低揮發(fā)性液體前體的飽和劑設(shè)計(jì)比較 Comparison of saturator designs for low volatility liquid precursor delivery

Comparisonofsaturatordesignsfordeliveryoflow-volatilityliquidprecursors

JamesE.Maslar,*,1WilliamA.Kimes,1VladimirB.Khromchenko,1BrentA.Sperling,2and

RavindraK.Kanjolia3

1NationalInstituteofStandardsandTechnology,100BureauDrive,Gaithersburg,MD20899

2EMDElectronics,Tamaqua,PA18252

3EMDElectronics,Haverhill,MA01832

*Correspondingauthor:E-mail:jmaslar@

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ABSTRACT

Numerouslow-volatilityprecursorsareutilizedinchemicalvapordepositionandatomiclayerdepositionprocesses.Suchprecursorsareoftendeliveredfromoneoftwocommonsaturatordesigns:abubbleroraflowovervessel.Previousreportsconcerningprecursordeliveryfromsuchvesselshavefocusedprimarilyoncontinuousdeliveryofmoderatetohighvolatilityliquidsandsolids.Fewreportshavefocusedoncyclicaldeliveryoflowvolatilityprecursorsatreducedpressures.Thislackofknowledgeconcerningsuchprocessescanbeahindrancetoefficientselectionofdepositionconditionsandvesseldesign.Theobjectiveofthisinvestigationwastocomparetheperformanceofthesetwosaturatordesignsforpulsedinjectionatreducedpressuresusingthelowvolatilityliquidprecursorμ2-η2-(But-acetylene)dicobalthexacarbonyl(CCTBA).ThebasisofthiscomparisonwasthemeasurementofCCTBAmasscarryoverperinjectionasafunctionofinjectionnumber,injectiontime,carriergasflowrate,systempressure,andvesselidletime.Themasscarryoverwasdeterminedfromabsorbancemeasurementsperformedusinganon-dispersiveinfraredgasanalyzer.Themeasuredmasscarryoverforbothvesselswascomparedtothetheoreticalmasscarryoverdeterminedusingasimpleanalyticalmodelbaseduponthe“bubblerequation”.Inthecaseofthebubbler,thismodeldescribedthevesselperformancewellwithknowledgeoftheprecursorvaporpressureandvesselheadspacepressure.Inthecaseoftheflowovervessel,thismodeldescribedtheoverallvesselperformancepoorlyunlessanadditionalvesselefficiencyfactorwasincluded,afactorthatisdifficulttopredictapriori.Furthermore,theefficiencyfactorwasnotnecessarilyconstantforaseriesofinjections:theefficiencyfactortendedtodecreasefromthefirstinjectionuntilastablevaluewasachieved,avaluethatdependedontheprocessconditions.Thislimitationofthemodelwasattributedtothespecificflowdynamicsassociatedwiththeflowovervesseldesign.Computationalfluiddynamicssimulationswereable

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toreproducethemasscarryoveroftheflowovervessel,afterestimatingtheCCTBA-carriergasbinarydiffusioncoefficient.Thesesimulationsalsoshowedthatalargerbinarydiffusioncoefficientandahighervaporpressurebothledtoanincreaseinmasscarryoverbutvesselefficiencycouldnotequalthatofthebubbler.WhiletheseresultswereobtainedwithCCTBA,thegeneralrelationshipsbetweenmasscarryoverandthevariousprocessparametersinthesesaturatorsareexpectedtobesimilarforotherlow-volatilityprecursors.

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1.Introduction

Numerouslow-volatilityprecursorsareutilizedinchemicalvapordeposition(CVD)andatomiclayerdeposition(ALD)processes.Suchprecursorsareoftendeliveredfromtheprecursorvesseltothedepositionsurfacebyevaporating(subliming)aliquid(solid)precursortogenerateavaporwhichisentrainedinacarriergas.Ideally,thecarriergasissaturatedinthevesselheadspacewiththeprecursorvaporattheprecursorvaporpressure.MostpreviousreportsdescribingsaturatordesignandperformancewerefocusedoncontinuousdeliveryofmoderatetohighvolatilityprecursorsforCVDororganometallicvaporphaseepitaxy(OMVPE)processes.1-27Whendescribingliquidprecursordelivery,previousreportshavenaturallyfocusedonbubblers.2,4,6-13,25-27(Inthiswork,a“bubbler”referstoavesselconfiguredwithadiptubeonthegasinletportthatextendsnearlytothebottomofthevessel.)However,evenwhendescribingsolidprecursordelivery,themajorityofpreviousreportsfocusedonsaturatordesignsinwhichthecarriergaswasdirectedthroughtheprecursorbed.Suchdesignsincludeinvertedorreversebubbler-typevesselsandsometimesincorporaterestrictedflowpathswithmultipletraysorchambers.1,3-6,10,13-24Whilesuchdesignshavebeenshowntoprovideexcellentperformance(atleastundersomeconditions),thesedesignscanbemorecostlytomanufactureandclean.Hence,simplerflowovervesselsareoftenutilizedforprecursordelivery.(Inthiswork,a“flowovervessel”referstoavesselthroughwhichcarriergasflowsbutwhichhasnodiptube:thegasinletandoutletportsopendirectlyintothevesselheadspace.)

PreviousprecursordeliverystudieshavehelpedtoidentifyprocessconditionsandvesseldesigncharacteristicsthataredesirableforcontinuousdeliveryofmoderatetohighvolatilityprecursorsforCVDorOMVPEprocesses,oftenatelevatedpressures.However,theprocessconditionsandvesselcharacteristicsthataredesirableforpulseddeliveryoflowvolatility

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precursorsatreducedpressureshavenotbeenwidelyidentified.Thereareafewreportsdescribingprecursordeliveryundersuchconditions,includingaliquidfromabubbler28andasolidfromaflowovervessel.29,30However,itisdifficulttocomparedefinitivelytheperformanceofabubblerandflowovervesselfromthesereportsbecausetheprecursorsandflowconditionsweredifferent.Itiswellknownthatanumberoffactorscanleadtonon-reproducibledeliveryofsolidprecursorsandthatthesefactorscanberelatedbothtothephysicochemicalpropertiesoftheprecursorandtheflowcharacteristicsoftherespectiveprecursorvessel.1,3-5,10,15,16,18,19,21,23,24,30-32Therefore,itissometimesdifficulttodifferentiatebetweentheimpactondeliveryofvesselflowcharacteristicsandprecursorproperties.Hence,amorestraight-forwardcomparisonofvesseldesignsforprecursordeliverywouldinvolvethesameprecursor.

Theobjectiveofthisinvestigationwastocomparedirectlytheperformanceofabubblerandaflowovervesselfordeliveryoflow-volatilityprecursorsduringreduced-pressure,cyclicaldepositionprocesses,e.g.,pulsedCVDandALDprocesses.Thesameliquidprecursor,μ2-η2-(But-acetylene)dicobalthexacarbonyl(CCTBA),wasutilizedinbothvessels.Aliquidwasexaminedtoavoidanyadditionalcomplicationsthatcanbeassociatedwiththeuseofsolids,therebypermittingamorestraight-forwardcomparisonofthevesselperformance.ThebasisofthiscomparisonwasthemeasurementofCCTBAmasscarryoverperinjectionasafunctionofinjectionnumber,durationofprecursorinjection(tinj),carriergasflowrate,systempressure,anddurationofthevesselidlebetweeninjections(tidle).Massvalueswereobtainedfromdirectabsorbancemeasurementsperformedusinganon-dispersiveinfrared(NDIR)gasanalyzer.Themeasuredmasscarryoverforbothvesselswascomparedtothetheoreticalmasscarryoverdeterminedfromamodelbaseduponthe“bubblerequation”.2,7-11,33Themasscarryoverfromtheflowovervesselwasalsocomparedtothatobtainedfromcomputationalfluiddynamics(CFD)

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simulations.Thefocusofthisinvestigationwasonthefollowingdeliveryconditions:tinj≤2s,tidle≤8sortidle≥180s,vesselheadspacepressuresbetween1.2kPaand7.8kPa,andcarriergasflowratesrangingfrom0.25L/minto0.75L/min.Theresultsofthisstudyshouldhelpelucidatetheimpactofprocessconditionsandvesseldesignonprecursordeliveryfortwocommonsaturatordesignsoperatingunderprocessconditionsthatarenotwidelyreportedupon.

2.Experimentalprocedure

2.1.Materials

Astainlesssteelbubblerandflowovervesselwerecompared.Eachvesselhadnominallythesame必1.5Lvolumeandspecificdimensions,asdescribedelsewhere.30Approximately200gofmicroelectronics-gradeCCTBA(EMDElectronics?)wassuppliedineachvessel(theCCTBAwasusedasreceived).Ultra-high-puritygradeargonwasusedasthecarriergasandwasfurtherpurifiedwithapoint-of-usepurifier.

2.2Flowsystem

Thedesignandoperationoftheflowsystemhavebeendescribedpreviously34,35andwillonlybedescribedbriefly.AschematicoftheflowsystemusedforeachvesselisshowninFig.1.Thecarriergasflowratewascontrolledwithamassflowcontroller(MFC)andthesystempressurewasmeasuredusingonecapacitancediaphragmgaugeupstreamoftheprecursorvessel(CDG1)andonedownstream(CDG2).ThetotalpressureatCDG1andCDG2aredesignatedbyPCDG1andPCDG2,respectively.Opticalaccesstothegasflowwasachievedwithoneoftwoopticalflowcells

?Certaincommercialequipment,instruments,andmaterialsareidentifiedinthispublicationtoadequatelyspecifytheexperimentalprocedure.Suchidentificationinnowayimpliesapproval,recommendation,orendorsementbytheNationalInstituteofStandardsandTechnology,nordoesitimplythattheequipment,instruments,ormaterialsidentifiedarenecessarilythebestavailableforthepurpose.

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(FC1andFC2)locateddownstreamoftheprecursorvessel.Theconductanceoftheflowsystemwasadjustedusingamanualthrottlevalve(TV).Fivevalveswereusedtocontrolgasdistribution:threepneumaticvalves(PVin,PVby,andPVout)tocontrolgasswitchingduringarunandtwomanualvalves(MVinandMVout)toisolatethevesselwhennotinuse(themanualvalveswereopenforallmeasurements).PVinandMVinandPVoutandMVoutwerelocatedontheinletandoutletlinesofthevessel,respectively.PVbywaslocatedonthelinethatbypassesthevessel.Forthebubbler[seeFig.1(a)],PVin,PVby,andPVoutwere2-portvalveswhileMVinandMVoutwere3-portvalves.The3-portvalvesonthebubblerwereconfiguredina“T”inwhichonesideofthearmofthe“T”wasvalvedandflowwasunimpededfromthestemofthe“T”throughthenon-valvedsideofthearm.Fortheflowovervessel[seeFig.1(b)],PVby,MVin,andMVoutwere2-portvalveswhilePVinandPVoutwere3-portvalves.The3-portvalvesontheflowovervesselwereconfiguredina“T”inwhichthestemofthe“T”wasvalvedandflowwasunimpededthroughthearmofthe“T”.Gasflowwasinitiatedinthevessel-idle/line-purgeconfiguration(noflowthroughthevessel)byopeningPVby(whilePVinandPVoutwereclosed),settingtheMFCtothedesiredflowrate,andadjustingTVtoobtainthedesiredpressureatCDG2.Intheinjectionconfiguration,carriergaswasdirectedthroughthevesselbyopeningPVinandPVout(whilePVbywasclosed).Theargonflowratesemployedinthisworkwere0.25L/min,0.50L/min,and0.75L/minatstandardtemperatureandpressure(STP),definedas0°Cand101.33kPa,respectively.Insubsequentdiscussions,flowratesarereferencedtoSTP.TheTVwassettoprovideeither1.3kPaor4.7kPaatCDG2fora0.50L/minflowrateandnotadjustedsubsequently.TheflowconditionsaresummarizedinTableI.AllsurfacesfromCDG1toTVwereheated.Thesublimator,FC1,andFC2wereencasedinaluminumjacketswhichwereheatedwithstripandcartridgeheaters,respectively.Linesandvalveswerewrappedandheatedwithheating

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tapes(thevalvesweremountedonaluminumblockstofacilitateheatdistribution).Allheatedcomponentswereinsulatedwithhigh-temperaturesiliconefoam.Thetemperaturesetpointforthevessel,thevalvesandinletline,andtherestoftheflowsystemwere50°C,55°C,and63°C,respectively.

TableI.TheTVdesignationsandtheassociatedargonflowrateandtotalpressureatCDG2used

forsettingtheconductanceandthecorrespondingconditionsduringmeasurements.

Designation

Conditionsforsettingconductance

Conditionsformeasurements

Arflowrate

(L/min)

PCDG2

(kPa)

Arflowrate

(L/min)

PCDG2

(kPa)

TV-1

0.50

1.3

0.250.7to1.0

0.501.1to1.6

0.751.6to2.1

TV-2

0.50

4.7

0.252.6to2.9

0.504.4to4.9

0.756.0to6.6

2.3NDIRgasanalyzer

TheNDIRgasanalyzerhasbeendescribedelsewhere35andwillonlybedescribedbriefly.AnalyzeroperationwasbasedonadirectabsorptionmeasurementofCCTBAintheC≡O(shè)stretchingmodespectralregion.Analyzerdesignincludedabroadbandinfraredsource,a4.95mcenter-wavelengthbandpassfilter,andacryogenically-cooledindiumantimonidedetector.MeasurementswereperformedinasinglepassthroughFC1(theopticalaxiswasperpendicularto

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thedirectionofgasflow).TheCCTBAvolumetricflowrateatSTP(F)wascalculatedusing

thebubblerequation2,7-11,33

(1)

FSTP=FSTPPCFCT1BA

CCTBAAr(P?PCFCT1BA)

whereFTPisthecarriergasvolumetricflowrate(STP),PCFCT1BAistheCCTBApartialpressureatFC1,andPisthetotalpressureatFC1.PCFCT1BAwasdeterminedfromtheabsorbancemeasurements35andPwasobtainedfromPCDG2bycalculatingthepressuredropthatexistsbetweenCDG2andFC1usingtheHagen-Poiseuilleequation.34,35

2.4.CalculatingCCTBAMassDelivered

ThecalculatedCCTBAmassdeliveredperinjection(mj)isdescribedby33,36

m=FBARTSTPtinj=FTPCCTPHArARTSTPtinj=FTP(PtSS?CCTBABA)RTSTPtinj(2)

(PSTPMPHS(PSTPMnPVP(PSTPM

wherePSTPisthestandardpressure,Mistheprecursormolarmass,Risthegasconstant,TSTPistheabsolutestandardtemperature,PCHCSTBA,S,andParetheprecursorpartialpressure,carriergaspartialpressure,andtotalsystempressure,respectively,inthevesselheadspace(P=PCHCSTBA+S),nSistheaveragesourceefficiencyfactor,andPCVCPTBAistheCCTBAvaporpressure.ThetermnSrepresentsthedegreetowhichtheconditionPCHCSTBA~PCVCPTBAisrealizedandisdefinedas36

nS==tinjj0nS(t)dt=tinjj0dt(3)

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P

wheremisthemeasuredCCTBAmassdeliveredperinjection,andmjisthemassperinjectionfromaperfectlyefficientvesselascalculatedusingEq.(2)withnS=1,nS(t)representsthetime-

dependentinstantaneoussourceefficiency,andPCHCSTBA(t)representsthetime-dependentPCHCSTBA.

ThetotalpressureintheheadspacewasassumedtobetheaverageofPCDG1andthepressureatalocationdownstreamofthelastoutletvalve.Thislocationwas≈18cmfromMVoutand≈6cmfromPVoutforthebubblerandflowovervessel,respectively(≈114.5cmfromCDG2inbothcases).ThepressureattherespectiveoutletlocationwascalculatedbytakingintoaccountthepressuredropbetweenthislocationandCDG2usingtheHagen-Poiseuilleequation.ThepressureincreasefromCDG2tothislocationwas≤10%and≤1%forTV-1andTV-2,respectively.WhentabulatingthePvalues,anaveragevaluewascalculatedoveratimeintervaldeterminedfromtheinflectionpointsofthederivativeofPCDG2,with0.1sand0.175saddedtothestartandsubtractedfromtheendoftheinterval,respectively,toreducetheeffectonthisestimationofpressuretransientsduringvalveswitching.Inthecaseofthebubbler,thehydrostaticpressure,Phydro,wassubtractedfromPCDG1priortocalculatingtheaveragevalue33

Phydro=pCCTBAgl(4)

wherepCCTBAistheCCTBAdensity(assumedtobe1440kg/m3),gistheaccelerationofgravity,andlisthelengthofthediptubebelowtheCCTBAlevel(thereisa2mmdistancebetweenthebottomofthediptubeandbottomofthevessel).Dependingonthemassinthebubbler,theestimatedPhydrovaluerangedfrom127Pato79Pafor200g(themassasreceived)to139g(themassremainingafterthemeasurementsdescribedhere),respectively.Forsimplicity,theaverage

HS

Phydro=103Pawasusedforallestimations.Thismethodofestimatingttlassumesanequalpressuredropacrosseachofthefourvalvesduringinjection.Thishasbeenshowntobea

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3(4冗kBTmAB)1232HS

reasonableassumptionforatleastoneemptybubblerwithPCDG2必5.2kPa.34However,valve

conductancecanvaryfromvalvetovalvesotherelevanceofthispreviousreportisuncertain.ThevalueofPCVCPTBAisdescribedbytheAntoineequation:

log10PCVCPTBA=AA?BAT(5)

whereTistheabsolutetemperatureandAAandBAareconstantsequalto11.39and3209.3,respectively.28Fromthisexpression,PCVCPTBA=28.8Paat50°C.

2.5.Computationalfluiddynamicssimulations

CFDsimulationsofdeliveryfromtheflowovervesselwereperformedusingCOMSOLMultiphysicsversion6.0,asdescribedpreviouslyforalowvolatilitysolidinanidenticalvesseldesignasutilizedinthisstudy.30Tosimplifythesesimulations,itwasassumedthatthegaspropertieswerethoseofargon(CCTBAwasdilute),thatthepressurewasconstant(givenbyP),thattheonlysourceofCCTBAwasvaporabovetheliquidatthebottomofthevessel,andtheCCTBApartialpressurewasequaltothevaporpressure.Thepropertiesofargonwereobtained

fromREFPROP.37Thebinarydiffusioncoefficient(DAB)wascalculatedfrom38

D=f=dTP

AB16n冗BDD0ttl

(6)

wherekBistheBoltzmannconstant,mAB=2(1mA)+(1mB)?1wheremAandmBarethemolecularmassofmoleculeAandB,nisthenumberdensityofmolecules,σABisthecharacteristiclength,ΩDisthecollisionintegral,andfDisacorrectionterm.Tosimulatem,avalueofd0=3.5×10-5kg·m·s-3·K-3/2(mD)at50°Cwasselected.Usingthisd0value,themassdifferencebetweenm

andmDforfifteeninjectionswithFTP=0.75L/min,tinj=2s,tidle=8s,andintheTV-2flow

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configurationwas<2%foreachinjectionnumberfourthroughfifteen(seeFig.6andassociateddiscussion).

3.Resultsanddiscussion

Figure2showsthemvaluesasafunctionofinjectionnumberforthebubblerandflowovervesselswithFTP=0.50L/min,tinj=2s,tidle=8s,andintheTV-2flowconfiguration.Alsoshownaredashedanddot-dashedlinesthatrepresentthemjvaluesforthebubblerandflowovervessel,respectively,calculatedwiththenSvaluesindicatedoneachline.Thereisgoodagreementbetweenmandmjasexpected.28Inthecaseofthebubbler,themasscarryoverdecreasesslightlyfromthefirstinjectiontoastablemasscarryoverafteraboutthreeinjections.Thesmalldecreaseinmassforthefirstonetotwoinjectionsisattributedtothetimeittakesforthepressureinthesystemtostabilizefrompulsetopulse(seeFig.3andassociateddiscussion).Onceastablemasscarryoverisobservedafterthefirstonetotwoinjections,themjvaluesareabout3%lowerthanthemvalues,adifferencewhichisattributedtothesimplisticmethodusedtoestimateP(seeSec.2.4).Inthecaseoftheflowovervessel,thereisrelativelypooragreementbetweenmandmjashasbeenobservedpreviouslyforasolidinsuchavesseldesign.29ThenSvaluesrangefromabout0.77forthefirstinjectiontoabout0.44onceastablemasscarryoverhasbeenachievedafterabouttwentytothirtyinjections.Asnotedpreviously,themethodusedtoestimatePresultsinanunderestimationofmjinthecaseofthebubbler.Presumably,thisalsoisthecasefortheflowovervessel.Hence,thecalculatednSvaluesarelikelyoverestimatedbyanamountcorrespondingtothedegreeofunderestimationofmj.Theobserveddecreaseofmasscarryover

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withinjectionnumberuntilastablemasscarryoverisachievedischaracteristicofaflowovervessel.Thisbehaviorisexplainedasfollows.Priortothefirstinjection,thevesselwassubjected

toa>300sidleduringwhichCCTBAvapordiffusedintothevesselheadspaceuntilPCHCSTBA=PCVCPTBA,themaximumCCTBApartialpressureachievable.ThemvaluedecreasesfromthatofaprecedinginjectionwhentheamountofCCTBAremovedduringaninjectionisgreaterthanthesumoftheamountofCCTBAdiffusingintotheheadspaceduringtheprecedingidle(an8sidleisinsufficienttoresultinPCHCSTBA=PCVCPTBA)plustheamountbeingentrainedintotheflowingcarriergasfromtheprecursorreservoir.AstablemasscarryoverisachievedwhentheamountofCCTBAremovedduringaninjectionequalsthesumoftheamountdiffusingintotheheadspaceplustheamountbeingentrained.Asdescribedinthecaseofthebubbler,pressurestabilizationeffectsledtothefirstonetotwoinjectionsexhibitingahighermthansubsequentinjections.Inthecaseoftheflowovervessel,similareffectsarepresent,butitisdifficulttodifferentiatetheeffectsonmofpressurestabilizationandgasflowdynamics(seeFig.3andassociateddiscussion).However,thepressurestabilizationprocesspresumablyresultsinalesssharpdecreasefromthefirstinjectionthanwouldhavebeenobservedintheabsenceofthiseffect.Becauseoftheseflowcharacteristics,Eq.(2)withaconstantnSvaluedoesnotdescribetheflowovervesselperformanceforallinjections.However,thisequationwithaconstantnSvaluecanadequatelydescribetheperformanceonceastablemasscarryoverisachieved,asillustratedbythedot-dashedlinelabeledwithnS=0.44(avalueobtainedfromtheaveragenSvalueforinjections51to100).

Figure3showsthetime-dependent(a)PCFCTBAand(b)PCDG2valuesforthefirstfiveinjectionsfromthebubblerand(c)PCFCTBAand(d)PCDG2forthefirstteninjectionsfromtheflowovervessel,allwithFTP=0.50°L/min,tinj=2s,tidle=8s,andintheTV-2flowconfiguration

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(thesameconditionsasforFig.2).Inthecaseofthebubbler,thetime-dependentPCFCTBAprofileisrectangularanddoesnotvarysignificantlywithinjectionnumberwhilePCDG2increasesslightlyoverthefirsttwotothreeinjections.ThesetrendsareconsistentwiththoseobservedinFig.2:themvalueisrelativelystableexceptforthefirsttwoinjectionsduringwhichthesystempressureisincreasing,leadingtoadecreaseinmatconstantPCHCSTBAasexpectedfromEq.(2).Inthecaseoftheflowovervessel,thetime-dependentPCFCTBAprofileisalsorectangularbutdecreaseswithinjectionnumberformorethanthefirstteninjections.Inaddition,thetime-dependenceofPCFCTBA

isdifferentforfirstinjectioncomparedtotheotherfour,thetime-dependenceofwhicharesimilar.ThePCDG2valueincreasesoveronlythefirstfourinjections.TheseresultsareconsistentwiththeexplanationofthetrendsobservedinFig.2:pressurestabilizationmayimpactthemvalueforthefirstonetofourinjectionsbutthemvaluecontinuestodecreasebeyondfourinjectionsduetothegasdynamicsintheflowovervessel,drivenbythecontinueddecreaseofCCTBApartialpressure.ThedifferenceinPCFCTBAforthefirstinjectioncomparedtothatofsubsequentinjectionsisattributedtopressurestabilizationinthevalvemanifoldafteralongidle.Presumably,thiseffectisnotobservedforthebubblerbecausethevolumeassociatedwiththebubblervalvemanifoldissmallerthanthatoftheflowovervessel(seeFig.1).

ThedependenceofthemasscarryoverontinjisdepictedinFig.4whichshowsthemvalueasafunctionoftinjfortheTV-1andTV-2flowconfigurationswiththebubblerforFTP=(a)0.25L/min,(b)0.50L/min,and(c)0.75L/minandtheflowovervesselforFTP=(d)0.25L/min,(e)0.50L/min,and(f)0.75L/min.Foreachinjection,tidle=4×tinj.Thelargermvaluesatthetopoftheverticalstackcorrespondtoearlierinjectionswhilethegroupingofsymbolsatthe

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smallermvaluescorrespondstoastateofstablemasscarryover.Thedashedanddot-dashedlinesrepresentthemjvaluesforTV-1andTV-2,respectively,calculatedwiththenSvaluesindicatedoneachline.Inthecaseofthebubbler[Fig.4(a)to4(c)],themvalueincreaseswithincreasingtinjandFTPanddecreasingPCDG2.AlloftheserelationshipsaredescribedwellbyEq.(2)withnSequaltounity.AswasthecaseforthedatashowninFig.2,themjvaluesareslightlylowerthanthemvaluesforsomeconditions,particularlyatlowerPCDG2.ThisunderestimationagainisattributedtothesimplisticmethodusedtoestimatePThedifferencebetweenthemandmjvaluesisgreaterintheTV-1configurationcomparedtotheTV-2configurationbecausethepressuredropacrossthevalvemanifoldisgreaterintheformer,resultinginapoorerestimateofPInthecaseoftheflowovervessel[Fig.4(d)to4(f)],forthefirstinjectionthemvalueincreaseswithincreasingtinjandFTPanddecreasingPCDG2.Onceastablemasscarryoverisachieved,themvalueincreaseswithincreasingtinj,however,themvalueincreasesrelativelylittlewithdecreasingPCDG2(intherangeinvestigatedhere)anddecreasesslightlywithincreasingFTP(incontrasttothebehaviorobservedwiththebubbler).TherelativelyweakdependenceofmonpressureandtheinversedependenceonflowratearecontrarytothedependenceexpectedbasedonEq.(2).Thesecharacteristicsareattributedtotheflowdynamicsoftheflowovervessel.ThemvaluesatastablemasscarryoverarereasonablywelldescribedbyEq.(2)withconstantnSobtainedfromtheaveragenSvalueforinjections51to100oftherespectiverun(aswasillustratedinFig.2).Fortheflowovervessel,therespectivenSvaluedecreaseswithdecreasingPCDG2andincreasingF

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ThedependenceofthemasscarryoverontidleisillustratedinFig.5whichshowsthemvalueasafunctionoftidlefortinj=0.5sintheTV-1andTV-2flowconfigurationswiththebubblerforFTP=(a)0.25L/min,(b)0.50L/min,and(c)0.75L/minandtheflowovervesselforFTP=(d)0.25L/min,(e)0.50L/min,and(f)0.75L/min.Thedashedanddot-dashedlinesrepresentthemjvaluesforTV-1andTV-2,respectively,calculatedwiththeindicatednSvalues.Inthecaseofthebubbler[Fig.5(a)to5(c)],themassdeliveredisindependentoftidle,indicatingthattheheadspace