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HighPowerImpulseMagnetronSputtering
HighPowerImpulse MagnetronSputtering Fundamentals,Technologies,Challenges andApplications
Editedby
DanielLundin
LaboratoiredePhysiquedesGazetPlasmas-LPGP UMR8578CNRS,UniversitéParis–Sud UniversitéParis–Saclay,OrsayCedex,France
TiberiuMinea
LaboratoiredePhysiquedesGazetPlasmas-LPGP UMR8578CNRS,UniversitéParis–Sud UniversitéParis–Saclay,OrsayCedex,France
JonTomasGudmundsson
DepartmentofSpaceandPlasmaPhysics
SchoolofElectricalEngineeringandComputerScience
KTHRoyalInstituteofTechnology
Stockholm,Sweden
ScienceInstitute,UniversityofIceland
Reykjavik,Iceland
Elsevier
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CoverphotobyDr.MarcusMorsteindisplayingaHiPIMSplasmanearthesurfaceofacylindricalrotatable magnetroninsideaPLATITindustrialPVDcoatingchamberequippedwithanIonauticsHiPIMSpowersupply.
Contributors
1Introductiontomagnetronsputtering 1 JonTomasGudmundsson,DanielLundin
1.1Fundamentalsofsputtering1
1.1.1DCglowdischarge2
1.1.2Electricalbreakdown8
1.1.3Thecathodesheath10
1.1.4Secondaryelectronemission11
1.1.5Electronenergydistributionfunction14
1.1.6Electricpotentials15
1.1.7Sputteryield16
1.1.8Energydistributionofsputteredatoms18
1.1.9Collisionsingases19
1.1.10DCglowsputtersource22
1.2Magnetronsputtering23
1.2.1DCmagnetronsputtering25
1.2.2Additionofmagneticfields25
1.2.3Electronconfinementandtargetutilization26
1.2.4Electronheating27
1.3Magnetronsputteringconfigurations30
1.3.1Balancedandunbalancedmagnetrons31
1.3.2Rotatingmagnetrons31
1.4Pulsedmagnetrondischarges32
1.4.1Definitionofpulsedmagnetronsputteringdischarges33
1.4.2Asymmetricbipolarmid-frequencypulsing34
1.4.3Magnetronsputteringwithasecondarydischarge36
1.4.4Highpowerimpulsemagnetronsputtering37
1.4.5Modulatedpulsepowermagnetronsputtering38
1.4.6Summary38 References39
2Hardwareandpowermanagementforhighpowerimpulse magnetronsputtering 49 ZdenˇekHubiˇcka,JonTomasGudmundsson,PetterLarsson, DanielLundin
2.1Briefhistoryofhighpowerpulsedmagnetronsputtering49
2.2Pulsegenerators52
2.2.1Basicpulsegenerators52
2.2.2Thyristor-diode-basedpulsers55
2.2.3IGBT-basedpulsers57
2.2.4Pre-ionization63
2.2.5Pulsedelay63
2.3Substratebias64
2.3.1Biassolutions64
2.3.2SynchronizedpulsedHiPIMSbias68
2.4AdvancedHiPIMSconfigurations69
2.4.1Multicathodeconfigurations69
2.4.2Superposition71
2.4.3Pulsetrains/multipulses/choppedpulses74
2.4.4Summary75 References75
3Electrondynamicsinhighpowerimpulsemagnetronsputtering discharges 81
Martin ˇ Cada,JonTomasGudmundsson,DanielLundin
3.1Techniquesforcharacterizingplasmaelectrons81
3.1.1Langmuirprobe82
3.1.2Emissiveprobe86
3.1.3Tripleprobe88
3.2Fundamentalelectroncharacteristics91
3.2.1Electronenergy,density,andtemperature91
3.2.2Plasmaexpansionandreflection94
3.3Influenceoftargetmaterialandworkinggas95
3.3.1Electronenergy,densityandtemperature95
3.3.2Plasmapotential98
3.3.3Reactiveplasmas102
3.4Multiplesourcesandhybridsystems103
3.4.1Electronpropertiesinmultisourcesystems103
3.4.2Electronpropertiesinhybridsystems104 References106
4Heavyspeciesdynamicsinhighpowerimpulsemagnetron sputteringdischarges 111
Martin ˇ Cada,NikolayBritun,AnteHecimovic,JonTomasGudmundsson, DanielLundin
4.1Theplasmaions111
4.1.1Techniquesforcharacterizingplasmaions112
4.1.1.1 Energy-resolvedmassspectrometry 112
4.1.1.2 Retardingfieldenergyanalyzers 115 4.1.1.3 Modifiedquartzcrystalmicrobalance(ionmeter) 116
4.1.1.4 Laser-basedmethodsforiondetection 118
4.1.2Spatialandtemporaldistributionofionsinthebulkplasma118
4.1.3Ionenergydistributioninthevicinityofthesubstrate123
4.1.3.1 Time-averagedIEDF 124
4.1.3.2 Time-resolvedIEDF 127
4.1.3.3 ReactiveHiPIMS 127
4.1.3.4 Time-evolutionoftheionflux 130
4.1.4Ionizedfractionofdepositingparticles132
4.1.5IonizedfluxfractioninHiPIMS133
4.1.5.1 ReactiveHiPIMSdischarges 136
4.1.5.2 Hybridsystems 137
4.1.5.3 Influenceofthemagneticfield 138
4.1.5.4 Massspectrometryresults 139
4.1.6Ionizeddensityfraction140
4.2Theplasmaneutrals141
4.2.1Spatialandtemporalevolutionofplasmaneutrals141
4.2.2Gasrarefaction146 References151
5Modelingthehighpowerimpulsemagnetronsputteringdischarge
TiberiuMinea,TomášKozák,ClaudiuCostin,JonTomasGudmundsson, DanielLundin
5.1Modelingapproaches159
5.1.1Pathwaymodels160
5.1.2Steady-stateglobalmodels162
5.1.2.1 Ionizationandreturnofsputteredtargetmaterial
5.1.2.2 Depositionparameters
5.1.2.3 Limitationsofthisapproach
5.1.3Time-dependentglobalmodel,IRM165
5.1.3.1 Particlebalance
5.1.3.2
5.1.3.3
5.1.3.4
5.1.3.5
5.1.3.6
5.1.4Particle-in-cell177
5.1.4.1 ChallengesofHiPIMSPICsimulations
5.1.4.2 Pseudo-3DPIC
5.1.5MonteCarlosimulations184
5.1.5.1 MonteCarlocollisionsimulations
5.1.5.2 MonteCarlosimulationofneutralparticletransport
5.1.5.3 DirectsimulationMonteCarlo(DSMC)forneutral particlestransport
5.1.5.4 Aposteriori MonteCarlo
5.1.6Othermodels188
5.1.6.1 Afeedbackmodel
5.1.6.2 EEDFassolutionofBoltzmann’sequation
5.1.6.3 Modelsforspokes
5.2Importantmodelingresults192
5.2.1Depositionrate192
5.2.2Currentandvoltagewaveforms195
5.2.2.1 Time-dependentglobalmodels 196
5.2.2.2 Self-consistentPICmodel 201
5.2.3Time-dependentplasmaproperties202
5.2.3.1 Temporalevolutionofneutralandchargedspecies 202
5.2.3.2 Excitedstatesevolution 207
5.2.3.3 Electronenergydistributionfunction(EEDF) 208
5.2.3.4 Ionenergydistributionfunction(IEDF) 211
5.2.3.5 Electrontransportcoefficientsandplasma deconfinement 212
References214
6Reactivehighpowerimpulsemagnetronsputtering 223 TomášKubart,JonTomasGudmundsson,DanielLundin
6.1Introductiontoreactivesputterdeposition223
6.1.1Workingpoint224
6.1.2Processcontrol227
6.2Fundamentalsofreactivesputtering227
6.2.1Moleculargasandplasmachemistry228
6.2.2Secondaryelectronemission231
6.2.3Sputteryieldsforcompounds232
6.2.4Reactivegasimplantationandthicknessofthecompound layer235
6.2.5Balance(Berg)modelofhysteresisreactivesputtering236
6.3HysteresisinreactiveHiPIMS240
6.3.1Experimentalobservations241
6.3.2Dynamicsofthehysteresis244
6.3.3ModelsofhysteresisinreactiveHiPIMS245
6.4ImportantaspectsofreactiveHiPIMS246
6.4.1Dischargewaveforms247
6.4.2Processstabilityanddepositionrate249
6.4.3Dynamicsofthesputtertargetsurface250
6.4.4Plasmacharacteristicsinthemetalandcompoundmode253
6.4.5NegativeionsinR-HiPIMS256
References257
7Physicsofhighpowerimpulsemagnetronsputteringdischarges 265
DanielLundin,AnteHecimovic,TiberiuMinea,AndréAnders, NilsBrenning,JonTomasGudmundsson
7.1Thedischargecurrent265
7.1.1Thedischargecurrentcomposition266
7.2Dischargemodes269
7.2.1Thedischargecurrentamplitude270
7.2.1.1 Thegeneralizedrecyclingmodel(GRM) 272
7.2.1.2 Dischargeanalysis 276
7.2.2Temporalevolutionofthedischargecurrent280
7.2.3Ohmicheatingversussheathacceleration288
7.3Transportofchargedparticles289
7.3.1Classicalionandneutralspeciestransport291
7.3.1.1 Iontransport
7.3.1.2 Classicalelectrontransport 294
7.3.2Anomaloustransport296
7.3.2.1 Anomalouselectrontransport 296
7.3.2.2 Anomalousiontransport 298
7.4PlasmaInstabilities300
7.4.1Spokesandbreathinginstabilitiesinmagnetronsputtering discharges301
7.4.2Thepotentialstructure308
7.4.3Effectofspokesonchargedparticletransport311
7.4.3.1 Transportnearthetarget
7.4.3.2 Transportinthebulkplasma
7.4.3.3
7.5Depositionrate315
7.5.1Physicsofdepositionrateloss316
7.5.2Increasingthedepositionrate320
7.5.3DepositionratesinreactiveHiPIMS323 References323
8Synthesisofthinfilmsandcoatingsbyhighpowerimpulse magnetronsputtering 333
KostasSarakinos,LudvikMartinu
8.1Introductiontothefundamentalsofthinfilmgrowth333
8.1.1Thinfilmgrowthfromanatomisticpointofview333
8.1.2Effectofenergeticionsonthinfilmmicrostructuralevolution337
8.1.3Effectofpulsedvaporfluxesonthinfilmgrowthdynamics337
8.2Depositiononcomplex-shapedsubstrates339
8.3Interfaceengineering341
8.4Thinfilmmicrostructureandmorphology343
8.4.1Filmdensityandsurfaceroughness344
8.4.2Filmtextureandmorphologicalevolution345
8.4.3Synthesisofself-organizednanostructures348
8.5Stressgenerationandevolution349
8.5.1Atomisticviewonstressgenerationandevolution350
8.5.2Effectofhighlyionizedfluxesonstressgenerationevolution351
8.5.3TailoringofstressinopticalcoatingsbyHiPIMS353
8.6Phasecomposition354
8.6.1Phasecompositiontailoringinelementalthinfilmmaterials: theTacase355
8.6.2Phasecompositiontailoringinfunctionaloxidefilms355
8.6.3Phasecompositiontailoringinmetastableternaryceramic films357
8.6.4Phaseformationtailoringviacontrolofchemicalcomposition358
8.7Time-domaineffectofHiPIMSonfilmgrowth360
8.8Summary361
Contributors AndréAnders
LeibnizInstituteofSurfaceEngineering(IOM),Leipzig,Germany
NilsBrenning
DepartmentofSpaceandPlasmaPhysics,SchoolofElectricalEngineeringandComputerScience,KTHRoyalInstituteofTechnology,Stockholm,Sweden
NikolayBritun
ChimiedesInteractionsPlasma-Surface(ChIPS),CIRMAP,UniversitédeMons, Mons,Belgium
Martin ˇ Cada
InstituteofPhysicsv.v.i.,AcademyofSciencesoftheCzechRepublic,Prague, CzechRepublic
ClaudiuCostin
AlexandruIoanCuzaUniversity,FacultyofPhysics,Iasi,Romania
JonTomasGudmundsson
DepartmentofSpaceandPlasmaPhysics,SchoolofElectricalEngineeringandComputerScience,KTHRoyalInstituteofTechnology,Stockholm,Sweden ScienceInstitute,UniversityofIceland,Reykjavik,Iceland
AnteHecimovic
Max-Planck-InstitutforPlasmaPhysics,Garching,Germany
Zden ˇ ekHubi ˇ cka
InstituteofPhysicsv.v.i.,AcademyofSciencesoftheCzechRepublic,Prague, CzechRepublic
TomášKozák
DepartmentofPhysicsandNTIS–EuropeanCentreofExcellence,UniversityofWest Bohemia,Plze ˇ n,CzechRepublic
TomášKubart
SolidStateElectronics,TheÅngströmLaboratory,UppsalaUniversity,Uppsala,Sweden
PetterLarsson
IonauticsAB,Linköping,Sweden
DanielLundin
LaboratoiredePhysiquedesGazetPlasmas-LPGP,UMR8578CNRS,Université Paris–Sud,UniversitéParis–Saclay,OrsayCedex,France
LudvikMartinu
DepartmentofEngineeringPhysics,PolytechniqueMontréal,Montréal,Quebec, Canada
TiberiuMinea
LaboratoiredePhysiquedesGazetPlasmas-LPGP,UMR8578CNRS,Université Paris–Sud,UniversitéParis–Saclay,OrsayCedex,France
KostasSarakinos
NanoscaleEngineeringDivision,DepartmentofPhysics,ChemistryandBiology, LinköpingUniversity,Linköping,Sweden
Preface HighPowerImpulseMagnetronSputtering:Fundamentals,Technologies,Challenges andApplications isanin-depthintroductiontoHighPowerImpulseMagnetronSputtering(HiPIMS)withanemphasisonhowthisnovelsputteringtechniquediffersfrom conventionalmagnetronprocessesintermsofhardware,dischargephysics,thinfilm growth,andresultingthinfilmcharacteristics.Thebookisaresultofaninvitation fromElsevierin2016towriteafirstbookentirelydedicatedtoHiPIMS.Roughlytwo andahalfyearslaterthisistheresult.
Thereisundoubtedlyworkthathasbeenoverlookedornotsufficientlydealtwith inthisbook.Ourambition,however,hasbeentopresentacomprehensivetextonthe HiPIMSprocess,ratherthanacollectionoflooselyconnectedresultsfoundinthe scientificliterature.ThemainmotivationisthatHiPIMS,likesomanytopicsinscience,isafieldinrapiddevelopment.Withagreatnumberofnewfindingspresented everyyear,resultsaresometimesmisinterpretedorcontradictory.Inaddition,differentdescriptionsofHiPIMSusetheirownterminology,whichunfortunatelyvaries dependingonwhatsourceyouarelookingat.Altogetherthispresentsasignificant thresholdforsomeonenewtothefield.IfthisbookinanywaycanlowerthatthresholdandstimulatemoreworkonHiPIMS,thenwehavesucceededinourtask.
Sowhoshouldreadthisbook?Wehopethatanyoneinvolvedinionizedphysical vapordepositionwillbenefitfromreadingit,oratleastafewchapters,dependingon interestandexpertize.Thematerial,however,isaimedatabroaderaudienceofprofessionals,practitioners,andstudents,whoarefamiliarwithbasicconceptsofplasma physicsandthinfilms.Wehavetriedtointroducevarioustopicsinsuchawaythat someonenewtoHiPIMSwillstillbeabletofollowandpossiblybeevenmoremotivatedtotryoutthispromising(butchallenging)technology.
WestartthisbookbyanintroductiontomagnetronsputteringinChapter 1,where weintroducethebasicconceptsneededtoexploreHiPIMS.Chapter 2 presentsan overviewofthehistoricaldevelopmentoftheHiPIMStechniquealongwithvarious highpowerpulsersthathavebeendevelopedovertheyears.Chapters 3 and 4 arefocusedonexperimentalprocesscharacterizationinHiPIMSanddescribetheroleof electronsandheavyspecies(neutralsandions),respectively.Typicalcharacteristics ofthesespeciesarepresentedtoprovideasolidunderstandingofthemostimportantfundamentalpropertiesoftheHiPIMSdischarge.Thesefindingsarefollowed upinChapter 5 usingcomputationalmodeling.Themainmodelsarepresentedand comparedtoeachotherwhenpossible.Wealsohighlightsomeimportantmodeling results,whichhavebeenselectedtoemphasizetheaddedunderstandingbroughtby computationalmodeling,butalsotovalidatecertainmodelapproachesorhighlight model-specificresults.Chapter 6 extendsthefundamentalknowledgegainedinthe previouschapterstoreactiveHiPIMSprocesses,whichinvolvesanintroductionof
basicsputteringphysicsinreactivegasmixturesaswellasmorespecificaspectsof surfaceanddischargeprocessesrelatedtoreactiveHiPIMS.Chapter 7 isanattempt atunifyingandsummarizingthemostimportantconceptspresentedinmainlyChapters 3 – 6,anddescribestheunderlyingphysicalandchemicalmechanismsgivingrise totheobservedprocessresultsandtheconsequencesthereof.Finally,Chapter 8 discussestheuseofHiPIMStodepositthinfilms.Thechapterissubdividedintoseveral sections,eachfocusingonadifferentprocess-specificaspectrelatedtocertainfilm characteristics,whereHiPIMShavebeenshowntohaveagreatimpact.Eachchapter containsanextensivelistofreferencestostimulatefurtherreading.
Abooklikethisonewouldnotbepossiblewithoutthecontributionsandinvaluableinputbyalltheexpertcoauthorsandbymanycolleaguesandfriends.Wedo notlistalltheauthorsoftheindividualchapters,whohave,besidestheirowntexts, madegreatcontributionstothebookasawhole.Withtheriskofforgettingsomeone, wewouldstillliketomentionafewcolleaguesoutsidetheauthorlist,whodeserve specialrecognition.Inparticular,wearedeeplygratefultothetalentedT.J.Petty,who patientlylistenedtoourdescriptionsanddiscussionsandconvertedthemintofantastic illustrations.WealsoacknowledgeFelipeCemin,whoreadandcommentedsomeof thechapters,whilewritinghisPh.D.thesisatUniversitéParis-Sud.AdrienRevelis acknowledgedforhisinputonthenumericalmodeling,mainlyrelatedtothe2Dand 3DparticlesimulationsofshortHiPIMSpulses.
Finally,wewouldliketoconcludebythankingourfamiliesforallthesupportthey haveshownusduringthecourseofwritingthisbookand,inparticular,forunderstandingwhywehadtoworkallthoseevenings(andmostweekends).
DanielLundin TiberiuMinea
JonTomasGudmundsson Paris–Linköping–Stockholm,June2019
Introductiontomagnetron sputtering JonTomasGudmundssona,b ,DanielLundinc
1 a DepartmentofSpaceandPlasmaPhysics,SchoolofElectricalEngineeringandComputer Science,KTHRoyalInstituteofTechnology,Stockholm,Sweden, b ScienceInstitute, UniversityofIceland,Reykjavik,Iceland, c LaboratoiredePhysiquedesGazetPlasmasLPGP,UMR8578CNRS,UniversitéParis–Sud,UniversitéParis–Saclay,OrsayCedex,France
Plasma-basedphysicalvapordeposition(PVD)methodshavefoundwidespreadusein variousindustrialapplications.Inplasma-basedPVDprocesses,thedepositionspecies areeithervaporizedbythermalevaporationorbysputteringfromasource(thecathodetarget)byionbombardment.Sputterdepositionhasbeenknownfordecadesasa flexible,reliable,andeffectivecoatingmethod.Initially,thedcglowdischargeorthe dcdiodesputteringdischargewasusedasasputtersourcefollowedbythemagnetron sputteringtechnique,whichwasdevelopedduringthe1960sand1970s.Magnetron sputteringhasbeentheworkhorseofplasma-basedsputteringapplicationsforthepast fourdecades.Intheplanarconfiguration,themagnetronsputteringdischargeissimplyadiodesputteringarrangementwiththeadditionofmagnetsdirectlybehindthe cathodetarget.Withtheintroductionofmagnetronsputtering,thedisadvantagesof diodesputtering,suchaspoordepositionrate,wereovercomeastheoperatingpressurecouldbereducedwhilemaintainingtheenergyofthesputteredspecies,often resultinginimprovedfilmproperties.Herewediscussthebasicsofthesputtering process,giveanoverviewofthedcglowdischarge,andreviewthebasicphysics relevanttothemaintenanceofthedischargeandthesputterprocesses.Thenwediscussthedcglowdischargeanditsroleasasputtersourceandhowitevolvesinto themagnetronsputteringdischarge.Wealsodiscussvariousmagnetronsputtering configurationsinuseforawiderangeofapplicationsbothunderlaboratoryandindustrialarrangements.Finally,weintroducepulsedmagnetrondischargesincluding highpowerimpulsemagnetronsputtering(HiPIMS)discharges.
1.1Fundamentalsofsputtering Animportantprocessthattakesplaceinaglowdischargeissputtering,whichcan occurifthevoltageappliedtothecathodeissufficientlyhigh.Whentheionsandfast neutralsfromtheplasmabombardthecathodetarget,theynotonlyreleasesecondary electrons,butalsoatomsofthecathodematerial.Thisisreferredtoassputtering. Whenspeciesaresputteredoffacathodetargetandsubsequentlyusedasfilmformingmaterial,theprocessbelongstowhatisreferredtoasaphysicalvapordeposition
(PVD).Sputteringismosteasilyperformedbyexposingacathodetargettoagas discharge:eitheradcdischarge(Kay, 1962)oramagnetronsputteringdischarge (Waits, 1978),whereasionbeamsputterdepositionisalsoawell-establishedPVD technique(BundesmannandNeumann, 2018).OtherPVDtechniquesincludeevaporation,pulsedlaserdeposition,cathodicarcdeposition,andionplating.Sputteringin gasdischargeswasdiscoveredinthemid-19thcentury(Grove, 1852).Filmformation utilizingsputterdeposition,wherethecathodetargetisthesourceofthefilmforming material,wasfirstreportedbyWrightinthe1870s(Wright, 1877a,b).Sputterdepositionofthinfilmshadalreadyfoundcommercialapplicationbythe1930s(Fruth, 1932, Hulburt, 1934),butgainedsignificantinterestinthelate1950sandearly1960swith improvedvacuumtechnologyandtherealizationthatawiderangeofmaterialscould bedepositedusingdcsputtering(Kay, 1962,Westwood, 1976)aswellasrfsputtering utilizedmainlyfordielectrics(Andersonetal., 1962).
Herewediscusssomeofthefundamentalsofdischargephysicsandsputtering.We introducethedcglowdischarge,includingitsvoltage–currentcharacteristicsandthe variousregionsobservedinitsoperation,andtheirpropertiesandrole.Wediscuss someofthefundamentalsofplasmaphysicsrelevanttosputteringdischarges,includingelectricalbreakdown,therelationbetweenthesheathvoltagedropandthesheath thickness,andthesecondaryelectronemission,essentialforthemaintenanceofthedc glowdischarge.ThesputteryieldisthendiscussedinSection 1.1.7,theenergydistributionofthesputteredatomsinSection 1.1.8,andcollisionswithinplasmadischarges inSection 1.1.9.Finally,weintroducethedcglowsputteringdischargeorthedcdiode sputteringdeviceinSection 1.1.10.Thisdiscussionisintendedtogiveanoverviewof thefundamentalconceptsandparametersthatareneededtounderstandtheoperation ofthemagnetronsputteringdischarge.
1.1.1DCglowdischarge Thetermgasdischargereferstoaflowofelectriccurrentthroughagaseousmedium. Foracurrenttoflow,someofthegasatomsandmoleculeshavetobeionized.Furthermore,thiscurrent,thedischargecurrent,hastobedrivenbyanelectricfield. Thedischargecurrent,whichprovidespowertothedischarge,hastobecontinuous throughoutthelengthofthedischarge.Thereisatransitioninthedischargewithregardstowhichchargedspeciescarriesthedischargecurrent.Infrontofthecathode, thereisaregion,thecathodeglow,inwhichmostoftheionizationoccurs.Outside thisregionthedischargecurrentismainlycarriedbyelectronstowardtheanodeand byionstowardthecathode.Energyisneededfortheionizationinthecathodeglow. Inthedcdischarge,thisisresolvedbysecondaryelectronemissionfromthecathodetarget.Thiselectronemissionisessentialforthemaintenanceofthedischarge (seeSection 1.1.4).Thedischargecurrentisbuiltupbyionizationwithinthecathode sheath,whichisduetothesecondaryelectronsthatareacceleratedbythelargeelectricfieldsinthisregion.Thustodescribethecurrentinadcdischarge,theinteraction ofchargedparticleswiththeelectrodesurfaceshastobetakenintoaccount.
Letusassumetwoparallelelectrodesseparatedbyadistance L andwithapplied potential VD .Thegapbetweentheelectrodesisfilledwithgasatpressure p ,the
Figure1.1 Thedischargecurrent ID versusthedischargevoltage VD foralow-pressuredcdischarge. Thevariousoperatingregimesarenoted,withincreasingcurrent,Townsendregime,subnormalglow,normalglow,abnormalglow,andarcregime.ReprintedfromGudmundssonandHecimovic(2017).©IOP Publishing.Reproducedwithpermission.Allrightsreserved.
workinggaspressure.Thetypeofdischargethatisformedbetweenthetwoelectrodes dependsuponthepressureoftheworkinggas,thenatureoftheworkinggas,the appliedvoltage,andthegeometryofthedischarge.Inthefollowingdiscussionofthe dcdischarge,wefollowthediscussiongiveninarecentreviewonthefoundationsof thedcdischarge(GudmundssonandHecimovic, 2017).
Thedischargecurrentisshownversusthevoltageacrossalow-pressuredcdischargeinFig. 1.1.Adescriptionoftherelationbetweenthecurrentandvoltagefor thedcdischargecanbefoundinreviewpaperssuchasbyFrancis(1956)andIngold (1978)andinanumberoftextbooksincludingthoseofHowatson(1976,Chapter4), Raizer(1991,Section8.2),andRoth(1995,Chapter9)andcanbesummarizedas follows:Whenavoltageisfirstapplied,thedischargecurrentisverysmall.Thiscurrentconsistsofcontributionsfromvariousexternalsourcessuchascosmicradiation generatingfreeelectronsandions.Whenthevoltagehasbecomelargeenoughtocollectallthesechargedparticles,thiscurrentremainsnearlyconstantwithincreased voltage.Asthevoltageisfurtherincreased,thechargedparticleseventuallyachieve enoughenergytoproducemorechargedparticlesthroughcollisionswiththeworking gasatomsorbybombardmentoftheelectrodesleadingtogenerationofsecondary electrons.Asmorechargedparticlesarecreated,thecurrentincreases,whereasthe voltageislimitedbytheoutputimpedanceofthepowersupplyandremainsroughly constant.ThisregioniscommonlyreferredtoastheTownsenddischarge.ThecharacteristicsoftheTownsenddischargeareverysmalldischargecurrents.TheTownsend dischargeisnotluminoussincetheelectrondensityislow,andthereforethedensity ofexcitedatoms,whichemitvisiblelight,iscorrespondinglysmall.Furthermore,it
isnotaself-sustaineddischargeinthesensethatitdoesnotentirelyprovideitsown ionizationbutrequiressomeexternalassistancetoproduceelectronseitherwithinthe gasitselforfromanegativelybiasedelectrode.
Iftheappliedvoltageisincreasedfurther,thenthedischargecurrentincreases,and eventuallythisleadstoasituationwheretheplasmadensityishighenoughforthedischargetoreorganizethevacuumpotentialstructureandformacathodesheath,which enablesmoreefficientionizationandthereforeahighercurrentatagivenvoltage. Thenthecurrentincreasessharplybyseveralordersofmagnitudeandbecomesindependentoftheexternalseed.Thisiswhatisreferredtoasthebreakdownpoint VB (see Fig. 1.1)orsubnormalglowandoccursatvoltagesrangingfromtwoorthreehundred voltsandupward,dependingonthenatureoftheworkinggas,thegaspressure,and theseparationoftheelectrodes.
Oncebreakdownhasoccurred,thedischargebecomesself-sustainingandtakes theformofaglow,andthegasbecomesluminous.Asionsbombardtheelectrode, secondaryelectronsareemitted.Theseelectronsimpactandionizetheatomsofthe workinggas.Thusmoreionsareavailabletobombardthecathodeandcreatemore secondaryelectrons.Atthispoint,thevoltagedrops,andthedischargecurrentincreasesabruptly.Electronimpactexcitationcollisionsfollowedbydeexcitationwith theemissionofradiationareresponsibleforthecharacteristicglow.Thisregimeis referredtoasthenormalgloworthedcglowdischarge.
Theionbombardmentofthecathodesurfaceisinitiallynotuniform.Thedischarge currentarrangesanoptimumcurrentdensity,and,asthecurrentincreasesfurther, moreandmoreofthecathodetargetsurfaceissubjecttoionbombardment.This continueswithincreasedsuppliedpoweruntilanearlyuniformdensityisachieved coveringtheentirecathodearea.Whenthewholecathodeiscoveredbyionbombardment,furtherincreaseinthepowerleadstoadischargewithacurrentdensityatthe cathode,whichisnolongeroptimal.Highercurrentscanthereforeonlybeachieved withhighervoltagesoverthecathodesheath.Thereisthereforeanincreaseinboth voltageandcurrent.Thisoperationregimeisreferredtoastheabnormalglowandis theregimeusedforsputtering,whichisfurtherdiscussedinSection 1.1.10.Theabnormalglowdischargelooksmuchlikethenormalglowdischargebutismoreintensely luminous,andsometimesthestructuresnearthecathodemergeintooneanother.As thecurrentdensityatthecathodebecomeslargeenoughfortheformationofcathodespots,thedischargemakesatransitionintothearcregime.Thecathodespots can,throughacombinationoffieldemissionandthermoionicemission,emitelectronsmoreefficientlythanthesecondaryelectronemissionprocess,whichleadstoa secondavalanche,increaseddischargecurrent,andadropinthedischargevoltageas seeninFig. 1.1.Eventuallyalow-voltagehigh-currentarcdischargeforms.
Thedcglowdischargeisimportanthistoricallybothforstudyingthepropertiesof theplasmaandforvariousapplicationswherethedcdischargeisusedtoprovidea weaklyionizedplasma.Thesimplicityofthedcglowdischargegeometrymadeita commonlyusedplasmagenerationmethodforfundamentalresearchinbothdischarge physicsandatomicandmolecularphysics(GudmundssonandHecimovic, 2017).As seeninFig. 1.1,thedcglowdischargeoperatesinthecurrentrangefromµAtohun-
Figure1.2 Aschematicofthedcglowdischargeshowingseveraldistinctregionsthatappearbetween thecathodeandtheanode.Thecolorsofthevariousregionsassumeaneondischarge.Thedarkspacesare abbreviatedasDS.
dredsofmA(currentdensityrange10 5 –10 3 A/cm2 ),andtheworkinggaspressure istypicallyintherange0.5–300Pa.
Earlystudiesofthedcglowdischargerevealedthatitconsistsofseveraldifferentregionsbetweentheelectrodes,whichhavebeenillustratedinmoreorlessthe samewaybyseveralauthors(Francis, 1956,Ingold, 1978,Raizer, 1991,Roth, 1995, Nasser, 1971).InFig. 1.2,wepresentaschematicofthenormalglowdischargein a0.5mlongtubeusingneonat133Paastheworkinggas,whichisduetoNasser (1971).Thecathodeistypicallymadeofanelectricallyconductivemetal.Thecathode metalhasaninfluenceonthevoltagerequiredtomaintainthedischarge.Forametal thatisagoodemitterofelectrons(seediscussioninSection 1.1.4)lowervoltagesare sufficient.Immediatelynexttothecathodeisathindarklayer,theAstondarkspace. TheAstondarkspaceisfollowedbythecathodeglow,whichhasarelativelyhigh iondensity.Thesecondaryelectronsreleasedfromthecathodesurfaceareaccelerated awayfromthecathode.Thesehigh-energyelectronsundergocollisionswithneutral workinggasatomsatadistanceawayfromthecathodecorrespondingtotheionizationmeanfreepath.Inthisregionthesecondaryelectronsparticipateinexcitation andtherebygeneratethecathodeglow.Thecathodeglowisfollowedbythecathode (CrookesorHittorf)darkspace.TheregionsthatextendfromtheAstondarkspaceto thecathodedarkspacetogetherconstitutethecathodesheath.Heretheelectricfield isdirectedtowardthecathode,andthespacechargeispositiveandofrelativelyhigh density.Thecathodedarkspaceisfollowedbythenegativeglow(infact,aregionwith positivepotential),whichexhibitsasignificantlightintensity.Mostoftheionization occurshere.Theboundarytowardthecathodedarkspaceisratherabruptwhileitis diffuseontheanodesidetowardtheFaradaydarkspace.TheelectricfieldandtheenergyoftheelectronsarelowintheFaradaydarkspace.Theelectronenergyavailable forexcitationandionizationishereexhausted.Beforeenteringthisdarkregion,the potentialgradientisslightlynegativeasthespacechargereverses.Herethedensityof electronshasbecomehighenoughtocarrytheentiredischargecurrentandtomake thespacechargenegative.Theelectrondensityfallswithinthisdarkspaceregiondue torecombinationanddiffusionuntilthenetspacechargeiszeroandtheelectricfield approachesasmallconstantvalueandthepositivecolumnbegins.Thepositivecolumnisaquasineutralplasmawheretheelectricfieldisverylow.Thepositivecolumn issimplyalonguniformglow,exceptwhenstriationsareformed.Thepositivecolumn actsasaconductingpathbetweenthenegativeglowregionandtheanode.Theanode
Table1.1 Thecolorofselectedluminouszonesinthedcglowdischarge.
Gas Cathodelayers
He red pink red/pink
Ne yellow orange red/brown
Ar pink darkblue darkred
H2 red/brown paleblue pink
N2 pink blue red/yellow
Air pink blue red/yellow
BasedonFrancis(1956).
glowisabrightregionthatappearsattheendofthepositivecolumn.Oftenathindark spaceisobservedattheendofthepositivecolumn(theanodedarkspace),andaglow closetothesurfaceoftheanode(theanodeglow).
Thesize,intensity,andcolorofalltheregionsdescribedabovedependonthenatureoftheworkinggas,gaspressure,andappliedvoltage.Also,someofthefeatures maybeabsentoverparticularparameterranges.Thevariousgasesgiveadischargeof acharacteristiccolor.Thecolorsofthelightemittedfromthevariouszonesofthedc glowdischargearelistedinTable 1.1.Ifthepressureisreduced,thenthecathodedark spaceexpandsattheexpenseofthepositivecolumn.Thisisduethefactthatnowthe electronshavetotravelfarther(meanfreepathislonger)toproduceefficientionization.Forasecondaryelectronemissionyieldintherange0.05–0.1,eachsecondary electronmustinitiateanavalanchethatproducesroughly10–20ionstomaintain thedischarge.Anelectronavalancheispossiblewithinthecathodesheathofglow discharges,becausetheelectronmeanfreepathforionizingcollisionsisheresmaller thanthesheaththickness.AswewillseeinSection 7.2.3,ionizationavalancheswithin thesheathregionarenotpossibleinHiPIMSdischargesduetolowerpressuresand thinnercathodesheaths.Howmanyionseachsecondaryelectronactuallyproduces dependsontheionizationmeanfreepathandthedistancebetweentheanodeand cathode.ThisrelationisqualitativelythestatementofPaschen’slaw,whichrelates thebreakdownvoltage VB totheproductofgaspressureandelectrodeseparationand willbediscussedinSection 1.1.2.Thisalsoshowsthattheionizationprocessesinthe cathodedarkspaceareessentialforthemaintenanceofthedischarge.
Thepotentialdifferenceappliedbetweenthetwoelectrodesisgenerallynotequally distributedbetweencathodeandanode.Thespatialvariationsofthepotential,the electricfield,particledensities,spacecharge,andcurrentdensitiesalongtheaxisofa dcglowdischargeareshowninFig. 1.3.Thespatialvariationoftheplasmaparameters shownherewasfoundbyparticle-in-cellsimulationofanargondcdischargeat50Pa whenavoltageof400Visappliedacrossthe5cmdischargegap(Budtz-Jørgensen, 2001).Asthepotentialprofileindicates(Fig. 1.3A),theelectricfieldislargeinthe vicinityoftheelectrodesandalmostzerowithinthepositivecolumn.Thusalmostall theappliedvoltagedropscompletelywithinthefirstfewmillimetersinfrontofthe cathode.Thisregionadjacenttothecathode,whichisthuscharacterizedbyastrong electricfield,isthecathodefall,oroftenreferredtoasthecathodesheath.Weseein
Figure1.3 Spatialprofilesof(A)theplasmapotential,(B)theelectricfield,(C)ionandelectrondensity, (D)space-chargedensity,and(E)ionandelectroncurrentdensity.Fromparticle-in-cellsimulationofan argondcdischargeat50Pa,electrodeseparationof5cm,and 400Vappliedtothecathode.Reprinted fromBudtz-Jørgensen(2001).©Budtz-Jørgensen.Reproducedwithpermission.Allrightsreserved.
Fig. 1.3Cthatthesheathregionisdepletedofelectrons,andinFig. 1.3D,weseethat thenetspacechargeispositiveinthesheathregioninlinewithourpreviousdiscussion ofthedarkspace.ThespacechargeshowninFig. 1.3Disfoundbysubtractionofthe electrondensityfromtheiondensity.Intheplasmabulk,theplasmaisquasineutral, andtheelectronandiondensitiesarethesame.Thisspacechargedensityleadstothe electricfielddistributionseeninFig. 1.3B.
1.1.2Electricalbreakdown Electricalbreakdownisanimportantphenomenonindischargephysics.Herewederivethebreakdownvoltageasafunctionoftheproduct pL,where p istheworking gaspressure,and L isthedistancebetweentheelectrodes,whichiscommonlyreferredtoasthePaschencurve.Asimilardiscussioncanbefoundinvarioustextbooks suchasbyLiebermanandLichtenberg(2005,Section14.3),Raizer(1991,Chapter7), andRoth(1995,Section8.6).
Theelectrondensityandfluxgrowexponentiallyaswemoveaxiallyawayfrom thecathode.Thustheincreaseintheelectronfluxisproportionaltotheflux,or
where e istheelectronflux,and α isknownasTownsend’sfirstionizationcoefficient andistheinverseofthemeanfreepathforionization,thatis, α(z) ≡ 1/λiz .The electronfluxinthedirectionalongthedischargeaxis(orthedirectionoftheelectric field)is
Duetothecontinuityofthetotalcharge(creationofequalnumbersofelectron–ion pairs),wecanwrite
where e (L) fromEq.(1.2)hasbeeninserted.Sincethedischargemustbeselfsustaining,wehave e (0) = γsee i (0) and i (L) = 0.Then
istheconditionforself-sustainability.Inavacuumregion,theelectricfield E isa constant,anditfollowsthattheelectrondriftvelocity μe E isalsoaconstant.Hence theelectronenergy Ee isaconstant,allowingustotreat α asaconstantinEq.(1.4). Inthatcase,takingthelogarithmofbothsidesofEq.(1.4)gives
whichisthebreakdownconditionforadcdischarge.Theionizationcoefficientis usuallyexpressedintheform
Table1.2 ConstantsfortheTownsendionizationcoefficient.
FromLiebermanandLichtenberg(2005).
where A and B aredeterminedexperimentallyandfoundtoberoughlyconstantovera rangeofpressuresandfieldsforagivengastype.Thecoefficients A and B forvarious commongasesarelistedinTable 1.2.
Iftheminimumvoltageatwhichthedischargeinitiates,thebreakdownvoltage,is writtenas VB = EL,then
whichsolvedfor VB gives
whichisafunctionoftheproduct pL.Theproductofpressureanddistancebetween theelectrodes(pL)isasuitableparametertocharacterizethedischarge.Thecurve thatshows VB asafunctionoftheproduct pL iscalledthePaschencurve.Thusfora fixeddischargelength L,thereisanoptimumgaspressureforplasmabreakdown.By differentiatingtheexpressionforthebreakdownvoltage,Eq.(1.8),withrespectto pL andsettingthederivativeequaltozero,wecanfindthevalueof pL thatcorresponds totheminimumbreakdownvoltage(Raizer, 1991,Chapter7)
andtheminimumvoltageis
whichisreferredtoastheminimumsparkingpotential,andistheminimumvoltage atwhichelectricalbreakdowncanoccurinagivengas.
AccordingtoEq.(1.8),thebreakdownvoltageishighforlowandhighpressure andaminimumat pL givenbyEq.(1.9).Atthelowerpressurestheionizationprocess isineffectiveduetothelowelectron-neutralcollisionprobability,whereasathigher pressureselasticcollisionspreventtheelectronsfromreachinghighenoughenergy forionizationtooccur.Thenumberofgasatomsormoleculesinthespacebetween
theelectrodesisproportionalto pL.Atlowerpressure,thedistancebetweencathode andanodehastobelongertocreateadischargewithpropertiescomparabletothose ofhighpressurewithsmalldistancebetweentheelectrodes.Forlowpressure,the electronmeanfreepathislarge,andmostelectronsreachtheanodewithoutcolliding withgasatomsormolecules.Thus,atlowpressure,ahighervalueof VB isrequired togenerateenoughelectronstocausethebreakdownofthegas.Athigherpressures, theelectronmeanfreepathisshort.Theelectronsdonotgainenoughenergyfromthe electricfieldtoionizethegasatomsormoleculesduetotheirfrequentcollisionswith thegasmolecules.Therefore VB increasesasthepressureincreases.
1.1.3Thecathodesheath Allplasmasareseparatedfromthesurroundingwallsbyasheath.Wehaveseenin Section 1.1.1,andinparticularinFig. 1.3A,thatmostofthepotentialdropovera dcglowdischargeappearsacrossthecathodesheath.Therelationbetweenthesheath thickness dc ,thedischargecurrentdensity J ,andthevoltagedropacrossthecathode sheath Vc wasderivedbyChild(1911),assumingthattheinitialionenergyisnegligiblecomparedtothesheathpotential(seealsoLiebermanandLichtenberg(2005, Section6.2)),giving
where Mi istheionmass.Eq.(1.11)isreferredtoastheChildlaworthecollisionlessChild–Langmuirlaw.TheChildlawisvalidwhenthesheathpotentialislarge comparedtotheaverageenergyoftheelectrons.Asimilarrelationwasderivedby Langmuir(1913)forelectronsemittedfromahotcathodeapproachingacoldanode (nothermionicemission).Inthecollisionalregime,wherethepressureishighenough thatthechargedspeciesinteractfrequentlywithneutralgasspecies,wecanassume thattheion-neutralmeanfreepath λi isindependentoftheionvelocity(Lieberman andLichtenberg, 2005,Section6.6).ThisgivesthecollisionalChildlaw
Alternatively,assumingthatthediffusionofionsisnegligible,comparedtothedrift duetoanelectricfield,andassumingthattheionmobility μi isindependentoftheion velocity,weget
whichisreferredtoastheMott–Gurneylaw.Itwasderivedtodescribethecurrentat theinterfaceofasemiconductorandinsulator(MottandGurney, 1948,ChapterV)and lateradaptedtodescribethecurrentthroughthedischargesheathbyCobine(1958).
Equation(1.13)isvalidonlyatveryhighpressures(lowdriftvelocities).Therelation betweenthecurrentdensity,sheathvoltagedrop,andthesheaththicknessgivenby Eqs.(1.12)and(1.13)issometimesreferredtoasthecollisionalChild–Langmuir law.Wenoteherethatthescalingsofthecurrentdensitywithboth Vc and dc in Eq.(1.12)aredifferentfromEq.(1.13).Ithasbeendemonstratedbyexperiments thattheMott–Gurneylaw(Eq.(1.13))appliestoadcglowdischargeinhydrogen (Lisovskiyetal., 2016)andnitrogen(Lisovskiyetal., 2014)formostofthepressure rangefrom10to333Pa.
1.1.4Secondaryelectronemission Theemissionofsecondaryelectronsasaresultofionsorneutralsbombardinga metallicsurfaceplaysanimportantroleindischargephysics.Thesecondaryelectron emissionyieldorcoefficient γsee isdefinedasthenumberofsecondaryelectronsemittedperincidentspecies.Thesecondaryelectronemissionyieldgenerallydependson thematerialbeingbombarded,itssurfacecondition,thetypeofbombardingspecies, andthekineticenergyofthebombardingspecies.Thesputtertargetsareheldathigh negativepotentials,andthusthesecondaryelectronsareacceleratedawayfromthe targetsurfacewithinitialenergyequaltothetargetpotential.Inmanycases,these electronssustainthedischargebyionizationoftheneutralworkinggas.Theseions thenbombardthecathodetargetandsubsequentlyreleasemoresecondaryelectrons.
Asafirstapproximation,thesecondaryelectronemissionyieldisindependentof thevelocityofthebombardingparticlewhiletheirenergyislow,sincetheelectron emissionoccursduetotransferofthepotentialenergyoftheincomingionoratom toanelectroninthetarget(Hagstrum, 1954,Abroyanetal., 1967).ThisconstantsecondaryelectronemissionyieldisattributedtoanAugerprocessandisreferredtoas potentialemission.Theenergy-dependentportionofthesecondaryelectronemission yieldiscalledkineticemission.Kineticemissionoccurswhenabombardingparticle transferssufficientkineticenergytoanelectroninthetarget.Typically,itstartscontributingtothetotalsecondaryelectronemissionyieldatathresholdenergyofaround afewhundredelectronvolts.Thisprocessdominatesathigherenergies.Bothexperimentaldataandtheorypredictalineardependenceofthesecondaryelectronemission yieldonthebombardingparticleenergyclosetothethresholdenergy,andlineardependenceonthebombardingvelocityathigherenergies(Abroyanetal., 1967,Parilis andKishinevskii, 1960,Cawthron, 1971,Baragiolaetal., 1979,Hasselkamp, 1992). Atmuchhigherenergies,experimentaldatashowthattheelectronyieldstartsdecreasingwithincreasingbombardingvelocity.Thisoccursforabombardingenergy ofaround100keVforH+ (Hasselkamp, 1992).Thetwodifferentmechanismsare consideredtobedetachable,sothetotalelectronemissionyieldiswrittenas
where γp and γk arethecontributionsfrompotentialandkineticemissiontothetotal yield,respectively.Inadditiontotheenergyoftheimpactingparticle,thesecondary
