Computer simulation of electronic excitation in atomic collision cascades [Elektronische Ressource] / von Andreas Duvenbeck

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Computer Simulation of Electronic Excitation inAtomic Collision Cascadesvom Fachbereich Physikder Universita¨t Duisburg-Essenzur Erlangung des akademischen Grades einesDoktor der Naturwissenschaften(Dr. rer. nat)genehmigteDissertationvonAndreas Duvenbeck aus DorstenReferent: Prof. Dr. A. WucherKorreferent: Prof. Dr. M. SchlebergerTag der Einreichung: 20.12.2006Tag der mu¨ndlichen Pru¨fung: 05.04.20072Contents1 Introduction 52 Fundamentals 112.1 Sputtering Models . . . . . . . . . . . . . . . . . . . . . . . 112.1.1 Single Knock-On Regime . . . . . . . . . . . . . . . 122.1.2 Linear Cascade Regime . . . . . . . . . . . . . . . . 122.1.3 Spike Regime . . . . . . . . . . . . . . . . . . . . . . 142.2 Formation of Ions in Sputtering . . . . . . . . . . . . . . . . 173 MD-Simulation 253.1 History of MD-Simulations . . . . . . . . . . . . . . . . . . 253.2 Today’s Role of MD . . . . . . . . . . . . . . . . . . . . . . 263.3 MD-Simulation of Collision Cascades . . . . . . . . . . . . . 283.3.1 Potentials . . . . . . . . . . . . . . . . . . . . . . . . 293.3.2 Numerical Integration . . . . . . . . . . . . . . . . . 344 SPUT93 394.1 Model Crystal . . . . . . . . . . . . . . . . . . . . . . . . . . 404.2 Initial and Boundary Conditions . . . . . . . . . . . . . . . 404.3 Impact Zone. . . . . . . . . . . . . . . . . . . . . . . . . . . 414.4 Numerical Integration . . . . . . . . . . . . . . . . . . . . . 434.5 Trajectory Analysis . . . . . . . . . . .

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• Physik

Informations

• Publié par: universitat_duisburg-essen
• Publié le: 01 janvier 2007
• Nombre de lectures: 17
• Poids de l'ouvrage: 3 Mo

Extrait

ComputerSimulationofElectronicExcitationin
AtomicCollisionCascades

vomFachbereichPhysik
derUniversita¨tDuisburg-Essen
zurErlangungdesakademischenGradeseines
DoktorderNaturwissenschaften
(Dr.rer.nat)
genehmigte
Dissertation
novAndreasDuvenbeckausDorsten

Referent:Prof.Dr.A.Wucher
Korreferent:Prof.Dr.M.Schleberger

TTaaggddeerrmEiu¨nnredilicchhuenng:P2r0u¨.f1u2n.g2:00065.04.2007

2

Contents

1Introduction5
2Fundamentals11
2.1SputteringModels.......................11
2.1.1SingleKnock-OnRegime...............12
2.1.2LinearCascadeRegime................12
2.1.3SpikeRegime......................14
2.2FormationofIonsinSputtering................17
3MD-Simulation25
3.1HistoryofMD-Simulations..................25
3.2Today’sRoleofMD......................26
3.3MD-SimulationofCollisionCascades.............28
3.3.1Potentials........................29
3.3.2NumericalIntegration.................34
4SPUT9339
4.1ModelCrystal..........................40
4.2InitialandBoundaryConditions...............40
4.3ImpactZone...........................41
4.4NumericalIntegration.....................43
4.5TrajectoryAnalysis.......................43
4.6Visualization..........................45
5LinearTransportModel49
5.1Introduction...........................49
5.2Description...........................51
5.2.1Excitation:Principle..................52
5.2.2Excitation:NumericalImplementation........58
5.3ApplicationoftheModel...................59
5.3.1DiusionCoecient..................59
5.3.2ApplicationonAg...................61
5.4Conclusion...........................68

3

4

CONTENTS

6NonlinearTransportModel69
6.1DescriptionoftheModel....................70
6.1.1DiusionCoecient..................70
6.1.2NumericalImplementation..............74
6.2ApplicationonSilver......................76
6.3Conclusion...........................82

7NonlinearTransportModelII85
7.1DescriptionoftheModel....................85
7.2Results..............................91
7.3Conclusion...........................99

8EnergyPartitioning101
8.1DescriptionoftheCalculation.................101
8.2Results..............................101
8.3Conclusion...........................105

9Conclusion

ASnapshotsofTraj.207

107

109

Chapter1

Introduction

Everybodyknowsthegame”poolbilliard”,whichismostcommonlyplayed
onarectangulartablewithalengthof7feetandawidthof3.5feet.At
thebeginningofeachgame,atotalnumberofnineorfteenbilliardballs
arearrangednexttoeachotherintriangularshapenearthefootofthe
table.Therstplayeropensthematchwiththeso-called“breakshot”,i.e.
thewhitecueballisshotintothetriangleofbilliardballs.Asthecueball
crashesintooneoftheouterballsoftheformationwithsucientvelocity,
thebilliardballsareknockedoutfromtheiroriginalpositionsandbecome
scatteredalloverthetable.Thisphenomenoncanbeexplainedinterms
ofasequenceofcollisionsamongthebilliardballsthatisinducedbythe
cueballimpact.
Inanalogytothismacroscopicbilliardgame,arathersimilarscenario
canbefoundinmodernsurfaceanalysis,however,onananometerlength
scale:Thesecondary-ion-mass-spectrometry(SIMS)[1],oneofthemost
versatilesurfaceanalysistechniques,maybeconsideredasakindofatomic
billiard.Morespecically,theSIMStechniqueusesenergeticatomicpar-
ticlesasprojectilesforthebombardmentofasolidsurfaceplacedwithin
avacuumchamber.Thisbombardmentinducesacomplexseriesofcolli-
sionsamongthenear-surfacetargetatoms.Thissequenceofcollisionswill
inthefollowingbereferredtoas“atomiccollisioncascade”.Thespatial
evolutionofthisatomiccollisioncascadewithinthetargetmaterialtakes
placewithinsomepicosecondsandtypicallyamountstoafewnanometer
dependingonthebombardingconditionsaswellasonmaterialparameters.
Inthecourseofthecollisioncascade,someoftheatomssetintomotion
maystrikenearbyparticleslocatedontheoutermostatomicmonolayers
ofthetargettherebyejectingthemothesurfaceintothevacuum.This
processisusuallycalled“sputtering”.
ThebasicideaoftheaforementionedSIMStechnologyistousethe
uxofsputteredparticlesasasourceofinformationonthemicroscopical
stoichiometricstructureintheproximityofthebombardedsurfacespot.
Bylaterallyvaryingthebombardingspotonthesurface,theentiresurface
canbescannedandchemicallyanalyzed.

5

6CHAPTER1.INTRODUCTION
However,theparticledetection,whichbasesupondeectioninelectric
elds,islimitedtothosespeciesthatleavethesurfaceinanionizedstate.
Duetothefactthattheionizedfractionofthetotaluxofsputtered
atomsoftenonlyamountstoafewpercentorevenless,thedetectionis
oftenhamperedbyratherlowsignals.Moreover,itiswellknown,that
theionizationprobabilityofemittedparticlesdoesnotonlydependonthe
elementaryspecies,butalsoonthelocalenvironmentfromwhichaparticle
leavesthesurface.Therefore,themeasuredsignalsfordierentsputtered
speciesdonotnecessarilyrepresentthestoichiometriccompositionofthe
sample.Intheliterature,thisphenomenonisknownasthe“MatrixEect”
inSIMS.
InordertocircumventthisprincipalshortcomingofSIMS,thereexist
twodierentconcepts.
(i)Fromanexperimentalpointofview,onewell-establishedapproachis
toemploycertaintechniquestoionizetheneutralatomsdirectlyafterthey
havebeenejectedfromthesurface.Thisismostcommonlyrealizedeither
bymeansofphotoionizationusinglaserirradiation[2],orbyelectronim-
pactionizationinanoblegasdischargechamber[3].Bothpost-ionization
techniquesavoidcomplicatedmatrixeectsinSIMSbydecouplingthe
emissionprocessandtheionizationprocessfromeachother.However,
bothoftheaforementionedtechniquesconstituteadirectinterventioninto
thenascentuxofsputteredparticles,whichmayalsoconsistofagglom-
eratesofatomssuchasmoleculesorclusters.Thelatter,inturn,maybe
fragmentedduringthepost-ionizationprocessand,therefore,signicantly
distortthemeasuredmassspectrum.Inparticular,thequantitativeanal-
ysisofspectrafromorganicsamplesishamperedbythecomplexityofthe
post-ionizationinducedfragmentationprocesses.
(ii)AnalternativeansatztotacklethequanticationprobleminSIMS
isthetheoreticalaccountoftheionizationprobabilityofsputteredparticles,
whichconstitutesavivideldofresearchandhasbeenrecentlyconsidered
sa“themosturgentunsolvedprobleminatomiccollisionsinsolids.”
R.BaragiolainInvitedreview:Somechallengingunsolvedproblemsinatomic
collisionsinsolids,Nucl.Instr.andMeth.B237(2005)520
Itiswellknown[4],thattheionizationprobabilityofparticlesejected
fromthesurfaceisdirectlyrelatedtothegenerationandtransportofki-
neticallyinducedelectronicexcitationsinthecollisioncascade.Thesesub-
strateexcitationsdonotonlyplayacrucialroleinthedeterminationof
thechargestateofsputteredatoms,butalsomanifest,forinstance,inion
inducedkineticelectronemission[5]orintheexperimentaldetectionofhot
electronsasinternaltunnelcurrentsinmetal-insulator-metaljunctions[6].
Fromatheoreticalpointofview,thetwoexcitationmechanismsusu-
allytakenintoaccountduringkeV-bombardmentofmetalsare(i)direct

7collisionsoftheprojectilewithconductionelectronsclosetotheFermi-
leveland(ii)electronpromotionincloseatomiccollisions.Thecollective
electronexcitationinducedbyprocess(i),i.e.thedirectcollisionaltransfer
ofkineticenergyfromboththeprojectileandlow-energyrecoilstoelec-
trons,cantorstorderbedescribedintermsoftheLindhard-Scharff-
Schiott(LSS)model[7]givingrisetoavelocity-dependentfrictionforce,
whereaselectronpromotionismostlytreatedwithintheFano-Lichten
model[8]ofquasi-molecularorbitalcrossing.
Duetothefactthatanab-initiocalculationoflargescaleparticledy-
namics,whichwoulddirectlyincludeelectronicexcitations,isstilltoocom-
plexandthereforenotfeasibleforasputteringscenario,severalattempts
[9,10,11,12,13]havebeenmadetoincorporateelectronicexcitationpro-
cessesintostandardcomputersimulationsofatomiccollisioncascades1.
However,inalloftheseapproacheselectronsonlyplayapassiverole
eitherasastaticmediumactingasafrictionforce,whichiscalculated
withintheframeworkoftheLSS-modelorsimilarapproachesemploying
localelectrondensities[14],leadingtoaslowingdownofmovingatomic
particles,orasanon-relevantby-productaccompanyingthedeeplevelcore
holegenerationinahardbinarycollisionevent[13].Inaddition,itshould
beemphasizedherethatpublishedmodelsneitherfeatureasimultaneous
quantitativetreatmentofbothexcitationsourcesnordotheytakeinto
accountanyexcitationenergytransport.
Inordertoclosethisgap,thepresentthesisdevelopesanalternative
computersimulationconcept,whichtreatstheelectronicenergylossesof
allmovingatomsasexcitationsourcesfeedingenergyintotheelectronic
sub-systemofthesolid.Theparticlekineticsdeterminingtheexcitation
sourcesaredeliveredbyclassicalmoleculardynamics.Theexcitationen-
ergycalculationsarecombinedwithadiusivetransportmodeltodescribe
thespreadofexcitationenergyfromtheinitialpointofgeneration.Cal-
culationresultsyieldaspace-andtime-resolvedexcitationenergydensity
proleE(r~,t)withinthevolumeaectedbytheatomiccollisioncascade.
ThedistributionE(r~,t)isthenconvertedintoanelectrontemperatureTe,
whichinafurtherstepcanbeutilizedtocalculatetheionizationprobabil-
itiesofsputteredatomsusingpublishedtheory.
Thepresentthesisisorganizedasfollows:
Chapter2givesanoverviewofthestandardmodelsforparticleemis-
sionfromion-bombardedsurfaces.Thestandardsputteringscenariosare
introducedanddiscussedintermsoftheirvaliditytakingintoaccount
recentexperimentaldataaswellasmolecular