1050

|¸0.0

|¸0.2|¸0.4

|¸0.6

|¸0.8

|¸1.0 |¹ |¹ |¹ |¹

|» |» |» |» |» |»

Temperature'

Act

ive

Fra

ctio

n(Data from Seidel et al.)

2.5 x 1014

2 x 1015

150 keV B, 30 mins

* * **

*

+ + + + ++

+

Figure4.21: Comparisonof experimentally-measuredactive fraction [87] to model for150keV, 2 ³ 1014cm 2 and2 ³ 1015cm 2 boronimplantsannealedfor 30min. atvarioustemperatures.Linesrepresentmodelpredictions,andsymbolsrepresentdata.

79

, Data B sub

|¶ |¶ |¶|¸0.0

|¸0.2|¸0.4

|¸0.6

|¸0.8

|¸1.0 |¹ |¹ |¹

|» |» |» |» |» |»

Time (sec)'

Act

ive

Fra

ctio

n(Data from Pelaz et.al.)

10-2 100 102

30keV, 2 x 1014 cm-2 B

- - - - -

Figure4.22: Comparisonof simulatedandexperimentallymeasuredactive fraction for a2 ³ 1014cm 2 boronimplantannealedat 800§ C. Datafrom Pelazet al. [84].

80

SIMS. SRP B total B sub

|

0.0Å |

0.2Å |

0.4Å|« |ª |ª |ª |ª |ª |ª |ª |ª |«|ª |ª |ª |ª |ª |ª |ª |ª |« |ª

|ª |ª |ª |ª |ª |ª |ª |« |ª |ª

|ª |ª |ª |ª |ª |ª |« |¬ |¬ |¬

|® |­ |­ |­ |­ |­ |­ |­ |­ |® |­ |­ |­ |­ |­ |­ |­ |­ |® ||­ |­ ||­ |­ |­ |­ |® |­ ||­ |­ |­ ||­ |­ |®

Data from Pelaz et al.°

1016

1017

1018

1019

1020

Depth (Æ µm)

B C

once

ntra

tion

(cm

�

-3)

30keV B implant,/800² oC anneal

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0Figure4.23:Comparisonof simulationwith SIMSandSRPdatafrom Pelazetal. [84] fora2 ³ 1014 cm 2 implantannealedat800§ C for 1 s. Notethatmostof theboronis alreadyin clusters.

81

SIMS1 SRP B total B sub

|

0.0Å |

0.2Å |

0.4Å|« |ª |ª |ª |ª |ª |ª |ª |ª |«|ª |ª |ª |ª |ª |ª |ª |ª |« |ª

|ª |ª |ª |ª |ª |ª |ª |« |ª |ª|ª |ª |ª |ª |ª |ª |« |¬ |¬ |¬

|® |­ |­ |­ |­ |­ |­ |­ |­ |® |­ |­ |­ |­ |­ |­ |­ |­ |® ||­ |­ ||­ |­ |­ |­ |® |­ ||­ |­ |­ ||­ |­ |®

Data from Pelaz et.al.°

1016

1017

1018

1019

1020

Depth (Æ µm)

B C

once

ntra

tion

(cm

�

-3)

30 keV B implant,/800² oC anneal

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2Figure4.24:Comparisonof simulationwith SIMSandSRPdatafrom Pelazetal. [84] fora2 ³ 1014cm 2 implantannealedat 800§ C for 1000s.

82

4.9 Summary

We have found that considerationof eithera finite setof discreteclustersor a moment-basedmodelsuchasKPM canmatchexperimentaldatasatisfactorily for mediumdoses.For mediumandlow energy boronimplants,wehavedevelopedasimpleclustermodelformodelingboroninterstitial clusters.This systemwasderivedfrom a multi-clustermodelbasedon ab-initio calculationsperformedat LawrenceLivermoreNationalLabs [102].Basedonanalysisof clusterkineticsandenergetics,weareableto matchtheresultsof thefull multi-clustermodel,while reducingthenumberof clustercontinuityequationsfromten to just two. Theresultingmodelclearly illuminatesthecritical processesinvolved inboronclustering. Despiteits simplicity, the modelaccuratelydescribesboronclusteringandanomalousdiffusionoverarangeof experimentalconditions.Thismodelalsoyieldedcorrectqualitativebehavior in matchingboronmarker layerexperiments.

Wealsofoundthatwecanmodelborondeactivationkineticsduringlow andmoderatetemperatureannealingafter implantation.Themodelis ableto capturethekineticsof thedeactivationandactivationprocessesandthuspredictelectricalactivationduringannealingoverawide rangeof temperaturesandtimes.

83

Chapter 5

Ultra Shallow Boron Junctions

Accordingto the InternationalTechnologyRoadmapfor Semiconductors[1], it is neces-saryto producehighly activatedandshallow junctionsfor continueddevice scaling. Forexample,it is estimatedthatdevicesproducedin theyear2006with gatelengthsof 100nmwill havesub-40nm junctiondepths.However, apparentlynew phenomenahavebeenobservedunderthefar from equilibriumconditionsnecessaryfor forming thesejunctions.In this chapter, we show thatby carefulconsiderationof modelsdevelopedin Chapter4for muchdeeperjunctions,thedependenceof junctiondepthonprocessingconditionscanbeunderstoodfor ultra-shallow junctionsaswell.

5.1 Rapid thermal soakanneals

Transientenhanceddiffusion(TED) hasbeenthedominanteffect in determiningjunctiondepthsfor thepastdecadeandwill continueto beimportant.However, theuseof ultra-lowenergy implantsandshorttime, high temperatureRTP annealinghasgreatlydiminishedthe importanceof TED in ultra-shallow boron junctions. Reducingthe implant energyis particularlyeffective asit putsthe damagecloserto the surfacewhereit canbe morereadilyannihilated,thusreducingthetimeperiodoverwhichTED is present.Recentwork[2, 3, 7] showsthatTED canbenearlyeliminatedfor implantenergiesbelow about1 keV.However, the reductionin TED hasrevealedother effects controlling boron diffusivity(andthusjunctiondepth)for ultra-shallow profiles.Thissectionfocusesonunderstandingandmodelingof theseeffects.

Agarwal etal. [2, 3, 7] foundthatalthoughsiliconimplantsat1 keV andbelow resultedin normal marker layer diffusion, boron implantswith similar dosesand rangesled tosignificantly( ì 4 ³ ) enhanceddiffusion. They termedthis effect BED (boronenhanceddiffusion) and associatedit with the formation of a boron-richphasenearthe surface.However, applying the modelsdevelopedin earliersectionsto this datawe find a goodmatchto this dataasshown in Fig. 5.1. The solid solubility asevident in the dataand

84

as impl

simulation

|304 |3

255 |3504 |3

75|3

1004 |31256 |3

1505 |31757|8 |z |z |z |z |z |z |z |z |8

|z |z |z |z |z |z |z |z |8 |z |z

||z |z |z |z |z |8 ||z |z |z |z |z |z

|z |8 ||z |z |z |z |z |z |z |8 |{ |{ |{ |{ |{ |{ |{ |{

|} |9 |9 |9 |9 |9 |9 |9 |9 |} |9 |9 |9 |9 |9 |9 |9 |9 |} |9 |9 |9 |9 |9 |9 |9 |9 |} |9 |9 |9 |9 |9 |9 |9 |9 |} |9 |9 |9 |9 |9 |9 |9 |9 |}

Depth (nm)

1050oC/10s

1017

1018

1019

1020

1021

1022 C

once

ntra

tion

(cm

:

-3)

500eV -- 5 keV, 1 x 10; 15 cm-2 B Data from Agarwal et al.

Figure5.1: Simulatedandmeasuredboronprofilesfollowing 1015cm 3 boronimplantsat0.5to 5 keV. Datafrom Agarwal etal. [3].

simulationswasmodeledusinga solid solubility modelasdiscussedin Section4.6. Ascanbeseen,thesimulationsaccuratelypredicttheobservedboronjunctiondepthsand/ormarker layerbroadening,notonly for implants,but alsofor borondepositedonthesurfacevia MBE (Figs.5.2,5.3). Thereis indeedsignificantlyenhanceddiffusion in this system(Fig. 5.4),drivenby thesamepair injectionprocesswhich leadsto enhancedtail diffusionasdiscussedin Section2.5.

It wasnotedby Agarwal et al. [2, 3, 7] that therewasa slightly greaterdiffusionen-hancementfor highertemperatures(e.g.,factorof 3 at 950§ C versus4 at 1050§ C), whilecoupleddiffusioneffectsgive smallerenhancementsat highertemperatures.For coupleddiffusioneffects,the interstitial super-saturation(andthusdiffusionenhancement)in thetail region dependson thebalancebetweeninterstitial injection,which is proportionaltoborondiffusion,andinterstitialdiffusionbackto thesurface,which is proportionalto theself-diffusioncoefficient. Sinceborondiffusionhasa smalleractivationenergy (andthussmallerincreasewith temperature)thantheself-diffusion,smallersuper-saturationsareex-pectedat highertemperaturesfor thesameboronsurfaceconcentration.However, for thehigh boronconcentrationsin theseexperiments,thesurfaceconcentrationis not constantdueto thechangesin thesolubility with temperature.We find from our simulationsthat

85

As-grown

simulation

|

0© |

50© |

100© |

150< |

200© |

250< |

300© |

350<|« |ª |ª |ª |ª |ª |ª |ª |ª |«|ª |ª |ª |ª |ª |ª |ª |ª |« |ª |ª

|ª |ª |ª |ª |ª |ª |« |ª |ª |ª |ª |ª |ª

|ª |ª |« |ª |ª |ª |ª |ª |ª |ª |ª |« |¬ |¬ |¬ |¬ |¬ |¬ |¬ |¬

|® |­ |­ |­ |­ |­ |­ |­ |­ |® |­ |­ |­ |­ |­ |­ |­ ||® |­ |­ |­ |­ |­ |­ |­ |­ |® |­ ||­ |­ ||­ |­ |­ |® |­ |­ |­ |­ |­ ||­ |­ |®

Depth (nm)¯

950oC/30s anneal

1017

1018

1019

1020

1021

1022 C

once

ntra

tion

(cm± -3 )

Figure 5.2: Comparisonbetweensimulatedand measuredbroadeningof boron delta-dopedsuper-latticesin the presenceof an MBE-depositedboron layer andannealingat950§ C for 10 sec.Datafrom Agarwal et al. [3].

theincreasedsolubility athighertemperaturesapproximatelycompensatesfor thechangesin theborondiffusionto self-diffusionratio, leadingto very little changein enhancementwith temperature.As canbeseenfrom Figs.5.1–5.4,our simulationsaccuratelypredictthe experimentalbehavior. Fig. 5.4 shows the changein diffusion enhancementversusimplantdose.Agarwal etal. [2, 3, 7] suggestedthattheratherabruptincreasein diffusionenhancementwith dosemight bedueto theformationof a boridephase.However, it canbeseenthat thedosedependenceis reasonablypredictedsimply basedon coupleddiffu-sionasthe increasedboronconcentrationwith doseleadsto largerfluxesof BI pairsintothesubstrate.

More recently, Agarwal et al. presentednew experimentalresultson the temperatureandtime dependenceof BED, againusinganMBE depositedlayer [6]. They found thatisochronal10 s annealsshow a B marker layerdiffusionenhancementthat increaseswithtemperatureto a peakvalueandthendecreases.Samplesannealedat 800§ C do not showany measurableenhancementwhile samplespreannealedat 1050§ C andthenannealedat800§ C show apronouncedenhancement.As they agree,suchbehavior cannotbeexplainedbasedonly on coupleddiffusioneffects. This is becausecoupleddiffusionenhancementsincreasewith decreasingtemperature.For example,the diffusion enhancement(S) from

86

As-grown

simulation

|

0© |

50© |

100© |

150< |

200© |

250< |

300© |

350<|« |ª |ª |ª |ª |ª |ª |ª |ª |«|ª |ª |ª |ª |ª |ª |ª |ª |« |ª |ª

|ª |ª |ª |ª |ª |ª |« |ª |ª |ª |ª |ª |ª

|ª |ª |« |ª |ª |ª |ª |ª |ª |ª |ª |« |¬ |¬ |¬ |¬ |¬ |¬ |¬ |¬

|® |­ |­ |­ |­ |­ |­ |­ |­ |® |­ |­ |­ |­ |­ |­ |­ ||® |­ |­ |­ |­ |­ |­ |­ |­ |® |­ ||­ |­ ||­ |­ |­ |® |­ |­ |­ |­ |­ ||­ |­ |®

Depth (nm)¯

1050oC/10s anneal

1017

1018

1019

1020

1021

1022 C

once

ntra

tion

(cm± -3 )

Figure 5.3: Comparisonbetweensimulatedand measuredbroadeningof boron delta-dopedsuper-latticesin the presenceof an MBE-depositedboron layer andannealingat1050§ C for 10 sec.Datafrom Agarwal et al. [3].

coupleddiffusioncanbeestimatedto bearound:

S Ï DBCBssÝ pÜ ni Þ

DIC ÔI ∝ exp Ò 0 × 7kT Ó (5.1)

Theobservationscan,however, beexplainedby includingtheformationof boronclustersat the lower temperatures.For example,using the boron interstitial clustermodel fromprevious chapter, we find small clusters(suchasB3I) form at lower temperatures,thusreducingtheeffective solubility of boron. This decreasesthemeasuredenhancementsatlower temperatures.Increasingthe temperatureleadsto dissolutionof theseclustersandhencemorepronouncedcoupleddiffusioneffects.Thus,asshown in Fig.5.5,it is possibleto explain the behavior observed by Agarwal et al. [6], at leastqualitatively. The hightemperaturepreannealleadsto formationof largerboronprecipitates(solubility phase).Itwill alsodissolveany of theas-grown smallerclusters.Henceduringthesubsquent800§ Cannealthedriving forcefor theformationof smallerclustersismuchlower(sincesolubilityis now governedby the solubility phase),while muchmoreenhancementis observed inthesamplewith the1050§ C preannealin agreementwith experiments.

87

= Data Simulation

|· |· |· |· |· |¶ |· |· |· |· |· |· |· |· |¶ |· |· |· |· |· |· |· |· |¶ |· |· |· |·|¸0

|¸2

|¸4

|¸6

|¸8 |º |º |º |º |º |¹ |º |º |º |º |º |º |º |º |¹ |º |º |º |º |º |º |º |º |¹ |º |º |º |º

|»

|»

|»

|»

|» E

nhan

cem

ent>

1013 1014 1015

Boron Implant Dose (cm? -2)

@ @ @ @@ @

Figure5.4: Predictedandmeasureddiffusivity enhancementof boronmarker layersforvarious0.5 keV boron implant dosesand annealingat 1050A C for 10 sec. Data fromAgarwal et al. [2].

Agarwal et al. [6] alsopresentedthe time dependenceof theseenhancements.Theyfoundthediffusivity enhancementlastsfor over100sat950and1000A C andincreasesforup to 30 s at 1050A C (e.g. 3 B at 3 s to 5 C 5 B at 30 s duringa 1050A C anneal).Althoughour simulationspredict roughly constantenhancementsover time at lower temperaturesconsistentwith theexperimentalobservations,we find it is not possibleto predictthe in-creasingenhancementobservedat1050A C. Notethattheoverallenhancementobservedat1050A C is alsosignificantlyhigherthanthepredictionof our model(Fig. 5.5). This sug-geststhat thepoint defectconcentrationsmaybeaffectedby changesin theboridephaseat highertemperatures.The implicationsof the formationandsubsequentdissolutionoftheboridephaseis thusnot fully understoodandremainunderactive research.

88

D Data E Simulations

|F700G |F

900G |F1100

|H0

|H2

|H4

|H6 |I |I |I

|J

|J

|J

|J E

nhan

cem

entK

Data from Agarwal et al.

Temperature (L oC)

1050oC,10s pre-annealMN O

P PP

P PQ Q

Q Q Q

Figure5.5: Temperaturedependenceof MBE marker layersasreportedby Agarwal et al.[6] andcomparedto simulations.As observedat800A C thereis noenhancement,howevera preannealat 1050A C maintainsanenhancement.Theenhancementsat highertempera-tureareplottedfor 10 s.

5.2 Spikeanneals

Theachievementof sub-40nmultra-shallow source/drainextensionsrequireslow energyimplantsalongwith fastspikeannealsto minimizediffusion.Theadvantageof usingfasterramp-upratecanbeunderstoodfrom a simpleanalysisof TransientEnhancedDiffusion(TED). Basedon the experimentalobservationsdiscussedin Section3.3, it is possibleto comeup with a simplemodel for the estimationof TED effects. If the formationofR311S defectsis associatedwith an effective interstitial solubility C311

I which is main-tainedthroughoutthe growth/dissolutionof thesedefects,thenthe flux of interstitialstothesurfacecanbeapproximatedby:

JTEDI TU DIC

311I V Rp W (5.2)

89

whereRp is the averagedepthof net interstitial distribution (approximatelythe implantrange).Theperiodoverwhich TED laststhenis just:

τTED U QI

JTEDI

U QIRp

DIC311I

W (5.3)

wherethenetexcessimplantdoseQI U NQimplant basedon a “ X N” model.During TED,theinterstitialsupersaturationis C311

I V C YI , sotheamountof excessdiffusionexpecteddur-ing TED is givenby: Z

Dt [ TED U D YAτTED fIC311

I

C YI U D YA fIQIRp

DIC YI W (5.4)

whereD YA is thedopantdiffusivity underequilibriumconditions.Note that theactivationenergy of boron diffusion ( T 3.6 eV) is lessthan that of self-diffusion via interstitials(DIC YI T 4 C 8 eV), sothatdiffusiondueto TED is actuallydecreasedastheannealingtem-peratureis increased(aslongassufficienttimeis allowedfor completionof TED). It is alsonotablethatTED dependsprimarily on theDIC YI productratherthantheindividual terms.Hence,usinga higher ramp-uprate is moreeffective in producingshallower junctions.Thusit is temptingto producefasterandfasterramp-upfurnacesto minimize diffusionwhile maintaininggoodactivation.

AlthoughTED effectsreducewith implantenergy, theachievablereductionin junctiondepthwith increasingramp-upratehasbeenfoundto decreasewith increasingimplanten-ergy [4, 30]. Sub-1keV implantsshow amorepronounceddecreasein junctiondepthwithincreasein ramprates,while thereductionin junctiondepthfor higherenergy implantshasbeenfoundto saturatefor largerramprates.In thissection,weapplythemodelsdevelopedin earlierchaptersto understandandmodeltheeffect of RTP annealingcycle on junctionbehavior sothatRTP processescanbeoptimizedfor shallow, low resistancejunctions.

Fig. 5.6 shows a schematicillustration of the temperatureversustime profile duringa ramp-up.For thesimulations,a linear ramp-upis assumed.After the lampsareturnedoff, it is assumedthatthewafertemperaturedropschiefly by radiatingheatto thefurnacewalls, andhencethe ramp-down ratedecreasesat lower temperatures.During the cooldown, theheatlossis proportionalto T4, so:

T U Tf \ 1 ] 3tRcool

Tf ^`_ 0 a 33

(5.5)

where,Tf is themaximumattainedtemperature,Rcool is thecooling rate(K/s) at Tf (K)andt is timeelapsedafterreachingTf .

Sincethe experimentsconsideredwereperformedunderlow ambientoxygenlevels,oxidationenhancedandretardeddiffusionwasmodeledasin previouswork [34]. For lowoxygenpartial pressures,diffusion is retardedratherthanenhanced[31]. At 1050A C, a

90

|F-10b |F

-5c |F0G |F

5c |F10

|H600

|H800

|H1000

|H1200 |I |I |I |I |I

|J

|J

|J

|J

Time (s)d

radiativee

100oC/s 100 oC/s

T

empe

ratu

re (f oC

)

Tg

f

100 o C/s

50 h o C/s

cooling

Figure5.6:Temperatureversustimeprofilesusedfor thesimulations.Ramp-upismodeledaslinearwhereascooldown is radiative.

33ppmoxygenpartial pressureand16 A initial oxide film resultsin CI at the interfaceequalto about0 C 2C YI . Simulationsof themodelthusincludingtheORDeffect is comparedto datafrom Lerchet al. [65] in Fig. 5.7.

Firstwe look at thequalitativebehavior of junctionmovementdueto spikeannealsforultra low energy B implants.Thesimulationspredicta reducedeffect of ramprateon x j

(asseenexperimentally)[5, 30] andsaturationin thejunctiondepthwith increasingramp-up rates(Fig. 5.8). This saturationoccursat larger rampratesfor lower energy implants.For higherenergies,thefasterramp-upsretainmoreof theinterstitialclustersandmoreoftheTED actuallyoccursduringtheramp-down, thusnegatingany reductionpossibledueto the fasterramp-up. In fact, for higherenergies,junction depthincreasesslightly withincreasedramprates,asTED persiststo lower temperaturesduring the ramp-down. Forvery fastramp-uprates,the ramp-upis only a small fractionof the total thermalbudget,and hencethe cooling rate dominatesthe total junction movement. Thus, asshown inFig. 5.9, higherramp-down ratesareeffective in reducingjunctiondepth,if the ramp-uprate is fast enoughthat TED is not completed. Figs. 5.10 – 5.12 shows comparisontoRTP annealsfrom Downey et al. [30] usingtwo differentramp-upratefor threedifferent

91

simulation

|i0j |i

25|i

50j |i

75|i

100j|k |l |l |l |l

|l |l |l |l |k |l |l

|l |l |l |l |l |l |k |l

|l |l |l |l |l |l |l |k

|l |l |l |l |l |l |l |l |k |m |m |m |m |m

|n |o |o |o ||o |o |

|o |n |o ||o |o |o |

|o |o |n |o |o |o |o ||o |o |o |n |o |o |o |o |o |o |o |o |n

Depth (nm)pas q

1050oC/10s anneal

1018

1019

1020

1021

1022 C

once

ntra

tion

(cm

r

-3)

imps

102 ppmt 103

ppmt104 ppmt

Figure5.7: Boronprofilesversusoxygenpartialpressurefor 1keV, 1015cm_ 2 boronim-plants annealed10 s at 1050A C (Lerch et al. [65]) are shown along with simulationsmatchedto theseprofilesby varyingthesurfaceinterstitialconcentration.

implantenergies.Thesimulationsgiveagoodmatchto theobservedboronjunctiondepthsacrossthespectrumof conditions[21].

92

250 eV 1 KeV 2 KeV

|F10

|u |u |u |u |u |u |u |u |F100G |u |u |u |u |u |u |u |u |F

1000|u|H-1

|H1

|H3

|H5

|I |v |v |v |v |v |v |v |v |I |v |v |v |v |v |v |v |v |I |v

|J|J

|J

|J

Rampup rate (Cw o/s)

Xj -

Xj(2

000

Co/s

) (n

m)

Figure5.8: The effect of ramprateon reductionin junction depthfor 1 B 1015cm_ 2 Bimplantsfollowing 1050A C spike anneals.Thedifferencein junctiondepth(x j@5B 1018

cm_ 3) relative to a ramp-uprateof 2000A C/sis shown for variousimplantenergies.

93

|F10

|u |u |u |u |u |u |u |u |F100G |u |u |u |u |u |u |u |u |F

1000|u|H25

|H28

|H31

|H34 |I |v |v |v |v |v |v |v |v |I |v |v |v |v |v |v |v |v |I |v

|J|J

|J

|J

Xj (

nm)x

87 oC/s 150 oC/s

Rampup rate (y oC/s)

250 eV Bz +, 1050oC/spike

Figure5.9: The effect of ramprateon reductionin junction depthfor 1 B 1015cm_ 2 Bimplantsfollowing1050A C spikeanneals.Theeffectof changingthecoolingrateis shown.Notethatincreasingtheramp-downrategivesagreaterjunctiondepthreductionfor higherramp-uprates,sincemoreof theTED thenoccursduringramp-down.

94

Data Simulations

|i0j |i

20j |i

40j |i

60j|k |l |l |l

|l |l |l |l |l |k |l|l |l |l |l |l |l |l |k

|l |l |l |l |l |l |l |l

|k |l |l |l

|l |m |m |m |m

|n |o |o |o |o |o |o |o |o |n |o |o |o |o |o |o |o |o |n |o |o |o |o |o |o |o |o |n |o |o |o |o

Depth (nm)

Data from Downey et al.

1018

1019

1020

1021

Con

cent

ratio

n (c

m

r

-3)

425 oC/s

50 { oC/s

250 eV B+, 1050oC/spike

Figure5.10: Comparisonof simulationandexperimentfor a 1 B 1015cm_ 2 250 eV B |implantfor a1050A C spikeannealin 33ppmO2 in N2 ambient.Ramp-upratesare50A C/sand425A C/s,andinitial ramp-down rateis 87A C/s. Datafrom Downey et al. [30].

95

Data Simulations

|i0j |i

20j |i

40j |i

60j|k |l |l |l

|l |l |l |l |l |k |l|l |l |l |l |l |l |l |k

|l |l |l |l |l |l |l |l

|k |l |l |l

|l |m |m |m |m

|n |o |o |o |o |o |o |o |o |n |o |o |o |o |o |o |o |o |n |o |o |o |o |o |o |o |o |n |o |o |o |o

Depth (nm)

Data from Downey et al.

1018

1019

1020

1021

Con

cent

ratio

n (c

m

r

-3)

425 oC/s

50 { oC/s

500 eV B{ +, 1050oC/spike

Figure5.11: Comparisonof simulationandexperimentfor a 1 B 1015cm_ 2 500 eV B |implantfor a1050A C spikeannealin 33ppmO2 in N2 ambient.Ramp-upratesare50A C/sand425A C/s,andinitial ramp-down rateis 87A C/s. Datafrom Downey et al. [30].

96

Data Simulations

|i0j |i

20j |i

40j |i

60j|k |l |l |l

|l |l |l |l |l |k |l|l |l |l |l |l |l |l |k

|l |l |l |l |l |l |l |l

|k |l |l |l

|l |m |m |m |m

|n |o |o |o |o |o |o |o |o |n |o |o |o |o |o |o |o |o |n |o |o |o |o |o |o |o |o |n |o |o |o |o

Depth (nm)

Data from Downey et al.

1018

1019

1020

1021

Con

cent

ratio

ns (

cm}

-3)

425 ~ oC/s

50 { oC/s

1 KeV B+, 1050oC/spike

Figure5.12: Comparisonof simulationandexperimentfor a 1 B 1015cm_ 2 1 keV andimplantfor a1050A C spikeannealin 33ppmO2 in N2 ambient.Ramp-upratesare50A C/sand425A C/s,andinitial ramp-down rateis 87A C/s. Datafrom Downey et al. [30].

97

5.3 Summary

In summary, we have investigatedthephenomenawhich control junctiondepthfor ultra-low energy boronimplants.We find it is possibleto modeltheextentof diffusionduringbothsoakandspike RTA (rapid thermalanneals)with varyingrampratesby consideringthefull thermalcyclewith modelsdevelopedin previoussections.Thesemodelsallow theoptimizationof RTP annealingcyclesconsideringthe trade-offs betweenjunction depthandsheetresistance.For example,with 1050A C spike anneals,theactive dose(andthussheetconductivity) variesapproximatelylinearly with junction depth. However, fasterrampratesallow the useof higherspike temperatures,with associatedhigheractivationandreducedsheetresistancefor thesamejunctiondepth.

98

Chapter 6

High Energy Implants and VacancyClustering

Understandingandmodelingvacancy clustersis essentialto modelingdiffusionfollowingwell formationandexploringthenoveluseof vacanciesin theformationof next generationdevices.For example,useof higherenergy sub-amorphizingSi implantshasbeenfoundtoreducetransientenhanceddiffusionfor mediumdoseboronimplants[92]. Fig. 6.1showsexperimentsby Sultanet al. [92] in which a Si pre-implantwasusedto obtainshallowerboronjunctions.In this chapter, we modeltheformationandsubsequentannealingof thevacancy rich layerproducedfrom highenergy implants.

6.1 Vacancycluster model

Bongiornoet al C performedtight binding moleculardynamics(TBMD) calculationstoobtainformationandthusbindingenergiesfor vacancy clustersin silicon for n � 35 [11].Their resultsshow thatdifferentgrowth patternsfor clusterformationexist. Thebindingenergy Eb

Zn[ for addinga vacancy to a n ] 1 size cluster is not a smoothfunction of

size but rather it is non-monotonic. As shown in Fig. 6.2 for small clustersizes(n �24), HexagonalRing Clusters(HRC, clustersgrown by removing Si atomsfrom the 6-memberedringspresentin theSi crystalstructure)aremoreenergetically favorablewithrespectto SpheroidalClusters(SPC,clustersgrown removing Si atomsfrom successiveshellsof neighborsof givenatoms).Hence,we usevaluesfor SPCfor largerclustersandHRCfor smallerclusters.In theabsenceof TBMD calculationsfor clusterslargerthan35,we usea functionalform for thebindingenergy from Jaraizet al C [59]. Discretereactionsaresolvedat eachclustersize.Clusterscangrow or dissolvewith additionor releaseof avacancy,

Vn _ 1 X V � Vn C (6.1)

99

5 keV B only 100 keV Si + 5 keV B only

|i0j |i

500j |i

1000j |i

1500j |i

2000j|k |l |l |l |l

|l |l |l |l |k |l |l

|l |l |l |l |l |l |k |l

|l |l |l |l |l |l |l |k

|l |l |l |l |l |l |l |l |k |m |m |m |m |m

|n |o |o |o ||o |o |

|o |n |o ||o |o |o |

|o |o |n |o |o |o |o ||o |o |o |n |o |o |o |o |o |o |o |o |n

Depth (A)� p1016

1017

1018

1019

1020 C

once

ntra

tion

(cm

r

-3)

2 x 10� 14 cm-2 B,800� oC/60s + 1000oC/15sData from Sultan et al.

Figure6.1: Boronprofilesformedfrom a2 B 1014 cm_ 2, 5 keV B implantaftera two-stepannealat 800A C/60secandthen1000A C/15sec.A shallower junction is formedif a 100keV Si pre-implantis usedprior to theboronimplantation.

Vacancy clusterscanalsodissolveby annihilationwith interstitials,

Vn X I � Vn _ 1 C (6.2)

Thenetrateof formationof sizen clusterfrom sizen ] 1 is givenby thesumof theratesof Eqs.6.1and6.2as:

Rn U RV � Vn � 1Vn

] RI � VnVn

C (6.3)

All reactionkineticsareassumeddiffusion limited, andhencethe rateof formationRV � Vn � 1

Vnof Vn from Eq.6.1 is givenby,

RV � Vn � 1Vn U 4πσV � Vn � 1

n _ 1 DV �� CVn � 1CV ] CVn

KV � Vn � 1Vn

�� W (6.4)

whereDV is thevacancy diffusivity andσV � Vn � 1n _ 1 is thecaptureradiusof thereactionand

100

HRC SPC

|F0G |F

10|F

20|F

30|F

40

|H0

|H10

|H20

|H30

|H40 |I |I |I |I |I

|J

|J

|J

|J

|J

Vacancy Cluster Size (n)yTBMD Calculations

6� 10

14

18

24z

Ef (

eV)

Bongiorno et al.

Figure6.2: Clusterenergeticscalculationsfrom Bongiornoetal. [11]. It canbenotedthatfor smallclusters(n � 24),HexagonalRingClustersaremoreenergeticallyfavorablewithrespectto SpheroidalClusters.

is definedas

σV � Vn � 1n U AV � Vn � 1

cap

4πahopC (6.5)

ahop is thehopdistanceandis takento beequalto ao, thelatticeconstantof silicon. Ancap

is thecapturecross-sectionandis givenby,

AV � Vn � 1cap U π

ZrV � Vn � 1cap [ 2 U 4π

Zn ] 1[ 2� 3a2

0 C (6.6)

KV � Vn � 1Vn

is theequilibriumconstantfor Eq.6.1andis givenas,

KV � Vn � 1Vn U \ 1

5 B 1022 cm_ 3 ^ exp � Eb

Zn[

kT � (6.7)

101

Thereactionratefor Eq.6.2 is givenas,

RI � VnVn U σI � Vn

n DI �� CVnCI ] CVn � 1

KI � VnVn

�� C (6.8)

Theequilibriumconstantfor this reactioncanbeobtainedas,

KI � VnVn � 1 U 1

KV � Vn � 1Vn

C YI C YV C (6.9)

Weassumea smallbarrierEI � V of 0.2eV to I/V recombination[33] andhence

σI � Vnn U AI � Vn

cap

ahopexp ��] EI � V

kT � (6.10)U 4π

Zn[ 2� 3a0 exp � ] EI � V

kT � C (6.11)

Thevacancy clusterenergiesfrom Bongiornoet al C [11] areshown in Table6.1. Forlargersizedvacanciesthebindingenergy usedfrom Jaraizet al C [59] is

Eb

Zn[ U 3 C 65 ] 5 C 15 � n � 2� 3� ] Z

n ] 1[�� 2� 3��� (6.12)

Net I andNet V concentrationsfrom TRIM [10] areusedasinitial conditions.We useananalyticalmodelfor interstitialtypeextendeddefectsfrom previouswork by Genceret al C[40, 41,42,43] As perthis model,interstitialsagglomerateinto

R311S defectsandfurther

transforminto loops. TheR311S andloop modelsarecalibratedto transmissionelectron

microscopy (TEM) data[35, 81].

6.2 Comparison to Au-labeling experiments

Oneof the primary problemsassociatedwith modelingvacancy clustersis the difficultyof directly observingthedefects.Most of theavailableexperimentsprovide indirectevi-denceof thepresenceof vacancy clusters.In this paper, we useAu in-diffusiondata[96]from MeV Si implants. In the experiments[96] considered,Si wasimplantedto a doseof 1016cm_ 2 at differentMeV energies. The implantswereperformedat 300A C to pro-moterecombinationof pointdefectsandthusavoid amorphization.Thesampleswerethenannealedat differenttemperaturesandtimes. Finally, they wereimplantedwith Au andannealedata lower temperature(750A C). Au from theimplantwasfoundto getteraroundRp/2 andwasmeasuredby RBS.Thefinal Au concentrationwasreportedto berelativelyinsensitive to the time of Au drive-in diffusion and is muchhigher than its equilibrium

102

Table6.1: Parametersfrom Bongiornoet al C [11] usedfor the simulations.Ef

Zn[ is the

formationenergy andEb

Zn[ is thebindingenergy in eV. We useSPCformationenergies

for n � 24andHRC for theclusterssmallerthan25.

Size 1 2 3 4 5 6 7 8 9 10Ef

Zn[ 3.40 5.20 7.14 9.36 10.68 11.37 13.7 14.08 14.72 15.58

Eb

Zn[ - 1.60 1.46 1.18 2.08 2.71 1.07 3.02 2.76 2.54

Size 11 12 13 14 15 16 17 18 19Ef

Zn[ 17.84 18.27 18.86 19.61 22.03 22.44 23.05 23.79 25.27

Eb

Zn[ 1.14 2.97 2.81 2.65 0.98 2.99 2.79 2.66 1.92

Size 20 21 22 23 24 25 26 27 28Ef

Zn[ 26.31 26.91 28.36 29.86 30.06 30.71 31.04 31.38 31.51

Eb

Zn[ 2.36 2.80 1.95 1.90 3.20 2.75 3.07 3.06 3.27

Size 29 30 31 32 33 34 35Ef

Zn[ 31.87 32.67 33.45 34.22 35.00 36.12 36.4

Eb

Zn[ 3.04 2.6 2.62 2.63 2.62 2.28 3.12

solubility in silicon. TEM imagesrevealAu relatedprecipitatesapproximately150A indiameterdistributedoveradepthsimilar to thatindicatedby theRBSprofiles.Au diffusesrapidly in Si via an interstitial mechanism.Hence,an increasein vacancy concentrationmovesAui morestronglyontosubstitutionalsites,eithervia Aui X V � Aus or by decora-tion of vacanciescluster/voids.ThetotalAu concentrationis dependenton theinteractionof theAui with vacanciesandvacancy clusters.Sincetheexactnatureof thekineticsof Auprecipitationis not clear, we cannotquantitatively determinethevacancy clusterconcen-trationsusingtheseexperiments.Recentresultsindicatethattheratioof gold to vacanciesis infactcloseto 1 [61].

Simulationsshow thatvacancy clustersarefairly stablein thevacancy rich layerandcan lead to enhancementof vacancy diffuserslike Sb. For example,we obtain a timeaveragedvacancy supersaturation( � CV V C YV � ) of T 20 aftera 950A C/600s annealof a2 MeV 1016 cm_ 2 Si implant. Fig. 6.3shows a typical sizedistribution aftera shorttimeannealat 750A C. As shown here,the moststableclustersareof clustersizesn U 6, 10,14, 18 and24. Also shown in the sameplot is the distribution at 950A C. It is clearthatlargerclustersplayamoreimportantroleathighertemperaturesfor which thereis a rapidgrowth to largersizes.Fig.6.4showsa2 MeV 1016 cm_ 2 Si implantannealedat750A C forvaryingtimesandcomparedto experimentaldata[96]. We obtaina very goodpredictionof thedepthdistribution of theclusteredvacancies.At 750A C, theclustersarevery stableandalmostnochangein total clusteredvacancy concentrationis seenbetween10min and

103

|i1� |i

10j |i

100j|k

|k

|k

|k |m |m |m

|n

|n

|n

|n

Cluster Size �

950oC 750oC

108

1010

1012

1014

Tot

al V

acan

cies

in C

lust

er (

cm-2)

Figure6.3: Simulatedsizedistribution of clustersaftera shorttime annealat 750A C and950A C. Clustersareripeninginto largerclustersmorepredominantlyat thehighertemper-ature.Thisalsoshowsthemoststablesmallclustersizesto bearound6, 10,14,18and24dueto thenon-monotonicbindingenergy.

1 h anneals,consistentwith experimentalobservations[96]. Fig.6.5showscomparisonstodataat 950A C. Notethatthesimulationsagreewell with thetime dependenceof thedata.At higher temperatures,vacancy clustersare annihilatedby an increaseddissolutionofinterstitialdefectsfrom thebulk andsurfaceannihilationof vacancies.Shown in Fig. 6.6is thecomparisonto 1000A C data.TheclustersaroundRp/2 arethe largestandthereforethemoststable.Hence,thereis a peakin clusterconcentrationat Rp/2 in thesimulationssimilar to thatobservedin theexperimentaldata[96]. We canfurtheranalyzeour resultsto seethe fraction of vacanciesin smallersizedclusters(n � 36). Note that thesewerethe clustersfor which we usedTBMD resultsfrom Bongiornoet al C [11]. Figs.6.7 and6.8shows thesignificanceof theadditionof largersizedclusters.At 750A C, a significantfraction of smallersizedclustersare present. However, at 950A C most of the clusters,especiallyaroundRp/2 haveripenedinto largerclusters(n � 35).

An important factor in matchingthe vacancy clusteringis relatedto the interstitialclusteringmodelused.Sincethesesimulationsinvolvea high implantdoseof 1016 cm_ 2,we canexpectto seeconsiderabletransformationto loops. Indeed,in all thesimulationsmostof the

R311S defectstransforminto loops. If we useonly a

R311S modelanddo not

104

� Au RBS

|i0.0� |i

0.5� |i1.0� |i

1.5�|k |l |l |l

|l |l |l |l |l |k |l

|l |l |l |l |l |l |l |k

|l |l |l |l |l |l |l |l

|k |l |l |l

|l |m |m |m |m

|n ||o |o |o |o |o |

|o |n |o |o |o |o |o |o |o |o |n |o |o |o |o |o |o |o |o |n |o |o |o |oData from Venezia et al.

Simulation (750oC/10 min) Simulation (750oC/1 hr)

1017

1018

1019

1020

Depth (� µm)

Con

cent

ratio

n (c

m

r

-3)

750� oC/10 mins� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �Figure 6.4: Simulatedclusteredvacancy concentrationscomparedto Au RBS datafor750A C annealsof 10 min and1 h. Simulationshow that thereis very litle changein theclusteredvacancy concentrationbetween10min and1 h. This is in agreementwith resultsfrom Veneziaet al C [96] who also report that Au concentrationsarenearlyconstantforlongerannealsup to 8 h at 750A C. Notethatthesurfacepeakin thedatais becauseof theAu implantusedfor thein-diffusion.

considerloop formation, the vacancy clustersarequickly annihilatedby the interstitialsfrom thebulk at thehighertemperatures.As seenin Fig. 6.9, usingonly a

R311S model

without any loop formationleadsto dissolutionof all the clustersin a time spanof lessthan60 s,contraryto theexperimentalobservations.

105

|i0.0� |i

0.5� |i1.0� |i

1.5�|k |l |l |l |l |l |l|l |l |k |l |l |l |l

|l |l |l |l |k |l |l |l|l |l |l |l |l |k |l |l

|l |l |l |l |l |l |k |l

|l |l |l |m |m |m |m

|n |o |o |o |o |o |o |o |o |n |o |o |o |o |o |o |o |o |n |o |o |o |o |o |o |o |o |n |o ||

|o |o |o |o |o |n |o |o |o |o Au Conc (950oC/10 s) Au Conc (950oC/10 min) Simulation (950oC/10 s) Simulation (950oC/10 min)

1016

1017

1018

1019

1020

Depth (� µm)

Con

cent

ratio

n (c

m

r

-3)

Figure6.5: Simulatedandclusteredvacancy concentrationscomparedto Au RBS dataafter950A C annealof 10 s and10 min. At 950A C, vacancy clustersareannihilatedby anincreaseddissolutionof interstitialdefectsfrom thebulk andlossto thesurface.Notethatthesimulationsagreewell with thetimedependenceof thedata.

106

� Au RBS Simulation

|i0.0� |i

0.5� |i1.0� |i

1.5�|k |l |l |l|l |l |l |l |l |k |l

|l |l |l |l |l |l |l |k|l |l |l |l |l |l |l |l

|k |l |l |l

|l |m |m |m |m

|n |o |o |o |o |o |o |o |o |n |o |o ||

|o ||o |o |n |o |o |o |o |o |o |o |o |n |o |o |o |o

Data from Venezia et al.

1017

1018

1019

1020

Depth (� µm)

Con

cent

ratio

n (c

m

r

-3)

1000oC/10 mins� � � � � � �� � � � � � � � � � � � � � � �

� � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � �

Figure6.6: Simulationandclusteredvacancy concentrationscomparedto Au RBS dataafter a 1000A C annealof 10 min. At 1000A C, the vacancy clustersare increasinglyan-nihilated from the surfaceand the dissolutionof interstitial defectsfrom the bulk. TheclustersaroundRp/2 arethe largestandthereforethemoststable.Hencethereis a peakin clusterconcentrationat Rp/2 (0.9µm) in thesimulationssimilar to thatobservedin theexperimentaldata[96].

107

Au RBS Total V in All Clusters Total V in Small

|i0.0� |i

0.5� |i1.0� |i

1.5�|k |l |l |l |l |l |l|l |l |k |l |l |l |l

|l |l |l |l |k |l |l |l|l |l |l |l |l |k |l |l

|l |l |l |l |l |l |k |l

|l |l |l |m |m |m |m

|n |o |o |o |o |o |o |o |o |n |o |o |o |o |o |o |o |o |n |o |o |o |o |o |o |o |o |n |o ||

|o |o |o |o |o |n |o |o |o |oData from Venezia et al. 

Clusters (2 -- 35)

1016

1017

1018

1019

1020

Depth (� µm)

Con

cent

ratio

n (c

m

r

-3)

(750¡ oC/10 min)

Figure6.7: At 750A C,aconsiderablefractionof thevacanciesarein smallersizedclusters.

108

Au RBS Total V in All Clusters Total V in Small

|i0.0� |i

0.5� |i1.0� |i

1.5�|k |l |l |l |l |l |l|l |l |k |l |l |l |l

|l |l |l |l |k |l |l |l|l |l |l |l |l |k |l |l

|l |l |l |l |l |l |k |l

|l |l |l |m |m |m |m

|n |o |o |o |o |o |o |o |o |n |o |o |o |o |o |o |o |o |n |o |o |o |o ||o |o |o |n |o |o |o |o |o |o |o |o |n |o |o |

|oData from Venezia et al. 

Clusters (2 -- 35)

1016

1017

1018

1019

1020

Depth (� µm)

Con

cent

ratio

n (c

m

r

-3)

(950¡ oC/10 min)

Figure6.8: Theabovefigureshowsthesignificanceof theadditionof largersizedclusters.At 950A C most of the clustersespeciallyaroundRp/2 have ripenedinto larger clusters(n � 35).

109

¢£ {311} + Loops¤ {311}

|i1

|i10

|i100¥ |i

1000

|k|k

|k

|k |m |m |m |m

|n|n

|n

|n

Time (s)¦Equilibrium vacancy dose

Au Dose (950oC)

108

1010

1012

1014

Tot

al V

acan

cy D

ose(

cm

-2)

950§ oC simulations using

¨ ¨ ¨ ¨ ¨ ¨© © © © © ©ª ª ª

ª ª ª

Figure6.9: Time dependenceof vacanciesin system(depthof 1000µm). Using only aR311S modelwithout any loop formationleadsto dissolutionof all theclustersby about

60 s, contraryto experiments.It shouldbenotedthat theexperimentalvaluereportedbyVeneziaet al C [96] is measuredbetween0.2 – 1 µm to avoid including the Au implantprofile. This methodalso leaves out the doseof vacanciesbelow 0.2 µm. Hencetheexperimentalresultsareexpectedto belower thanthesimulationresultsdespitehaving agoodagreementin thedepthdistributions.Also, without loopsthevacancy concentrationdropsbelow theequilibriumvaluedueto theinterstitialsupersaturationfrom thedissolvingR311S defects.

110

6.3 Moment basedmodels

The physicalrateequationmodeldescribedin the previous sectionsis computationallyveryexpensivesincethefull sizedistributionis trackedateachpoint in space.Evenif onelimits thenumberof precipitatesizesthatwill besolvedfor, thenumberof variablesis stillvery large for efficient solutionof theequationsystem.If thesystemhasmultiple spatialdimensions,the numberof solutionvariablesbecomesprohibitively large. Clejanet al.developeda moreefficient approachbasedon consideringthe sizedistribution in termsof a smallnumberof moments[23]. Only theevolution of thosemomentsareconsideredratherthanthefull distributionateachpoint in space.Werestatetheequationsasdescribedin Section4.1againfor convenience.Themomentsaredefinedas[23]:

mi U ∞

∑n« 2

ni fn W (6.13)

wherei U 0 W 1 W 2 W C¬C¬C . Thezerothordermomentof thedistribution is simply theprecipitatedensity, while the first momentcorrespondsto the densityof precipitatedsoluteatoms.Higherordermomentsfurtherdescribetheshapeof thesizedistribution. This transformsthesystemof equationsto thefollowing set[23]:

∂mi

∂t U 2iR2 X ∞

∑n« 2 ­

Zn X 1[ i ] ni ® Rn (6.14)

NotethatthesumsovertheRn canall bewritten in termsof sumsover fn, nfn, etc.Hence,they canbecalculatedfrom themomentsif momentsareusedto describethedistribution.This reducesthesystemof equationsto besolvedto:

∂mi

∂t U DV ­ 2iλ1C2V X m0CVγ |i ] m0Cssγ _i ®

γ |i U ∞

∑n« 2 ­

Zn X 1[ i ] ni ® λn fn (6.15)

γ _i U λ1C Y1 f2 X ∞

∑n« 2 ­ ni ] Z

n ] 1[ i ® λn _ 1C Yn _ 1 fn

whereC Yn U C Yn V Css and fn U fn V m0.

If we allow interstitialsreactwith the vacancy clusters,we would needto addextratermsto themomentequations.Wecanfurtherneglectthegenerationof interstitialsfromvacancy clusters(backwardreactionof Eq. 6.2). Thus,with thesamedefinitionsof γi asbeforeandsettingγ0 U λ2 f2 themomentscanbederivedto be:

∂m0

∂t U DV ­ λ1CV2 ] m0Cssγ0

® ] DICIm0γ0 (6.16)

111

∂m1

∂t U DV ­ 2λ1CV2 X m0CVγ |1 ] m0Cssγ _1 ® ] DICIm0 ­ γ0 X γ |1 ®

∂m2

∂t U DV ­ 4λ1CV2 X m0CVγ |2 ] m0Cssγ _2 ® ] DICIm0 ­ γ0 X γ |2 ] 2γ |1 ®

∂CV

∂t U ] DV ­ 2λ1CV2 X m0CVγ |1 ] m0Cssγ _1 ® X DICIm0γ0

∂CI

∂t U ] DICIm0 ­ γ0 X γ |1 ®Sinceany finite numberof momentsis insufficientto describeanarbitrarydistribution,

it is necessaryto adda closureassumption,which is anassumptionabouttheform of thedistribution, fn U f

Zn W zi [ . The zi areparametersof the distribution which canbe deter-

minedfrom the moments.The numberof momentswe needto keeptrack of equalsthenumberof parametersin thedistribution function.

Sincewe want to develop the mostcomputationallyefficient model,we considerthepossibilityof representingthesystemin termsof its first two momentsfollowing theworkof GencerandDunham[43]. Thevaluecanbefoundapproximatelyfrom aweightedsumof λn. Therefore,our systemreducesto:

∂m0

∂t U R2 U Dλ ¯ C2V ] m0Cssγ0 ° ] DIλCIm0γ0

∂m1

∂t U 2R2 X Dλm0

ZCV ] Cssγ1 [±] DIλCIm0

Z1 ] γ0 [ (6.17)

∂CV

∂t U ]³² 2R2 X Dλm0

ZCV ] Cssγ1 [´X DIλCIm0γ0 µ

∂CI

∂t U ] DIλCIm0

Z1 X γ0 [

with

γ0 U C Y1 f2γ0 U f2 U γ0 V C Y1 (6.18)

γ1 U ∞

∑n« 2

C Yn fn| 1

Usingthefull setof rateequations,it is now possibleto calculateγi numerically. Thefullrateequationmodelwassimulatedat a singlegrid point. A largemaximumsizeof 1000waschosento remove any errorsdueto pile-up at the largestsize. The simulationwasrun for different timesto extract γi andm1. Figs. 6.10 and6.11show γi plottedagainstm1 extractedfrom the full model. It canbe notedthat γi satisfy the following limits as

112

expected[43]:

limm1 ¶ 2

γ0 U C Y1lim

m1 ¶ ∞γ0 U 0 (6.19)

limm1 ¶ 2

γ1 U 0

limm1 ¶ ∞

γ1 U 1

For larger m1, γi are found to have only a weak dependenceon temperature.Further,γi seemto be uniquefunctionsof m1 within reasonableerrors. However to confirm thishypothesisit is necessaryto beableto obtainthesameγi irrespectiveof its thermalhistory.Figs.6.10and6.11alsoshow comparisonsbetweentwo-stepanneal.It wasfoundsamplessimulatedat 1000A C with and without a 400A C preannealgave very similar γi , givingcredenceto thepossibilityof usingonly thefirst two momentsto modelthis system.It isnow possibleto find analyticexpressionsto fit theobtainedγi . For example,we cannowusethe obtainedγi in the setof equationsgiven by Eqns.6.18. Thereareno other freeparametersin this system.NotethatCss canbetakenasC YV andis not a fitting parameter.Usingtheγi thusderived,wehoweverfoundthesimulationto benumericallyunstabledueto thestrongchangein γi at smallaveragesizes.Hencea new setof γi wereconstructedneglectingsmallsizeeffects.A kinetic barriercanbeaddedto correctfor thegrowth rateatsmallsizes.Figs.6.12and6.13show suchγi values.A barrierof 0.4eV wasaddedto allreactionsasa correctionto includesmallsizeeffects.This systemwasnow foundto givegoodmatchto experimentaldataandthefull rateequationmodel. As shown in Fig. 6.15the AKPM modelmatchesthe full rateequationmodelfairly well over both dissolutionanddepthat 1000A C. FurtherFig. 6.14shows annealsat 950A C showing goodtime andtemperaturedependence.

113

·

|i1� |i

10j |i

100j|k

|k|k

|k |m |m |m

|n|n

|n

|n

Average Size (n)

400 oC 800 oC 1000 oC 400 oC +

100

104

108

1012

γ0

1000 oC

¸¸¸¸¸ ¸ ¸ ¸ ¸ ¸ ¸¸¸¸ ¸ ¸ ¸ ¸¸¸ ¸Figure6.10: γ0 valuesextractedfrom simulationsof the full systemof rateequationsforthreedifferenttemperatures(400,800,1000A C) . Also shown in thesameplot is γ0 valuefor a 1000A C annealaftera preannealat 400A C. Notethattheγ0 is almostindependentofits thermalhistory.

114

¹

|i1� |i

10j |i

100j|k

|k|k

|k

|k |m |m |m

|n|n

|n

|n

|n

Average Size (n)

400 oC 800 oC 1000 oC 400 oC

100

104

108

1012

1016

γ1

+ 1000 oCº º º º º º º º º ººº º

Figure6.11: γ1 valuesextractedfrom simulationsof the full systemof rateequationsforthreedifferenttemperatures(400,800,1000A C) . Also shown in thesameplot is γ1 valuefor a 1000A C annealaftera preannealat 400A C. Notethattheγ1 is almostindependentofits thermalhistory.

115

AKPM

|i0j |i

25|i

50j |i

75|i

100j|k

|k|k |m |m |m |m |m

|n|n

|n

Average Size (n)

1000 oC

100

102

104

γ0

Figure6.12: Analytic fit to γ0 neglectingsmall sizeeffects. This wasdoneto avoid theexponentialchangein γi values.

116

AKPM

|i0j |i

20j |i

40j |i

60j |i

80j |i

100j|k

|k|k |m |m |m |m |m |m

|n|n

|n

Average Size (n)

1000 oC

100

104

108

γ1

Figure6.13:Analytic fit to γ1 neglectingthenearexponentialchangenearsmallsizes.

117

|i0.0� |i

0.5� |i1.0� |i

1.5�|k |l |l |l |l |l |l|l |l |k |l |l |l |l

|l |l |l |l |k |l |l |l|l |l |l |l |l |k |l |l

|l |l |l |l |l |l |k |l

|l |l |l |m |m |m |m

|n |o |o |o |o |o |o |o |o |n |o |o |o |o |o |o |o |o |n |o |o |o |o |o |o |o |o |n |o ||

|o |o |o |o |o |n |o |o |o |o Au Conc (950oC/10 s) Au Conc (950oC/10 min) AKPM Simulation (950oC/10 s) AKPM Simulation (950oC/10 min) FKPM Simulation (950oC/10 s) FKPM Simulation (950oC/10 min)

1016

1017

1018

1019

1020

Depth (� µm)

Con

cent

ratio

n (c

m

r

-3)

Figure6.14:Comparisonof AKPM andfull discreteclustermodelat 950A C

118

» Au RBS AKPM Simulation FKPM Simulation

|i0.0� |i

0.5� |i1.0� |i

1.5�|k |l |l |l|l |l |l |l |l |k |l

|l |l |l |l |l |l |l |k|l |l |l |l |l |l |l |l

|k |l |l |l

|l |m |m |m |m

|n |o |o |o |o |o |o |o |o |n |o |o |o |o |o |o |o |o |n |o |o |o |o ||o |o |o |n |o |

|o |oData from Venezia et al. 

1017

1018

1019

1020

Depth (� µm)

Con

cent

ratio

n (c

m

r

-3)

1000oC/10 mins¼ ¼ ¼ ¼ ¼ ¼ ¼¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼

¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼

Figure6.15:Comparisonof AKPM andfull discreteclustermodelat 1000A C

119

6.4 Summary

A setof discreteclustersareusedto modelvacancy clusterevolution after high energyion-implantationin Si. Theparametersfor this systemarefrom atomisticcalculations.Itwasfoundthat this systemis ableto predictthetemperature,time anddepthdependenceof vacancy clustersseenin the experimentalresults. A procedurehasbeenproposedtoreducethis complex model into a simple two-momentmodel. The parametersfor thistwo momentmodelarederived from the full rateequationmodelandarefound to givegoodpredictionto data.This efficient two-momentmodelcanbeeasilyincorporatedintotechnologymodelingtoolsandappliedto modelmorecomplex situations.

120

Chapter 7

Conclusionsand Futur eWork

7.1 Summary

Our aim in this work wasto understandandmodeltheevolution of ion implantedsiliconduring annealing,particularlywith respectto the characteristicsshown by boron. In ourwork, wehavecontributedoverarangeof topicsnecessaryto helpin theunderstandingoftheevolutionof anion implantedSi wafer.

Weevaluatedmetaldiffusionexperimentsto betterunderstandpointdefectproperties.Usingaconsistentmodelingapproach,we foundthevacancy diffusivity to beof thesameorderof magnitudeastheinterstitialdiffusivity. Theresultingvacancy diffusivity is muchfasterthan derived from previous analysisbut is much closerto atomisticcalculations.However, we foundit wasnot possibleto identify vacancy transportpropertiesaccuratelyfrom metaldiffusionexperimentsalone.

To understandtheinitial conditionsfor our simulations,we simulatedtheinitial dam-ageannealingprocessto determinethepoint defectconcentrationspresentafterrecombi-nationwithin thedamagecascade.It wasfoundthatfor low doseor highenergy implants,thenumberof interstitialsremainingafter this recombinationcanstronglydeviatefrom a“+1” of the implantdosedueto diffusionof vacanciesto thesurface.We alsosimulatedthefull damageto understandtheeffectof formationof interstitialandvacancy clusters.Itwasfoundthatthoughvacancy clusterscansurviveto relatively long timesat low temper-atures,thechangein observedsupersaturation(relative to usinga“+1” model)is neglible,andhencea “+1” modelcanbeusedeffectively underthesecircumstances.

We evaluateddifferentapproachesto modelingboron/interstitialclustering. In par-ticular, we lookedat modelingboronclustersusinga moment-basedkinetic precipitationmodelandclusterbasedmodels.Wefoundthatbothmodelscanpredictexistingdatawellif necessaryparameterscanbeoptimized.Sinceab-initio calculationshave emergedasapowerful tool to helpdetermineclusterprecursors,clusterbasedmodelshave theadvan-

121

tageof beingmorephysically-basedfor modelinginitial stagesof clustering. A simpleclustermodelwasderived from an extensive modelbasedon atomisticcalculationsper-formedat LawrenceLivermoreNationalLabs[60]. This simplemodelwassuccessfullyusedin modelingboroninterstitialclusters,wasfurtherextendedto includechargestatesof clustersandunderstandmarker experiments.This modelwasalsoableto matchelec-trical activationdata.

Theboronmodelwasusedsuccessfullyin understandingandmodelingultra low en-ergy boron implantsfor both soakandspike anneals.It wasfound that it is possibletomodelnew behavior like saturationof obtainableminimum junction depthin agreementwith experimentalresults. We alsolooked at modelingthe excessvacancy layer formedafterhigh energy implantation.For this,a vacancy clustermodelwasdevelopedbasedonclusterenergeticsvaluesfrom Tight Binding MolecularDynamics(TBMD) calculations[11]. Thismodelwasfurthersimplifiedusingamoment-basedapproachto enableefficientincorporationinto industrialprocesssimulators.

7.2 Futur eDir ections

In recentyears,progressin atomisticcalculationshavemadeit possibleto obtainformationenergies of dopant/defectclusters. However, thesetechniquesbecomecomputationallyprohibitive for largersizedclustersthatcanevolve during theannealingprocess.Hence,althoughthey help us understandthe clusterprecursors,no calculationsexist for largerclustersizes.Thebehavior of largerclusterscanoftenbeestimatedfrom experimentalob-servations,andthepropertiesexhibitedby suchlargerclusterscanbemodeledefficientlyby usingmoment-basedapproaches.Effective modelingof suchsystemsshouldincludediscreteclustersat small sizesandmomentsto representlarger sizedclusters.This situ-ation is complicatedfor two componentsystemslike boron-interstitialclusters.Heretheclusterscangrow into largerinterstitialor boronrich phases,andthemomentbasedmodelitself needsto bederivedcarefully. This canbesimplifiedby working with a full discretemodelasa basisfor deriving thecouplingbetweenthemoments.It canbeexpectedthatthesemaydependon theform chosenfor theformationenergy of theseclusters.

Ultra low energy implantshave beenfoundto form anamorphouslayerwhich formsa new boridephase.Theimplicationsof theformationof this new phasearenot yet fullyclearwith regardto contributing to point defectsupersaturationsor electricalactivation.New experimentsareneededto highlight the effect of the formationof this new phase.Experimentalresearchgroupsarefocussedon increasingtheactivationbeyond the solidsolubility of boronby differentmethodslike laseranneals,pre-amorphizationimplants.The underlyingphysicalactivation mechanismsduring theseprocessesis an importantareafor futurestudy.

Accordingto theInternationalTechnologyRoadmapfor Semiconductors[1], devicesproducedaround2010with gatelengthsof 50nmwill needhighly activesub-20nmjunc-

122

tion depths(around100–200monolayers).As the channellengthdecreases,lateraldif-fusionbecomesmoreimportant. However, accordingto currentunderstandingof dopantdiffusion, suchjunctionsareunattainablefor boron. Overcomingthesebarriersrequiresa betterunderstandingof all processesat an atomisticlevel. This not only includesin-teractionof boronwith point defectsbut alsoincludesinteractionwith interfaces(oxide,silicides)andotherbulk trapsandimpurities.

123

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VITA

EDUCATION½ Ph.D. in Manufacturing Engineering 2001BostonUniversity, Departmentof ManufacturingEngineering,Boston,MA.½ Bachelorof Technologyin Metallur gical Engineering 1995Instituteof Technology, BanarasHinduUniversity, Varanasi,India.

EXPERIENCE½ BostonUniversity, Boston,MA 1996–2000ResearchAssistantfor Assoc.Prof. ScottDunhamin the Departmentof ElectricalandComputerEngineering.½ Intel Corporation, Hillsboro,OR 1997TCAD Engineer(summerintern).½ BostonUniversity, Boston,MA 1995–1996TeachingAssistantin theDepartmentof ManufacturingEngineering.

PUBLICATIONS½ S.Chakravarthi andS.T. Dunham,“A SimpleContinuumModel For BoronClus-teringBasedon Atomistic Calculations”,Submitted(afterrevision) J.Appl. Phys.,(2000).½ S. Chakravarthi andS.T. Dunham,A PhysicalModel for Simulationof VacancyClustersin Ion ImplantedSilicon, in Preparation.to besubmittedto J.Appl. Phys.½ S.T. Dunham,A.H. GencerandS. Chakravarthi , “Modeling of DopantDif fusionin Silicon”, IEICE Trans.Electron.E82C(6) 800-812June(1999).½ S. Chakravarthi andS.T. Dunham,“Modeling of Boron Deactivation/ActivationKinetics during Ion-implantAnnealing”, InternationalConferenceon Simulationof SemiconductorProcessandDevices(SISPAD) 2000,TechnicalDigest,(2000).½ S. Chakravarthi , A.H. Gencer, S.T. Dunhamand D.F. Downey, “UnderstandingandModeling RampRateEffectson Shallow JunctionFormation”, Si Front-EndProcessingPhysicsandTechnologyof Dopant-DefectInteractionsII, MaterialsRe-searchSocietyProceedings,(2000).½ S. Chakravarthi andS. T. Dunham,“Modeling Of Vacancy ClusterFormationinIon ImplantedSilicon”, in Fifth Intl. Symp. On ProcessPhys. andModeling inSemiconductorDevice Manufacturing,ElectrochemicalSocietyMeetingProceed-ings,(1999).

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½ S.Chakravarthi andS.T. Dunham,“A SimpleContinuumModel for SimulationofBoronInterstitialClustersbasedon Atomistic Calculations”, InternationalConfer-enceonSimulationof SemiconductorProcessandDevices(SISPAD) 1998,Techni-calDigest,p.55(1998).½ S. T. Dunham,S. Chakravarthi , andAlp H. Gencer, Beyond TED: Understand-ing BoronShallow JunctionFormation,In InternationalElectronDevicesMeeting1998,TechnicalDigest,IEEE(1998).½ S.Chakravarthi andS.T. Dunham, “Point DefectPropertiesFromMetalDif fusionExperiments- Whatdoesthedatareally tell us”, in DefectsandDiffusionin SiliconProcessing,V.469(MaterialsResearchSocietyProceedings,Pittsburgh,PA, 1997)½ S. Chakravarthi andS. T. Dunham,Influenceof ExtendedDefectModelson Pre-diction of Boron TransientEnhancedDiffusion, In Silicon Front EndTechnology— MaterialsProcessingandModelingEE3.5,(MaterialsResearchSocietyMeeting,1998).½ A.H. Gencer, S.Chakravarthi , I. ClejanandS.T. Dunham,FundamentalModelingof TransientEnhancedDiffusionthroughExtendedDefectEvolution,in DefectsandDiffusion in Silicon Processing,V. 469 (MaterialsResearchSocietyProceedings,Pittsburgh,PA, 1997)½ A.H. Gencer, S. Chakravarthi andS.T. Dunham,PhysicalModelingof TransientEnhancedDiffusion andDopantDeactivation via ExtendedDefectEvolution, In-ternationalConferenceon Simulationof SemiconductorProcessandDevices(SIS-PAD) 1997,TechnicalDigest,(IEEE,Piscataway, NJ,1997).

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