DEVELOPMENTOFASINGLE-ATOMMICROSCOPEFOROPTICALDETECTIONOF ATOMICNUCLEARREACTIONPRODUCTS By BenjaminThomasLoseth ADISSERTATION Submittedto MichiganStateUniversity inpartialful˝llmentoftherequirements forthedegreeof PhysicsDoctorofPhilosophy 2020 ABSTRACT DEVELOPMENTOFASINGLE-ATOMMICROSCOPEFOROPTICALDETECTIONOF ATOMICNUCLEARREACTIONPRODUCTS By BenjaminThomasLoseth Developmentofincreasinglysensitivedetectiontechniquesisnecessaryforthemeasurementof extremelysmallnuclearcrosssectionsthatarecrucialtounderstandingmanynucleosynthesis processes.Tothatend,thisthesispresentsthe˝rststepstowardthecommissioningofanovel detector,calledthesingle-atommicroscope,withacrosssectionmeasurementforthereaction 84 Kr ¹ p ; º 85 Rb,byopticallyimagingrubidiumatomsinsolidkrypton.Techniquesforthegrowth ofhighlytransparent 100 mthick˝lmsofsolidnoblegasesaredemonstrated.Theabsorption crosssectionformatrix-isolatedrubidiuminsolidkryptonismeasuredtobeontheorderof 8 10 15 cm 2 ,witha˛uorescencecrosssectionontheorderof 2 10 16 cm 2 .The˛uorescence crosssectionofrubidiumatomsembeddedinsolidkryptonasa1.7MeV/uionbeamwasmeasured tobe ¹ 9 4 º 10 16 cm 2 .Theneutralizatione˚ciencyofrubidiumionsimplantedinsolidkrypton ismeasuredtobeontheorderofunity.Thenextstepstowardimagingindividualrubidiumatoms insolidkryptonarepresented. ACKNOWLEDGEMENTS Firstofall,Iamespeciallygratefulfortheguidanceandsupportofmyadvisor,Prof.Jaideep Singh,andwillbeforeverthankfultohimfortheopportunitytoparticipateinthisinterestingand challengingscienti˝cresearch.WorkinginSpinlabhasreinvigoratedmyloveforphysics,andIwill lookbackonthetimespentherewithagreatfondness.Ithavegreatlyenjoyedworkingalongside theotherSpinlabgroupmembers,includingRoy,Erin,andthemanyotherbrilliantgraduateand undergraduatestudentsIhavehadthepleasuretoworkwith.IwanttoespeciallythankFryFang forthemanylongdayshespentworkingwithmeonpSAM-Icouldnothavemadeitthisfar withouthim. DuringmylongtenurehereatMSUIhavehadtheprivilegetogettoknowKimCrosslanand BrendaWenzlick-Thankyoubothforyourfriendshipandhelp!ThankyoutoProfs.Johannes Pollanen,MartinBerz,KyokoMakino,PavelSnopokforsupportingmewithyourkindness, knowledge,andadvice.WorkingattheNSCLhasbeenaneye-openingexperience,andIcouldnot imagineworkinginamoreexcitingfacilitysta˙edwithsuchkindandprofessionalsta˙.Iwant tothankTonySwartz,BradPowell,ChuckGaus,andKimGwinnfromNSCLfacilitiesfortheir excellentworkinpoweringandsupportingtheSAMproject.ThankstoBenArend,Je˙Wenstrom, MorganBurr,andCodyNoratfortheirexcellentdesignwork.AhugethankstoKenPlath,JayPline, andtheNSCLmachineshopsta˙fortheirtremendouslyskilledworkandlifesavinglast-minute modi˝cations. Iwanttoo˙ermysincerethankstothemembersofmyguidancecommittee,Profs.Luke Roberts,HendrikSchatz,StuartTessmer,andKirstenTollefsonfordevotingtheirvaluabletime andenergytoadviseandreviewthisresearch,andsupportmeinmyendeavors. Iamdeeplygratefulforthelove,support,andkindnessofmyfamilyandfriends(Kairi,Alyssa, Aimee,Phil,Jon,andmanyothers)throughoutmytimehereatMSU,withoutwhichIcouldnot haveaccomplishedthisdreamofmine. iii TABLEOFCONTENTS LISTOFTABLES ....................................... vi LISTOFFIGURES ....................................... viii CHAPTER1INTRODUCTION ............................... 1 CHAPTER2DETECTIONOFATOMICNUCLEARREACTIONPRODUCTSVIA OPTICALIMAGING ............................. 3 2.1Motivation.......................................3 2.2CrossSectionSensitivity...............................6 2.2.1Smallcross-sectionreactions.........................6 2.2.2Low-beam-currentreactions.........................7 2.3TechnicalChallenges.................................8 2.3.1Captureinnoblegassolids..........................9 2.3.1.1Noblegas˝lmdamage.......................9 2.3.1.2Productionneutralizationandtrapping..............11 2.3.2Opticalsignal-to-backgroundestimates...................13 2.3.2.1Single-atomsignalrate.......................13 2.3.2.2Signal-to-backgroundestimation..................15 2.4LimitationsandSummary...............................18 2.5Acknowledgements..................................19 CHAPTER3THEPROTOTYPESINGLE-ATOMMICROSCOPE ............ 20 3.1Requirements.....................................20 3.1.1HeatLoad...................................20 3.1.2BeamlineandOpticalAccess.........................22 3.2Components......................................23 3.2.1Overview...................................23 3.2.2AssemblyandCleaningProtocol.......................24 3.2.3CryocoolerandColdComponents......................27 3.2.4TemperatureControl.............................29 3.2.5FeedthroughVacuumAccess.........................34 3.2.6LinearShiftMechanismandPositionControl................35 3.2.7GrowthChamber...............................36 3.2.8Vacuumcontrol................................36 3.2.9ImagingChamber...............................39 3.2.10GasHandlingSystem.............................39 3.3NobleGasFilmGrowth................................42 3.3.1Background..................................42 3.3.2Experimentalsetup..............................43 3.3.3Results....................................45 iv 3.3.3.1GrowthRate............................48 3.3.3.2OpticalClarity...........................52 3.3.3.3FringeContrast...........................58 3.3.3.4Filmuniformity..........................60 3.3.3.5Filmpurity.............................64 3.3.3.6NobleGasUseandStickingProbability..............65 3.3.4Conclusions..................................66 CHAPTER4CALIBRATEDFLUORESCENCESPECTROSCOPYOFMATRIXISO- LATEDRUBIDIUMATOMS ......................... 68 4.1Introduction......................................68 4.2ExperimentalSetup..................................69 4.3Results.........................................71 4.3.1VacuumRubidiumSpectrum.........................72 4.3.2RubidiumDepositionRate..........................72 4.3.3RbinKrAbsorptionSpectra.........................78 4.3.4RbinKrFluorescenceSpectroscopy.....................78 4.4Conclusions......................................84 CHAPTER5BEAMLINEFEASIBILITYSTUDIES .................... 86 5.1Introduction......................................86 5.2Experimentalsetupandprocedure..........................87 5.3Results.........................................89 5.3.1Beame˙ectson˝lmclarity..........................89 5.3.2Ion-Beaminducedluminescence.......................91 5.3.3FilmSputtering................................92 5.3.4Laserinduced˛uorescenceofionimplanted˝lms..............93 5.3.5Molecularoxygen˛uorescenceline.....................101 5.4Conclusions......................................102 CHAPTER6CONCLUSIONANDFUTURESTEPS .................... 104 6.1Rubidium˛uorescencecrosssection.........................104 6.1.1NeutralRubidiumbeam............................104 6.1.2Rubidiumionbeam..............................105 6.2Progresstowardssingle-atomsensitivity.......................106 6.3Futureoutlook.....................................113 APPENDICES ......................................... 114 APPENDIXAANDORCLARACCDCALIBRATION ................ 115 APPENDIXBPULSETUBECRYOCOOLERS .................... 120 APPENDIXCTEMPERATUREPROBECALIBRATIONS .............. 126 APPENDIXDLINEARSHIFTMECHANISM(LSM)COMMANDS ........ 128 BIBLIOGRAPHY ........................................ 129 v LISTOFTABLES Table2.1:Candidatereactionsforthesingle-atommicroscope,withapproximatebeam currents,targetarealdensities,andexpectedyields.................6 Table2.2:Propertiesofnoblegassolids............................10 Table2.3:Selectedmatrix-isolatedabsorptionandemissionspectraofSAM-friendly species.ItalicizedlifetimesarevacuumvaluesfromtheNISTAtomicSpectra Database(physics.nist.gov).............................12 Table2.4:Potentialsourcesofopticalbackground,withknownexcitationwavelengths....16 Table3.1:Propertiesofnoblegassolids............................21 Table3.2:Tableofmaterialproperties.Valuestakenfrom[1].................29 Table3.3:TableofpSAMcon˝gurations............................49 Table3.4:Tableofsolidnoblegas˝lmproperties. T subl isde˝nedasthetemperatureat whichthevaporpressureis 10 4 Torr........................57 Table3.5:Purityofnoblegases˛owingintopSAMasmeasuredwiththeRGA.......65 Table4.1:TableofABFlaserscanparameters.........................70 Table4.2:RubidiumD 1 hyper˝nestructure.Referencedataistakenfrom[2].Reference valueuncertaintiesaregenerallylessthan100kHz.Wavelengthmeasurements arepreciseto7MHz,withanabsolutecalibrationaccuracyof600MHz.....73 Table4.3:Summaryofrubidiuminkryptonsampleconcentrations..............77 Table4.4:RubidiuminKryptonabsorptionpeaks.......................78 Table4.5:Tableoflaser-induced˛uorescencescanparametersforspectrainFigure4.9...80 Table4.6:RubidiuminKryptonlaserinduced˛uorescencepeaks,withuncertainties giveninparenthesis.Resonancestrengthisgivenwithrespecttotheamplitude ofthestrongestresonanceat730nm........................80 Table4.7:Measuredcrosssectionsandquantume˚cienciesat excitation = 730 nm.....85 vi Table5.1:Ion-beaminducedluminescencespectrumpeaks.Peaklocationshavean uncertaintyof0.5nm................................92 Table5.2:Tableoflaser-induced˛uorescencescanparameters................94 Table5.3:Listofrubidiuminkryptonlaserinduced˛uorescencepeaks,comparing neutralandionbeamimplantedrubidium......................98 Table5.4:Maximumcrosssectionsof 85 Rbimplanted˝lms,with excitation = 750 nm...98 Table5.5:Tableofmolecularoxygenresonancescanparameters...............101 Table5.6:Comparisonofquantume˚cienciesforneutralandion-implantedmatrix- isolatedrubidiuminsolidkrypton.Neutralabsorptionand˛uorescencecross sectionswerecalculatedfromanaverageofthe25 Cand116 Cmeasure- mentsinTable4.7,andtheion-implanted˛uorescencecrosssectionisan averageofallthemeasurementsinTable5.4....................103 Table6.1:Listoftechniquesforreducingtherequiredintegrationtime t forsingle-atom detection.......................................113 TableA.1:CCDcountperphotoncalibration..........................118 TableC.1:pSAMTemperatureSensorCalibrationData....................126 TableC.2:pSAMTemperatureSensorCalibrationData....................127 TableD.1:CommonlyusedLSMcommands.RefertoMcLennanPM1000MotionCon- trollermanualformoreinformation.The'1'beginningeachcommandrefers totheaxisofmotion,ofwhichthereisonlyoneinthecaseofpSAM,but couldbehigherifmultiplelinearmotionmechanismsareeverimplemented...128 vii LISTOFFIGURES Figure2.1:GraphicalrepresentationoftheSAMconcept(nottoscale,noblegas˝lm thicknessexaggeratedforclarity).Left:Basiccapturingschemewithout arecoilseparator.Thenuclearreactiontakesplaceininversekinematics, wheretherecoilingproductsandlowintensityunreactedbeamarecaptured inanoblegas˝lm.Right:Schematicofopticalexcitationand˛uorescence imagingofthecapturedrecoilatomsontoaCCDcamera.Theexcitation lightisseparatedfromtheemitted˛uorescencelightusingopticalbandpass ˝lters........................................5 Figure2.2:Genericenergyleveldiagramforathree-levelsystemwithgroundstate a , excitedstate b ,andmetastablestate m .Excitationislabeledbythedouble arrow;emission,bysinglearrows;andnonradiativetransferisdenotedbythe dashedarrow....................................15 Figure2.3:O˙-resonancesuppressionfactor ˙ i ¹ ºš ˙ i 0 forGaussianabsorptionline- shapes.Farfromresonance,theprobabilityofexcitationdecreasesexponen- tially,suppressingtheprobabilityofimpurity˛uorescence............17 Figure3.1:Top-downandside-viewoftheopticalimagingsystemforcreatinga1:1 imageofthesubstrateontheAndorClaraCCDcamerasensorwithasolid anglee˚ciencyof2.3 % ..............................23 Figure3.2:ArenderingoftheoriginalprototypeSingleAtomMicroscopedesign.left: exteriorofpSAMwithanatomicsourceattached.Thecryocoolerismounted onalineardrive,capableofpositioningthesubstrateintheupper`growth' positionorloweringitintothe`imaging'position.right:crosssectionof pSAM,showingthetwostagesofthecoldheadandthesubstrateinthe `imaging'position.Thesubstrateispositionedclosetoalargeviewport tomaximizethelightcollectione˚ciency.....................24 Figure3.3:ApictureoftheassembledpSAMwhilemountedtoalasertableintheSpinlab attheNSCL.Anarrayofopticscanbeseeninfrontoftheimagingchamber fordirectinglaserlightthroughthesubstrate...................25 viii Figure3.4: leftpanel. PictureofthepSAMsubstratemountasattachedtothe2ndstage heatexchanger.Aheaterandtemperatureprobecanbeseenontheleftside, withwiressecuredtothemountandheatexchangerwithcoppertapetobest ensurethermalgrounding.Thisthermalgroundingensuresthewiresareat thesametemperatureasthesubstratemount,whichpreventsanyerroneous readingsduetoheatconductionalongthewires.Theheaterisquitelong, andextends1inchintothesubstratemountasoutlinedbyadashedline. rightpanel. NearlyfullyassembledpSAMcoldheadstructure.The1-inch diametersubstrateisvisiblethroughtheholenearthebottomofthecopper shieldassembly,asisthethingastubingOD)fordepositingthenoble gasesonthesubstratesurface.Aluminizedmylarshieldinghasnotyetbeen appliedtotheoutercoppershieldinthispictureexceptinonesmallspot.The substratehasmounthasbeenshieldedwithaluminizedmylar(barelyvisible). Seealso:AppendixCformorepicturesofthecoldhead.............26 Figure3.5:a)OriginalpSAMsubstratemount,whichutilizedaremovablethreaded coppersubstrateholdertomakeiteasiertoinstallandremovethesubstrate. However,thethreadswerefoundtopoorlyconductheatatlowtemperatures andlimitedtheultimatesubstratetemperatureunlesscryogenicvacuumgrease (Apiezon-N)wasappliedduringinstallation.b)Currentsubstratemountthat clampsthesubstratedirectlytothemount,eliminatingtheneedforApiezon-N application.Indiumwireisappliedasagasketingmaterialateachsubstrate- copperinterface.Alsofeaturedisthecoppershieldtubetoreduceblackbody irradiationonthefrontsubstratesurface......................28 Figure3.6:AdvertisedcoolingpowercapabilitiesofthepSAMcryoocoler..........30 Figure3.7:PressureandTemperaturemeasuredinsidepSAMasafunctionoftimerelative tocryocoolerstart.Thepressureinitiallyincreasesasthetopofthecoldhead getshotasheatispumpedoutofthecoldcomponents,leadingtoincreased outgassing.Thesubstratemountiscooledbelow6Kin50minutes,butit takesroughly70minutesforbothstagestostabilize................31 Figure3.8:PlotofTemperaturevs.Heaterpowerasreadbythesubstratemounttem- peraturesensor.Relationisreasonablywellrepresentedbyalinear˝twitha slopeof1K/W...................................32 Figure3.9:PlotofpSAMpressure,substratemounttemperature,andheaterpowerover aperiodof6seconds.Theoscillationintemperature(middletrace)is clearlyevident,aswellasacorrespondingoscillation(toptrace)inpressure associatedwithavariationinvaporpressureforresidualgasesfrozenonthe coldparts.ThebottomtraceshowstheLakeshoretemperaturecontrolis unabletovarytheheaterfastenoughtocounteracttheoscillation.........33 ix Figure3.10:Pinoutofelectricalfeedthrough˛angeonpSAM,denotingpinassignments fortheheaterandtemperatureprobeleads.....................34 Figure3.11:Typicalpartialpressureasafunctionofmass/chargeasmeasuredbytheRGA withpSAMatroomtemperature(top),andwiththesubstratemountat5.9K (bottom).Withthecryocooleratbasetemperature,thepressureisreduced byanorderofmagnituderelativetoroomtemperature.Theprinciplepeaks oftheresidualgasesarelabeledinthebottomplot.................37 Figure3.12:RGAscanstakenduringnoblegas˝lmgrowths,wherethenaturallyabundant isotopesofneon,argon,andkryptondominatethescans.............38 Figure3.13:Diagramofthegashandlingsystemusedtodepositnoblegasesontothe substrateinpSAM.Thegeneraldirectionof˛owisfromlefttoright,and startsatacylinderofresearchgrade(99.999%purity)noblegas.After ˛owingthroughanoptionalpuri˝er,itentersabu˙ervolumethroughan electronicallycontrolledvalve.Thenoblegassubsequentlypassesthrough aliquidNitrogencoldtrapforfurtherpuri˝cation(removalofwatervapor) beforeenteringpSAM,whereit˛owsthroughastainlesssteelcapillarytubing endingapproximately2cmfromthesurfaceofthesubstrate.Duringa˝lm growth,thevalvetothevacuumpumpsystemisclosed..............40 Figure3.14:PlotoftheGasHandlingbu˙ervolumepressureasafunctionofPfei˙ervalve ˛owratesettingduringacollectionofneon,argon,andkrypton˝lmgrowths. TheunitsforthePfei˙erValve˛owratearenottheactualgas˛owrate(Torr L/s)throughthePfei˙ervalve,butratherthe˛owratesettingusedtocontrol howopenthevalveis.Theactual˛owratethroughthePfei˙ervalvehasbeen measuredtoberoughlyafactorof20higher,andstronglydependsonthe di˙erenceinpressureacrossthevalveandisrelatedtothenoblegascylinder regulatorsetting(typically 18 20 psig)......................41 Figure3.15:Top-Downschematicofathin˝lmthicknessmeasurementduringnoblegas deposition.Lightfromadiodelaserissentthroughthecombinationofabeam expanderandiristoreducethelightintensitybelow 1 mW/cm 2 .Afterward thelightpassesthrougha50:50beamsplitterandoneofthebeamsisfocused ontoaphotodiodetomonitorthebeampower.Thesecondbeamisdirected andfocusedontothecenterofthefrontsurfaceofthesubstratelocatedin themiddleofthepSAMgrowthchamberata45degreeangletothebeam path.Thelighttransmittedthroughthesubstrateisfocusedontoasecond photodiodetomonitorthelasertransmissionasafunctionoftime........44 x Figure3.16:Exampledatafroma 15 1 mKrypton˝lmgrowth.Thelasertransmission (red)isplottedalongsidethegashandlingpressure(blue)asreadbythe Baratronpressuregauge.Aftertheinitial15minutedepositionperiodatlow pressure,depositingapproximatelyhalfofafringe(roughly140nm),thegas handlingpressureisrampedupto150Torrandthefringefrequencyincreases drastically.Alsopicturedaretheminimaandmaximaintheinterference pattern(greenXs).Amuchlowerfrequencyoscillationisvisibleathigh growthratesduetothin˝lminterferenceinthesecondary˝lmdepositionon thebacksurfaceofthesubstrate..........................46 Figure3.17:Top-Downschematicofawhitelighttransmissionmeasurement.Lightis ˝ber-coupledfromtheDH-2000andcollimatedbeforepassingthroughthe substrateinthepSAMimagingchamber.Transmittedlightisgatheredbya focusinglensand˝bercoupledtothespectrometer................46 Figure3.18: Top: TypicalroombackgroundspectraasmeasuredbytheUV-VISandVIS- NIRspectrometers. Middle: TypicalDH-2000lightsourcetransmission throughthesubstrate(no˝lm)inthepSAMimagingchamber.Thepeaksin thespectracorrespondtotheBalmerseriestransitionsfromthedeuterium lampintheDH-2000. Bottom: Mercury-Argoncalibrationsource(Ocean OpticsHG-1)spectrumasmeasuredbyeachspectrometer.Peaklocations generallyagreebetweenthespectrometerstowithin0.5nm...........47 Figure3.19:MeasuredNeon,Argon,andKryptongrowthratesasafunctionofGasHan- dlingpressure(leftcolumn)andpSAMpressure(rightcolumn)fordi˙erent pSAMcon˝gurationsanddepositiontemperatures.................51 Figure3.20:Intensityoflighttransmittedthrough6separatekrypton˝lmsdepositedat di˙erenttemperatures(two˝lmsdepositedat36Kareplotted),relativeto theintensityoflighttransmittedthroughthebaresubstrate(no˝lm),asa functionofwavelength.Theoscillationsevidentineachtraceareduetothin ˝lminterferenceinthesecondary˝lmonthebackofthesubstrate.Theinset plotshowstheaveragetransmission(errorbarsdenotethestandarddeviation) foreach˝lmasafunctionofdepositiontemperature...............52 Figure3.21:Collectionofgrowthparametersasafunctionofdepositiontemperature. Toprow:growthraterelativetopSAMpressure.Middlerow:average transmissionof˝lmandsubstraterelativetoonlysubstrate.Theerrorbars denotethetransmissionovertherangeofwavelengthsmeasuredwiththe spectrometer.FilmsweregenerallymoretransparenttoIR,andmoreopaque toUV.Bottomrow:thicknessesof˝lmsanalyzedinthiswork..........53 xi Figure3.22:Filmclarityasafunctionoftimeandtemperatureforneon,argon,andkrypton. Filmclarityisrelativetotheinitialtransmissiontodecouplevariationsin initial˝lmtransmissionfromthetimedependentbehavior.Holdinga˝lmat lowertemperaturestendsto'freezein'theinitial˝lmtransparency........54 Figure3.23:Picturesof˝lmsexhibitingdi˙erentcharacteristics.Thepicturesweretaken throughtherearviewportonthepSAMimagingchamber(exceptforthe bottomright),sothe˝lmisonthefarsideofthesubstrate............57 Figure3.24:Initialfringecontrast,contrastdecay,andmaximumthicknesswithanob- servedfringeplottedasafunctionofdepositiontemperature...........59 Figure3.25:ThicknessofaKrypton˝lmasafunctionofpositionalongaverticalline throughthecenterofthesubstrate,asmeasuredinpSAMv1.4(left)and v2.1(right).Theincludedlinesdepictthepredictedthicknessdistribution assuminguniformandcosineintensitydistributionsforgasleavingtheend ofthecapillarytubing.Itshouldbenotedthattheverticalandhorizontalaxis havedi˙erentscales.Forv2.1,interferencefringeswereonlyobservedatthe topofthesubstrate.Attemptsatotherpositionsnearthemiddleandbottom ofthesubstrateyieldednointerferencepattern,andasecondmeasurement wasperformedafterdepositinganadditional5 montothe˝lm,similarly yieldinginterferencefringesonlynearthetop...................62 Figure3.26:SetofwavelengthscansfortheKrypton˝lmuniformitymeasurementper- formedinpSAMv1.4,whichillustratestypicalinterferencepattersfora wavelengthscan.Theamplitudeofthefringeswaslargestatthetopofthe substrate.......................................63 Figure4.1:Experimentalsetupforrubidiumatomicbeam˛uorescenceandwhitelight absorptionofmatrixisolatedrubidiumduringasolidkrypton˝lmgrowth....70 Figure4.2:Experimentalsetupfor˛uorescenceimagingofmatrixisolatedrubidium samples.Includedisanactualimageofthesubstrateilluminatedbyback- groundlightfromtheiongauge.Thecapillarytubingfornoblegasdeposition isjustvisibleatthebottomedgeofthesubstrate(theimageisinverted).....71 Figure4.3:FluorescencepowerasmeasuredbytheAPDasthefrequencyofexcitation lightisscannedthroughtheRubidiumD 1 transition................73 Figure4.4:Angularintensitydistributionmodelsplottedasafunctionofanglerelative tothecenterline( = 0 )intensity..........................75 Figure4.5:IntegratedAPDvoltageasafunctionoflaserintensity.Abest˝ttothisdata yieldsasaturationintensity I 0 = 13 : 6 2 : 9 mW/cm 2 ..............76 xii Figure4.6:PlotofthemodeledpowerdensityasviewedbytheAPDforeachangular distribution.TheplottedvaluesaretheintegrandofEquation4.3inthe y = 0 plane,wherethecenteroftheatomicbeamandlaserintersect.Inthis coordinatesystem,thenozzletipislocatedat z = 35 mm,andthelaser beamisalongthe x -axiscenteredat z = 0 mm.TheAPDsensorislocated abovetheplotted x - z planeat y = 96 mm.....................77 Figure4.7:Absorptionspectraofthethreerubidiumdopedkrypton˝lms.Theab- sorbancefor˝lmswithalowerconcentrationofrubidiumhavebeenmulti- pliedby10toaidinvisibility...........................79 Figure4.8:Absorptioncrosssectionofrubidiuminsolidkryptonassumingthecosine (upperlimit)and j ¹ º (lowerlimit)angulardistributionsoutoftherubidium source........................................79 Figure4.9:Laser-induced˛uorescencespectrumforrubidiuminsolidkrypton.The y - axisunitsarethetotalCCDcountratesummedovertheentiresubstrateand normalizedtothelaserpower............................81 Figure4.10:CCDimagesofthesubstrateunder1mWof730-nmlaserlightwitharoughly Gaussianpro˝le.Thetopimageisofasubstratewithakrypton˝lm,while thebottomimageisofarubidium-dopedkrypton˝lm.Thewhitecircles denotetheextentofthesubstrate..........................82 Figure4.11:Fluorescencepowerperatomasafunctionoflaserintensityforeach˝lmand fortheupperandlowerboundsonthepredictednumberofatomsinthe˝lm. Theslopeofeachlineisthe˛uorescencecrosssection ˙ f ............83 Figure4.12:Fluorescencecrosssectionmeasurementsforeachofthethreerubidium- dopedkrypton˝lms,plottedvs.theaveragenumberdensitycalculatedfrom thetwoatomicangulardistributionmodels....................84 Figure5.1:Diagramofthewhitelighttransmissionmeasurementduringion-beamim- plantation......................................88 Figure5.2:Diagramofthelaser-induced˛uorescenceimagingsetup.............88 Figure5.3:Initialtransmissionoflightthroughthesubstrateandsolidkrypton˝lms relativetotransmissionthroughjustthesubstrate.Theoscillationinthe transmissionisduetothin˝lminterferenceintheroughly400-nmthick krypton˝lmwhichformsonthebackofthesubstrate...............90 Figure5.4:Averagetransmissionofthe˝lmsasafunctionoftimeduringionimplanta- tion.Thespikesanddiscontinuitiesareduetoalightsourceinstabilityand notduetosuddenchangesinthe˝lm........................90 xiii Figure5.5:Left:Asthe 84 Krbeamcollideswiththe˝lm,visible˛uorescencelightis emitted.Thewhitelightsourcewasblockedforthispicture.Right:After50 hr,the 84 Krbeamisfocusedontoadi˙erentspotonthe˝lm.Theimpression ofthebeaminthepreviouslocationisalargeclearareaintheotherwise cloudy˝lm.Thenewbeamlocationcanbeseenasagreenspottotheright oftheprevious.Thewhitelightsourcewasonandisclearlyvisibleasan ovalshapeoccupyingmostofthesubstratearea..................91 Figure5.6:Ion-beaminducedluminescencespectrum.....................92 Figure5.7:Decayofthegreenluminescencepeakassociatedwithatomicnitrogen,which wasmeasuredtohavearoughly10-seconddecayconstant............93 Figure5.8:Top:CCDimageofafreshlygrownKrypton˝lm.Bottom:CCDimageof thesamekrypton˝lmafter53hoursof 84 Krionimplantation.Theregionof interestisshownbythewhitecircle........................95 Figure5.9:Top:CCDimageofafreshlygrownKrypton˝lm.Bottom:CCDimageof thesamekrypton˝lmafter11hoursof 85 Rbionimplantation.Theregionof interestisshownbythewhitecircle........................96 Figure5.10:Top:Laser-induced˛uorescencespectrumforafreshlygrown100- mkryp- ton˝lm.Middle:Spectrumfor 84 Krimplanted˝lms.Bottom:Spectrumfor 85 Rbimplanted˝lms................................97 Figure5.11:Timedependenceof˛uorescencespectraforakrypton˝lmembeddedwith 85 Rbions......................................99 Figure5.12:Total˛uorescenceyieldduringannealingto38Kandsubsequentcooldown to30K.......................................99 Figure5.13:Fluorescencecrosssectionfor˝lmsembeddedwith 85 Rbions.Theshaded bandsarefroma10%uncertaintyinthenumberofatomsimplanted.......100 Figure5.14:Energyleveldiagramformolecularoxygentransition.Afterexcitationat756 nm,molecularoxygennonradiativelytransfersviainter-systemcrossing(IC) toanadjacentlowerlyingstate,andemitsnear1300nm.............101 Figure5.15:Background˛uorescencelineforakrypton˝lmwithrubidiumionsembed- ded.Thesmallspikesinthespectrumdenotetheendsoflaserscansegments andarenotactualfeaturesofthespectrum.....................102 Figure6.1:Requiredintegrationtime t asafunctionofsignal-to-backgroundratio for di˙erentcon˝dencelevels,assumingatotalsignalrateof1Hz..........108 xiv Figure6.2:TransmissionofSemrock˝ltersutilizedin˛uorescenceimaging.Thetrans- missionofthedichoicbeamsplitter,measuredatanincidentangleof45 wasstronglydependentonthepolarizationoftheincidentlightasshownby theshadedblueregion.Thetransmissionoftheindividualelementsmetor exceededthemanufacturer'sspeci˝cations.....................110 Figure6.3:SetupusedtomeasurethetransmissionoftheSemrock˝ltersinseries......110 Figure6.4:TransmissionoftheSemrock˝ltersmeasuredatdi˙erentlaserpowers.The combinedtransmissionofthe˝ltersisafactorof 10 4 largerthanpredicted, basedontheindividualtransmissions.......................111 Figure6.5:ProposedchangestothepSAMimagingsystemdesignedtodrasticallyreduce thebackgroundrate.................................112 FigureA.1:ExperimentalsetupfortheExtendedIRAndorClaraCCDcalibration......116 FigureA.2:SampleimagefromtheCCDcalibrationat750nm,with˝ttoanAirydisk...117 FigureA.3:Measuredcountsperphotonasafunctionofwavelengthfordi˙erentClara CCDsettings....................................119 FigureB.1:DiagramoftheStirlingCycle.Arrowsindicatepistonmotionandheat exchangerenergy˛ow................................120 FigureB.2:Basicpulsetubecryorefrigeratorwithanexternalcompressorsystem.The graphillustratesthetemperaturebehaviorofgaspassingthroughtheheat exchangersateitherendofthepulsetubeduringonepressurecycle.......121 FigureB.3:Standardcon˝gurationformoderntwo-stagepulsetubecryocoolers.Figure takenfrom[3]....................................122 FigureB.4:PictureofthepSAMcryocoolercoldhead.Externalreservoirvolumesnot pictured.......................................124 FigureB.5:DimensioneddrawingofthepSAMcryocooler(CryomechmodelPT415), withremotemotor..................................125 xv CHAPTER1 INTRODUCTION Thisthesisdescribesthe˝rststepsundertakeninthedevelopmentofanewmethodformeasuring thecrosssectionoflow-yieldnuclearreactions.Thedetector,calledthesingle-atommicroscope, worksbycapturingtheproductatomsofthenuclearreactioninacryogenicallyfrozennoblegas solid.Onceembeddedinthenoblegassolid,whichisopticallytransparent,theproductatomsare selectivelyidenti˝edwithlaser-induced˛uorescenceandindividuallycountedviaopticalimaging todeterminethenuclearcrosssection.Single-atomsensitivitybyopticalimagingisfeasible becausethesurroundinglatticeofnoblegasatomsfacilitatesalargewavelengthshiftbetweenthe excitationandtheemissionspectrumoftheproductatoms.Thisnoveldetectionschemehasthe potentialfornear-unitye˚ciency,ahighdegreeofselectivity,single-atomsensitivity,andcould beusedtodetermineanumberofastrophysicallyimportantnuclearreactionrates. Thistechniquewill˝rstbeimplementedinmeasuringthecrosssectionforthereaction 84 Kr ¹ p ; º 85 Rb.Thisreactionisanidealchoiceforacommissioningexperimentbecausethe beam, 84 Kr,isanoblegasandwillbeopticallyinvisiblewhencapturedinasolidkrypton˝lm.The productnuclei, 85 Rb,haveastrongtransitionatareadilyaccessiblewavelength,whichishelpfulin achievingsingle-atomsensitivity.Beforeimplementation,anumberoftasksmustbeaccomplished inordertodemonstratetheabilitytocountatomsinasolidnoblegas˝lmvia˛uorescenceimaging. First,itisnecessarytorepeatablygrowandmaintainopticallytransparentsolidkrypton˝lmsof su˚cientthicknesstostopanenergeticion.Second,asthenumberofproductatomswillbeat leastpartiallydeterminedbytheamountof˛uorescencelightemittedinthe˝lmunderresonant laserexcitation,theintrinsicbrightnessofrubidiumatomsembeddedinsolidkryptonmustbe determined.Third,anumberofopenquestionsexistregardingimplementingthetechniqueinan actualbeamlineexperiment,includingdeterminingtheneutralizationfractionofionsstoppedin the˝lm,aswellasthedurabilityofsolidnoblegasthin˝lmsunderheavyionirradiation,among others. 1 Thisthesisisorganizedintothefollowingtopics.InChapter2thesingle-atommicroscope detectiontechniqueisdescribedindetail,includingadiscussionofopenquestionsandtechnical challengestobeaccomplished.Chapter3detailsthedesignandcomponentsoftheprototype single-atommicroscope,aswellasresultsofnoblegas˝lmgrowthstudies.Chapter4describesthe atomicbeam˛uorescencetechniqueformeasuringtheintensityofanatomicbeam,andsubsequent measurementoftheabsorptionand˛uorescencecrosssectionofmatrix-isolatedrubidiuminsolid krypton.Chapter5encompassesthe˝rstbeamlinetestsfortheprototypesingle-atommicroscope, includinge˙ectsofenergeticheavy-ionbeamimplantationonasolidkrypton˝lm,ionbeam- inducedluminescence,andthe˛uorescencecrosssectionofion-implantedrubidiuminsolid krypton.Chapter6describesthenextstepsforthesingle-atommicroscopeproject,including improvingtheabsorptionand˛uorescencecrosssectionmeasurementofmatrix-isolatedkrypton, aswellasdetailingwhatisnecessaryforachievingsingle-atomsensitivity. 2 CHAPTER2 DETECTIONOFATOMICNUCLEARREACTIONPRODUCTSVIAOPTICAL IMAGING ThischapterisadaptedwithpermissionfromapublishedworkbyB.Loseth et.al. in Phys.Rev. C. 99 065805(2019).Copyright © 2019byAmericanPhysicalSociety. 2.1Motivation Instarsandduringstellarexplosions,andoverbillionsofyears,intricatenetworksofnuclear reactionssynthesizednearlyeverynaturalchemicalelementthatweobservearoundus.Nucle- osynthesisofmostelementsheavierthanironarenotproducedbystellarfusionbutratherby neutroncapture,whetheritbeslowandgradualindividualneutroncapturesduringstellarburning (s-process)ortherapidcaptureofmanyneutronssuchasisbelievedtooccurduringneutronstar mergers(r-process).Thereare35stableisotopesinaccessibletoneutron-captureprocessesand believedtobeproducedthrough -inducedphotodisintegration(p-process)[4,5,6,7]. Thereareasigni˝cantnumberofnuclearreactionsthathaveastrongin˛uenceonnuclide abundancesandwhosecrosssectionsareeitherunknownorpoorlyunderstoodatastrophysically relevantenergies.Measuringthesecrosssectionsisoftentechnicallychallengingforavariety ofreasons.Atastrophysicalenergies(intheso-calledGamowwindow),thecrosssectioncanbe extremelysmallduetothedi˚cultyinovercomingtheCoulombbarrieratstellartemperatures.In ordertomeasureextremelysmallcrosssectionsdirectlyandwithinanacceptabletimeperiod,high beamcurrentsanddensetargetsarerequiredfortheproductionofonlyahandfulofreactionsper day. Aninversekinematicscon˝gurationisoftenutilized,wherethebeamnucleihaveahighermass thanthetargetnucleisothatthereactionproductsscatterforwardinanarrowcone.Basedon theirchargeandmass,thefewproductnucleiarethenseparatedfromthebeamandsecondary nucleibyelectricandmagnetic˝eldsinrecoilseparatorsystems[8,9].Alternativeandoften 3 complementarymethodsinvolvethedetectionoftheproton,neutron,orgammacreatedbythe reactionwithanarrayofscintillatingdetectorsaroundthereactionsite[10].Unfortunatelysuch methodsaresensitivetocosmicray,natural,andbeam-inducedbackgroundsources,theratesof whichcanbesigni˝cantlyhigherthanthatofthereactionofinterest.Someexperimentale˙orts havemoveddeepunderground,wherethecosmic-ray-inducedbackgroundratesaresigni˝cantly lower.Forundergroundfacilities,CASPARatSanfordUndergroundResearchFacility[11],and LUNAinItaly[12],backgroundratesbecomelimitedbyradioactiveelementsinthesurrounding rock,andare 10 2 10 4 timeslowerthanonthesurface. Forreactionsinvolvingrareisotopes,itcanbedi˚culttoachievesu˚cientstatisticsdueto inadequatebeamintensities.Rareisotopebeamscanalsobesigni˝cantlycontaminatedwithother nucleiasaconsequenceofproductionmechanisms,whichcandrasticallyincreasebackground rates.Furthermore,heavynucleihavesubstantialmagneticrigidityandrelativelyslightdi˙erences incharge-to-massratios,makingthemcumbersometoseparateduetothelongdistancesandhigh magnetic˝eldsrequired.Typicalrecoilseparatorsarelesse˙ectiveathighmassesforthesame reasons. Noveldetectionschemescapableofbypassingtheaforementionedchallengescreateanoppor- tunitytomeasureexceptionallylowyieldnuclearreactionsorothersuchlowyieldnuclearevents, suchasneutrinolessdouble- decay.Suchadetectionschemeshouldexhibitsingle-atomsensi- tivitytothereactionproductswhilebeingunsusceptibletotraditionalbackgroundsources.The detectionmethodsshouldexhibitahighdegreeofselectivitybetweenatomicspeciestoovercome beamcontaminationorseparationissues.Ahighdetectione˚ciencyisalsohighlydesirableto maximizetheprobabilityofdetectingrareevents. Weproposeatechniqueformeasuringcrosssectionsoflowyieldnuclearreactionsbydetecting theatomicproducts optically ,calledthesingle-atommicroscope(SAM).TheSAMisintended forreactionsperformedininversekinematics,suchthatmostoralloftherecoilingproductatoms arecapturedinsideacryogenicallyfrozennoblegassolid(suchasneon,argon)depositedona transparentsubstrate.Oncetrapped,anatomicresonanceisexcitedintheproductatomswith 4 Figure2.1:GraphicalrepresentationoftheSAMconcept(nottoscale,noblegas˝lmthickness exaggeratedforclarity).Left:Basiccapturingschemewithoutarecoilseparator.Thenuclear reactiontakesplaceininversekinematics,wheretherecoilingproductsandlowintensity unreactedbeamarecapturedinanoblegas˝lm.Right:Schematicofopticalexcitationand ˛uorescenceimagingofthecapturedrecoilatomsontoaCCDcamera.Theexcitationlightis separatedfromtheemitted˛uorescencelightusingopticalbandpass˝lters. alaser,andtheemitted˛uorescencelightiscollectedbyaCCDcamera-basedimagingsystem. Guestatomsthatareisolatedinanoblegasmatrixgenerallyexhibitblue-shiftedabsorptionand red-shiftedemissionbandsrelativetothewavelengthinvacuumforagivenatomictransition.This wavelengthshiftbetweenabsorptionandemissionbands(Stokesshift[13])canbeaslargeas hundredsofnanometers.Todetecttheisolatedproductatoms,theirred-shifted˛uorescenceis isolatedfromtransmittedorscatteredexcitationlightwithoptical˝lterstopickouttheemission wavelengthrangeofinterest. AschematicofthemethodisincludedinFig.2.1.Wearguethatsingle-atomsensitivity isfeasiblewiththeSAM,notingthatsingleatomdetectionofbariumatomsinsolidxenonhas beendemonstrated[14,15].Themainadvantageofthisapproachisthatthedetectionmechanism isnota˙ectedbytraditionalbackgroundsources.Neutronand -raybackgroundsdonota˙ect the˛uorescencespectraordetectionthereof,andtheproductatomsareidenti˝edbytheirunique 5 atomictransitions,whicharedistinctfromanycodepositedatomsfromthebeam. InSec.IIwediscusspromisingcross-sectionsensitivitiesfortwoclassesofnuclearreactions. Wethendescribespeci˝cdetailsregardingthecaptureanddetectionofatomicspeciesinanoble gassolidinSec.III.Finally,inSec.IVthemethodissummarizedandthebene˝tsandlimitations oftheSAMdetectionschemearediscussed. 2.2CrossSectionSensitivity Table2.1:Candidatereactionsforthesingle-atommicroscope,withapproximatebeamcurrents, targetarealdensities,andexpectedyields. ReactionBeamTargetCrossApprox.Reaction currentdensitysectionyieldimportance (pps)(atoms/cm 2 )(b)(products/day) 22 Ne ¹ ; n º 25 Mg 10 15 10 19 10 15 1s-process n source 10 15 10 17 10 11 100 91 Nb ¹ p ; º 92 Mo 10 4 10 20 10 5 1Productionofp-nucleus 92 Mo 10 7 10 20 10 3 10 5 WeenvisiontwoclassesofreactionswheretheSAMdetectionschemeisapplicable:(i) extremelysmallcross-sectionreactionswithahigh-currentstableisotopebeam-and(ii)low-current rareisotope(radioactive)beamreactions.Table2.1listsapproximateexperimentalparametersfor examplereactionsofeachtype. 2.2.1Smallcross-sectionreactions 22 Ne ¹ ; n º 25 Mgisakeyreactionfors-processnucleosynthesis,andithasanextremelysmall predictedcrosssectionintheGamowwindow,oftheorderoffemtobarns( 10 15 b)[16].Assuming ahigh-intensity 22 Nebeamofcurrent 10 15 ppsincidentonawindowless 4 Hegasjettargetwithan arealdensityof 10 19 atoms/cm 2 (JENSAtarget[17]),theexpectedyieldfora1-fbcrosssection isonlyasingle 25 Mgatomperday.Duetothesesmallyields,single-atomsensitivitytothe product 25 Mgatomswithnegligiblebackgroundratesisnecessarytomeasureacrosssectionfor 6 thisreactioninareasonableamountoftime,evenatthehighestachievablecurrentsandtarget densities. FortheSAMtomeasurethisreaction,itshouldbenotedthatsuchhighbeamcurrentsrequire thattheunreactedbeamintensity( 10 15 pps)beattenuatedbyafactorof 10 6 inordertoavoid meltingacryogenicnoblegas˝lm,asdiscussedinSec.III.Withanappropriaterecoilseparator toattenuatetheunreactedbeamintensity,thisreactioniswellsuitedfortheSAM,asthebeam ( 22 Ne)isanoblegasandthusanyunseparated 22 Nebeamatomswouldnotcontributebackground ˛uorescenceduringopticalimagingoftheproduct 25 Mgatoms.Anadvantageisthat,unlike sometraditionaldetectionmethods,theSAMdetectionschemewouldbeimmunetoleakybeams orothernon-magnesiumbeamcontaminants,whichcanbedi˚culttocompletelyeliminatefrom high-intensitybeamlinesystems.Itis,furthermore,desirabletohaveanalternativetechnique,which theSAMdetectionschemecanpotentiallysatisfy,withdi˙erentsystematicsthantheforthcoming undergroundmeasurementsduetotheimportanceofthisreaction. 2.2.2Low-beam-currentreactions Thelowintensityofrareisotopebeamsisoftenthelimitingfactorinthecross-sectionsensitivity fortraditionaldetectionmethods.Withsingle-atomsensitivityandatomicspeciesselectivity,the SAMschemecanimproveuponcross-sectionsensitivitiesevenwithlow-intensitybeams.Asan example,thereaction 91 Nb ¹ p ; º 92 Mohasbeenidenti˝edasakeyreactionintheproductionof thep-processnuclei 92 Mo[18].AHauser-Feshbachmodel(NON-SMOKERdatabase)predicts crosssectionsfrom1 bto1mbintheGamowwindow[19].AttheNationalSuperconducting CyclotronLaboratory(NSCL),a 91 Nbbeamcanbeproducedwithacurrentoforder 10 4 pps, whichwillbefurtherimprovedto 10 7 ppsattheupcomingFacilityforRareIsotopeBeams(FRIB). AnadvantageofsuchsmallcurrentsforSAMisthatnobeamrejectionorrecoilseparatorwill benecessarytoprotectthenoblegas˝lm,easilyallowingforacapturee˚ciencyapproaching unity.Usingaprotontarget(CH 2 ,ofdensity0.25mg/cm 2 ),fora10- bcrosssectionroughlyone 92 MoatomisproduceddailyatNSCLbeamintensities,andthesameyieldallowsfor10-pbcross 7 sectionstobeprobedwithFRIBbeamcurrentsassumingnegligiblebackgroundrates. Gamma-baseddetectionmethodsarehandicappedbylowere˚cienciesandaresusceptibleto cosmicrayandenvironmental sources,requiringmorebeamtimetoachievesu˚cientcounts abovebackground(typicallyhundredsofcountsforgoodstatistics).Similardi˚cultiesexistfor low-energyneutrondetection.Reactionsinvolvinghighermassnuclides,suchas 91 Nb ¹ p ; º 92 Mo, easilyexceedthedesignmagneticrigidityacceptanceofcontemporaryrecoilseparatorsystems [8,9]unlessahighchargestateisselected,alimitationontheoveralle˚ciencydespitethenear- unitydetectione˚ciencyofrecoilsaftertheseparator.TheSAMhasthepotentialtosigni˝cantly outperform ,neutron,andelectromagneticseparator-basedmethodsforsomerareisotopereactions duetoshorterbeam-timerequirementstoamasssu˚cientstatistics,especiallyforlowercross sectionswhereexpectedyieldsaresmall. 2.3TechnicalChallenges Anumberoftechnicalchallengesmustbeovercomebeforethismethodcanbeappliedto measuringthecrosssectionforalow-yieldreaction.Chiefamongthem,single-atomsensitivity mustbedemonstratedfortheproductspeciesofinterest,whichweargueisfeasibleformany species.Achievingsingle-atomsensitivityrequiresperformingtime-dependentcalibrated˛uores- cencespectroscopyofthespeciesofinterestinasolidnoblegas,aswellasopticalbackground characterizationatexcitationandemissionwavelengthsappropriatefortheproductspeciestobe detected.Aslaserintensityandopticalrequirementsmaynotallowforimagingtheentirearea containingproductatomssimultaneously,alaserscanningsystemwillbeimplementedtoraster acrossthesurfaceofthedepositedsolidnoblegas˝lm.Furthermore,single-atomdetectionshould beachievedforshortopticalintegrationtimes,sotheopticalsignal-to-backgroundrateshouldbe maximizedtoensurethatimagingtheentiresubstrateviarasterizedscanningisnotprohibitively time-consuming.Therearealsoafewoutstandingquestionsregardingcaptureandneutralization ofenergeticionsinacryogenicsolidnoblegas. 8 2.3.1Captureinnoblegassolids Tocapturetheproducts,generallyspeaking,asolidnoblegas˝lmofthickness100 missu˚cient tofullystopanionwithakineticenergyofafewMeVpernucleon[20],whichisatthehigher endoftheenergyrangeformostreactionsofastrophysicalinterest.Highlytransparentthin˝lms ofthickness100 mcanbedepositedinaboutanhourwithanareaof20cm 2 orlarger,which matchesthesizeofthefocalplaneforatypicalrecoilseparator.Thespeci˝cpropertiesofmost noblegasesinsolidformarelistedinTable3.1.Theselectionofwhichnoblegastouseforagiven reactionwilldependprimarilyonthematrix-isolatedspectraoftheproductatomstobedetected. Thepolarizabilityofthenoblegasatomshasasigni˝cante˙ectonthespectraoftrappedatoms [21]. Thereareafewimportantfactorstoconsiderregardingthecaptureofenergeticionsinanoble gassolid.First,someamountofdamagewillbein˛ictedonthenoblegas˝lmthroughdirect heatingandsurfacesputteringduetoexposuretoanenergeticionbeam.Second,allproductatoms arehighlyionizedandmaynotbecompletelyneutralizedbeforestoppinginthe˝lm.Asionsmay havedrasticallydi˙erentspectrathanneutralatoms,thefractionofproductatomswhichremain ionizedmaybeopticallyundetectable.Third,itisunclearwhattrappingsitethestoppedatoms willoccupyintheface-centeredcubic(fcc)latticeformedbynoblegasatoms(calledthenoblegas matrix),andtrappingsitesareknowntoa˙ectthespectraofthecapturedatoms[22]. 2.3.1.1Noblegas˝lmdamage Twoobviousmechanismsa˙ectthemaximumbeamintensityatwhichsigni˝cantdamageis in˛ictedonthenoblegasmatrix.Thekineticenergyofanyunseparatedbeamatomsisdeposited asheatinthenoblegas˝lm,whichwillcausethe˝lmtosublimeforsu˚cientbeamintensities. Thise˙ectmaybeespeciallysigni˝cantforneonduetothesingle-digittemperaturesrequired forsolidi˝cation,wherethecoolingpowerofcontemporarypulse-tubecryocoolersisonlyofthe orderof1W.Theheaviernoblegas˝lmswillbemoreresistanttodirect-heatingsublimation,as thecoolingpowerimprovestotensofwattsathighertemperatures.Itisimportanttonotethat 9 Table2.2:Propertiesofnoblegassolids. NeArKrXeRef.No. Latticestructurefccfccfccfcc[23] Latticeconstant(Å)4.4645.3115.6466.132[24] Triplepoint(K)24.5683.81115.78161.37[24] ˆ solid ,t.p.(g/cm 3 )1.4441.6232.8263.399[25] T solid (K, 10 6 Pa)7.327.438.451.3[26] Sublim.energy(meV)19.680116164[27] Polarizability(Å 3 )0.3941.6412.4844.044[23] Refractiveindex1.111.291.381.49[28] noblegasicesareelectricalinsulators,andwill,therefore,havepoorthermalconductivityatlow temperatures,whichmayprovetobealimitingfactordespitesu˚cientcoolingpower[1].Togeta senseofatypicalheatload,a3MeV/nucleon 91 Nbbeamwithacurrentof 10 8 ppswoulddeposit atolerable4mW. Alikelymoresigni˝cantdamagemechanismissurfacesputteringofthe˝lmbythebeam andproducts.Noblegasmatricesarerelativelylooselybound,andeachincomingenergeticion willejectsomenumberofnoblegasatomsfromthematrix,typicallycalledthesputteringyield. Thise˙ectcanbecompoundedunderhighbeamintensities,astheensuinghighertemperatures duetokineticenergydepositionincreasethenoblegasatommobilityande˙ectivelylowersthe surfacebindingenergy.Forlightions( p or )withakineticenergyoftheorderofMeVincident onsu˚cientlythick,lowtemperaturenoblegas˝lms,thesputteringyieldisdeterminedbythe sublimationenergyandtheelectronicstoppingpowerofthenoblegassolid[29,27]. Theliteratureonlyreportssputteringofnoblegas˝lmsbyheavyionsatalowkineticenergy,in therangeofkeV,wherethesputteringyieldisdominatedbynuclearstoppingpoweramong othere˙ects[30,31],incontrasttothelightioncase.Balaji etal. reportsputteringyieldsashigh as 10 3 10 5 with5-keVionsforvariouscombinationsofNe,Ar,Kr,andXeionsandtargets[31]. Togetamoremacroscopicunderstandingofthise˙ect,underabeamintensityof 10 9 ions/cm 2 /s, suchsputteringyieldscorrespondtoathicknesslossofroughly 0 : 002 0 : 2 m/hr.Studieshave notbeenperformedformedium-tohigh-massionsimpingentonnoblegassolidsatastrophysical 10 energiesofafewMeVpernucleon,wheretheelectronicstoppingpowerwillbedominant,and whereelectronicstoppingpowersareanorderofmagnitudehigherthaninthelight-ioncase. Extrapolatingthelow-energyheavy-ionsputteringyieldstoastrophysicalenergies,themaximum thicknesslosswouldincreaseto2 m/hr,assumingthatsputteringyieldsareproportionaltothe totalstoppingpower. 2.3.1.2Productionneutralizationandtrapping Forstudiesoftheopticalspectraofatomicspeciesinnoblegasmatrices,samplesaretypically preparedbydepositinganinitiallayerofthenoblegasmatrixonthecooledsubstrate,followedby alayerofco-depositednoblegasandguestspecies,and˝nishedwitha˝nallayerofnoblegasto ensurethateachguestatomisisolated(i.e.surroundedbynoblegasatoms).Theguestspeciesare usuallydepositedwitheitherane˙usiveoranionicsource;studiesofNa + ionsdepositedinAr [32]andBa + ionsinXe[33]haveshownspectraconsistentwiththoseoftheirneutralcounterparts, anditisknownthatthechargestateofenergeticionsstoppedinmediumapproaches0[34]. However,asnoblegassolidshavepoorelectricalconductivity,itisunknownwhetherthereisa su˚cientpopulationoflooselyboundelectronsforcompleteneutralization.Furthermore,itmay beadvantageousforsomespeciestoremainsinglyionizedduetomorefavorablespectroscopy. Theimplantationmechanismforenergeticnuclearreactionproductions,whichwillpenetrate somedepthintothe˝lm,isstarklydi˙erentfromthetypicalpreparationmethod.Inparticular, thereactionproductswillbehighlyionizedbeforeimplantationanditisnotclearwhatpercentage oftheproductionswillbecomefullyneutralizedduringandafterstoppinginthenoblegas˝lm. Furthermore,thetrappingsiteofthestoppedproductatominthenoblegasatomlatticemaybe unstableorsigni˝cantlydi˙erentfromthetrappingsitesfortypicalnoblegasmatrixsamples. Fortunately,annealingnoblegas˝lmshavebeenshowntorecoveratomsinunstabletrapping sites[22].ThesequestionsrequirefurtherinvestigationastheydirectlylimittheSAMdetection e˚ciency. 11 Table2.3:Selectedmatrix-isolatedabsorptionandemissionspectraofSAM-friendlyspecies. ItalicizedlifetimesarevacuumvaluesfromtheNISTAtomicSpectraDatabase(physics.nist.gov). AtomZVacuumtransitionMatrixisolatedLifetime(ns)Ref.No. assignment (nm)absorption (nm)emission (nm) Li32p 2 P 2s 2 S671.0Ar656.5-679.0900 26 [35] Na113p 2 P 3s 2 S589.2,589.8Ar536.0-594.5670-710 13 28 [36] K194p 2 P 4s 2 S766.7,770.1Ar666.4-746.7850-950 20 75 [37] Rb375p 2 P 5s 2 S780.2,795.0Ar705-755877 ˘ 20[21,38] 4d 2 D 5s 2 S516.5Ar420-540630 ˘ 100[38] 6p 2 P 5s 2 S420.5Ar420-540630 ˘ 100 Cs556p 2 P 6s 2 S852.3,894.6Ar822-845970 30.5 , 35 [38] 5d 2 D 6s 2 S685.1Ar610-670762 2 : 2 10 10 7p 2 P 6s 2 S455.6Ar440-520762 543 Be42p 1 P 2s 1 S234.9Ne232.0232 1.8 [39] Ar235.0-237.0465 1 : 33 10 9 Kr240.5464.7 9 : 5 10 7 Mg123p 1 P 3s 1 S285.3Ne275.3296.52.03[40] Kr277.0-296.0297-326 1 : 25 2 : 25 [41] 3p 3 P 3s 1 S472 8 : 91 10 6 Ca204p 1 P 4s 1 S422.8Ar422.0432.9 4.6 [42] 4p 3 P 4s 1 S647.6 8 : 6 10 5 Sr385p 1 P 5s 1 S460.9Ar447466.2 5 [43] 5p 3 P 5s 1 S689.4709.2 2 : 1 10 4 Ba566p 1 P 6s 1 S553.7Ar532550 8.4 [33] Xe561-566570-591 Zn304p 1 P 4s 1 S213.9Ne205.4212.81.15[40] Xe219.9356,399 > 10 4 [44] 4p 3 P 4s 1 S307.7Ar297 2 : 6 10 4 [45] Cd485p 1 P 5s 1 S228.9Ne216.5-221.7227.21.26[40] 5p 3 P 5s 1 S326.2Ar312.4 2 : 5 10 3 [45] Hg806p 3 P 6s 1 S253.7Xe253.2 119 [45] Al133d 2 D 3p 2 P308.3Ne260.0 17 [46,47] 4s 2 S 3p 2 P394.5Ne320.0 20 S163p 1 S 0 3p 3 P 1 459.0Ar456.9 3 : 3 10 9 [48] 3p 1 S 0 3p 1 D 2 772.7785 2 : 3 10 5 Mo425pz 7 P 5sa 7 S379.8Ar341.3399.0 > 10 3 [49] 5sb 5 D 5sa 7 S496.8 1 : 5 10 5 Yb706p 1 P 6s 1 S398.8Ne388.2394.9 5.2 [50] 6p 1 P 6s 1 S555.8546.0 6 : 8 10 2 [51] 12 2.3.2Opticalsignal-to-backgroundestimates Aftercapture,theproductatomsmustbeidenti˝edanddetectedinthenoblegas˝lmbased ontheiratomicspectra.Itisadvantageousthatthespectralbehaviorofatomsandmolecules isolatedinnoblegasmatriceshasbeena˝eldofstudyinchemicalphysicsfordecades,andsothe spectraofmanyatomicspecieshavebeenmeasuredinavarietyofmatrices.Broadlyspeaking,the transitionsofatomicspeciesisolatedinnoblegasmatricesarequalitativelysimilartothetransitions invacuum,however,transitionwavelengthscanbeshiftedbytenstohundredsofnanometersand exhibitsigni˝cantlybroadenedlinewidths(typicallynm).Table2.3listsasubsetofthe availableatomicspectrainnoblegasmatricesalongwiththevacuumtransitionwavelengths.The lifetimesofallowedtransitionsarenotsigni˝cantlya˙ectedinmedium[51],andsotransitions lackinganyavailablelifetimedatainmediumarelistedwiththeirvacuumlifetimes.Thistable isnotexhaustive,asmanyspeciesandtransitiondatahavebeenomittedforbrevity,butitdoes includespeciescompatiblewiththeSAMdetectionscheme. Thephysicsofatomsandtheirelectronicspectrainteractingwithnoblegasatomsisthoroughly reviewedin[22].Ourproposedopticaldetectionschemereliesontheshiftbetweenexcitation and˛uorescencespectraexhibitedbymostspeciesinmedium(seeFig.2.1),whichallowsfor theselectiveoptical˝ltrationofanytransmittedorscatteredexcitationlight.Divalentatoms,in particular,canexhibitconsiderableshiftsduetoanintersystemcrossingbehavior,suchasYbin Ne[52],MginKr[41],andHginArandKr[53],wheretheperturbativee˙ectofthenoblegas latticefacilitatesaradiationlesstransitionfromanexcitedstatetoanadjacentorlower-lyingstate. 2.3.2.1Single-atomsignalrate Thenetopticalsignalrateduetoasingleresonantlyemittingatomissimplythe˛uorescence intensity F (numberofphotonsisotropicallyemittedperunittime)peratommultipliedbythe e˚ciencyoftheopticalimagingsystem,whichweestimatetobeoftheorderof 10 2 10 3 . Opticalimaginge˚ciencyincludesfactorsduetothesolidangle,transmissione˚ciencyofoptical ˝ltersforwavelengthseparationoftheexcitationfromemissionlight(Semrock,Rochester,NY), 13 andwavelength-dependentquantume˚ciencyofCCDcameras.Laser-coolableatomsareideal,as theyaregenerallycharacterizedbycyclingtransitionswithnoorminimalrepumping.Foranalkali atomunderresonantexcitationfromthegroundstate a tothe˝rstexcitedstate b ,the˛uorescence intensity F ishalftheinverseoftheexcitedstatelifetime,assumingthattheexcitationlightisof su˚cientintensity.ConsultingTable2.3,the 2 S ! 2 P transitionofRbatomsinsolidArexhibits a20-nslifetime,correspondingtoanopticalsignalrateofroughly 25 250 kHzdependingonthe imaginge˚ciency. Thealkalineearthelements,withtwovalence s -shellelectrons,areslightlymorecomplicated. AsdepictedinFig.2.2,uponresonantexcitationfrom a ! b ,thereissomechanceoftransfer from b toalower-energymetastablestate m withasigni˝cantlylongerlifetime.Mgatomsinsolid Krexhibita2-nslifetimeforthe 1 S ! 1 P transition,correspondingtoanopticalsignalrateof 0 : 25 2 : 5 MHz.However,emissionfromthetriplet 3 P statewasalsoobservedwitha9-mslifetime ( 0 : 5 -Hzopticalsignalrate)[41].DetectionofaMgatomviathe 1 P emissionappearsfeasible basedontheselifetimes,asasu˚cientnumberofphotonswillbedetectedbeforetheatomtransfers tothemetastable 3 P state.Waitingforthemetastablestatedecayorrepumpingtheatomwitha secondarylightsourceshouldallowforrecoveryofthe 1 P emissionband.Thisblinkingintoand outofmetastablestatesischaracteristicofasingleemitter,andobservationofblinkingbehavior wouldgotowardscon˝rmationofsingle-atomsensitivity.Itshouldbenotedthatdetectionofthe 3 P emissionistechnicallyfeasible,astheopticalsignalratesarestillwellabovethedarkcountrate oforder1mHzforstate-of-the-artCCDcameras(Andor,Belfast,UnitedKingdom).Furthermore, backgroundratesmaybesigni˝cantlyloweratthe472-nm 3 P Mgemissioncomparedtothe 297 -to 326 -nm 1 P emission,whetheritbeduetothee˙ectivenessofoptical˝ltersforintense ultravioletexcitationlight,therelativewavelengthshiftbetweenexcitationandemissionbands,or the˛uorescenceofimpuritiesinthewindowsandoptics. Detectionofatransitionmetallikemolybdenumisexpectedtobemorechallengingthanthe previouscases,witha 4 d 5 5 s 1 electroniccon˝gurationand a 7 S groundstate.Studiesofmatrix isolatedMoinsolidArandKrbyPellin etal. [49]reportsubstantialnonradiativetransferto 14 Figure2.2:Genericenergyleveldiagramforathree-levelsystemwithgroundstate a ,excited state b ,andmetastablestate m .Excitationislabeledbythedoublearrow;emission,bysingle arrows;andnonradiativetransferisdenotedbythedashedarrow. metastablestateswidelyseparatedingaseousMoatomsdespitethespin,parity,or J selection rules.Emissionfrommetastable b 5 D , a 5 P ,and a 5 F stateswereobservedwithsimilarlifetimes afterexcitationto z 7 P inanargonmatrix.Takingthereportedin-mediumlifetimesatfacevalue (Table2.3),observationofthe z 7 P ˛uorescencewillyieldkHzsignalrates,whilethemetastable b 5 D statewouldyield30-Hzsignalrates.Thechallengebecomesdetermininganexcitationscheme thate˙ectivelymimicsthethree-levelsystemdepictedinFig.2.2,analogoustothemagnesium case. 2.3.2.2Signal-to-backgroundestimation Estimatingtheopticalbackgroundrateisamorechallengingtask.Thehighnumberofpossible opticalbackgroundsourceshampersthedeclarationofageneralquantitativeassertionaboutthe backgroundrate,andultimatelyitwillhavetobemeasuredandminimizedforagivenspecies throughadjustmentsinopticalspectroscopygeometryandmaterialsselection.Instead,wecatalog somepossiblesourcesofbackgroundlightandestimatetheirrelativeimportance(seeTable2.4). Anyscatteredorre˛ectedexcitationlaserlightisexpectedtobesu˚cientlyattenuatedthrough 15 Table2.4:Potentialsourcesofopticalbackground,withknownexcitationwavelengths. BackgroundLocation/SourceWavelengthNote ScatteredlightLaserexcitationSpeciesdependentAttenuatewithoptical˝lter(s) unreactedbeamNoblegas˝lmSpeciesdependent BeamcontaminantNoblegas˝lmSpeciesdependent N 2 Film/residualgas < 200nmO˙resonance NFilm/residualgas523,1047nm[54]Unknownconcentration O 2 Film/residualgas763nm[55]1-nmFWHM,24-mslifetime OFilm/residualgas296,558,630nmUnknownconcentration H 2 OFilm/residualgas < 200nmO˙resonance CFilm/residualgas462,872,980nmUnknownconcentration Cr 3 + Sapphireimpurity693.0,694.4nm[56]Impurityinsubstrate theuseofoptical˝lters.Theprimarysourcesofbackgroundlightareexpectedtobecontaminant atomsormoleculesthat,undertheexcitationwavelengthoftheproductatomofinterest,happen to˛uoresceatwavelengthswithinthebandpassoftheoptical˝lters.Thesecontaminantscouldbe impuritiesinthesubstrate,noblegas˝lm,vacuumwindows,oroptics.Furthermore,thebeamcan becontaminatedbyisotopeswithsimilarcharge-to-massratios,whichwillbeimplantedalongside theproductatoms. Theoverallbackgroundratewillberelatedtothesumofthe˛uorescenceratesforallbackground sources.Assumingexperimentalconditionswithexcitationlightata 500 -nmwavelength,withan intensity(powerperunitarea)of P š A = 1 W/cm 2 ,theopticalsignal-to-backgroundratio S š B foroneproductatomwitha ˝ = 5 nsexcited-statelifetimeisapproximately S š B = " 2 ˝ P h Õ i n i ˙ i 0 ˙ i ¹ º ˙ i 0 !# 1 (2.1) ˇ 4 10 14 " Õ i n i ˙ i 0 ˙ i ¹ º ˙ i 0 !# 1 ; (2.2) wherethesumisoverallbackgroundspecieswitharealdensity n i ,peakabsorptioncrosssection ˙ i 0 ,andwavelength-dependentabsorptioncrosssection ˙ i ¹ º atalaserfrequency ,and h isthe Planckconstant. Equations(1)and(2)statethat S š B isinverselyproportionaltothearealnumberdensity n i andtheabsorptioncrosssection ˙ i ¹ º ofbackgroundspecies.Theabsorptioncrosssectionis 16 Figure2.3:O˙-resonancesuppressionfactor ˙ i ¹ ºš ˙ i 0 forGaussianabsorptionlineshapes.Far fromresonance,theprobabilityofexcitationdecreasesexponentially,suppressingtheprobability ofimpurity˛uorescence. dependentonthein-mediumlineshapefactor,whichisafunctiondescribingtheprobabilityof absorptionasafunctionofthewavelength,andistypicallyGaussianformatrixisolatedspecies. Figure2.3illustratestheo˙resonancesuppressionfactorasafunctionofthelinewidthsfromthe transitionresonance,assumingthatthein-mediumlineshaperemainsGaussianfarfromresonance. Ifthepeakabsorptionwavelengthofabackgroundspeciesissu˚cientlyfarfromtheexcitation wavelength,thebackgroundatomexcitationratewillbeexponentiallysuppressed.Itisimportantto notethatlinewidthsforabsorptionandemissionareverybroadinmediumduetophononexcitation ofthenoblegaslattice,andareoftheorderof 10 3 10 4 GHzorroughly 1 10 nm,whichisorders ofmagnitudelargerthaninvacuum. Asanexample,themostabundantpotentialbackgroundsourcewillbecomponentsofair trappedasimpuritiesinthenoblegas˝lm.Noblegasesarecommerciallyavailablewithppm 17 puritiesandcanbefurtherpuri˝edtoppblevelswithgettering.Foranargon˝lmof100 m thickness,therewillberoughly 2 10 20 argonatoms/cm 2 ,with 10 14 moleculesofairassuming appmpurity.Toachieve S š B = 1 wouldrequireano˙-resonantsuppressionfactorofroughly 10 28 ,adistanceofalmost5linewidthsfromresonanceforaGaussianabsorptionlineshape.As themolecularcomponentsofairdonotabsorbuntilwellintotheultraviolet,theyarenotexpected tocontributesigni˝cantlytothebackgroundrate,withtheexceptionofO 2 near763nm. 2.4LimitationsandSummary SeverallimitationsexistfortheSAMdetectionscheme.First,whileatomicspeciescanbe selectivelyexcited,thismethodisincapableofdistinguishingbetweendi˙erentisotopesofthe samespecies.Althoughsmallisotopedi˙erencesexistintheatomichyper˝nestructuredue tothenuclearspin,thelinewidthsinmediumaresobroadthatanyisotopicvariationbecomes obscured.Second,whilethismethodispotentiallyapplicabletoawiderangeofspecies,species withoutopticallyaccessibletransitionscannotbedetected,whicheliminatesthenoblegaselements alongwithelementslike˛uorine,whoselowest-lyingtransitionoccursat97.7nminvacuum. Third,itisnotsuitedtodetectproductsthatareabundantinavacuumsystem,suchasoxygen, nitrogen,andcarbon,asitwouldbeimpossibletogrowasolidnoblegas˝lmwithoutthousands ofsuchcontaminantatomsevenwiththehighestachievablenoblegaspurity.Fourth,thedetection mechanismisslowfortheSAMrelativetotraditionalmethodssincetheproductsarenotdetected immediatelyaftercreationbut,rather,atalatertimewhentheyareimaged.Thereforeshort-lived isotopes( ˝ 1 š 2 < 1 day)arenotsuitableunlessthedaughternucleiarealsoopticallydetectableand thedaughtersareadi˙erentspeciesfromthebeamatomsandanybackgroundatoms. Tosummarize,importantreactionsfornucleosynthesisprocessesareoftendi˚culttomeasure becauseoftheirlowyield,whetheritbeduetoextremelylowcrosssections,low-intensityrare isotopebeams,orhighbackgroundrates.Weproposeanoveldetectionmethodforlow-yield nuclearreactionsthatcapturestheproductatomsinacryogenicallyfrozen˝lmofasolidnoble gaswheretheyareopticallyimagedandcounted.Thismethodcano˙eranear-unitycaptureand 18 detectione˚ciency,feasiblyachievesingle-atomsensitivity,andispotentiallyapplicabletomany astrophysicallyimportantnuclearreactions.Thechiefadvantageofthesingle-atommicroscopeis thatitisnotsensitivetoneutron, ,orchargedparticlebackgroundsourcesandcould,therefore, outperformtraditionaldetectionmethods. 2.5Acknowledgements SpecialthankstogoSamAustin,ArtemisSpyrou,HendrikSchatz,andXiao-DongTang forhelpfuldiscussions.Thisworkbene˝tedfromsupportbytheNationalScienceFoundation underGrantNo.PHY-1430152(JINACenterfortheEvolutionoftheElements).Thisworkwas supportedbyMichiganStateUniversity,theDirector'sResearchScholarsProgramattheNational SuperconductingCyclotronLaboratory,andtheU.S.NationalScienceFoundationunderGrantNo. #1654610. 19 CHAPTER3 THEPROTOTYPESINGLE-ATOMMICROSCOPE Thischapterdescribesthedesign,construction,andperformanceoftheprototypesingle-atom microscope(pSAM).The˝rstsection,3.1,describesthedesignrequirementsandconsiderations foralowtemperaturecryostatwithlargeopticalaccess.Section3.2describestheconstructionand individualcomponentsoftheprototypeSingleAtomMicroscope(pSAM).Section3.3reportson thegrowthofthin˝lmsofsolidNeon,Argon,andKryptoninpSAM. 3.1Requirements ThepSAMhasthreefundamentaldesignconsiderations.First,itshouldbecapableofgrowing transparentthin˝lmsofsolidnoblegasesonacoldsubstrate.Second,thereshouldbeaccessto the˝lmsurfaceforanexternalsource(beamline)toembedtheatomicspeciesofinterestintothe noblegas˝lm.Third,itshouldprovidesubstantialopticalaccesstothe˝lmforacharge-coupled device(CCD)camera-basedimagingsystem. 3.1.1HeatLoad AcentralrequirementforthepSAMistheabilitytogrowandmaintainthin˝lmsofsolidnoble gases.Thefreezingpointofthenoblegasesincreasewithmass,ascanbeseeninTable3.1along withanumberofotherproperties.Heliumsolidi˝esonlyunderhighpressure(0.95Kelvinat2.5 MPa[23]),andisthereforetechnicallyinaccessibleforthispurpose.Neonhasthelowestfreezing pointamongthenoblegasesusedinpSAM,andrequirestemperaturesinthesingledigits(Kelvin) atultra-highvacuum(UHV, < 10 7 Torr).Traditionally,coolingtolowtemperaturesinvolved cryostatsystemsusingliquidheliumasarefrigerant[28].Theinventionoftheclosed-cycle cryorefrigerationsystems(cryocoolers)revolutionizedmanyaspectsoflowtemperaturephysics, ascryocoolersarecapableofcoolingtoliquidheliumtemperatureswithoutthematerialsexpense andoverheadofusingliquidhelium.Closed-cyclecryocoolersdeliverlongterm,stable,and 20 Table3.1:Propertiesofnoblegassolids. NeArKrXeref latticestructurefccfccfccfcc[23] latticeconstant(Å)4.4645.3115.6466.132[24] triplepoint(K)24.5683.81115.78161.37[24] ˆ solid ,t.p.(g/cm 3 )1.4441.6232.8263.399[25] T solid (K, 10 6 Pa)7.327.438.451.3[26] Sublim.energy(meV)19.680116164[27] polarizability(Å 3 )0.3941.6412.4844.044[23] refractiveindex1.111.291.381.49[28] lowmaintenancecoolingtoliquidheliumtemperatures,andarethereforeanidealchoiceforthis purpose. Blackbodyradiationisthemainsourceofexternalheatingincryogenicvacuumsystemsas thereisinsu˚cientresidualgastoconductheatfromthevacuumvesseltothecoldparts.Cryostats andcryocoolersutilizethin-walledstainlesssteelforstructuralsupport,whichsimilarlyconductsa negligibleamountofheatinthetemperaturerangeofinterest.Achievingsingledigittemperaturesat thesamplelocation,inthiscasethesubstrateuponwhichthenoblegas˝lmsaredeposited,requires shieldingfromthewallsofthevacuumvessel,whichatroomtemperatureareanintensesource ofradiativeheat.Theradiativeheat˛owbetweentwosurfacesisgivenbytheStefan-Boltzmann equation[1], P rad = ˙ EA ¹ T 4 2 T 4 1 º ; (3.1) where ˙ = 5 : 67 10 8 W š m 2 K 4 istheStefan-Boltzmannconstant,Aisthearea(dependingonthe geometry)ofthetwosurfaces, T 1 and T 2 arethetemperaturesofthetwosurfaces,and E isafactor dependingontheemissivitiesofthetwosurfaces.Theemissivity( )isameasureofhowabsorptive amaterialistoradiation(light)andisrelatedtohowre˛ective( R )asurfaceisby = 1 R .A perfectblackbody( = 1 )at T = 300K hasaradiativeintensityof ˙ ¹ 300K º 4 = 46mW š cm 2 onto thesubstrateandmounting˝xturesatsingledigittemperatures.Tobecapableofgrowingsolid neon˝lms,thecoolingsystemshouldhavesu˚cientcoolingpowerattemperaturesbelow10Kto o˙settheincomingblackbodyradiation. 21 3.1.2BeamlineandOpticalAccess Fluorescencephotonsfromatomscapturedonthesubstratesurfacewillbeemittedisotropically,and sotheopticalsignalsizefordetectionwillbeproportionaltotheaccessiblesolidanglearoundthe sample.Imagingsingleatomsismoree˚cientiftheimagingopticsareplacedclosetothesample inordertomaximizethenumberof˛uorescencephotonscollected.Usinglargediameterviewports andlensesislikewisebene˝cial.Thechallengebecomesoptimizingthedistanceanddiameterso astomaximizethecollectione˚ciencywithoutaddingsigni˝cantheatloadtothesubstrate.As astartingpoint,designofavacuumchamberandsubstratemountisintendedforthesinglelens imagingsolutiondisplayedinFigure3.1.Inprinciple,theimagingcanbeperformedwithasingle 50mmdiameterasphericlenswithane˙ectivefocallengthof40mm(EdmundOpticsNo.84- 340).Creationofa1:1imageontheCCDcamera(AndorCLARACCD),requiresthesubstrate frontsurfacetolensdistancebeequaltothelenstocameradistance,whichistwicethefocallength (80mm).Thelightcollectione˚ciencyforthissetupisestimatedby š 4 ˇ = ¹ 1 cos ºš 2 ,where ishalftheangleoccludedbythelens.Inthiscase, tan = 25mm š 80mm ,resultinginalight collectione˚ciencyofroughly 2 : 3% .Incontrast,atypicalopticalcryostathase˚cienciesaround 0 : 1% orlower[50]. Unimpededaccesstothefrontsurfaceofthesubstrateisessentialforachievingunitycapture e˚ciencyofrecoilingproductatoms.However,itisdi˚culttoimagineasinglechamberdesign whichfeaturestherequisitebeamlineaccessandgoodopticalaccesstoembeddedatomswithout signi˝cantcompromise.Opticalcryostatsforsimilarapplicationsanglethesubstratebetweenthe viewportsandsampledepositionportasacompromise[57].Instead,atwo-chamberdesignwas chosentoensureidealaccessibilityforboth,withthesubstratemountedonalineardrivefortransfer betweenchambers.Thiswillallowforthedesignofanimagingchamberwithidealopticalaccess withoutobstructingatomimplantation. 22 Figure3.1:Top-downandside-viewoftheopticalimagingsystemforcreatinga1:1imageofthe substrateontheAndorClaraCCDcamerasensorwithasolidanglee˚ciencyof2.3 % . 3.2Components 3.2.1Overview AttheheartofpSAMisapulsetubecryocooler,necessaryforcoolingasubstratetothecryogenic temperaturesrequiredtosolidifynoblegases.Thesubstrateisclampedtoacoppersubstratemount attachedtothecryocoolerandsurroundedbyacooledcoppershieldassemblyinordertoblock mostblackbodyradiationfromtheroomtemperaturevacuumvesselwalls.Thecryocooleritself ismountedonalineardrive(linearshiftmechanism)usedtopositionthesubstrateineitherthe growthorimagingchamber.Thelineardriveismountedontopofthegrowthchamber,wherenoble gas˝lmsaregrownandproductatomsareembedded.Thegrowthchamberfeaturesviewportsfor monitoringduringsamplegrowthandalsocontainstheturbomolecularvacuumpumpandvacuum 23 sensors.Theimagingchamberismountedbelowthegrowthchamberandisofcustomdesign, featuringlargediameterviewportsincloseproximitytothesubstrate.Figure3.2and3.3containa renderingofthepSAMmodelandapictureofthedetector. Figure3.2:ArenderingoftheoriginalprototypeSingleAtomMicroscopedesign.left:exterior ofpSAMwithanatomicsourceattached.Thecryocoolerismountedonalineardrive,capableof positioningthesubstrateintheupper`growth'positionorloweringitintothe`imaging'position. right:crosssectionofpSAM,showingthetwostagesofthecoldheadandthesubstrateinthe `imaging'position.Thesubstrateispositionedclosetoalargeviewporttomaximizethe lightcollectione˚ciency. 3.2.2AssemblyandCleaningProtocol Itisgoodpracticetothoroughlycleanallvacuumcomponentsbeforeassembly.Componentsare oftencontaminatedwithoilsfromfabricationandhandlingthatoutgasundervacuumandlimitthe ultimatevacuumpressure.Furthermore,anyimpuritiescapturedina˝lmorcontaminationonthe substratehasthepotentialtobeasigni˝cantsourceofbackgroundlightunderlaserexcitation.The 24 Figure3.3:ApictureoftheassembledpSAMwhilemountedtoalasertableintheSpinlabatthe NSCL.Anarrayofopticscanbeseeninfrontoftheimagingchamberfordirectinglaserlight throughthesubstrate. 25 Figure3.4: leftpanel. PictureofthepSAMsubstratemountasattachedtothe2ndstageheat exchanger.Aheaterandtemperatureprobecanbeseenontheleftside,withwiressecuredtothe mountandheatexchangerwithcoppertapetobestensurethermalgrounding.Thisthermal groundingensuresthewiresareatthesametemperatureasthesubstratemount,whichprevents anyerroneousreadingsduetoheatconductionalongthewires.Theheaterisquitelong,and extends1inchintothesubstratemountasoutlinedbyadashedline. rightpanel. Nearlyfully assembledpSAMcoldheadstructure.The1-inchdiametersubstrateisvisiblethroughthehole nearthebottomofthecoppershieldassembly,asisthethingastubingOD)fordepositing thenoblegasesonthesubstratesurface.Aluminizedmylarshieldinghasnotyetbeenappliedto theoutercoppershieldinthispictureexceptinonesmallspot.Thesubstratehasmounthasbeen shieldedwithaluminizedmylar(barelyvisible).Seealso:AppendixCformorepicturesofthe coldhead. 26 pSAMcomponentswerecleanedbeforeassemblybyhandcleaningallsurfaces˝rstwithacetone, andthenwithisopropylalcohol.Afterward,theyweresubmergedinanultrasoniccleanerforone hourat60 Celsius,rinsedwithdistilledwater,andlefttoairdryinacleanarea.Assemblyof pSAMwasperformedinaClass-100cleanroomtominimizetheamountofdustandparticulates aswellasminimizethechanceforsurfacecontaminationinsidethevacuumvessel. 3.2.3CryocoolerandColdComponents ThepSAMcryocoolerisaCryomechPT415Cryorefrigerator[58],whichistwo-stagePulseTube typecryocoolerwithacoolingpowerof40Wattsat45Kelvinand1.5Wattsat4.2Kelvinatits ˝rstandsecondstageheatexchangers,respectively(seeFigure3.6).Thetheoryofoperationand speci˝cdetailsofthecryocooler`coldhead'(mainbodyofthecryorefrigerationsystem,separate fromthecompressedheliumgassystem)aredetailedinAppendixB.Thenoblegas˝lmsaregrown onthesurfaceofasubstratethatismountedtothe2ndstageheatexchangeronthecoldhead.The substratemount,picturedintheleftpanelofFigure3.4,ismachinedfromablockofoxygen-free electrolytic(OFE,C10100CopperAlloy)copper,whichisacommonlyusedmaterialincryogenic applicationsduetoitsexceptionalthermalconductivityatlowtemperatures.Thesubstrateitself issyntheticsapphire,whichhasbothexcellentopticalqualitiesandamongthehighestthermal conductivitiesofanymaterialatlowtemperature.Table3.2containspropertiesaboutvarious materialsusedinpSAMatcryogenictemperatures.Thesubstrateis˝rmlyclampedtothesubstrate mountwithacopperring,andalayerofindiummetalisusedasagasketingmaterialtoimprove thermalcontactwiththesubstratemount.Indiumalsohasexcellentcryogenicpropertiesandisa verysoftmetal,makingitidealforthispurpose.Firmlyclampingthesubstratetoitsmountwith Indiumasagaskete˙ectivelycold-weldsthemtogether,˝llinginanygapsorirregularitiesbetween thematingsurfaces[1].Acrosssectionoftwodi˙erentsubstratemountsthathaveseenusein pSAMisincludedinFigure3.5. Ashieldingstructuremadeofseveralcopperpartsisconstructedaroundthe2ndstageofthecold head,includingthesubstratemount,andispicturedintherightpanelofFigure3.4.Thisshieldis 27 Figure3.5:a)OriginalpSAMsubstratemount,whichutilizedaremovablethreadedcopper substrateholdertomakeiteasiertoinstallandremovethesubstrate.However,thethreadswere foundtopoorlyconductheatatlowtemperaturesandlimitedtheultimatesubstratetemperature unlesscryogenicvacuumgrease(Apiezon-N)wasappliedduringinstallation.b)Currentsubstrate mountthatclampsthesubstratedirectlytothemount,eliminatingtheneedforApiezon-N application.Indiumwireisappliedasagasketingmaterialateachsubstrate-copperinterface. Alsofeaturedisthecoppershieldtubetoreduceblackbodyirradiationonthefrontsubstrate surface. thermallyanchoredtothe1ststageheatexchangerandcompletelycoversthesubstratemountexcept forapairof2indiameterholescenteredoneithersideofthesubstratetoallowforgoodoptical access.Thepurposeofthisshieldistoprotectthe2ndstagefromblackbodyradiationemanating fromtheenclosingvacuumvessel,whichisatroomtemperature.Assumingaperfectblackbody ( = 1 ),thepairof2indiameterholesallowaradiativepowerof ¹ 46mW š cm 2 º¹ 2 º¹ 20cm 2 º = 1 : 84W throughtheshielding, Tofurtherreducethee˙ectofblackbody,alayerofaluminizedmylaristapedtothesurfaceof thesubstratemountandtheoutsideoftheshieldingstructure.Aluminizedmylarisathinlayerof plasticsheetingthathasbeencoatedwithaluminumononeside.Thealuminumisveryre˛ective (emissivity ˇ 0 : 01 [1])comparedtotheunpolishedcoppersubstratemount(emissivity > 0 : 02 [1]), 28 Table3.2:Tableofmaterialproperties.Valuestakenfrom[1]. ThermalconductivitySpeci˝cheatThermalcontraction W/(m K)J/(g K) L š L (%) 4K295K4K295K 293 K 4 K Brass2860.000150.3770.384 CopperOFHC6303970.000090.3860.324 Stainlesssteel0.27150.000170.480.296 Polyimide(Kapton TM )0.0110.190.000790.7550.44 Sapphire23047 < 0.000090.7790.079 reducingtheamountofblackbodyradiationabsorbedbythesubstratemount.Thecombination ofthecoppershieldstructureandaluminizedmylarshieldingallowsforopticalaccessandthe substratemounttoreachtemperaturesbelow6K,whichiscoldenoughtogrow˝lmsofsolid Neon.Theheaviernoblegases'temperaturerequirementsaremucheasiertoachieve.Thenext lowestfreezingpointisforArgonat27K,wherethecoolingpowerofthecryocoolerisimproved totensofWatts.AplotofthecoolingcapacityofthecryocoolerisincludedinFigure3.6,and thepressureandtemperatureinsidepSAMduringatypicalcooldownfromroomtemperatureis includedinFigure3.7 3.2.4TemperatureControl Monitoringandcontrollingthetemperatureisdonewithatemperaturesensorandheatermounted tothesubstratemount(picturedinFigure3.4).ThesensortypeisaCernoxresistor(Lakeshore ModelCX-1050-AA,SN:X103297)andprovidesatemperaturemeasurementviaitstemperature dependentelectricalresistance.Itiscalibratedovertherangeoftemperaturesfrom 1 : 4 325K , withanuncertaintyoflessthan20mKattemperaturesbelow50K.Thetemperaturesensoris mountedinaholeonthebottomendofthesubstratemount,belowthesubstrate.Thislocationis furthestfromthe2ndstageheatexchangerandnearbythesubstrate,wherethetemperaturereading shouldbeclosetotheactualsubstratetemperature.Measuringthesubstratetemperaturedirectly isnotdoneinpSAMduetothedi˚cultyofmountingatemperatureprobewithoutcontamination 29 Figure3.6:AdvertisedcoolingpowercapabilitiesofthepSAMcryoocoler. 30 Figure3.7:PressureandTemperaturemeasuredinsidepSAMasafunctionoftimerelativeto cryocoolerstart.Thepressureinitiallyincreasesasthetopofthecoldheadgetshotasheatis pumpedoutofthecoldcomponents,leadingtoincreasedoutgassing.Thesubstratemountis cooledbelow6Kin50minutes,butittakesroughly70minutesforbothstagestostabilize. orobstructionofthesubstrate.AnotherCernoxsensor(LakeshoreModelCX-1050-CU-HT, SN:X134596)ismountedtothe1ststageheatexchangerfordiagnosticpurposes.Thetemperature sensorcalibrationdataisincludedinAppendixC. Theheaterisan 50 Ohmresistorinacylindricalhousing(LakeshorepartnumberHTR-50) thatisusedtoraisethetemperatureofthesubstratemountbysimplysendingcurrentthroughit. Theheaterismountedjustabovethesubstrate,adistanceof3inchesfromthe2ndstageheat exchanger.Theheatercartridgeisquitelarge(1/4inchindiameter,1inchlong),penetratingmore thanhalfwayintothesubstratemount.Thisplacementoftheheaterensuresthatthetemperature 31 Figure3.8:PlotofTemperaturevs.Heaterpowerasreadbythesubstratemounttemperature sensor.Relationisreasonablywellrepresentedbyalinear˝twithaslopeof1K/W. ofthemountaroundthesubstrateisuniform,sincetheheatsourceisbetweenthesubstrateandthe sourceofcooling(2ndstageheatexchanger).Sendingcurrent I throughtheheaterwithresistance R injectsheatenergyintothesubstratemountatarateof P = I 2 R ,where P isthepowerin Watts.Atemperatureismaintainedwhenthetotalheatloadismatchedbythecoolingpowerof thecryocooler. Thetemperaturesensorsandheaterarewiredtoanelectricalvacuumfeedthrough˛ange thatisexternallyconnectedtoaLakeshoreModel331Temperaturecontroller.TheLakeshore 331measurestheresistanceofeachtemperaturesensorandconvertstoatemperaturewitheach sensor'suniquecalibrationcurve.Italsoiscapableofsendingupto1Ampofcurrentthroughthe heater,correspondingtoamaximumpowerof50Watts.Aplotofthesubstratemounttemperature asafunctionofheaterpowerisincludedinFigure3.8.TheLakeshore331canbesettomaintaina speci˝ctemperaturethroughtheuseofaProportional-Integral-Derivative(PID)controlalgorithm, whichadjuststheheaterpowerautomaticallytomaintainaspeci˝ctemperature.Altogether,with thetemperaturecontrolsystem,thetemperatureofthesubstratemountcanbesettoanytemperature intherangefrom5-60K. 32 Figure3.9:PlotofpSAMpressure,substratemounttemperature,andheaterpoweroveraperiod of6seconds.Theoscillationintemperature(middletrace)isclearlyevident,aswellasa correspondingoscillation(toptrace)inpressureassociatedwithavariationinvaporpressurefor residualgasesfrozenonthecoldparts.ThebottomtraceshowstheLakeshoretemperature controlisunabletovarytheheaterfastenoughtocounteracttheoscillation. Thecryocoolercoolingpoweriscreatedbycyclingbetweenhigh(280psi)andlow(100psi) pressuresofcompressedheliumatafrequencyofroughly1.4Hz.Thisoscillatorybehaviorofthe coolingpowermanifestsitselfinanobservabletemperatureoscillationbelow20K.Atsuchlow temperatures,thespeci˝cheatofcopperfallsdrastically,sothesmalloscillationinheatenergy correspondstoanoticeabletemperatureoscillation.ThisoscillationisdepictedinFigure3.9, whichshowstheautomatedheatercorrections(controlledbytheLakeshore331)areinsu˚ciently fasttoaccommodatetherapidswingsintemperature,whichreachamaximumamplitudeofnearly 1degreeKnear10K.Thistemperaturevariationisnotexpectedtosigni˝cantlya˙ectspectroscopy ofsamplesdepositedonthesubstrate.However,shoulditprovenecessary,itispossibletodampthe oscillationsbyincreasingthetotalthermalmassorinstallingalargeheatcapacityspacerbetween 33 Figure3.10:Pinoutofelectricalfeedthrough˛angeonpSAM,denotingpinassignmentsforthe heaterandtemperatureprobeleads. thesubstratemountand2ndstageheatexchanger.Alayeredspacerofleadandcopperhasbeen showntodamptheoscillationstothemilliKelvinscale[59]. 3.2.5FeedthroughVacuumAccess ExternalaccesstotheinteriorofpSAMisprovidedthroughasetoffeedthrough˛angesattached toanadapting˛angebetweentheLinearShiftMechanismandcoldhead˛angenearthetopof pSAM.ThestainlesssteelcapillarytubingOD,usedtodepositnoblegaseson thesubstratesurfaceisconnectedtoastainlesssteelfeedthroughtubeonaConFlat (CF)˛ange(Leskerpart:LFT212TEFV).Thesectionsofstainlesssteeltubingareconnectedwith custom˝ttingsthataresilversoldered(brazed)tothetubing.The˝ttingsarefastenedtogetherwith brassscrewsandanindiumo-ringsealiscompressedbetweenthe˝ttingstoensurealeak-tight sealevenatlowtemperature.Thenoblegasfeedthroughtubingisexternallysealedwithastainless bellowsvalve(SwagelokpartSS-4H).Thenoblegases˛owthroughthisinletvalvefromaseparate gashandlingvacuumsystem,describedlaterinthischapter. ApressurereliefvalveonaCF˛angeisalso˝ttedtotheadapting˛angeasasafety 34 measureincaseofrapidsublimationoflargeamountsoffrozengasesinsidepSAM.Thepressure reliefvalve(Accu-GlassModelPRV-133)isdesignedtoopenatwhentheinternalpressureexceeds 2psiaboveatmosphere,therebypreventingahazardousoverpressurizationsituation.Theelectrical feedthrough˛ange(MDC23PinSubmini-C1.33DS)forthetemperaturesensorsandheaterisalso attachedtotheadapting˛ange. 3.2.6LinearShiftMechanismandPositionControl Asmentionedintheoverview,thecoldheadandadapting˛angearemountedtoaUHVDesign HLSM150LinearShiftMechanism(LSM),whichiscapableof300mmoflinearmotion(300 mmstroke).ThepurposeoftheLSMistomovethesubstratebetweenthegrowthandimaging chamber,describedinsubsequentsections.TheLSMconsistsofanexpandableedge-welded bellowsassemblywithCF˛angessupportedinakinematicguidesystem.Linearexpansion orcontractionofthebellowsisdrivenbyaMcLennansteppermotor(23HT18C230)˝ttedtoa 50:1IP57gearbox,whichdrivesaprecisionstainlesssteeltrapezoidallead-screw(with2mm pitch).ControloftheLSMpositionisdonethroughaMclennanSim-Stepsteppermotordrive andcontroller,whichutilizesaMclennanPM1000motioncontrollertocommandaMSE570M microsteppingbipolarsteppermotordrive.TheSim-Stepisoperatedthroughacommandline interfaceandiscapableofpreciselytranslatingtheLSMthroughoutitsfullstrokerangeatadjustable speeds,alongwithexecutionofuser-de˝nedmotionsequences. Thesteppermotordividesafullrevolutioninto200steps,whichisimprovedbytheMSE570M drivewhichimplementsamicrostepping( step)resolutionfactorof16,therebydividingafull rotationinto3200 steps.Thesteppermotordrivesa50:1gearboxcoupledtothe2mmpitch lead-screw(2mmperrevolution),whichpropelstheactualexpansionandcontractionoftheLSM. ConvertingstepstoLSMdisplacementisastraightforwardcalculation: 200steps 1rev 16 step 1 step 50 rev 1 screwrev 1 screwrev 2 mm = 80 ; 000 steps mm (3.2) Thiscorrespondsto12.5nm/ step,wellbeyondtheresolutionoftheRenishawLM10magnetic 35 encoderattachedtotheLSMforprecisionpositionmeasurements.TheLM10hasaresolutionof 1 m,correspondingto80 stepsor5motorsteps.PositioningtheLSMrepeatablywithmicron precisionistypicalwiththissetupalthoughthepositionhasbeenobservedtodriftasfaras10 m overaperiodofaweek,likelyduetothermalcontractionandexpansion.RefertoAppendixDfor alistofcommoncommandsusedincontrollingtheLSM. 3.2.7GrowthChamber ThegrowthchamberisanIDsphericalsquaredesigncommerciallyavailablefromKimball Physics,withfourandfourports.Acrosssectionofthegrowthchamberis includedlaterinFigure3.15.Twoportsareoccupiedbyapairoflargediameterfused silicaviewportsviewdiameter)fromTorrScienti˝cLtdonopposingsidesofthesubstrateat a45-degreeangle,forthepurposeofmonitoringnoblegas˝lmgrowth,aprocessdescribedlater inthePerformancesectionofthischapter.Oneportisoccupiedbyavacuumpump,and twoportsbyvacuumsensors.Thebeamlineportdirectlyin-linewiththefront surfaceofthesubstrate,issealedwithapneumaticallyactuatedMDCgatevalve(GV-1500M-P) ona˛angeforisolationfromthebeamline.Theadditionalportsinthegrowthchamber areunused. 3.2.8Vacuumcontrol ThevacuumpumpsystemconsistsofanOerlikonTurboVac50turbomolecularpump(55l/s),with anAnestIwata250Coil-freescrollpump(9.1CFMdisplacement)forroughvacuum.Vacuum pressureismonitoredwithanMKSSeries392Micro-IonGauge,accurateforpressuresranging from 10 9 760 Torr.Inaddition,pSAMfeaturesanSRSRGA200ResidualGasAnalyzer(RGA) forvacuumdiagnosticsandnoblegaspartialpressuremeasurements.TheRGAiscapableof measuringthepartialpressuresofresidualgasesinpSAMinthepressurerangeof 10 4 10 10 Torr ( 10 6 10 12 Torr withtheelectronmultiplieron).TheRGAfunctionsbyionizingresidualgas atomsandmoleculeswithahot˝lamentandseparatingthembasedonthemass-to-charge( m š q ) 36 Figure3.11:Typicalpartialpressureasafunctionofmass/chargeasmeasuredbytheRGAwith pSAMatroomtemperature(top),andwiththesubstratemountat5.9K(bottom).Withthe cryocooleratbasetemperature,thepressureisreducedbyanorderofmagnituderelativetoroom temperature.Theprinciplepeaksoftheresidualgasesarelabeledinthebottomplot. ratio.TheSRSRGA200issensitiveintherangefrom m š q = 0 200amu ,althoughtypically nopeaksaredetectedabovethebackgroundfor m š q > 86 ,whichistheheavieststableisotopeof Krypton.TypicalRGAscansforpSAMatroomtemperatureandatbasetemperaturearedisplayed inFigure3.11.Partialpressuremeasurementscanalsobeperformedduring˝lmdeposition,where thescanisdominatedbythenoblegasbeingdeposited,asdisplayedinFigure3.12. 37 Figure3.12:RGAscanstakenduringnoblegas˝lmgrowths,wherethenaturallyabundant isotopesofneon,argon,andkryptondominatethescans. 38 3.2.9ImagingChamber Theimagingchamberfeaturestwolargefusedsilicaviewportsviewdiameter)fromTorr Scienti˝cLtdwithananti-re˛ectivecoating(partVPZ64QBBAR,700-1100nm)mountedto portsoneithersideofthesubstrate.Thevacuumchamberwasdesignedwitha crosssectionwiththe˛atsectionparalleltothesubstrate,andisdetachableincaseanewdesign isrequired.Therearviewportispositionedjustfromthefront(noblegas˝lm)sideofthe substrate,correspondingtoapproximately10%totalsolidanglee˚ciencyoutoftherearviewport fromthecenterofthesubstrate. 3.2.10GasHandlingSystem Thepurposeofthegashandlingsystemistotransfernoblegasesfromacompressedgascylinder topSAMinacontrolledfashionandatthehighestpurity.Adiagramofthesystemisincluded inFigure3.13.Thenoblegasesusedareofresearchgradepurity,purchasedfromPraxair(Neon 99.999%,Kr99.999%)andAirgas(Argon99.998%).Thegascylindersare˝ttedwithastandard dual-stageregulatingvalve(Matheson3120A)andconnectedtoanoblegaspuri˝er(SAESGC50 Puri˝er)whichiscapableofreducingimpuritiesinthenoblegasestoconcentrationsbelow10parts perbillion(ppb),or99.99999%purity.Thepuri˝erwasbypassedwithisolatingandbypassvalves forthemajorityof˝lmgrowthsdescribedinthisthesis.Thenoblegasesthen˛owthroughan electronicallycontrolledneedlevalve(Pfei˙erEVR116controlvalve)intothemainbu˙ervolume, whichisaCon˛at(CF)6-waycross.Mountedtothebu˙ervolumeisthevacuumpump system(OerlikonTurboVac50withEdwardsnXDS10iforevacuumpump),whichcanbeisolated fromthebu˙ervolumewithananglevalve(LeskerSA0150MCCF).Pressureinthebu˙ervolume ismeasuredwithacoldcathodeionizationvacuumsensor(HPSSeries423I-MAG)validinthe range 10 11 10 2 Torr,andacapacitancemanometer(MKSBaratron626C)thatisaccuratein therange 0 : 1 100 Torr.Thecoldcathodesensorispoweredo˙during˝lmgrowthforprotection. Afterthebu˙ervolume,thegas˛owsthroughaliquidnitrogencoldtraptofreezeoutwater vaporpresentinthegas.Thecoldtrapconsistsofalongdiameterstainlesssteeltube(approx 39 5metersinlength)coiledto˝tinsideadewar˝lledwithliquidnitrogen.Thegascompletes thejourneytopSAMthroughasectionof˛exibletubingthatisconnectedtoagasinlet˛ange, locatednearthetopofpSAM.OncethroughthepSAMinletvalve,thegasentersalongcapillary tubingOD,ID,approximatelyinlength)startingattheinlet,passinginsidethe coppershielding,andendingapproximately2cmfromthesubstratesurface.Thecapillarytubing isthermallyisolatedfromtheshieldingitselftoensureitstemperatureremainshighenoughto preventnoblegases(ArgonandKryptoninparticular)fromfreezinginsidethetubingandclogging it. Gas˛owintopSAMiscontrolledviacomputer,whichreadsthepressureinsidethebu˙ervol- umewiththeBaratron626CandadjuststhePfei˙ercontrolvalveinordertomaintainaspeci˝cally setpressurewithaPIDalgorithm,similartothetemperaturecontroldescribedpreviously.The pressuredi˙erentialbetweenthepuri˝ersectionandthebu˙ervolumecausesgasto˛owintothe bu˙ervolumeataratecontrolledbythePfei˙ervalve.Thepressuredi˙erentialbetweenthebu˙er Figure3.13:Diagramofthegashandlingsystemusedtodepositnoblegasesontothesubstratein pSAM.Thegeneraldirectionof˛owisfromlefttoright,andstartsatacylinderofresearchgrade (99.999%purity)noblegas.After˛owingthroughanoptionalpuri˝er,itentersabu˙ervolume throughanelectronicallycontrolledvalve.Thenoblegassubsequentlypassesthroughaliquid Nitrogencoldtrapforfurtherpuri˝cation(removalofwatervapor)beforeenteringpSAM,where it˛owsthroughastainlesssteelcapillarytubingendingapproximately2cmfromthesurfaceof thesubstrate.Duringa˝lmgrowth,thevalvetothevacuumpumpsystemisclosed. 40 Figure3.14:PlotoftheGasHandlingbu˙ervolumepressureasafunctionofPfei˙ervalve˛ow ratesettingduringacollectionofneon,argon,andkrypton˝lmgrowths.TheunitsforthePfei˙er Valve˛owratearenottheactualgas˛owrate(TorrL/s)throughthePfei˙ervalve,butratherthe ˛owratesettingusedtocontrolhowopenthevalveis.Theactual˛owratethroughthePfei˙er valvehasbeenmeasuredtoberoughlyafactorof20higher,andstronglydependsonthe di˙erenceinpressureacrossthevalveandisrelatedtothenoblegascylinderregulatorsetting (typically 18 20 psig). volumeandpSAMcausesthegasto˛owthroughthecoldtrap,capillarytubing,andontothe substratesurfaceataraterelatedtothepressuredi˙erentialandthee˙ectiveconductanceofthe coldtrapandcapillarytubing.Theregulatoronthenoblegascylindersistypicallysetat 18 20 psig,andthepressureinthebu˙ervolumeismaintainedat 100 150 TorrwiththePfei˙ervalve foratypical˝lmgrowth.Thepressureinthebu˙ervolumecanbeheldataconstantpressureto within0.2Torr,andthisstablepressurecontrolinthebu˙ervolumeensuresastable˝lmgrowth rateonthesubstrate.TheaveragedPfei˙ervalvesettingsusedduringacollectionof˝lmgrowths isincludedinFigure3.14. 41 3.3NobleGasFilmGrowth 3.3.1Background Noblegassolidso˙erastableandinertenvironmentforthecaptureandpreservationofatomic andmolecularspecies.Inthemature˝eldofmatrixisolationspectroscopy,guestspecies(atoms ormolecules)arecodepositedwithagaseousnoblegasessprayedontoacryogenicallycooled substrate,whereuponspectroscopicstudiescanbeperformed[60].Thestructureandproperties ofthenoblegasmatrixcanhaveasigni˝cante˙ectonthespectraofisolatedspecies[22].Itis importantthattechniquesforthedepositionofsuchsamplesresultinthin˝lmswithconsistently reproducibleproperties. TheSingleAtomMicroscoperequires˝lmsof100 minthickness,as100 missu˚cientto fullystopenergeticionsatmostastrophysicalenergiesinthenoblegas˝lmbasedontheoretical stoppingpowercalculations[20].Incontrast,thematrixisolationliteraturetypicallyutilizes samplesthicknessesoforder 1 10 m[44,33],signi˝cantlylessthanrequiredfortheSAM. Transparencyofthenoblegas˝lmisalsoanimportantfactor,asSchulzeandKolbreportthat whileNeandAr˝lmsaregenerallytransparentovertherangeofthicknessesstudied( < 30 m),Kr andXe˝lmsbecomeopaquewithincreasingthickness.Filmopacitymaynotplayasigni˝cantrole formatrixisolationstudies,asguestspeciesconcentrationaregenerallyhigh(1: 10 4 )tomaximize thesignalforbulkspectroscopy[61].Largeguestconcentrationsarenotaluxuryavailableforthe SAM,whichaimstoimageextremelysmallconcentrations(1: 10 20 ),whereindividualatomsmay beobscuredbynoblegas˝lmopacity.Itishighlydesirabletobeabletodeposittransparent˝lms ofallthenoblegastypes,asthespectralbehaviorofguestspeciescanvarysigni˝cantlybetween di˙erentmatrixtypes. Thenextsectiondescribesthesystemsandprocedurefordepositingnoblegas˝lmsonto thecryogenicallycooledsapphiresubstrateinpSAM.Theaforementionedgashandlingsystem, externaltopSAM,controlsthe˝lmgrowthrateando˙ersadditionalnoblegaspuri˝cationoptions. The˝lmgrowthrateismeasuredvialaserthin˝lminterference,andtheopticalqualityofthe 42 ˝lmsismeasuredaftergrowthviawhitelighttransmission.Afterdescribingtheequipmentand methods,observationsfromNeon,Argon,andKrypton˝lmgrowthsoverarangeofdeposition temperaturesarecatalogued. 3.3.2Experimentalsetup Thenoblegas˛owsintopSAMfromtheaforementionedgashandlingsystem,andisdirectedat thesubstratewithathincapillarytubeOD).Noblegasatomsexitingthecapillarytubing willcollidewithandhavesomeprobabilityoffreezingonthesurfaceofthecoldsubstrate,andin thismannerathin˝lmofsolidnoblegasgraduallybuildsup.Thethicknessofthe˝lmismeasured usingtheprincipleofthin˝lminterference,whereinextremaareevidentintheintensityoflaser lighttransmittedthroughthe˝lmandsubstrateasthe˝lmthicknessincreases.Thisphenomenais causedbyinterferenceofthecoherentlaserlightinthe˝lmandisquanti˝edbytheconditionfor extrema, M = 2 n 1 t cos 1 = 2 t q n 2 1 sin 2 0 ; (3.3) where isthewavelengthofthelight, 0 istheangleofincidence, n 1 istheindexofrefraction ofthe˝lmmaterial, t isthe˝lmthickness,and M = 1 ; 2 ; 3 ::: isaninteger.Whetherthisisthe conditionforaminimaormaxima,whichareseparatedonlybyahalfinteger( i.e. M + 1 š 2 ), dependsontheindexofrefractionofthesubstratematerial n 2 relativetothe˝lm n 1 andwhetherit isthere˛ectance R ortransmission T beingmeasured[62].Thisdistinctionisimmaterialforour purposes,astheconditionisusedtocalculateagrowthratefromthefrequencythatmaximaand minimaoccur. Theexperimentalsetupfora˝lmgrowthisdisplayedinFigure3.15,whichalsocontains detailedpartandequipmentinformation.FilmgrowthsoccurwiththesubstrateinthepSAM growthchamber,whichhasacircularcrosssectionand8accessports.Threeoftheportsare occupiedbyaturbomolecularvacuumpump,andanionizationpressuregaugeandresidualgas analyzerforvacuumdiagnostics.Twolargeviewportsonoppositesidesofthegrowthchamber allowopticalaccessthroughthesubstrateata45-degreeangle,andaredesignatedforathin˝lm 43 Figure3.15:Top-Downschematicofathin˝lmthicknessmeasurementduringnoblegas deposition.Lightfromadiodelaserissentthroughthecombinationofabeamexpanderandiris toreducethelightintensitybelow 1 mW/cm 2 .Afterwardthelightpassesthrougha50:50beam splitterandoneofthebeamsisfocusedontoaphotodiodetomonitorthebeampower.Thesecond beamisdirectedandfocusedontothecenterofthefrontsurfaceofthesubstratelocatedinthe middleofthepSAMgrowthchamberata45degreeangletothebeampath.Thelighttransmitted throughthesubstrateisfocusedontoasecondphotodiodetomonitorthelasertransmissionasa functionoftime. interferencemeasurementduringgrowth.Theportinlinewiththefrontsurfaceofthesubstrateis designatedforbeamlineaccess,tobeutilizedforimplantationofguestspeciesthatwillbedetected duringimaging.Thetworemainingportsareunused.Lightfromadiodelaserisfocusedonto thefrontsurfaceofthesubstratetogetalocalized˝lmthicknessmeasurementatthecenterofthe substrate.Thelaserpowerismeasuredbeforethesubstratewiththeuseofabeamsplitterand photodiodetocorrectforany˛uctuationsinlaserpower,andthelighttransmittedthroughthe˝lm andsubstrateismonitoredwithasecondphotodiode. 44 A˝lmgrowthbeginsbysettingthepressureinthegashandlingbu˙ervolumetoapproximately 5Torr( ˇ 0.3 m/hrgrowthrate)foraperiodof15minutesinordertogentlydepositaninitial thinlayerofnoblegasonthesurfaceofthesubstrate.Thegashandlingpressureissubsequently rampeduptoahigherpressure,typically100-150Torr( ˇ 100 m/hrgrowthrate)fortheremainder ofthe˝lmgrowth.Asanexample,aplotofthegashandlingpressureandnormalizedlaser transmissionisincludedinFigure3.16,whichclearlydisplaystheincreasingoscillationfrequency inthetransmissionasgashandlingpressureisincreased,correspondingtoagrowthrateincrease. Thegrowthrateisextractedfromthelasertransmissionwithapeak˝ndingfunctionthatlocatesthe minimaandmaximaintheinterferencepattern.Adjacent( M = 1 )maximaorminimacorrespond toathicknessincrease t = 1 2 ¹ n 2 1 sin 2 0 º 1 š 2 .Thediodelaserusedforthesemeasurements hasawavelengthof = 638 nmandisalignedata45-degreeangletothesubstrate,giving t ˇ 280 380 nmdependingonthe˝lmtype. The˝lmgrowthproceedsuntilathicknessofapproximately100 mhasbeendeposited.The opticalqualityofthe˝lmismeasuredaftergrowthbasedonthetransmissionofbroadband(white) lightasmeasuredbyaspectrometer.BroadbandlightisproducedbyanOceanOpticsDH-2000- S-DUV-TTLlightsource,employingdeuteriumandhalogenlampsforstablelightoutput(stability anddrift 0.1%/hr)inthewavelengthrangeof190-2500nm.LightfromtheDH-2000is˝ber coupledtoasinglecollimatinglens(OceanOptics74-UV)anddirectedthroughthesubstratein thepSAMimagingchamber.Thetransmittedlightiscollectedand˝bercoupledtoanOcean OpticsFLAME-S-ESSpectrometer,eitheraUV-VIS(200-850nm)orVIS-NIR(350-1000nm) modeldependingonapplication,witharesolutionbetterthan2nm.Aschematicofthe˝lmoptical qualitymeasurementisincludedinFigure3.17.Typicalspectrameasuredbybothspectrometers areincludedinFigure3.18. 3.3.3Results FilmsofNeon,Argon,andKryptonhavebeengrownoverarangeofdepositiontemperatures andforthreedistinctcon˝gurationsofpSAM.Theinitialcon˝guration(pSAMv1.4)featureda 45 Figure3.16:Exampledatafroma 15 1 mKrypton˝lmgrowth.Thelasertransmission(red)is plottedalongsidethegashandlingpressure(blue)asreadbytheBaratronpressuregauge.After theinitial15minutedepositionperiodatlowpressure,depositingapproximatelyhalfofafringe (roughly140nm),thegashandlingpressureisrampedupto150Torrandthefringefrequency increasesdrastically.Alsopicturedaretheminimaandmaximaintheinterferencepattern(green Xs).Amuchlowerfrequencyoscillationisvisibleathighgrowthratesduetothin˝lm interferenceinthesecondary˝lmdepositiononthebacksurfaceofthesubstrate. Figure3.17:Top-Downschematicofawhitelighttransmissionmeasurement.Lightis ˝ber-coupledfromtheDH-2000andcollimatedbeforepassingthroughthesubstrateinthepSAM imagingchamber.Transmittedlightisgatheredbyafocusinglensand˝bercoupledtothe spectrometer. 46 Figure3.18: Top: TypicalroombackgroundspectraasmeasuredbytheUV-VISandVIS-NIR spectrometers. Middle: TypicalDH-2000lightsourcetransmissionthroughthesubstrate(no ˝lm)inthepSAMimagingchamber.ThepeaksinthespectracorrespondtotheBalmerseries transitionsfromthedeuteriumlampintheDH-2000. Bottom: Mercury-Argoncalibrationsource (OceanOpticsHG-1)spectrumasmeasuredbyeachspectrometer.Peaklocationsgenerallyagree betweenthespectrometerstowithin0.5nm. 47 substratemountwitharemovablecoppersubstrateholder.Thev1.4substratemountandholder werethreaded(opticalSM1)foreaseofremoval,howeverthisledtothermalcontactissuesbetween thesubstratemountandholderatlowtemperatureduetothermalcontractions.Thethermalcontact issuewasresolvedbyapplicationofcryogenicvacuumgrease(Apiezon-N)betweenmountand holder,howeverconcernsregardinggreasecontaminationofthesubstratesurfaceledtothedesign ofanewsubstratemount.Fortheredesignedsubstratemount,installedforpSAMv2.0andv2.1, thesubstrateisclampeddirectlytothemountwithindiumasagasketingmaterial,eliminating theneedforgreasenearthesubstrate.InpSAMv2.0,anewgasfeedthroughandslightlylonger internalcapillarytubingwereinstalledto˝xasmallvacuumleak.Inaddition,pSAMv2.0and v2.1featureanewsectionofblackbodyshieldingattachedonthefront(˝lm)sideofthesubstrate mountshielding.Thenewshielding,acylindricalcoppertubeID),wasimplementedtoreduce thetotalamountofblackbodyradiationonthesurfaceofthesubstrateandtoserveasamounting ˝xturefortheendofthecapillarytubing.Theendofthenewcapillarytubingwas˝rmlymounted tothenewshieldtubewithacustomizedbrassclamp,butthisledtoissueswhen˛owingArgon asthetemperatureofthecapillarywaslowenoughtofreezeArgoninsidethecapillary,e˙ectively cloggingit.Asaresult,onlyNeon˝lmscouldbegrowninpSAMv2.0asthebasetemperatureof theshielding(31K),andthereforethecapillarytubing,isnotlowenoughtofreezeandbecome cloggedwithsolidNeon.ForpSAMv2.1,theendofthecapillarytubingwasremountedwith Kaptontape,whichhasverypoorthermalconductivity,insteadofbrassinordertothermally insulateitfromthecoppershielding.ThepSAMcon˝gurationsaresummarizedinTable3.3, whichalsoincludesthemeasureddistancebetweenthesubstrateandtheendofthecapillarytubing foreachcon˝guration.Figure3.5detailsthedi˙erencesbetweenthetwosubstratemounts. 3.3.3.1GrowthRate Thegrowthratefollowsanonlinearrelationshipwiththegashandlingpressureasisdisplayedin theleftcolumnofFigure3.19,whichincludesdatafromapproximately30separate˝lmgrowths. AsthepSAMvacuumismaintainedbypumpingduringgrowth( < 10 4 Torr),itisreasonable 48 Table3.3:TableofpSAMcon˝gurations. VersionTubingDistanceBaseTemp.PressureNotes v1.42.8cm5.4K 10 8 TorrOriginalsubstratemountwithcryo- genicgrease.Endofcapillarytubing isun˝xed. v2.01.9cm5.8K 10 8 TorrNewcapillarytube.Redesignedsub- stratemount.Endofcapillarytube clampedtonewshieldingtube.Cap- illaryclogswithfrozenArgon. v2.12.3cm5.8K 10 8 TorrRemountedendofcapillarytubewith Kaptontape.Cloggingproblem˝xed. v2.22.2cm4.4K 10 8 TorrReplacedAl-mylarshielding.Moved Temperaturesensorto 2 nd stageheat exchanger. toexpectagrowthratethatvarieslinearlywithgashandlingpressure,aswouldbeexpectedfor freely˛owinggases.Freemolecular˛owofgasesischaracterizedbythemeanfreepathbetween collisionsofgaseousatomsbeinglargecomparedtothesizeoftheenclosingvolume,butthatis generallyonlythecaseforpressuresbelow1Torr[63].AsthecapillarytubinginsidepSAMhas aninnerdiameterofonly1mmandisroughly50cminlength,andthegashandlingpressureisin excessof100Torr,weinterpretthenonlinearityasaconsequenceofgas˛owthroughthecapillary tubingbeingviscous. ThegashandlingsystemwasnotsubstantiallychangedbetweenpSAMcon˝gurations,sothe variationofgrowthratesbetweenpSAMcon˝gurationsisattributedtodi˙eringdistancesbetween theendofthecapillarytubingandthesubstratesurface.TheNeongrowthratevariationbetween pSAMcon˝gurationsisconsistentwiththenoblegasbeamintensityfollowinganinversesquare lawwithdistance.ThisbehaviorissimilarlyevidentintheArgongrowthratebutdoesnotappear tobetrueforKrypton,asthegrowthrateisobservedtovarybylessthan20%betweenv1.4 andv2.1whiletheinversesquarelawpredictsa 1 ¹ 2 : 8cm š 2 : 3cm º 2 ˇ 50% variation.One possibleexplanationforthisinconsistencycanbefoundbyconsideringthedi˙erentcondensation temperaturesbetweennoblegasesalongwiththepresencecryogenicshieldinginvicinityofthe 49 substrate. AlinearrelationshipisobservedifthegrowthrateisplottedasafunctionofpSAMpressure,as displayedintherightcolumnofFigure3.19.ThislinearityimpliesthatthepSAMpressureduring ˝lmgrowthcanbeusedasarelativemeasureoftheamountofgas˛owingintopSAMthatdoes notfreezeontoacryogenicsurface.Gasexitingthecapillarytubingwillhavesomeprobability ofstickingtothesubstrateorsubstratemount,thecryogenicshielding,orcollidingwithothergas atomsandescapingtobepumpedaway.Neonisthesimplestcasetoconsiderasitcanonlyfreeze onthesubstrateorsubstratemount,sincethebasetemperatureofthecryogenicshielding(31K) istoohightosolidifyNeon.Roughmeasurementssuggestthat80%ofNeonfreezessomewhere withtheremainderbeingpumpedaway,usingthemanufacturer'sadvertisedpumpingspeedofthe turbopumpandambientpressuretocalculatethevolumeofgaspumpedawayduringgrowth. Kryptonontheotherhandislikelytofreezeanywhereonthesubstrate,mount,orshielding structureduetoits'signi˝cantlyhigherfreezingpointaround40K.ThisresultsinlowerpSAM pressurerelativetoArgonorNeonduring˝lmgrowthasverylittlegasisabletoescapewithout freezing.AttachingthenewshieldtubeforpSAMv2.1resultedinsigni˝cantlylowerambient pressuresduringKryptongrowthrelativetov1.4duetotheadditionofacoldsurfacesurrounding thecapillarytubing.ThepictureforArgonisslightlymorecomplicated,asthetemperatureofthe cryogenicshieldingis35-36KwhenthesubstrateissettoArgon˝lmdepositiontemperatures, whichrangefrom24-36Kinthisstudy.ThevaporpressureofsolidArgonexceeds 10 6 Torr attemperaturesabove30K,resultinginnoticeablyhigherambientpSAMpressuresduring˝lm growthespeciallyathigherdepositiontemperatures.ThegrowthraterelativetopSAMpressure isplottedasafunctionofdeposition(substratemount)temperatureinthetoprowofFigure3.21, whereeachdatapointrepresentsasingle˝lmgrowth.Theparameter ˜ GR istheslopeextracted fromalinear˝ttothegrowthratevspSAMpressuredatain˝g3.19.Ingeneral,thegrowthrate isshowntobeindependentofdepositiontemperature,andtheArgonvaporpressureincreaseis clearlyevidentfordepositiontemperaturesabove30K. 50 Figure3.19:MeasuredNeon,Argon,andKryptongrowthratesasafunctionofGasHandling pressure(leftcolumn)andpSAMpressure(rightcolumn)fordi˙erentpSAMcon˝gurationsand depositiontemperatures. 51 Figure3.20:Intensityoflighttransmittedthrough6separatekrypton˝lmsdepositedatdi˙erent temperatures(two˝lmsdepositedat36Kareplotted),relativetotheintensityoflighttransmitted throughthebaresubstrate(no˝lm),asafunctionofwavelength.Theoscillationsevidentineach traceareduetothin˝lminterferenceinthesecondary˝lmonthebackofthesubstrate.Theinset plotshowstheaveragetransmission(errorbarsdenotethestandarddeviation)foreach˝lmasa functionofdepositiontemperature. 3.3.3.2OpticalClarity Theopticalclarityofa˝lmisquanti˝edbymeasuringtheintensityofbroadbandlightfrom theDH-2000transmittedthroughthe˝lmandsubstraterelativetoaclean(no˝lm)substrate,as measuredbyaspectrometer.Asetoftypical˝lmclaritymeasurementsforkrypton˝lmsisincluded inFigure3.20.Thenoblegas˝lmsbehaveasakindofanti-re˛ectivecoatingonthesubstrate,as thetransmissionof˝lmandsubstratecanbeashighas 110% forexceptionallyclear˝lms.The clarityof100 mnoblegas˝lmsissensitivetosubstratetemperatureduringdeposition.Though 52 Figure3.21:Collectionofgrowthparametersasafunctionofdepositiontemperature.Toprow: growthraterelativetopSAMpressure.Middlerow:averagetransmissionof˝lmandsubstrate relativetoonlysubstrate.Theerrorbarsdenotethetransmissionovertherangeofwavelengths measuredwiththespectrometer.FilmsweregenerallymoretransparenttoIR,andmoreopaqueto UV.Bottomrow:thicknessesof˝lmsanalyzedinthiswork. 53 Figure3.22:Filmclarityasafunctionoftimeandtemperatureforneon,argon,andkrypton.Film clarityisrelativetotheinitialtransmissiontodecouplevariationsininitial˝lmtransmissionfrom thetimedependentbehavior.Holdinga˝lmatlowertemperaturestendsto'freezein'theinitial ˝lmtransparency. 54 ˝lmsgenerallyremaintransparentbelow20 m,theybecomeincreasinglyopaquewithincreasing thicknessoutsideofasmalltemperaturewindowforeach˝lmtype,wherethetransmissionis maximized.Filmsshowinganyopacityaremoreopaquetoshorterwavelengthlightandgenerally remaintransparenttowavelengthslongerthan700nm,exceptfor˝lmshavingbelow90%average transparency.Theidealtemperatures T id areallabovethecharacteristictemperatures T ch reported in[28],includedinTable3.4,butbelowthetemperatureswheresublimationoftheaccumulated frozengasbecomessigni˝cant.Annealing˝lmsafterdepositioncausesthemtobecomemore opaque.TheaveragedtransmissionofwhitelightforNe,Ar,andKr˝lmsasafunctionof depositiontemperatureareplottedinFigure3.21.Figure3.23containspicturesof˝lmsthat exhibitcommoncharacteristics. Neon ˝lmsweregrownoveralimitedtemperaturerange,asthebase(lowest)temperature waslimitedto4.6KandsublimationofNeonbecomessigni˝cantattemperatureshigherthan9 K.TheonlyNeon˝lmsgrownduringv1.4con˝gurationwereatthebasetemperatureandwere highlytransparentbyeyeandtowhitelight.Interestingly,the˝lmswereslightlyopaqueatthe basetemperatureforthev2.0andv2.1con˝gurations,andthehighesttransparencydeposition temperaturewasachievedat8K.A˝lmgrownat4.6Kinv2.2shatteredatathicknessof60 mduringgrowth,butwasotherwisetransparent.Thespeci˝ccauseofthediscrepancybetween con˝gurationshasyettobeidenti˝ed.ThewhitelighttransmissionofNeon˝lmsmaintainedat depositiontemperatures( 6 8K )decreasedatarateof 0 : 02 0 : 1% š hr ,withlowertemperatures generallymaintaininginitialtransparencyforlonger(seethetopplotinFigure3.22).E˙ectsof coolingthe˝lmsaftergrowthwerenotstudiedduetothelimitedavailabletemperaturerange. Argon ˝lmsweredepositedattemperaturesrangingfrom24-36Kandshowastarkdi˙erence betweenpSAMcon˝gurations.Filmsduringv1.4weremosttransparentat25K,becomingsteadily moreopaquewithincreasingtemperature,andingeneralwerefoundtobeslightlylesstransparent tovisiblewavelengths < 700 nmthanNeonorKrypton.Filmsmaintainedatdeposition temperaturesbecameincreasinglyopaquewithtime,atarateof 0 : 02 4% š hr ,worseningwith increasingtemperature(seethemiddleplotinFigure3.22).Cooling˝lmsto 20K aftergrowth 55 allowedthetransmissiontoremainconstantformorethan12hours.Cooling 100 m ˝lmsbelow 20K wouldcausethemtoshatter. Filmsgrownduringv2.1weresigni˝cantlymoreopaquethanv1.4,scarcelybreaking50 % transparencyatthebestdepositiontemperature,anda˝lmdepositedat24Kwasnearlycompletely opaque(transmission < 0 : 5% ).SimilartoNeon, T id wasshiftedhigherbyafewdegreesforv2.1 relativetov1.4.The˝lmsduringv2.1arevisiblycloudyinthecenterofthesubstrateandbecome moretransparenttowardtheedge.Theopacityofthev2.1˝lmsislikelyrelatedtotheadditionof thecylindricalcoppertubetotheshieldingstructurearoundthefrontsubstratesurfaceandcapillary tube.Theshieldingstructureisatatemperaturecorrespondingtoahighvaporpressureforsolid Argon( T shield ˇ 36 K).ThepresenceoflowtemperatureArgongascontinuouslysublimingfrom theshieldingsurfacemaybenegativelya˙ectingthe˝lmtransparency. Krypton ˝lmsweredepositedattemperaturesrangingfrom29-44Kandshowclaritybehavior consistentacrossv1.4,v2.1andv2.2.Filmsexhibitedthehighestwhitelighttransmissionwhen depositednear34K,withaslightlydecreasingtransmissionwithincreasingtemperature.Films becomerapidlyopaqueattemperaturesbelow32K,whichcorrespondsto T ch reportedin[28]. Smallspecklingbecamevisiblein˝lmsattemperaturesof32Kandbelow.A˝lmgrownat6K wascompletelyopaqueandbrittle,takingontheappearanceofsnoworfrost,andasectionofthe ˝lmdislodgedfromthesubstrateduringgrowth.Curiously,krypton˝lmsgrownnear40-41K exhibitwispy,frost-likestructuresvisibleinthe˝lmthatdisappearwithtimeasthe˝lmsbecome cloudy.Filmsmaintainedtheirinitialtransparencyformorethan100hoursiftemperaturewas heldbelow30K.Filmsmaintainedat 35 36K exhibiteddecreasingtransparencyatarateof 0 : 1 0 : 2% š hr oftheirinitialtransparency(seethebottomplotinFigure3.22).Coolingthe˝lmsto afterdepositionwase˙ectiveinmaintainingtransparency,howevercooling 100 mKrypton˝lms below 30K causedthemtoshatterindependentlyofthecoolingrate. 56 Figure3.23:Picturesof˝lmsexhibitingdi˙erentcharacteristics.Thepicturesweretakenthrough therearviewportonthepSAMimagingchamber(exceptforthebottomright),sothe˝lmison thefarsideofthesubstrate. Table3.4:Tableofsolidnoblegas˝lmproperties. T subl isde˝nedasthetemperatureatwhich thevaporpressureis 10 4 Torr. NeonArgonKryptonSource T ch (K) 5 118 1 : 529 2 [28] v p ch (Torr) 9 : 4 10 15 1 : 1 10 17 6 : 5 10 14 [26] T id (K) 8 0 : 527 235 2 thiswork v p id (Torr) 2 : 2 10 7 5 : 4 10 9 3 : 0 10 10 [26] T subl (K)10.036.250.8[26] d 0 ( m)192227[28] d 0 ( m)202619thiswork 57 3.3.3.3FringeContrast Theamplitudeofinterferencefringesintransmittedlaserlightdecreaseswithincreasing˝lm thickness,aphenomenaalsoreportedin[28].Thefringecontrast,de˝nedasthedi˙erencein transmittedlaserpowerforanadjacentminimaandmaxima,istypically 10 15% fortheinitial interferencefringesasdisplayedinFigure3.24.Thiscontraststeadilydecayswithincreasing thicknessuntilamaximumthicknesswherefringesbecomeindistinguishable, d 0 .Thefringe contrastdecayandmaximumthickness( d 0 )asafunctionofdepositiontemperaturearealso displayedinFigure3.24.Themaximumthicknessesreportedin[28]areincludedinTable3.4 alongsidetheaverage d 0 ofall˝lmgrowthsreportedinthiswork.Thelossofcontrastisattributed in[28]toalossofintensitywithinthe˝lmduetoabsorptionandscattering.Sinceinterference fringesareindistinguishableformost˝lmsbeyondthicknessesof40 m,andthegashandling pressureisheldconstant,thegrowthrateisassumedtoremainconstantfortheremainderofthe growthforthepurposesofcalculatingthe˝nalthickness.Locationsofminimaandmaximaare extractedduringpost-growthanalysisusingthesignalprocessingalgorithm argrelextrema ,part oftheSciPypackageinPython[64].Thealgorithmtypicallybeginsreportingerroneousextrema whenthefringecontrastfallsbelow 0 : 5% ,wherefringeamplitudesapproachthenoise˛oorforthe photodiodes. Theinitialfringecontrastgenerallydecreaseswithincreasingdepositiontemperature,butin- terestinglythefringecontrastdecayincreasesproportionallywithtemperature,leadingtorelatively constant d 0 .Theinitialfringecontrastcanbeexceptionallylowathigherdepositiontemperatures, intherangefrom 1 5% ,butcontrastistypicallysustainedbeyond10 m.Krypton˝lmsde- positedinpSAMv2.1exhibitadrastic,lowfrequencyoscillationinfringecontrast,attributedto aninterferencebeatinge˙ectwithinthesecondary˝lmonthebackofthesubstrate,whichresults inasystematicallysmaller d 0 .Intheabsenceofthebeatinge˙ect,fringesareobservableout tothicknessesof 30 m.AsingleArgon˝lmdepositedat27Ksustainedobservablefringesat thicknessesbeyond80 m,suggestingalarger d 0 maybeachievable.Asigni˝cantchangewas observedbetweenpSAMcon˝gurationswhenconsideringthemaximumthicknessatwhichfringes 58 Figure3.24:Initialfringecontrast,contrastdecay,andmaximumthicknesswithanobserved fringeplottedasafunctionofdepositiontemperature. 59 couldbeobserved,consistentlyacrossall˝lmtypes.Valuesof d 0 inv1.4arelargerbyroughlya factorof2comparedtov2.0andv2.1ThelaserdiodesystemdetailedinFigure3.15waspartially disassembledbetweencon˝gurationsv1.4andv2.0toallowfortheremovalofpSAMfromthe lasertable.Aplausiblesourceofthesystematicdi˙erencebetweenpSAMcon˝gurationscould befoundintherealignmentofthelaserdiodesystemperformedaftersubsequentre-installationof pSAMonthelasertable.Aslightlylongerfocallengthlenswasutilizedasfocusinglens#2in v2.0andv2.1,mainlyforconvenience. 3.3.3.4Filmuniformity ThethicknessofaKrypton˝lmwasmeasuredalongseveralpointsalongaverticallinethroughthe centerofthesubstrate.Thin˝lminterferencefringeswereobservedwhenmonitoringtheintensity ofre˛ectedandtransmittedlaserlightfocusedonthesubstratefromacontinuouswaveTi:Sapphire laser(MSquaredSOLSTiS),whosewavelengthwascontinuouslyvariedbetween = 770 800 nm(487cm 1 ,or14.6THzscanwidth).Similartothethicknessmeasurementduringgrowth, ˝lmthicknesscanbedeterminedfromthepositionofextremausingtherelation t = M ab a b 2 ¹ a b º q n 2 1 sin 2 0 ; (3.4) where a and b arethewavelengthsoftwoextrema, 0 istheangleofincidence, n 1 istheindexof refractionofthe˝lmmaterial, t isthe˝lmthickness,and M ab isthenumberoffringesseparating theextrema[62].Forexample,adjacentmaximawouldcorrespondto M ab = 1 ,andamaximumat a separatedfromaminimumat b bytwominimaandmaximawouldcorrespondto M ab = 2 : 5 . Thenumberoffringesobserved,andconsequentlytheuncertaintyofagivenmeasurement,is determinedbythewidthofthescanandthethicknessofthe˝lm.Observationofonecomplete fringeinthe487cm 1 windowrequiresathicknessofatleast 7 : 6 mforaKrypton˝lm( n 1 = 1 : 38 , 0 = 7 ).Alargerscanwidth,therebyincreasingthenumberoffringesobserved,couldbeusedto reduceuncertaintyinthickness,butthewidthofscanswaslimitedto30nmintheinterestoftime (approximately10min/scan). 60 Nofringeswereobservedwhenthistechniquewasappliedfor 100 mArgonandKrypton ˝lms,consistentwithmaximumfringethicknessesreportedinthefringecontrastsection.The uniformitymeasurementwasperformedonKrypton˝lmsduringv1.4andv2.1withcenterthick- nessesmeasuredduringgrowthof 15 m.Thicknessmeasurementsweretakenatpointsalonga verticallinethroughthecenterofthesubstrate.Theinterferencefringesobservedinre˛ectionat eachpointforthev1.4uniformitymeasurementareshowninFigure3.26,andthethicknessateach pointisplottedinFigure3.25.The˝lmissigni˝cantlythickernearthetopofthesubstrateclosest totheendofthecapillarytubing,whichislocatedat y = 13mm andthehorizontaldistancelisted inTable3.3. Thefringesalsohadthegreatestcontrastnearthetopofthesubstrate.Althoughfringeswere observedacrosstheentiresubstrateforthev1.4measurement,thefringecontrastfellbelow 0 : 5% nearthebottom,relativetoanorderofmagnitudehighernearthetop.Interestingly,thev2.1 measurementonlyyieldedfringesatthetopofthesubstrate,andclearfringeswerenotobserved below5.4mmduringtheinitialscan.Toexplorethepossibilityofathicknessdependenceon thepresenceoffringes,anadditional 5 m ofKryptonwasdepositedandthescanwasrepeated, butfringeswereagainonlyobservednearthetopofthesubstrate,thoughatlowercontrastand disappearingaltogetherat5.4mm.Thethicknessmeasurementsplottedat y = 0 ; 5 : 4mm inthe rightpanelofFigure3.25comefromthefringesobservedduringtheinitialandsubsequentkrypton depositions.Itcanbeinferredfromthismeasurementthattherapiddisappearanceoffringesfor scansbelow7.2mmdoesnotseemtobedependentonthethicknessofthe˝lm.Thelackof fringescouldbeduetothelocalnonuniformityofthe˝lmwherethelaserinterferenceoccurs.This nonuniformityoverthebeamspotsizemaybesu˚cienttodestroyanymeasurableinterference signalonthedownslopeofthedistribution,whereasthe˝lmthicknessseemstohaveplateaued (moreuniform)atthetopofthesubstrate,allowingformeasurableinterferencefringes.Thisis consistentwithobservingfringesacrosstheentiresubstrateinv1.4,astheincreasedseparation betweensubstrateandcapillarytubingresultedinamoreuniform˝lm. Themeasuredthicknessdistributiononthe˝lmisfairlyconsistentwithbothuniformandcosine 61 Figure3.25:ThicknessofaKrypton˝lmasafunctionofpositionalongaverticallinethroughthe centerofthesubstrate,asmeasuredinpSAMv1.4(left)andv2.1(right).Theincludedlines depictthepredictedthicknessdistributionassuminguniformandcosineintensitydistributionsfor gasleavingtheendofthecapillarytubing.Itshouldbenotedthattheverticalandhorizontalaxis havedi˙erentscales.Forv2.1,interferencefringeswereonlyobservedatthetopofthesubstrate. Attemptsatotherpositionsnearthemiddleandbottomofthesubstrateyieldednointerference pattern,andasecondmeasurementwasperformedafterdepositinganadditional5 montothe ˝lm,similarlyyieldinginterferencefringesonlynearthetop. 62 Figure3.26:SetofwavelengthscansfortheKrypton˝lmuniformitymeasurementperformedin pSAMv1.4,whichillustratestypicalinterferencepattersforawavelengthscan.Theamplitudeof thefringeswaslargestatthetopofthesubstrate. intensitydistributionsfromoftheendofthecapillarytubing,whichimpliesthatthe˝lmuniformity isdominatedbyaninversesquarelawfromtheendofthecapillarytubing.Thecosinedistribution predictsaslightlysharperpeak,butthebehavioronthedownslopeofthepeakistoosimilarto theuniformdistributiontodistinguishwithintheprecisionofthesemeasurements.Thecapillary tubingforv2.1is 20% closertothesubstrate,likelycausingthe˝lmtobenoticeablylessuniform inv2.1,andsuggestiveofasharperintensitydistributionthanattributabletoacosine.Attaininga moreuniform˝lmcanbeaccomplishedbyincreasingthedistancebetweensubstrateandtubing, thoughatthecostofusingmoregas.Alternatively,increasingthenumberoftubessymmetrically aroundthesubstratecoulddecreasethenonuniformity. 63 3.3.3.5Filmpurity Quantifyingtheamountofimpuritiesinthenoblegases˛owingintopSAMcanbeaccomplished viadirectmeasurementwiththeresidualgasanalyzer(RGA).Neon,argon,andkryptongaseswere ˛owedintopSAMatroomtemperaturebysteppingthegashandlingsystembu˙ervolumepressure between 2 10 Torr,whilecontinuouslymeasuringthepartialpressuresofthemostabundant residualgasesinpSAMfor5minuteintervals.ThevacuumpumpsonpSAMwererunning,and thegashandlingpressurewaspurposelylimitedtolowpressure(10timeslowerthanduringa˝lm growth)tokeepthepressureinsidepSAMbelow 10 5 Torr,astheRGAislimitedtoamaximum pressureof 10 4 Torr(withtheelectronmultipliero˙).Thepurityofthegaswasmeasuredwithout anyadditionalpuri˝cationmeasures(getterpuri˝erwasbypassed,andliquidnitrogencoldtrapwas atroomtemperature)toestablishabaseline.ThepuritymeasurementsaresummarizedinTable 3.5.TheRGAissensitivetopartialpressuresontheorderof 10 9 Torrwiththeelectronmultiplier poweredo˙,whichisnecessarywhenoperatingatsuchhighpressures,andsothesensitivityof thepuritymeasurementswaslimitedto 0 : 3% . Asabaseline,neongaswas˛owedintopSAMwhileatatemperatureof20Kelvinwhich su˚cientlylowtofreezenearlyallimpuritygases.Asexpected,theresultingpuritymeasurements wereconsistentwiththelabeledgasbottlepurity(99.999%)withinthesensitivityoftheRGA, sincethemostabundantresidualgases(nitrogen,oxygen,water,CO 2 ,etc)wouldfreezetothe substratebeforehavingachancetocontacttheRGAsensor.However,measurementsperformed withpSAMatroomtemperatureshowedimpuritylevelswellinexcessofthelabeledgaspurity. Neonandkryptonweremeasuredtohaveimpuritiesatthelevelof 5% ,andargonsigni˝cantly betterat 1% .Inallcasestheimpuritieswereprimarilymolecularnitrogen,withtraceamounts oftheothercomponentsofair.Thepuritygenerallyimprovedwithgas˛owrate,suggestingthe impuritiesmaybeacquiredinthegashandlingbu˙ervolumeandcoldtrap,andthatthepurity maybesigni˝cantlybetteratthegas˛owratesusedduring˝lmgrowth(GasHandlingpressures above100Torr).Unfortunately,apuritymeasurementisnotpossibleatsuch˛owratesduetothe aforementionedpressurelimitationsoftheRGA. 64 Table3.5:Purityofnoblegases˛owingintopSAMasmeasuredwiththeRGA. G.H.PressureNeon(20K)Neon(r.t.)Argon(r.t.)Krypton(r.t.) Torr%%%% 299.4(9)94.8(3)98.8(5)94.9(7) 499.4(8)94.8(4)99.0(4)94.8(5) 699.5(9)95.3(4)99.1(3)95.1(4) 899.5(8)95.7(4)99.2(3)95.7(4) 1099.6(8)96.2(4)99.3(3)96.3(3) 3.3.3.6NobleGasUseandStickingProbability Onemethodtomeasurethetotalamountofgasusedduringa˝lmgrowthistousethevacuum pressureandthepumpingspeedoftheturbomolecularpump(TMP,anOerlikonTurboVac50). TheidealgaslawtranslatestheTMPpumpingspeed S = 55L š s andvacuumpressure P intoa molar˛owrate Û n via Û n = SP RT ; (3.5) whereTisthegastemperatureand R = 8 : 314 Jmol 1 K 1 .Integratingthisquantityoverthe durationofthe˝lmdepositionwillgivetheamountofgasthatiswastedduringgrowth(pumped away).Similarly,integratingthisquantityasthecoldcomponentsarewarmedwillyieldthetotal amountofgasthatisfrozensomewhereonthecoldcomponents.Itishowevernotclearwhat thetemperatureofthenoblegasis,eitherduringdepositionorsublimation.Duringgrowth,gas enteringpSAMisexpectedtobeatroomtemperature,butlikelycoolssomewhatinthenarrow capillarytubingthatsnakesinsidetheapproximately35Kcoppershieldingstructure.Thegas atomssublimingfromthesubstratemountasthe˝lmismeltedcanbeassumedtobethetemperature ofthesubstratemountonaverage,butitisnotclearwhattheaveragegastemperatureisinthe vicinityofthepressuregaugeandTMP,afterhavinginteractedwiththe35Kcoppershielding structureandthe300Kvacuumvessel.Themeanfreepathofgasatomsat 10 4 Torr(typical maximumpSAMpressureduringgrowth)isontheorderof 0 : 1 1 m,equaltoorlargerthanthe sizeofthevacuumvesselitself,sothegasatomsshouldnothavesu˚cientself-interactiontocreate atemperaturegradientbetweenthecoldcomponentsandthevesselwalls. 65 Neonisidealtouseforthismeasurementsinceits'lowsublimationtemperature(10K)means itwillonlyfreezetothesubstratemount,unlikeargonandkryptonwhichcanfreezetothecopper shieldingstructure.Neon's10Ksublimationtemperatureisalsosigni˝cantlyseparatedfromthe commoncomponentsofair,soitisreasonabletoassumethemeasuredvacuumpressureisalmost entirelyduetoneonandnotnitrogenoranyothergases.Fora100 m˝lmgrowninpSAMv1.4, atotalof 81 16 mmolofneonwasusedbasedonintegratingEquation3.5throughthegrowth andsublimation,assuminganeongastemperatureof 30 5 Kandincludinga 15% manufacturers uncertaintyinthepressure.Ofthattotal, 8 : 5 mmols( 10% )waspumpedawayduringgrowth,with theremaindercomingo˙duringsublimation.Asthemolar˛owrateisinverselyproportional totemperature,assuminganeongastemperatureof300Kwouldreducethetotalto8.1mmol. Itisreasonabletoexpectthetemperatureofneongasisthesameduringgrowthasitisduring sublimation,sothewastefactorof 10% islikelyindependentoftheassumedtemperature.Based onaroughcalibrationofthegashandlingsystem,anestimated 84 3 mmolofneonwasused, whichsuggeststhattheneongastemperatureinpSAMiscloserto30K. Thereareroughly3.6mmolofneonina1indiameter,100 mthicksolidneon˝lm,sothe amountofneonusedthatactuallyendsupfrozentothesubstrateisaround = 3 : 6 š 81 ˇ 4% . Withthecapillarytubingdistanceof2.8cminv1.4,theprobabilityofgasemanatingfromtheend ofthetubehittingthesubstrateisapproximately 9% assumingauniformdistribution,and 17% foracosinedistribution.Thereforethe'stickingprobability',de˝nedasthepercentageofatoms hittingthesubstratethatactuallyfreezetoit,isintherangeof 25 50% dependingontheintensity distributionoutofthetube. 3.3.4Conclusions AstudybySchulzeandKolb[28]reportsthedensityandrefractiveindexofNe,Ar,Kr,andXe solid˝lmsoverawiderangeofcondensationconditionsbyvaryingparameterssuchassubstrate temperature,growthrate,and˝lmthickness.Theyreportnosigni˝cantdependenceofthedensityor refractiveindexonthe˝lmgrowthrateorthickness.However,theyreportasigni˝cantdependence 66 onthedensityandrefractiveindexbelowacharacteristictemperatureforeachgas.Theyconclude thatattemperaturesabovethecharacteristictemperature(reproducedinTable3.4),thesolidifying noblegasatomshavesu˚cientmobilitytoform `well-orderedcrystalliteswithaclosepacked structure' .Attemperaturesbelowthecharacteristictemperature,thenucleationrateincreases, resultingina `reductionofthecrystallitesize' ,e˙ectivelyreducingthedensityandrefractiveindex. Theircommentaryon˝lmtransparencyislimited,otherthantosaythat˝lmsbecomecloudyabove thicknessesof20-30 m. ThoughthedensityandrefractiveindexwasnotmeasuredinpSAM,thecloudyandfrosted appearanceofargonandkrypton˝lmsgrownattemperaturesatorbelowthecharacteristictem- peratureisconsistentwiththedensitybehaviordescribedin[28].Incontrast,depositingoptically transparent100 m˝lmsofsolidnoblegasesinpSAMisconsistentlyachievedsolongasthe substrateisheldwithinatemperaturewindowduringdeposition,speci˝ctoeachnoblegas.The relevantwindowsare 7 : 5 8 : 5 Kforneon, 25 27 Kforargon,and 33 35 Kforkrypton.The initiallytransparent˝lmsbecomecloudyifthesubstratetemperatureismaintainedatthedeposition temperature,butcoolingthesubstrateaftergrowthby 3 4 degreesKe˙ectivelyfreezes-inthe initialtransparencyformorethan100hours.Coolingthe˝lmsbymorethanafewdegreesK causesthe˝lmstoshatter.E˚cientlydepositingthenoblegasontothesubstrateisbestachieved bysettingthetubingclosetothesubstrate,atthecostofamorenonuniform˝lm,astheintensity distributionofgasfromthecapillarytubingseemstobedominatedbytheinverse-squarelaw. 67 CHAPTER4 CALIBRATEDFLUORESCENCESPECTROSCOPYOFMATRIXISOLATED RUBIDIUMATOMS 4.1Introduction AsacommissioningexperimentforpSAM,acrosssectionmeasurementforthereaction 84 Kr ¹ p ; º 85 Rbhasbeenchosenduetoafewfavorableproperties.Sincethebeam(krypton)isa noblegas,anyunreactedbeamwillbeimplantedinthesolidnoblegas˝lm(alsokrypton,inthis case)andbeopticallyundetectable.Thisreactionhasalargecrosssection(oftheorder1mbat2.5 MeV/ucenterofmassenergy)whichwillensurerelativelyfastcreationofalargenumberofproduct atomstoaidindetection.Rubidiumisanalkaliatomwithacycling5s 2 S ! 5p 2 Ptransitionata readilyaccessibleexcitationwavelength,andexhibitsalargewavelengthshiftbetweenexcitation andemission(seeTable2.3)whenembeddedinsolidkrypton.Inthischapter,measurementsof theabsorptionand˛uorescencespectraofmatrixisolatedrubidiuminsolidkryptonarepresented andcomparedtopreviousmeasurements[21,38]. Inordertodetectthenumberofproductatomscapturedinthe˝lmforanuclearreaction crosssectionmeasurement,theintrinsicbrightnessofamatrixisolatedrubidiumatomneedstobe measured.Tothatend,the˛uorescencecrosssection ˙ f = P š I ofarubidiumatominkryptonwill bemeasured,where P isthepoweremittedbyanatomunderresonantexcitationlightofintensity I . Measuringthiscrosssectionrequiresimplantingaknownnumberofrubidiumatomsinakrypton ˝lmandmeasuringthetotal˛uorescencepoweremittedbythoseatomsunderlaserexcitation.The numberofatomsemittedbyasourceofrubidiumatomswillbemeasuredwithatechniquecalled atomicbeam˛uorescence(ABF),whereresonantlaserexcitationintersectstheatomicbeamin vacuum.Thevacuum˛uorescenceintensityfromthisintersectionregionisthenusedtocalculate theintensityoftheatomicbeam.Knowledgeoftheatomicbeamintensityandthekrypton˝lm growthrateallowsforcalculationoftherubidiumnumberdensityinthekrypton˝lm. 68 4.2ExperimentalSetup Adiagramoftheexperimentalsetupduringsolidkrypton˝lmgrowthwithrubidiumco- depositionisshowninFigure4.1.Rubidiummetaliscontainedinatitaniumcrucible˝ttedwitha cylindricalnozzle.Thehighvaporpressureofrubidiumensuresasigni˝cantdensityofrubidium gasinthecrucible,whiche˙usesoutthroughthenozzle.Thenozzleopeninghasdimensionsof10 cminlengthand1mmindiameterinordertocreateanarrow,collimatedbeamofrubidiumatoms. Thetotal˛uxofrubidiumoutofthenozzlecanbecontrolledbyincreasingthevaporpressureof thesourcerubidiumthroughadjustingthetemperatureofthetitaniumcrucible,whichcanbeset betweenroomtemperatureand400Celsiuswiththeuseofaresistiveheatingelement. LaserlightfromMSquaredSOLSTiSTi:Sapphirelaserwasalignednormaltotherubidium atomicbeamandtointersectitatadistanceof35mmfromtheendofthenozzle.Thelaser wavelengthismeasuredwithaHighFinesseWS6-600wavelengthmeter.Thelaserbeampro˝le wasGaussianwithadiameterof5.4mmwitha5MHzlinewidth.Thelaserwavelengthwas scannedthroughtheRubidiumD1transition,andtheemitted˛uorescencepowerwasmeasured withanavalanchephotodiode(APD,ThorlabsAPD410A2)located95mmabovetheintersection volume.Asthe˛uorescencesignalissmall,anopticalchopper(ThorlabsMC2000B)isemployed topulsethelaserexcitationatafrequencyof1kHz,andtheopticalchopperreferencesignaland theAPDoutputaresenttoalock-inampli˝er(SRSModelSR530)toimprovethesensitivityof themeasurement.Themeasured˛uorescenceintensityisutilizedtocalculatetheintensityofthe atomicbeam.ThetransmittedlaserpowerisalsomeasuredwithaThorlabsPM120VApower meter.TypicalABFscanparametersandsettingsarelistedinTable4.1. Therubidiumatomicbeamisimplantedinasolidkryptonduring˝lmdepositionontoasapphire substrateinthepSAMgrowthchamber.Krypton˝lmgrowthhasbeenpreviouslydescribedin Chapter3.OpticalabsorptionmeasurementsareacquiredwithanOceanviewDH-2000whitelight sourceandFlameSpectrometerduringgrowthandrubidiumimplantation.Flowofrubidiuminto the˝lmiscontrolledbyopeningandclosingagatevalvebetweentherubidiumsourceandthe substrate. 69 Table4.1:TableofABFlaserscanparameters. AvalanchePhotodiode(APD410A2)properties Responsivity@795nmTransimpedanceGainConversionGain 13 : 75 A W 500 kV A 6 : 875 10 6 V W Lock-inAmpli˝er(SRSSR530)settings(25 Crubidiumsource) laserpowersensitivitytimeconstantapprox.signalamplitude 0.3mW100 V30ms2V 4.0mW500 V30ms7V RubidiumD 1 laserscanparameters center (nm)scanwidthscanrate 794.976910GHz20 MHz s Figure4.1:Experimentalsetupforrubidiumatomicbeam˛uorescenceandwhitelightabsorption ofmatrixisolatedrubidiumduringasolidkrypton˝lmgrowth. 70 Figure4.2:Experimentalsetupfor˛uorescenceimagingofmatrixisolatedrubidiumsamples. Includedisanactualimageofthesubstrateilluminatedbybackgroundlightfromtheiongauge. Thecapillarytubingfornoblegasdepositionisjustvisibleatthebottomedgeofthesubstrate(the imageisinverted). After˝lmgrowththesubstrateismovedtotheimagingchamberfor˛uorescenceimaging,as showninFigure4.2.FibercoupledlightfromtheSOLSTiSiscollimatedbyanasphericlensand sentthroughafocusinglenstoexpandthebeampro˝letothesizeofthesubstrate.Thefront surfaceofthesubstrateisimagedontoanAndorClaraCCDcamerasensorwitha2inchAspheric lens(Edmund#67-281,f=40mm)placedtocreatea 1 š 4 -sizedimageofthesubstrateontheCCD sensor.Re˛ectedandscatteredlaserexcitationlightis˝lteredbytwoopticalcolor˝lters,adichroic beamsplitter(SemrockDi02-R830-25x36)andalong-passedge˝lter(SemrockBLP01-830R-25), bothofwhichpasslightofwavelengthlongerthan830nm. 4.3Results Threerubidium-dopedkrypton˝lmsweregrownatadepositiontemperatureof8Kelvinanda growthrateof5.3,4.7,and4.7 m/hr.Topreparethesamples,aninitial1- mlayerofkryptonwas depositedonthesubstrate,whichwasfollowedbyalayerofcodepositedrubidiumandkryptonfor adurationof1452,693,and1542s,respectively.Anotherlayerofonlykryptonwasthendeposited untilatotal˝lmthicknessofapproximately5 mwasreached.Thissamplepreparationprocedure 71 wasadaptedfrom[21].Sampleswereattemptedatkryptongrowthratesbetween 13 140 mand depositiontemperaturesof34Kand37K,butnoabsorptionorlaser-induced˛uorescencedueto rubidiumwasobserved. 4.3.1VacuumRubidiumSpectrum The˛uorescencepowerasmeasuredbytheAPDisplottedasafunctionofexcitationlaserfrequency inFigure4.3forasinglescan.Thescaniswellrepresentedwitha˝tofeightVoigtpro˝lesandthe measuredhyper˝nelevelsandsplittingsagreewiththeliteraturevalues,assummarizedinTable 4.2.TheVoightlinepro˝leisaconvolutionofGaussianandLorentzianlineshapes,andisde˝ned as V ¹ ; ˙; º = ¹ 1 1 ˙ p 2 ˇ exp 0 2 2 ˙ 2 ! š ˇ ¹ 0 º 2 + 2 d 0 ; (4.1) where isthefrequency, ˙ isthestandarddeviationoftheGaussian,attributedtoDoppler broadening,and = 2 : 875 MHzisthehalf-widthathalf-maximumoftheLorentzian,whichis halfthenaturallinewidthofthetransition. Basedontheamplitudeofthespectraforeachisotope,themeasuredisotopicratiofor 85 Rbis 0.637(69)andfor 87 Rbis0.363(39),whilethereferencedatareportsanisotopicratioof0.7217(2) and0.2783(2)for 85 Rband 87 Rb[2].The˝ttedVoigtpro˝leshaveanaveragestandarddeviationof 178MHzduetoDopplerbroadening,whichcorrespondstoavelocityspreadofv = c ˙ š 0 = 140 m/s. 4.3.2RubidiumDepositionRate Thenumberofatomsexitingthenozzlecanbecalculatedfromthemeasured˛uorescenceintensity. Thepoweremittedbyasingleatom P atom undertwo-levelresonantexcitationlightwithintensity I is P atom = h 2 I š I 0 1 + I š I 0 (4.2) 72 Figure4.3:FluorescencepowerasmeasuredbytheAPDasthefrequencyofexcitationlightis scannedthroughtheRubidiumD 1 transition. Table4.2:RubidiumD 1 hyper˝nestructure.Referencedataistakenfrom[2].Referencevalue uncertaintiesaregenerallylessthan100kHz.Wavelengthmeasurementsarepreciseto7MHz, withanabsolutecalibrationaccuracyof600MHz. RubidiumD 1 Transition( 5 2 S 1 š 2 ! 5 2 P 1 š 2 ) Wavelength = 794 : 979014933 ¹ 96 º nm Frequency 0 = 377 : 107385690 ¹ 46 º THz Lifetime ˝ = 27 : 679 ¹ 27 º ns Naturallinewidth = 2 ˇ 5 : 75 MHz Isotopeshift 0 ( 87 Rb)- 0 ( 85 Rb) = 77 : 583 MHz 85 Rb 0 ,F ! F'= 2 ! 32 ! 23 ! 23 ! 3 avg.shift reference(GHz)1.55991.9215-1.4758-1.1142 measured(GHz)1.59171.9715-1.4296-1.06180.0451 87 Rb 0 ,F ! F'= 1 ! 21 ! 12 ! 12 ! 2 avg.shift reference(GHz)3.87694.6717-2.9919-2.1359 measured(GHz)3.83884.6555-2.9958-2.17910.0253 levelsplitting 85 Rb 5 2 S 1 š 2 87 Rb 5 2 S 1 š 2 85 Rb 5 2 P 1 š 2 87 Rb 5 2 P 1 š 2 reference(GHz)3.03576.83470.36160.8166 measured(GHz)3.02746.83830.37380.8254 di˙erence(GHz)-0.00830.00360.01220.0088 73 where h isthePlanckconstant, isthefrequencyoftheemittedphoton, istheexcitedstatedecay rate,and I 0 isthesaturationintensity,whichisde˝nedastheintensityatwhichthe˛uorescence powerishalfofthesaturatedpower P sat = h š 2 .ThetotalpowermeasuredbytheAPDisgiven by P APD = ¹ ¹ x ; y ; z º P sat I ¹ x ; y ; z ºš I 0 1 + I ¹ x ; y ; z ºš I 0 n ¹ x ; y ; z º dV ; (4.3) wheretheintegralisoverthevolumewherethelaserlightofintensity I ¹ x ; y ; z º intersectsthe distributionofatomsemittedfromthenozzle,describedbythenumberdensity n ¹ x ; y ; z º .Thesolid anglee˚ciency istheratioofpowerdetectedbytheAPDsensortothetotalpoweremitted, = A APD 4 ˇ r 2 ; (4.4) validfor 4 ˇ r 2 ˛ A APD ,where A APD = 0 : 196 mm 2 istheareaoftheAPDsensor,and r ˇ 100 mm isthedistancefromtheAPDsensortoavolumeelement. Astheangularintensity J ¹ º ofrubidiumatomsoutofthenozzleisunknown,twodi˙erent modelsareusedtocalculateanupperandlowerlimitonthenumberofrubidiumatomscollecting inthekrypton˝lm.EachmodelisdisplayedinFigure4.4.The˝rstmodelisasimplecosine distributiontosimulateabroad,di˙useatomicbeam, J 1 ¹ º = S 1 cos ˇ (4.5) where J 1 istheangularintensityinatoms/sr/s, S 1 isthetotalrateofatomsemanatingfromthe nozzleinatomspersecond,and isthepolaranglewithrespecttotheaxisofthenozzle.The secondmodelistakenfrom[65],andisderivedfromthedistributionatomswhichtraversea cylindricalchannelofthesamedimensionsasthenozzlewithradius r = 0 : 5 mmand L = 100 mm,whileneglectinginteratomiccollisions, J 2 = S 2 C j ¹ º ; (4.6) where C isanormalizationconstant,and j ¹ º = 8 > > > >< > > > > : cos + 2 ˇ cos h ¹ 1 º R ¹ q º + 2 3 q ¹ 1 2 º¹ 1 ¹ 1 q 2 º 3 š 2 º i ; q 1 cos + 4 3 ˇ q ¹ 1 2 º cos ; q 1 (4.7) 74 Figure4.4:Angularintensitydistributionmodelsplottedasafunctionofanglerelativetothe centerline( = 0 )intensity. for q = L 2 r tan ; R ¹ q º = arccos q q q 1 q 2 ; (4.8) and = 1 2 1 3 2 © « 1 2 3 + 2 2 1 1 + 2 1 š 2 1 + 2 1 š 2 2 sinh -1 ¹ 1 º ª ® ® ® ¬ with = 2 r L : (4.9) Thenumberdensityiscalculatedfromtheangularintensityvia n ¹ x ; y ; z º = J ¹ º v 1 x 2 + y 2 + z 2 (4.10) where ¹ x ; y ; z º isthepositionrelativetotheendofthenozzle,andv = p 8 k B T š ˇ m istheaverage velocityoftherubidiumatomswithmass m andtemperature T . ThesaturationintensitywasdeterminedbyscanningthelaserthroughtheRubidium D 1 reso- nancefordi˙erentlaserpowers.Thesaturationintensityisextractedfromabest˝ttotheintegrated APDsignalasafunctionoflaserintensity,asdisplayedinFigure4.5.Withthesaturationintensity andtheintegratedAPDpower,thetotalatomicbeamcurrentforeachmodel, S 1 and S 2 ,canbe 75 Figure4.5:IntegratedAPDvoltageasafunctionoflaserintensity.Abest˝ttothisdatayieldsa saturationintensity I 0 = 13 : 6 2 : 9 mW/cm 2 calculatedfromEquation4.3.Thepowerdensityforeachangulardistributionmodelasdetected bytheAPDisplottedinFigure4.6. Threekrypton˝lmsweregrownwithdi˙erentquantitiesofrubidiumatomsembedded,con- trolledwiththerubidiumsourcetemperature(rubidiumcurrent)anddepositiontime.Theresults aresummarizedinTable4.3,includingtotalatomiccurrentoutofthesource S ,numberofatoms inthe˝lm N film ,rubidiumnumberdensityinthekrypton˝lm n film ,andrubidiumconcentration. Upperandlowerlimitsweredeterminedbythe J 2 and J 1 angulardistributions,respectively.The numberofrubidiumatomsimplantedinthekrypton˝lmwascalculatedbyintegratingtherubidium atomicbeamintensityoverthesubstrateinpSAM,assumedtobeacircleofradius1cmatadistance of85cmfromtherubidiumnozzle.Thelargest(anddominant)sourceofuncertaintyinthenumber ofatomsisfromtheuncertaintyinthesaturationintensity,whichcontributesaround 20 30% . Uncertaintyinthelaserbeamradiuscontributesasmallamount( < 5% ),andtheuncertaintyinthe 76 Figure4.6:PlotofthemodeledpowerdensityasviewedbytheAPDforeachangulardistribution. TheplottedvaluesaretheintegrandofEquation4.3inthe y = 0 plane,wherethecenterofthe atomicbeamandlaserintersect.Inthiscoordinatesystem,thenozzletipislocatedat z = 35 mm,andthelaserbeamisalongthe x -axiscenteredat z = 0 mm.TheAPDsensorislocated abovetheplotted x - z planeat y = 96 mm. Table4.3:Summaryofrubidiuminkryptonsampleconcentrations. T source dep.timeKrgrowthrate upper lo w er SN film n film Rbconc. ( C)(s)( m/hr)(Rbatoms/s)(Rbatoms)(Rbatoms/cm 3 )(ppm) 2514525.29 2 : 6 10 13 2 : 9 10 13 3 : 8 10 16 1.9 3 : 1 10 12 6 : 0 10 12 7 : 9 10 15 0.39 1166934.72 1 : 1 10 14 5 : 6 10 13 1 : 8 10 17 9.0 1 : 3 10 13 1 : 1 10 13 3 : 7 10 16 1.8 22015424.65 7 : 9 10 14 8 : 3 10 14 1 : 3 10 18 65 9 : 4 10 13 1 : 7 10 14 2 : 7 10 17 13 substratepositioncontributesapproximately 10% . 77 Table4.4:RubidiuminKryptonabsorptionpeaks. (nm)FWHMnote 65030highRbdensity 70516highRbdensity 72012bluetriplet 73112bluetriplet 74430bluetriplet 76524redtriplet 78724redtriplet 81324redtriplet 87975highRbdensity 4.3.3RbinKrAbsorptionSpectra AbsorptionspectraobtainedusingthesetupinFigure4.1forallthreerubidiumdopedkrypton˝lms aredisplayedinFigure4.7,andareingoodagreementwithpreviouslyreportedspectra[38,21]. Thepresenceoftheredandbluetripletsareobvious,andadditionalpeaksareobservedforthe˝lm withthehighestdensityofrubidium,T source = 220 C,thatarenotdetectedinthelowerdensity samples.TheobservedpeaksarelistedinTable4.4. Theabsorbance A ¹ º ofthe˝lmisde˝nedas A ¹ º = ln ¹ T ¹ ºº = ˙ a ¹ º nl (4.11) where T ¹ º isthetransmissionatwavelength , ˙ a ¹ º istheabsorptioncrosssection, n isthe numberdensityofrubidiumatomsinthe˝lm,and l isthepathlengthofoflightthroughthe ˝lm.Usingthecalculatednumberdensityofrubidiumatomsinthe˝lmandthethicknessofthe rubidium-dopedlayer,itispossibletoextractanupperandlowerlimitontheabsorptioncross section,plottedinFigure4.8.Theabsorptioncrosssectionagreeswellbetweenthethreesamples. 4.3.4RbinKrFluorescenceSpectroscopy Theobserved˛uorescencespectrumoftherubidiumdopedkrypton˝lmgrownwith T source = 220 CisplottedinFigure4.9forlaserwavelengthsintherangefrom 700 760 nm,withthelaserscan 78 Figure4.7:Absorptionspectraofthethreerubidiumdopedkrypton˝lms.Theabsorbancefor ˝lmswithalowerconcentrationofrubidiumhavebeenmultipliedby10toaidinvisibility. Figure4.8:Absorptioncrosssectionofrubidiuminsolidkryptonassumingthecosine(upper limit)and j ¹ º (lowerlimit)angulardistributionsoutoftherubidiumsource. 79 Table4.5:Tableoflaser-induced˛uorescencescanparametersforspectrainFigure4.9. CCDacquisitionparameters exposuretimeintegrationsmode 0.8s6ExtendedNIR PreAmpgainpixelreadoutratesensortemperature 1x1MHz(16-bit)-55 C laserscanparameters range(nm)scanrate 700760nm20 GHz s Table4.6:RubidiuminKryptonlaserinduced˛uorescencepeaks,withuncertaintiesgivenin parenthesis.Resonancestrengthisgivenwithrespecttotheamplitudeofthestrongestresonance at730nm. (nm)FWHMstrength 700.9(3)4.1(5)0.061(6) 714.3(5)9.6(1.1)0.240(9) 720.6(3)6.6(2)0.74(4) 730.0(3)8.0(2)1.000 742.5(3)10.9(2)0.940(8) parametersandCCDacquisitionsettingslistedinTable4.5.Thewavelengthofthe˛uorescence lightwasnotmeasured,butisassumedtobeabove830nmduetothelongpass˝ltersusedto attenuatestrayexcitationlight(seeFigure4.2).Arecentpaperreportstheemissionwavelength forrubidiuminkryptontobe923nmwitha37nmFWHMforexcitationinthebluetriplet[21]. Asthedetectione˚ciencyoftheCCDcameradropsrapidlyforwavelengthsabove950nm,it isassumedthe˛uorescencemeasuredbytheCCDis923nmlight.The˛uorescencespectrum iswellrepresentedbya˝tto˝veGaussianfunctions.Theaveragepeaklocations,widths,and amplitudesforallthreesamplesarereportedinTable4.6.Aftermeasurementswerecompletedon the˝rst˝lm,itwasevaporatedandakrypton˝lmwasgrownwhiletheatomicrubidiumsource wasblocked.Laserinduced˛uorescencescansperformedonthebaresubstrateandontheempty krypton˝lmshowednoappreciable˛uorescenceabovebackground. 80 Figure4.9:Laser-induced˛uorescencespectrumforrubidiuminsolidkrypton.The y -axisunits arethetotalCCDcountratesummedovertheentiresubstrateandnormalizedtothelaserpower. Foreachrubidium-dopedkrypton˝lm,the˛uorescencepowerwasmeasuredat730nmexci- tationwavelengthoverarangeoflaserpowers,withanapproximately1-cmradiusGaussianbeam pro˝le.Thethird˝lm's˛uorescenceyieldwasalsomeasuredwithahigherintensitylaserbeam withanapproximately0.25-cmradiusGaussianbeampro˝le.Forallthree˝lms,the˛uorescence yieldwasfoundtoincreaselinearlywiththelaserintensity,asdisplayedinFigure4.11.Duetothe linearrelationship,wecanassumetheatomsarefarfromsaturation,andthe˛uorescencepower peratomcanbewrittenas P total N = ˙ f I (4.12) where N isthenumberofatomsilluminatedbylaserlightwithintensity I , ˙ f isthe˛uorescence crosssection,and P total isthetotal˛uorescencepoweremittedfromthelaserregionasmeasured 81 Figure4.10:CCDimagesofthesubstrateunder1mWof730-nmlaserlightwitharoughly Gaussianpro˝le.Thetopimageisofasubstratewithakrypton˝lm,whilethebottomimageisof arubidium-dopedkrypton˝lm.Thewhitecirclesdenotetheextentofthesubstrate. 82 bytheCCDcamera.Thistotal˛uorescencepowerwascalculatedfrom P total = hc 925 nm R total C CCD ¹ = 925 nm º (4.13) where hc 925 nm istheassumedenergyofthe˛uorescencephotons, R total isthetotalCCDcount rateinthelaserregion, = 0 : 0027 isthesolidanglee˚ciencyoftheCCDsensorrelativetothe substratesurface,and C CCD ¹ º isawavelength-dependentcalibrationfactorforconvertingCCD countstonumberofphotons,whichhasbeenmeasuredseparately(seeAppendixA). Figure4.11:Fluorescencepowerperatomasafunctionoflaserintensityforeach˝lmandforthe upperandlowerboundsonthepredictednumberofatomsinthe˝lm.Theslopeofeachlineis the˛uorescencecrosssection ˙ f . Basedonthissimplemodel,theslopeofalinear˝ttothe˛uorescencepowerasafunctionof intensityyieldsthe˛uorescencecrosssection ˙ f .Interestingly,eachsampleexhibitsamarkedly di˙erent ˙ f asdisplayedinFigure4.12.The˝lmwiththehighestnumberdensityofrubidium wasmeasuredtohavea˛uorescencecrosssectionanorderofmagnitudelowerthantheothertwo ˝lms.Eventhehigh-andlow-intensitymeasurementsonthethird˝lm(lowestnumberdensity)are signi˝cantlydi˙erentifconstrainedtothesamerubidiumangulardistribution.Inthisthird˝lm, increasingtheintensitybyafactorof16yieldeda˛uorescencepowerincreaseofonlyafactorof 4. 83 Figure4.12:Fluorescencecrosssectionmeasurementsforeachofthethreerubidium-doped krypton˝lms,plottedvs.theaveragenumberdensitycalculatedfromthetwoatomicangular distributionmodels. 4.4Conclusions Theabsorptioncrosssectionforrubidiuminsolidkryptonisdominatedbytwotripletsofpeaks, correspondingtotwodi˙erenttrappingsitesinthekryptonlattice,ashasbeenreportedbyothers [21].Theabsorptioncrosssectionofrubidiumdopedsolidkrypton˝lmswasmeasuredforthree di˙erentrubidiumconcentrationsandallthreewerefoundtobeconsistentinmagnitude.Basedon this,theatomicbeam˛uorescencemethodisareasonablyaccuratetoolformeasuringtheintensity oftheatomicbeamsource.Thetwoextremecasesfortheangulardistributionofrubidiumatoms outofthesourceyieldafactorof5di˙erenceintheabsorptioncrosssection.Althoughtheactual angulardistributionisunknown,acosinedistributionmodelismostlikelytherealitybasedonthe DopplerwidthoftheABFspectra.TheDopplerwidthofpeakswasmeasuredtobeconsistentto avelocityspreadof 140 m/swhichroughlycorrespondstoanangularwidthof22degreesfor 220 84 Table4.7:Measuredcrosssectionsandquantume˚cienciesat excitation = 730 nm. T source ˙ a (cm 2 ) ˙ f (cm 2 ) QE ; emission > 830 nm ( C) cos ¹ º j ¹ º cos ¹ º j ¹ º cos ¹ º j ¹ º 25 1 : 2 10 14 2 : 4 10 15 2 : 8 10 16 5 : 8 10 17 2 : 3 10 2 2 : 4 10 2 7 : 9 10 17 1 : 6 10 17 6 : 6 10 3 6 : 7 10 3 116 1 : 3 10 14 2 : 5 10 15 4 : 9 10 16 1 : 0 10 16 3 : 8 10 2 4 : 0 10 2 220 1 : 3 10 14 2 : 6 10 15 1 : 1 10 17 2 : 3 10 18 8 : 4 10 4 8 : 8 10 4 Cgaseousrubidiumatomshavinganaveragevelocityof 345 m/s.Forthesharplypeaked j ¹ º distribution,angularwidthisexpectedtobeapproximately2degrees,whichwouldcorrespondto amuchsmallerDopplerwidthof 12 m/s. Thelaserinduced˛uorescencespectrumwaslikewisefoundtobeconsistentwiththeliterature, however,the˛uorescencecrosssectionwasnotfoundtobehavepredictablywithrubidiumconcen- tration.Althoughthe˛uorescencepowerwaslinearlydependentonthelaserintensityforallthree rubidiumdopedkryptonsamples,the˛uorescencecrosssectionvariedbymorethananorderof magnitudebetweenthedi˙erentsamples.Ifwede˝nethequantume˚ciencyastheratioofthe ˛uorescenceandabsorptioncrosssections, QE = ˙ f š ˙ a ,then QE canbeusedasameasureof theamountof˛uorescencelightemittedforacertainamountofexcitationlightabsorption.Ina vacuum, QE = 1 duetoenergyconservation.Inamedium,however, QE canbelessthan1since absorbedenergycanbetransferrednonradiativelythroughlatticephonons.Themeasuredquantum e˚ciencyforthesamplesinthisstudyaresummarizedinTable4.7.Asthequantume˚ciencies inthisstudyareontheorderof 0 : 08 4% ,itseemsnonradiativedecaydissipatesasigni˝cant portionoftheabsorbedlaserexcitation.Inaddition,thisquantume˚ciencyseemstovarygreatly between˝lmswithdi˙erentrubidiumconcentrations,aswellasfordi˙erentlaserbeamspotsizes orlocationsonthe˝lm. 85 CHAPTER5 BEAMLINEFEASIBILITYSTUDIES 5.1Introduction Thereareanumberofoutstandingquestionsregardingtheimplementationofthesingle-atom microscopemethod(SAM)inabeamlinenuclearreactioncrosssectionmeasurement.Most importantly,asproductionsarehighlyionized,itisnotclearwhatpercentageofthemwillbecome fullyneutralizedastheypenetrateandbecomestoppedinthesolidnoblegas˝lm.Dependingon theproductspecies,asinglyionizedchargestatecanrenderthetrappedatomopticallyundetectable duetounfavorablespectra.Determiningthisneutralizatione˚ciencyisnecessaryforanaccurate crosssectionmeasurement,anddependingonthespeciesofinterest,ensuringahighneutralization e˚ciencywillfavorablyimpacttheSAMdetectione˚ciency. Anotherunknownisthee˙ectthatunreactedenergeticionbeamwillhaveonthenoblegas thin˝lm.Atomsareknockedoutofthe˝lmaseachincomingioncollideswiththesolidnoble gaslatticeinaprocesscalledsputtering.Signi˝cantsputteringcouldbedeleterioustotheSAM detectione˚ciencybydamagingthelatticeorremovingsigni˝cantamountsofthe˝lmsuchthat thereisinsu˚cientremainingthicknesstotrapincomingproductatoms.Thesputteringyield, whichistheratioofejectedtoincomingatoms,hasnotbeenmeasuredforaheavyionbeamat astrophysicalenergiesoftheorderofafewMeVpernucleon.Resultsatlowerenergiessuggest signi˝cantthicknesslossesonlyforbeamintensitiesabove 10 9 ions/cm 2 /s,describedwithgreater detailinChapter2. Thischapterpresentstheresultsofthe˝rstbeamlinetestsfortheSAMdetectionscheme,in whichtheopticalpropertiesofakrypton˝lmarestudiedbefore,during,andafterbombardmentby energetickryptonandrubidiumionbeams.Thisrepresentsanimportant˝rststeptowardscommis- sioningpSAMbymeasuringthecrosssectionofthe 84 Kr ¹ p ; º 85 Rbreaction.Thecommissioning experimentwillutilizeakryptonbeamincidentonaprotontarget,andtheproductrubidiumatoms 86 andunreactedkryptonbeamarebothcapturedinakrypton˝lmonthepSAMsubstrate.Inthis precursorexperiment,thekryptonbeamwillbeusedtosimulatethee˙ectsoftheunreactedbeam onthe˝lm,andtherubidiumbeamwillbeusedtodeterminetheneutralizatione˚ciencyofthe productrubidiumionsaswellascon˝rmthespectrumofmatrixisolatedrubidiuminkrypton. 5.2Experimentalsetupandprocedure Forthemeasurementsdescribedinthischapter,theprototypesingle-atommicroscope(pSAM) wasattachedtothegeneral-purposeReA3beamlineattheNationalSuperconductingCyclotron Laboratory(NSCL)atMichiganStateUniversity[66,67,68].Theexperimentalsetupissimilar tothatinChapter4excepttheReA3beamlineisattachedtothepSAMgrowthchamberinplace oftheneutralrubidiumatomicsource,asshowninFigure5.1.During˝lmgrowthandion-beam implantation,thetransmissionofwhitelight,˝ber-coupledfromanOceanviewDH-2000white lightsource,iscontinuouslymonitoredwithaFlameSpectrometer(modelFlame-S-VIS-NIR-ES). TheionbeamfromtheReA3facilitypassesthrougha1-cmapertureconnectedtoanammeter usedtomonitortheportionofthebeamcurrentwhichstrikestheaperture.AretractableFaraday cupdownstreamoftheapertureisperiodicallyinsertedforabrieftimetomeasurethebeamcurrent passingthroughtheaperture.ThebeamcurrentwhiletheFaradaycupisretractedisinferredby correlationwiththeaperturecurrent,assumingtheportionofthetotalbeamthatisblockedbythe apertureremainsconstant. A 84 Kr 31 + beamwithanenergyof1.7MeVpernucleonand2-Hzbunchedcurrentofap- proximately 1 10 6 particlespersecond(pps)wasimplantedin100- mthickkrypton˝lmsfor durationsof3,12,and53hours.A 85 Rb 31 + beam,alsowithenergy1.7MeVpernucleonanda currentofapproximately 1 10 6 pps,wasimplantedinkrypton˝lmsfordurationsof0.7,10,15, and11hours.The0.7-hr 85 Rbimplantationwasperformedonthesame˝lmusedinthe53-hr 84 Kr implantation.Aftertheionbeamimplantation,thelaser-induced˛uorescencewasmeasuredfor excitationwavelengthsbetweennm.Followingtheion-implanted˝lm˛uorescencemea- surement,the˝lmwassublimedandafreshkrypton˝lmwasgrownforthesubsequentionbeam 87 Figure5.1:Diagramofthewhitelighttransmissionmeasurementduringion-beamimplantation. Figure5.2:Diagramofthelaser-induced˛uorescenceimagingsetup. 88 implantation.Laser-induced˛uorescencemeasurementswereperformedonthebaresubstrateafter sublimationandonthefreshkrypton˝lmtoestablishtheopticalbackground. Thesolidkrypton˝lmsweredepositedatarateof160 m/hrwithasubstratetemperatureof34 K,andwerecooledafterdepositionto30Katarateof1Kperminute.The˛uorescenceimaging setupusedisincludedinFigure5.2andisnearlyidenticaltothesetupusedinChapter4.Laserlight fromanMSquaredSOLSTiSlasertransportedthroughan85moptical˝ber(630HP),collimated withanasphericlens,anddirectedontothesubstratewithamirroranddichroicbeamsplitter. Upstream,thelaserbeamwasgivenadivergencewiththeuseofafocusinglenssuchthatitwas expandedtothesizeofthesubstrate,withanaverageintensityof1.5mW/cm 2 .Fluorescence lightfromthesubstrateiscollectedbyalargeasphericlensplacedbehindthesubstratesuchthat a1/4-sizedimageofthesubstratewasformedonthesensorofanAndorClaraCCDcamera.The dichroicbeamsplitterandalong-passedge˝lter,whichbothblocklightofwavelengthbelow830 nm,areusedtoattenuateanyscatteredorre˛ectedlaserlight. 5.3Results 5.3.1Beame˙ectson˝lmclarity Theinitialwhitelighttransmissionforthe˝lmsisincludedinFigure5.3,whichshowsexcellent agreementbetweenall˝lms,withanaverageof1.09inthewavelengthrangenm.A plotoftheaveragetransmissionforeach˝lmasafunctionoftimeduringallionimplantations isinFigure5.4,whichalsoincludestheaveragetransmissionfora˝lmwithoutanionbeam. Unfortunately,thewhitelightsourcedevelopedanintermittentinstability,however,thetrendis stillclear.Underionbeamirradiation,theclarityofthe˝lmdecreasesataslowerratethanunder noirradiation.Thisobservationiscon˝rmedwithavisualinspectionofthe˝lmafterasigni˝cant periodofbeamimplantation,showninFigure5.5.Theareainwhichtheionbeamisimplanted inthe˝lmappearstoremaintransparentwhiletheremainderofthe˝lmbecomescloudy.There wasnomeasurableabsorptionspectraforthe 85 Rb-implanted˝lms,likelyduetoaninsu˚cient numberofimplantedrubidiumatoms. 89 Figure5.3:Initialtransmissionoflightthroughthesubstrateandsolidkrypton˝lmsrelativeto transmissionthroughjustthesubstrate.Theoscillationinthetransmissionisduetothin˝lm interferenceintheroughly400-nmthickkrypton˝lmwhichformsonthebackofthesubstrate. Figure5.4:Averagetransmissionofthe˝lmsasafunctionoftimeduringionimplantation.The spikesanddiscontinuitiesareduetoalightsourceinstabilityandnotduetosuddenchangesinthe ˝lm. 90 Figure5.5:Left:Asthe 84 Krbeamcollideswiththe˝lm,visible˛uorescencelightisemitted. Thewhitelightsourcewasblockedforthispicture.Right:After50hr,the 84 Krbeamisfocused ontoadi˙erentspotonthe˝lm.Theimpressionofthebeaminthepreviouslocationisalarge clearareaintheotherwisecloudy˝lm.Thenewbeamlocationcanbeseenasagreenspottothe rightoftheprevious.Thewhitelightsourcewasonandisclearlyvisibleasanovalshape occupyingmostofthesubstratearea. 5.3.2Ion-Beaminducedluminescence AsshowninFigure5.5,theimpactoftheionbeamonthe˝lmproducesvisible˛uorescencelight. Theviolentcollisionoftheenergeticionscausesionizationoftheatomsinthe˝lm,andhighenergy electromagneticradiationisemittedastheliberatedelectronsarerecaptured.Thisinturncauses visible˛uorescenceinthe˝lmandsubstrate.Withthewhitelightsourceblocked,thespectrometer wasusedtotakespectrawithandwithoutionbeamirradiation.Thedi˙erenceofthetwospectra isplottedinFigure5.6fordi˙erentimplantationtimesduringthe54-hr 84 Krimplantation.The spectrumconsistsoffourmainfeatures,listedinTable5.1,andwasthesameforboththe 84 Krand 85 Rbbeams.Thepeakat694nmisattributedtothe˛uorescenceofacommonsapphireimpurity, chromium,andthebroadpeakat417isattributedtolatticedefectsinthesapphire.Thepeaksat 525nmand564nmareattributedtotransitionsofatomicnitrogenandoxygen,respectively,which areimpuritiesinthesolidkrypton˝lm.Theamplitudeoftheatomicnitrogenandoxygenlines increasesdrasticallyinthe˝rstfewhoursof˝lmirradiation,likelyasaresultofthemolecular 91 Table5.1:Ion-beaminducedluminescencespectrumpeaks.Peaklocationshaveanuncertaintyof 0.5nm. (nm)FWHMAssignment 416.547(4)sapphiresubstrate[69] 524.51.8(2)N˝lmimpurity( 2 D ! 4 S)[54] 563.812(3)O˝lmimpurity( 1 S ! 1 D)[54] 693.0,694.41.9(2)Cr 3 + sapphireimpurity[56] nitrogenandoxygenimpuritiesinthekrypton˝lmbecomingdisassociatedbytheionbeam.The ˛uorescenceofthe525nmpeakislong-livedwitha10-seconddecaytime(seeFigure5.7),and isvisibletotheeyeupto60secondsaftertheionbeamisblocked.Thedecaytimesoftheother peaksweretooshorttobemeasured. Figure5.6:Ion-beaminducedluminescencespectrum. 5.3.3FilmSputtering ThevacuumpressureinpSAMshowednomeasurabledi˙erencewheneitherbeamwasblocked bytheFaradaycupandwhenthebeamwashittingthesolidkrypton˝lm.Thevacuumpressurein pSAMwithakrypton˝lmat30Kistypically 2 10 8 TorrasmeasuredwiththeMKS392Ion 92 Figure5.7:Decayofthegreenluminescencepeakassociatedwithatomicnitrogen,whichwas measuredtohavearoughly10-seconddecayconstant. gauge,whichissensitivedownto 10 9 Torr.Anestimateofthe˝lmsputteringraterequiredto registerwiththeiongaugecanbefoundbyusingthemolar˛owrateinEquation3.5.Assumingthe pressureincreasesby 1 10 9 Torrwhentheionbeamishittingthe˝lmandapumpingspeedof 55L/s,the˝lmsputteringrateis 3 10 12 mol/s.Foraionbeamspotwithcrosssectionalareaof 0.2cm 2 ,thiscorrespondstothesmallestmeasurablekrypton˝lmthicknesslossratebeingonthe orderof0.01 m/hr.Thetypicalionbeamratewasontheorderof 10 6 pps,sowecanputanupper limitonthesmallestmeasurablekrypton˝lmsputteringyieldfortheseteststoberoughly 10 7 ˝lm atomssputteredperbeamion.Thislimitonthesputteringyieldisordersofmagnitudehigherthan thepredictedyieldof 10 3 10 5 .Improvingthismeasurementrequiresmuchhigherbeamcurrents oramuchmoresensitivevacuumgaugecoupledwithaloweroverallvacuumpressure. 5.3.4Laserinduced˛uorescenceofionimplanted˝lms Filmsimplantedwiththe 84 Krbeamdisplayednosigni˝cantlaserinduced˛uorescencewhen comparedtoafreshlygrown˝lm.Figure5.8containsCCDimagesofthesubstrateunderlaser 93 Table5.2:Tableoflaser-induced˛uorescencescanparameters. CCDacquisitionparameters exposuretimeintegrationsmode 5s2ExtendedNIR PreAmpgainpixelreadoutratesensortemperature 1x1MHz(16-bit)-55 C laserscanparameters range(nm)scanrate 700760nm20 GHz s excitationwithafreshlygrownsolidkrypton˝lmandthesame˝lmafter53hrof 84 Krion implantation( 1 : 3 10 11 totalions).Asexpected,the˝lmsimplantedwiththe 84 Krbeamare generallyindistinguishablefroma˝lmthathasnotbeenexposedtoanionbeam.Incontrast,a ˛uorescenceimageof 85 Rbimplanted˝lmsshowaclearlylocalizedionbeamspotasdisplayedin Figure5.9.ThelaserscanparametersandCCDacquisitionsettingsarelistedinTable5.2 TheCCDimagesareprocessedintoameasureoftheCCDcountrateperincidentlaserintensity, de˝nedasthe˛uorescenceyieldimage Y ¹ x ; y º Y ¹ x ; y º = ˆ ¹ x ; y º I ¹ x ; y º ; (5.1) where ˆ ¹ x ; y º istheCCDimagecountrateincountspersecond,atthearrayofpixelsatposition ¹ x ; y º ,and I ¹ x ; y º istheexcitationlaserintensityinmW/mm 2 .This˛uorescenceyieldissummed overallpixelswithinaregionofinterest(ROI)toarriveatatotal˛uorescenceyieldforeachimage. Themean˛uorescenceyieldovertheROImeasuredasafunctionoflaserexcitationwavelength isplottedinFigure5.10forfreshlygrown, 84 Krbeam,and 85 Rbbeamimplanted˝lms.For 84 Kr implanted˝lmstheROIencompassedtheentiresubstrate,whereasonlythelocalizedionbeam spotwasusedfor 85 Rb˝lmstoimprovethesignaltobackgroundratio. The˛uorescencespectrumforthe˝nal 85 Rbembedded˝lmwasstudiedoverseveraldaysunder thehypothesisthatsomeportionofthe 85 Rbions,whichremainedsinglyionizedafterstopping inthe˝lm,wouldgraduallyneutralizeovertime.Ifsuchahypothesisweretrue,the˛uorescence 94 Figure5.8:Top:CCDimageofafreshlygrownKrypton˝lm.Bottom:CCDimageofthesame krypton˝lmafter53hoursof 84 Krionimplantation.Theregionofinterestisshownbythewhite circle. 95 Figure5.9:Top:CCDimageofafreshlygrownKrypton˝lm.Bottom:CCDimageofthesame krypton˝lmafter11hoursof 85 Rbionimplantation.Theregionofinterestisshownbythewhite circle. 96 Figure5.10:Top:Laser-induced˛uorescencespectrumforafreshlygrown100- mkrypton˝lm. Middle:Spectrumfor 84 Krimplanted˝lms.Bottom:Spectrumfor 85 Rbimplanted˝lms. 97 Table5.3:Listofrubidiuminkryptonlaserinduced˛uorescencepeaks,comparingneutraland ionbeamimplantedrubidium. neutralionbeam (nm)FWHM (nm)FWHM 720.6(3)6.6(2)720(1)12(1) 730.0(3)8.0(2)733(1)14(1) 742.5(3)10.9(2)749(1)20(1) Table5.4:Maximumcrosssectionsof 85 Rbimplanted˝lms,with excitation = 750 nm. uncertainties(%) N ions n (atoms/cm 3 ) ˙ f (cm 2 ) N ions C CCD 3 : 1 10 9 1 : 5 10 12 1 : 4 10 15 10118 6 : 6 10 10 3 : 1 10 13 6 : 9 10 16 8 : 7 10 10 4 : 2 10 13 7 : 5 10 16 8 : 2 10 10 3 : 9 10 13 8 : 3 10 16 yieldwouldincreasewiththenumberofneutral 85 Rbatoms.Howeverthiswasnotthecase,as showninFigure5.11,whichshowsthe˛uorescenceyieldslowlydecreasingwhenthespectrum wasmeasuredonadailybasisforafewdaysaftercessationofionbeamimplantation.Aftertwo days,the˝lmwasannealedbyraisingitstemperatureto38Katarateof0.1K/min,heldat38K for10min,andcooledbackto30Kat1K/minwhilethelaserinduced˛uorescencewasmeasured atanexcitationwavelengthof735nm.Annealingresultedina˛uorescenceyielddecreaseofa fewpercentasshowninFigure5.12,whichisconsistentwiththeincreasedopacityofthe˝lmas aconsequenceoftheannealing.Amoreaggressiveannealingto44Khadasimilare˙ectonthe ˛uorescenceyield.Whencombinedwiththeslightdecreasein˛uorescenceyieldasthe˝lmaged, wecanconcludethatthe˛uorescenceyieldwasmostlikelya˙ectedbytheincreasingopacityof the˝lm,andthatneutralizationofanytrappedrubidiumionswasnotameasurablee˙ectasa consequenceofannealing. Afteroneday,thespectrumslightlychangedshapeasthethreepeaksbecamemoredistinct, suggestingthattheembeddedrubidiumatomsdoundergosomeformofrearrangementinthe ˝lm.Theindividualpeaksinthespectrumarebroader,lessdistinct,andslightlyred-shiftedfor 98 Figure5.11:Timedependenceof˛uorescencespectraforakrypton˝lmembeddedwith 85 Rb ions. Figure5.12:Total˛uorescenceyieldduringannealingto38Kandsubsequentcooldownto30K. 99 Figure5.13:Fluorescencecrosssectionfor˝lmsembeddedwith 85 Rbions.Theshadedbands arefroma10%uncertaintyinthenumberofatomsimplanted. ion-implanted˝lmscomparedtotheneutralrubidium˛uorescencespectrumdetailedinChapter 4.ThepeaklocationsarelistedandcomparedtotheneutralrubidiumspectruminTable5.3. Onemeasurementwasextendedoutto800nmexcitationtoexplorethetailofthethirdpeak,and the˝rstpeakoftheredtripletwasfound.Spectraatwavelengthslongerthan800nmwasnot possibletomeasureduetothelimitationsoftheoptical˝lters,andthewavelengthrangeofthe˝ber employedtotransportthelaserlight.Withthetotalnumberofimplanted 85 Rbions,itispossibleto calculatethe˛uorescencecrosssectiondisplayedinFigure5.13,fromthetotal˛uorescenceyield Y analogoustoEquation4.13, N ˙ f = Y hc 925 nm C CCD ¹ = 925nm º : (5.2) thepeak˛uorescencecrosssectionforeachsampleissummarizedinTable5.4.Thebackground ˛uorescencewassubtractedforeachmeasurement,calculatedbysummingthe˛uorescenceyield 100 Table5.5:Tableofmolecularoxygenresonancescanparameters. CCDacquisitionparameters exposuretimeintegrationsmode 5s2ExtendedNIR PreAmpgainpixelreadoutratesensortemperature 1x1MHz(16-bit)-55 C laserscanparameters range(nm)scanrate 755.74755.93nm50 MHz s Figure5.14:Energyleveldiagramformolecularoxygentransition.Afterexcitationat756nm, molecularoxygennonradiativelytransfersviainter-systemcrossing(IC)toanadjacentlowerlying state,andemitsnear1300nm. overanROIwherethe 85 Rbionswerenotimplanted. 5.3.5Molecularoxygen˛uorescenceline Throughthecourseofacquiring˛uorescencespectraofthe˝lms,asharp,brightresonancewas observedintheproximityof excitation = 755 nminmostspectra.Thisbackgroundresonanceis su˚cientlynarrowtohavenotbeenobservedwiththeCCDacquisitionsettingsforlaser-induced ˛uorescencespectrainChapter4,norisitpresentinanywhitelightabsorptionspectra.A˝ne wavelengthscanthroughtheresonanceproducedthespectrashowninFigure5.15,withthelaser scanparametersandCCDacquisitionsettingslistedinTable5.5.The˛uorescencelightinCCD 101 imagesofthesubstrateappearedtobedistributeduniformlythroughoutthe˝lm,andtheresonance wasnotobservedinspectrawithnokrypton˝lmonthesubstrate.Theresonanceiscenteredata wavelengthof755.835nmandhasaFWHMof0.017nm,andappearstoconsistofatleasttwo closely-spacedpeaks.Sincethe˛uorescencelightappearsuniformlydistributedthroughoutthe ˝lm,andduetoitsproximitytoamolecularoxygenvacuumresonance,thebackgroundresonance isattributedtomolecularoxygenimpuritiesinthekrypton˝lm[70,71,72].Themolecularoxygen attributioncanbefurthercon˝rmedwithameasurementofthe ˇ 1270 nmemissionwithan infraredspectrometer,modeledbytheenergyleveldiagramdisplayedinFigure5.14. 5.4Conclusions Whenembeddedasanenergeticionbeam,the˛uorescencespectrumofrubidiuminkrypton variesfromwhenneutralrubidiumisco-depositedwiththesolidkrypton˝lm.Intheiondeposition case,theindividualpeaksinthenmtripletarebroader,varyinrelativeamplitude,andthe Figure5.15:Background˛uorescencelineforakrypton˝lmwithrubidiumionsembedded.The smallspikesinthespectrumdenotetheendsoflaserscansegmentsandarenotactualfeaturesof thespectrum. 102 Table5.6:Comparisonofquantume˚cienciesforneutralandion-implantedmatrix-isolated rubidiuminsolidkrypton.Neutralabsorptionand˛uorescencecrosssectionswerecalculated fromanaverageofthe25 Cand116 CmeasurementsinTable4.7,andtheion-implanted ˛uorescencecrosssectionisanaverageofallthemeasurementsinTable5.4. ˙ n a ˙ n f ˙ ion f n QE ion QE (cm 2 )(cm 2 )(cm 2 ) ˙ n f š ˙ n a ˙ ion f š ˙ n a 7 : 7 10 15 1 : 7 10 16 9 : 2 10 16 0.020.12 smallerpeaksthatwereobservedintheneutralrubidiumsamplesarenolongerpresent.However, the˛uorescencecrosssectionfortheion-implantedsamplesarecomparableto,andevenlarger thanthelargestcrosssectionestimatefortheneutralrubidiumsamples( ˙ n f = 5 10 16 ),and thequantume˚ciencyforion-implantedrubidiumwassigni˝cantlyhigherwhenassumingthe sameabsorptioncrosssection,assummarizedinTable5.6.Thissuggeststhattheneutralization e˚ciencyforenergeticrubidiumionscouldbeclosetounity.Unfortunately,thelargevariationin neutralrubidium˛uorescencecrosssectionmeasurementsmakesitdi˚culttomakeaquantitative estimateoftheneutralizatione˚ciency.Sincethelargest˛uorescencecrosssectionsweregenerally measuredin˝lmswiththefewestnumberofimplantedrubidiumatoms,itispossiblethereare diminishingreturnswithincreasingionimplantationtimes. Thesolidkrypton˝lmswerenotsigni˝cantlydamagedbyheavyionirradiation.Sputtering ofthe˝lmwasnotcatastrophicallyhigh,nordidtheenergydepositedinthe˝lmbytheionbeam causesigni˝cantheatingorsublimation,andtheionbeamdidnotadverselya˙ectthetransparency ofthe˝lm.Instead,theionbeamcounteractedthenaturalcloudinessthat˝lmsacquirewithtime, andsothekrypton˝lmsremainedrelativelytransparentwherevertheionbeamwasimplanted. Furthermore,ionbeam-inducedluminescencelightwasobservedandcouldbeusedasacontinuous measureofthebeamcurrent,assumingtheamplitudeofthebeam-induced˛uorescenceisrelated tothepowerdepositedbythebeam. 103 CHAPTER6 CONCLUSIONANDFUTURESTEPS 6.1Rubidium˛uorescencecrosssection 6.1.1NeutralRubidiumbeam Anaccuratemeasurementoftheintrinsicbrightnessofmatrix-isolatedrubidiumisnecessaryin ordertobeabletocountthenumberofembeddedatomsina˝lm.Fluorescencecrosssection measurementsof 10 12 10 14 neutralrubidiumatomsthatwereco-depositedwiththesolidkrypton ˝lmvariedbyuptoafactorof50.Thelargestcauseofthevariationisduetouncertaintyinthe numberofrubidiumatomsemittedbythee˙usiveovensource.Sincerubidiumhasaveryhigh vaporpressure,along,narrownozzlewasselectedforthesourceinordertocreateacollimated andlowintensitybeamofrubidiumatoms.Someheatingisnecessarytobreakthroughthesurface oxidationlayeronthesourcemetal,however,therewasnomeasurableoutputfromthesource untilithadbeenheatedtoahightemperature,atwhichpointtheoutputbecameveryintenseand relativelyuncollimated.Whenthecruciblewasremovedafterwards,rubidiummetalwasfoundto haveleakedoutofaseaminthecrucible.Futureattemptswouldbene˝tfromasealedcrucibleto preventleaks,andashorternozzlewithawideropeningtoallowameasurablenumberofrubidium atomsoutofthesourcewithoutrequiringoverheating. Improvingourunderstandingoftheatomicbeamangulardistributioncouldbeaccomplished bymeasuringtheatomicbeam˛uorescence(ABF)atmultiplelocationsalongthebeamaxisto determinethedivergenceofthebeam.Ascanofanarrowlaserbeamintheplaneperpendicular totheatomicbeamwouldprovideaone-dimensionalbeampro˝le.Withapproximately 5 10 7 rubidiumatomsinthelaserinteractionregion,theABFmeasurementhadasignal-to-noiseratio of100,soareductioninthebeamintensitybyasimilarfactorshouldstillbemeasurablewithout drasticchangestotheexperimentalsetup.Furtherimprovementstothemeasurementcouldallow 104 fordetectionofevensmallerintensities.Withabrief1-secondimplantationtimeandassuming areductionbyafactorof100inthe 25 CrubidiumdepositionratefromChapter4,akrypton ˝lmcouldbeembeddedwithonly 10 7 rubidiumatoms.Distributedevenlyacrossthesubstrate, thiswouldcorrespondtoanarealdensityof0.03atoms/ m 2 inthe˝lm.Witha1:1imageof thesubstrateformedontheCCDsensor,withpixelareaof40 m 2 ,therewouldberoughlyone rubidiumatomperpixel.Basedontheseestimates,theABFmethodshouldbeappropriatefor creatingkrypton˝lmswithrubidiumconcentrationssmallenoughtoallowformeasurementsof individualatoms. Morethoroughstudiesofthe˛uorescenceyieldoftherubidium-dopedkrypton˝lmsare required,astwo˛uorescencemeasurementsonthesame˝lmbutfordi˙erentlaserintensities yieldedcrosssectionsthatdi˙eredbyafactorof3.The˛uorescenceyieldshouldbemeasuredfor signi˝cantlyhigherintensitiestoconstructacomprehensivemodelforthe˛uorescencedependence ontheintensityofthelaserexcitation.Measurementsofthe˛uorescenceyieldatseveralplaces onthesurfaceofthesubstratecouldalsoprovideanadditionalmeasureoftheangulardistribution outoftherubidiumsource.Thecombinationofanimprovedunderstandingofthematrix-isolated rubidium˛uorescenceandoftheatomicrubidiumsourcewillbenecessarytoreducetheuncertainty onthe˛uorescencecrosssection. 6.1.2Rubidiumionbeam Fluorescencecrosssectionmeasurementsof 10 9 10 10 ion-beamimplantedrubidiumatomswere consistenttowithinafactorof2,whichismarkedlybetterthanthecaseofneutralrubidium beam,mostlyduetoonlya10 % uncertaintyonthenumberofcapturedrubidiumions.However, thisuncertaintywasnotsu˚cienttoaccountfortheincreased˛uorescencecrosssectionofthe ˝lmimplantedwiththesmallestnumberofrubidiumions.Animprovedunderstandingofthe ˛uorescenceatvariouslaserintensities,asmentionedintheprevioussection,couldresolvethis discrepancy.Improvingameasureoftheneutralizatione˚ciencyforanenergeticrubidiumion beamwillrequireamoreprecisemeasurementof ˙ f forneutralrubidium. 105 Discoveryoftheion-beaminduced˛uorescenceaswellasthestrongbackgroundresonance ofmatrix-isolatedmolecularoxygeno˙ersunanticipatedtoolstoforthesingle-atommicroscope detectionscheme.Bothphenomenacouldbeusedasameasureoftheconcentrationofoxygen impuritiesinthe˝lm,shouldimpuritiesbecomeanimportantfactorforrubidiumsingle-atom detectionorforsomespeciestobestudiedinthefuture.Ion-beaminduced˛uorescenceofthe substratehasthepotentialtobeusedasameasureofthetotalpowerbeingdepositedbytheion beam,whichcanbeusedtoinferthetotalbeamcurrent,animportantparameterforcalculationof thenuclearcrosssection.Itmaybeworthwhiletoexplorethedependenceofthebeaminduced ˛uorescenceonthebeamintensityinfuturebeamlineexperiments. 6.2Progresstowardssingle-atomsensitivity Theabilitytoopticallydetecttheatomicnuclearreactionproductswithsensitivitiesoftheorder ofatomsiscrucialfortheusefulnessofthesingle-atommicroscope(SAM)detectionmethod, aswell-developedmethodsalreadyexistfornuclearcrosssectionmeasurementswithlargeproduct atomyields.Althoughthenumberofatomsdetectedinthisthesisvia˛uorescenceimagingis large( > 10 9 ),itispossibletoestimatethefeasibilityofachievingsingle-atomsensitivity.The con˝dencelevelatwhichwecandeclareasignalexistsabovethebackgroundisdependentonthe signaltobackgroundratio.Thenumberofbackgroundandsignalcountsmeasuredoveracertain integrationtimeissimplytheratemultipliedbytheintegrationtime.Theuncertaintyassociated withthesignalandbackgroundcountsaredeterminedaccordingtocountingstatistics, N s ˙ s = R s t p R s t ; N b ˙ b = R b t p R b t ; (6.1) where N s isthenumberofcountsmeasuredduringintegrationtime t ,duetoanatomemittingata rate R s ,and N b isthenumberofbackgroundcountsmeasuredduringintegrationtime t ,duetoa backgroundrate R b . Forlargecountrates,thedistributionofrepeatedsignalmeasurementsapproximatelyfollowsa normaldistribution[73].Theexpectedfraction( f )ofmeasurementsfollowinganormaldistribution 106 thatfallwithin k standarddeviations ˙ ofthemeanisgivenbytheErrorFunction: f ¹ k ˙ º = erf k p 2 ; (6.2) erf ¹ x º = 1 p ˇ ¹ x x e u 2 du : (6.3) Foragivenmeasurement N s ˙ s ,theprobability p thatthesignalissigni˝cantlydi˙erentfrom zero,calledthecon˝dencelevel,isdeterminedvia N s 0 = k ˙ s ! k = N s ˙ s (6.4) p = erf k p 2 : (6.5) Inreality,wehavenomeansofdistinguishingtheatomsignalfromthebackgroundduringan individualmeasurement.Havingmadeameasurementofthetotalsignal N T (atomandbackground), wemustmakeaseparatemeasurementofjustthebackgroundratewithnosourceatomsandsubtract togetthesingleatomsignal. N s = N T N b (6.6) ˙ s = q ˙ 2 T + ˙ 2 b = p R T t + R b t (6.7) FromEquation6.4, k = ¹ R T t R b t º p R T t + R b t = p R T t 1 1 + 1 q 1 + 1 + 1 = p R T t p 2 + 3 + 2 ; (6.8) where = R s š R b isthesignaltobackgroundratio.UsingEquation6.8wecandeterminethe integrationtime t necessarytoachieveacon˝dencelevel p asafunctionofsignaltobackground ratio ,whichisplottedinFigure6.1, t = 1 R T 2 h erf 1 ¹ p º i 2 2 + 3 + 2 2 : (6.9) Forthelargestmeasured˛uorescencecrosssection( ˙ f = 1 : 4 10 15 cm 2 ),overtheionbeam ROIwith 3 : 1 10 4 pixels(circularareaofradius100pixels),containingatotalof 3 : 1 10 9 rubidium 107 Figure6.1:Requiredintegrationtime t asafunctionofsignal-to-backgroundratio fordi˙erent con˝dencelevels,assumingatotalsignalrateof1Hz. atoms(givinganaverageof 10 5 atomsperpixel),andwithlaserintensity I = 2 : 5 mW/cm 2 ,theCCD measuredanaveragesignalrateperpixelof R T = 25 counts/swithabackgroundrateof R b = 17 counts/s.Thisgivesanaveragepixelsignal-to-backgroundratioof = ¹ R T R b ºš R b = 0 : 47 , andasignal-to-backgroundratioperatomof a = 4 : 7 10 6 .EvaluatingEquation6.9with a , R T = 25 Hz,andacon˝dencelevel p = 0 : 95 givesanintegrationtimeof 1 : 4 10 10 s = 440 yr.It isimportanttonotethatthesespectrawereacquiredunderconditionsnotspeci˝callyintendedfor single-atomdetection,andthatachievingamorereasonable60-secondintegrationtime,requiring reductionbyafactorof 2 10 8 ,canfeasiblybeaccomplishedbymaximizing andincreasingthe totalsignalrate.Incomparison,arecentpublicationdemonstratingsinglebariumatomdetection insolidxenonreported,under3-sexposuretolaserexcitationwithintensity I ˇ 10 5 mW/cm 2 ,a backgroundrateof R b =1000counts/(mW s)andaper-atomsignalrateof R s = 380 counts/(mW s), forasignal-to-backgroundratioof a = 0 : 38 [57]. Arelativelylowlaserintensitywasemployedintherubidium˛uorescencemeasurementsin 108 ordertoimagetheentiresubstrate.Focusingthelaserexcitationontoacircularareaofradius25 mcoulddrasticallyincreasethesignalratebyasmuchasafactorof 10 4 ,assumingboththesignal andbackgroundratescalelinearlywithlaserintensity.Tomakeamoreconservativeestimate, assumethesignalrateincreaseslinearlywithintensityuptoafactorof 10 2 .Afurtherfactorof tenincreasein R T canbefoundinincreasingthelightcollectione˚ciencyoftheimaginglens byplacingitclosertothesubstrate.Thelightcollectione˚ciencyfortheimagingsystemused during˛uorescenceimagingwasestimatedtobe0.0027,whichcanimprovetoashighas0.023 withthecurrentpSAMimagingchamber.Combiningtheseimprovementsresultsinuptoafactor of 10 3 10 5 increase R T ,andcorrespondingdecreaseintherequiredintegrationtime. Thegreatestreductionin t ,whichscaleswith 1 š 2 forsmall ,canbeaccomplishedthrough maximizing byminimizingthebackgroundrate R b ,whichshouldbereducedbyatleasta factorof 10 3 .ThemainsourceofbackgroundmeasuredbytheCCDismostlikelylaserlight re˛ectedbythesubstratethatisinsu˚cientlyattenuatedbytheoptical˝lters.Thetwo˝ltersare adichroicbeamsplitter(SemrockDi02-R830-25x36)usedtore˛ectthelaserexcitationontothe substrate,andalong-passedge˝lter(SemrockBLP01-830R-25)placedimmediatelyupstream oftheCCDsensor.Fromthemanufacturersspeci˝cations,theupperlimitforthetransmission at750nmforthedichroicbeamsplitterisapproximately 10 4 and 10 7 forthelong-pass˝lter. Thesetransmissionswereindependentlyveri˝edasisdisplayedinFigure6.2.Placingthe˝lters inseriesshouldprovideatransmissionontheorderof 10 11 ,howevermeasurementsoftheseries transmissionat725nm,usingthesetupinFigure6.3,resultsinacombinedtransmissionofonly 10 7 ,asshowninFigure6.4.ThelaserpowerfromtheSOLSTiSlaserwasmeasuredbeforeand afterthedichroicbeamsplitterusingcalibratedpower-meters(ThorlabsPM120VA),andthelaser powertransmittedbythelong-pass˝lterwasmeasuredbytheAndorClaraCCDcamera,whichwas previouslycalibrated(detailedinAppendixA).Thedichroicbeamsplitterbehavesaspredicted, withatransmissionof 10 4 ,butthelong-pass˝lterattenuatesthelaserlighttransmittedthrough thebeamsplitterbyonlyafactorof 10 3 insteadof 10 7 measuredpreviously.Thelong-pass˝lter issigni˝cantlylesse˙ectiveforlightalreadyattenuatedbythebeamsplitter. 109 Figure6.2:TransmissionofSemrock˝ltersutilizedin˛uorescenceimaging.Thetransmissionof thedichoicbeamsplitter,measuredatanincidentangleof45 wasstronglydependentonthe polarizationoftheincidentlightasshownbytheshadedblueregion.Thetransmissionofthe individualelementsmetorexceededthemanufacturer'sspeci˝cations. Figure6.3:SetupusedtomeasurethetransmissionoftheSemrock˝ltersinseries. 110 Figure6.4:TransmissionoftheSemrock˝ltersmeasuredatdi˙erentlaserpowers.Thecombined transmissionofthe˝ltersisafactorof 10 4 largerthanpredicted,basedontheindividual transmissions. Usingthemeasuredtransmissionofthe˝ltersinseries,wecanestimatethisbackgroundrate with R b = I hc T C CCD 1 M A pixel ˇ 9 counts/pixel/s(6.10) where I = 2 : 5 mW/cm 2 isthelaserintensity, š hc = 3 : 77 10 15 photons/mJ, = 0 : 08 is there˛ectanceofthesubstrate, = 0 : 1 isthelightcollectione˚ciencyassuming10 % ofthe re˛ectedlightiscollectedbytheimaginglens, T = 10 7 istheestimatedtransmissionoftheoptical ˝ltersat750nm, C CCD = 0 : 74 counts/photonistheCCDe˚ciency, M = 0 : 25 isthemagni˝cation oftheimagingsystem,and A pixel = 4 : 16 10 7 cm 2 istheareaofapixel.Thisroughestimate iswithinafactorof2ofthemeasuredbackgroundrate.Unfortunately,theAndorClaraCCD usedforthesemeasurementsisbiasedtowardthebackgroundlightinthiscase,sincethee˚ciency at750nmissigni˝cantlyhigherthanat925nm,whichistherubidiumemissionwavelength ( C CCD ¹ 750 nm ºš C CCD ¹ 925 nm ºˇ 5 ).Thebackgroundcouldalsobedueto˛uorescenceinthe 111 Figure6.5:ProposedchangestothepSAMimagingsystemdesignedtodrasticallyreducethe backgroundrate. sapphiresubstrateinducedbylaserexcitation,buttherearenoknownabsorptionlinesforsapphire inthiswavelengthregion. Assumingthebackgroundrateisduetoinsu˚cientattenuationoftheexcitationlight,some simplechangestotheimagingsystemwouldreducethebackgroundbythedesiredamount.The additionofasecond˝lterupstreamoftheCCD,withtheappropriateopticalproperties,could aloneprovidetherequisiteattenuationbyafactorof 10 3 .Apossiblymoree˙ectiveadjustmentis tochangethegeometryoftheimagingsystemsuchthattheexcitationlightisnolongeraligned alongtheimagingaxis.Suchachangewouldpreventre˛ectedlaserlightfromreachingtheCCD sensor.Thecurrentimagingsystemandapossiblemodi˝cationispresentedinFigure6.5.The improvementsinintegrationtimeforsingle-atomdetectionaresummarizedinTable6.1. 112 Table6.1:Listoftechniquesforreducingtherequiredintegrationtime t forsingle-atomdetection. ParameterReductionin t Technique R T 10Imaginglensclosertosubstrate,increasing . R T 10 2 10 4 Increaselaserintensity I . 10 6 Additionaloptical˝lter,decreasing R b . 10 6 Adjustlaserexcitationgeometry,decreasing R b . 25UseCCDwithfavorablee˚ciency. 6.3Futureoutlook Thisdissertationoutlinesthe˝rstexcitingstepsundertakenincommissioningthesingle- atommicroscopeasanoveldetectionmethodformeasurementofnuclearcrosssectionswith astrophysicalimportance.AssemblyandtestingofpSAMhasdemonstratedtheabilitytorepeatably depositopticallytransparentsolidnoblegas˝lmsofrequisitethicknesstocaptureenergeticheavy ions,akeyrequirementforthistechnique. 84 Kr ¹ p ; º 85 Rbhasbeenselectedasanidealnuclear reactionforcommissioningpSAM.Furtherdevelopmentoftheatomicbeam˛uorescencemethod fordopingasolidkrypton˝lmwithaknownconcentrationofrubidiumatomsisrequiredto arriveatamoreprecisemeasurementoftheabsorptionand˛uorescencecrosssectionofmatrix- isolatedrubidium.BeamlinetestsperformedattheReA3facilitydidnotidentifyanyunexpected problems,andshowedpromisingresultsfortheneutralizatione˚ciencyofhighly-ionizedenergetic rubidium.Beforeattemptingacrosssectionnuclearcrosssectionmeasurement,thesensitivityof opticaldetectionneedstoimprovebyseveralordersofmagnitude,thoughmostofthatimprovement appearsfeasible. 113 APPENDICES 114 APPENDIXA ANDORCLARACCDCALIBRATION CalibrationoftheAndorClaracharge-coupleddevice(CCD)involvesdeterminingthephoton- to-countconversionratio,whichisameasureofthenumberofphotonsrequiredtoregistera singlecountonapixeloftheCCDsensor.TheCCDsensorhasdimensionsof8.98x6.71mm, subdividedintoWxH=1392x1040(=1447680)pixels,eachpixelhavingdimensionsof6.45x 6.45 m.Thepixelsaresemiconductorcapacitorswhichconvertincomingphotonstoelectrons whicharethenreadout,ampli˝ed,anddigitizedafteragivenexposuretime.TheClaraCCD haspixelreadoutratesof20MHz(14-bitdigitization)or1MHz(16-bitdigitization),allowing forpixelstotakeavaluebetween 2 14 1 = 16383 or 2 16 1 = 65535 counts.AllCCDs exhibitaconstantbaselinesignalwhichisindependentofexposuretimethatshouldbesubtracted fromagivenimage,hereafterreferredtoasdarkcounts.FortheClaraCCD,thedarkcountis approximately500countsperpixel.Thedarkcountsareasmallerportionofthemaximumpixel valuewhenusinga1MHzpixelreadoutrate(16-bit),allowingforamoresensitivemeasurement. Thedownsideisthatreadoutoftheimagetakessigni˝cantlylonger,roughly1.5secondsat1MHz readoutratecomparedto0.07secondsat20MHz. TheClaraCCDpossessesan'ExtendedIRMode'whichsigni˝cantlyincreasesthesensitivity ofthesensortoinfraredlight,thoughitisonlyusefulforexposuretimeslongerthan10ms.The e˚ciencyoftheAndorClaraCCDcamerahasbeenmeasuredforbothNormalandExtendedIR mode,inthewavelengthragefrom700-1000nmusingtheMSquaredSOLSTiSlaser.Asthe outputofthelaserisfairlyhighpower(4watts),thepowerneedstobeattenuatedsigni˝cantlyto avoidoverexposingthesensitiveCCD.TheinfraredoutputfromtheSOLSTiSwassteppeddown inintensitythroughtheuseofa10xbeam-expander,whoseoutputwasspatially˝lteredwitha 500 mpinhole.FortheExtendedIRmodecalibration,thepowerwasfurtherattenuatedusinga glan-laserpolarizer(ThorlabsGL10-B),beforebeingsteeredintoa10xsecondbeam-expanderand a200 mpinholetofurtherreducetheintensityandtotalpower.Theoutputofthesecondbeam 115 pinholewaselevatedandsteeredontothesensoroftheClaraCCD,whichisencasedinalight-tight boxtoeliminatebackgroundlight.ThissetupispicturedinFigureA.1. FigureA.1:ExperimentalsetupfortheExtendedIRAndorClaraCCDcalibration. Forthiscalibration,theSOLSTiSwastunedbetween700and1000nmmostlyin10nm increments(30total).Aftertuningtoawavelength,thepowerimmediatelybeforetheCCDwas measuredwithacalibratedpower-meter(ThorlabsPM120VA),atthepositionmarkedTinthe diagramabove.Thepower-meteriscapableofcorrectingforitsownwavelengthdependence,and sothecurrentwavelengthwasenteredintothepower-meterbeforeeachpowermeasurement.The laserbeampro˝lewaswellrepresentedbyanAiryDisk[74](patternresultingfromdi˙raction throughthe200micronpinhole),displayedinFigureA.2. Foreachwavelength,theCCDtookakineticacquisitionof20framesoftheincidentbeam spot,withanexposuretimeof300milliseconds,andwiththePreAmpgainsetto 1 inExtended IRmode,and1MHzreadoutrate.FortheNormalmodecalibration,100framesweretakenwith a10msexposuretimeandwiththePreAmpgainsetto 1 : 5 .Laserpowermeasurementswere 116 FigureA.2:SampleimagefromtheCCDcalibrationat750nm,with˝ttoanAirydisk. recordedbeforeandaftereachmeasurement. Themeasuredlaserpowerwasconvertedtoaphotonratevia: R = P hc ; (A.1) where R isthephotonrateinHz,PisthelaserpowerinWatts, isthewavelengthinm, c = 2 : 9979 10 8 m š s isthespeedoflightinm/s,and h = 6 : 626 10 34 J s isthePlanckconstant. Itisassumedthattheentirelaserbeam-spotwascapturedbythepower-meter.Iassumedthe manufacturersuncertaintyforthelaserpowermeasurement(3 % fornm,7 % for 1100nm).Uncertaintyinwavelengthwasnegligible.Thekineticseriesimageswereaveraged intoasingleaverageframeforthedark,background,and30calibrationmeasurements.The averageddarkcountframewassubtractedfromboththebackgroundframeandthe30calibration measurements.The30calibrationmeasurementframesalsohadtheaveragedbackgroundframe subtracted,thoughthebackgroundwasnegligibleforthesemeasurements.Thecountsfromall pixelweresummedtogetatotalnumberofcounts( N CCD ). Thee˚ciencyofthecameraistherefore = N CCD R t exp ; (A.2) where t exp istheCCDexposuretime.TheresultsofbothcalibrationsareplottedinFigureA.3. ThemeasurementsarealsolistedinTableA.1. 117 TableA.1:CCDcountperphotoncalibration. NormalMode,14-bit,1.5xGainExtendedIRMode,16-bit,1xGain (nm) (countsperphoton) (nm) (countsperphoton) 7000.900570.04271 7100.189120.00750 7100.853680.03765 7200.180470.00713 7200.818930.03415 7300.170470.00106 7300.824070.03383 7400.163410.00668 7400.780490.04651 7500.150750.00601 7500.742700.04215 7600.137940.00545 7600.758870.04522 7700.131600.00520 7700.660400.03588 7800.120130.00472 7800.639820.03226 7900.114190.00465 7900.621490.02990 8000.103540.00409 8000.568240.02624 8100.095500.00380 8100.518060.02261 8200.085950.00340 8200.466270.02015 8300.079970.00319 8300.462740.01930 8390.070730.00278 8390.406000.01382 8500.064260.00254 8500.367910.01405 8600.057460.00226 8600.336890.01259 8700.053050.00209 8700.319510.01176 8800.044940.00179 8780.271280.01184 8900.039770.00157 8900.241700.00837 9000.033400.00133 9000.209270.00704 9100.030940.00124 9100.190010.00631 9200.027960.00111 9200.171350.00565 9300.023470.00094 9300.144390.00515 9400.019440.00078 9400.120980.00418 9500.017080.00068 9500.104050.00334 9600.013850.00055 9600.088170.00291 9700.011650.00046 9700.071860.00241 9800.009300.00037 9800.060170.00208 9900.007550.00056 9900.047480.00336 9990.006270.00047 9960.040820.00290 118 FigureA.3:Measuredcountsperphotonasafunctionofwavelengthfordi˙erentClaraCCD settings. 119 APPENDIXB PULSETUBECRYOCOOLERS Theworkingprincipleofmostclosed-cyclecryorefrigerationsystemsissimilartotheStirling cycle.Aworkinggas(typicallyhelium)iscompressedatroomtemperature,wheretheheatof compressionisremoved,andsubsequentlyexpandsandcoolsnearacoldheatexchangerwhere heatisextractedfromwhateverisbeingcooled.FigureB.1graphicallydescribestheidealStirling coolingcycle,whichcanbedividedintofourbasicsteps: 1. Compression: Thecoldpistonbeginsthecycleclosetothelowtemperatureheatexchanger. Thewarmpistoncompressesthegasisothermally,andtheheatofcompressionisexpelledto theexternalenvironmentthroughthehightemperatureheatexchangeratambienttemperature. 2. Transfer: Bothpistonsmovetogethertoisochorically(withconstantvolume)transferthe roomtemperaturecompressedgasthroughtheregenerator,coolingthegastothelowtem- peraturebydepositingheatintheregenerator. FigureB.1:DiagramoftheStirlingCycle.Arrowsindicatepistonmotionandheatexchanger energy˛ow. 120 FigureB.2:Basicpulsetubecryorefrigeratorwithanexternalcompressorsystem.Thegraph illustratesthetemperaturebehaviorofgaspassingthroughtheheatexchangersateitherendofthe pulsetubeduringonepressurecycle. 3. Expansion: Thecoldpistonisretractedtoexpandthegasinthecoldvolume,coolingthe gasandabsorbingheatfromthelowtemperatureheatexchanger.Thisstepremovesheat fromanysamplemountedtothelowtemperatureheatexchanger. 4. ReturnTransfer: Bothpistonsagainmovetogethertoisochoricallytransferthecoldgas throughtheregenerator,whereitreabsorbstheheatdepositedduringstep2.Afterthisstep, thesystemhasreturnedtoitsoriginalcon˝guration. ThecryocoolerinpSAMisoftheGi˙ord-McMahon(GM)pulsetubevariety[75],which hasanori˝ceandareservoirvolumeinsteadofthecoldpistonasinthebasicStirlingsystem. AschematicofasingleGMpulsetubecoolingsystemisdisplayedinFigureB.2.Anexternal compressor(C)providesambienttemperature(T W )compressedheliumattwopressures(P H ,P L ) whichamotorizedrotatingvalve(RV)alternatesbetween,creatinganoscillatingpressureinthe regeneratorandpulsetube.AsthepressurerisestoP H ,theworkinggascoolsbydepositingheatin theregeneratorbefore˛owingthroughthecoldheatexchanger(X C )andenteringthepulsetubeat T C andP H .Whenthevalve(RV)switchestolowpressure(P L ),thegasinthepulsetubeexpands, cools,and˛owsbackthroughX C atT < T C ,extractingenergyfromthesamplebeingcooled. 121 Thereverseprocessoccursatthewarmheatexchanger(X W ),whichisconnectedtoareservoir volume(V R )byanori˝ce(O).Theori˝ceisavalveusedtoregulate˛owintoandoutofV R .At thehighpressurepartofthecycle,gasatthewarmendofthepulsetubecompresses,heats,and ˛owsintoV R throughthewarmheatexchanger(X W )atT W ,whereitdepositstheheatenergydue tocompression.Whenpressureinthetubesubsequentlydrops,gasattemperatureT W ˛owsfrom thereservoirintothepulsetubeuntilequilibriumisachieved.The˛owofgasintoandoutofV R iscrucialtoe˚cientcooling,aswithout˛ow,thecoolingduetoexpansioninthetubewouldbe canceledbythesubsequentcompression. Thepurposeofthepulsetubeistoisolatethetwoprocessesoccurringattheheatexchangers. Gasinthemiddleofthepulsetubeneverleavesthetubesincethe˛owisreversedbeforeitcan traversetheentirelengthofthetube.Thepurposeoftheregeneratoristopre-coolthegasentering thepulsetubeandreheatthegasexitingthepulsetube.Theregeneratorusuallyconsistsofahigh heatcapacitymaterialwithlargesurfaceareatomaximizeheatexchangewiththegas.Thelack ofmovingpartsnearthecoldheatexchangermakespulsetubecryocoolershighlyreliable,have longlifetimes,andresultsingreatlyreducedvibrationatthecoldheatexchanger.Lowvibration FigureB.3:Standardcon˝gurationformoderntwo-stagepulsetubecryocoolers.Figuretaken from[3]. 122 isespeciallyimportantforopticalapplications,wheresamplestabilityiscrucial.ForthepSAM cryocoolersystem,thecompressorisconnectedtothemotorizedrotatingvalvebytwo100ft.long ˛exibleheliumlines,whichserveasthehighandlowpressurevolumesinthecompressorsystem. Themotorizedvalveisisolatedfromthecoldhead(regeneratorandpulsetubes)bya2ft.˛exible heliumline. Contemporarysingle-stagepulsetubecryocoolerscanachievebasetemperaturesnear30K, wheretheyarelimitedbyheatconductionalongtheregenerator.Toreachthesingle-digitbasetem- peraturesnecessarytofreezeNeon,pSAMusesamoreadvancedtwo-stagepulsetubecryocooler. Inthiscon˝gurationtheregeneratorsareinseriesandthepulsetubesareinparallel,asdisplayed inFigureB.3from[3].ThesecondstageheatexchangerforthepSAMcryocooleriscapableof achievingabasetemperatureof2.8Kundernoheatload.AdrawingandpictureofthepSAM coldheadareincludedinFigureB.4andB.5.Amorethoroughdescriptionofmoderncryocooler designanddevelopmentcanbefoundin[76,77,3,78]. 123 FigureB.4:PictureofthepSAMcryocoolercoldhead.Externalreservoirvolumesnotpictured. 124 FigureB.5:DimensioneddrawingofthepSAMcryocooler(CryomechmodelPT415),withremotemotor. 125 APPENDIXC TEMPERATUREPROBECALIBRATIONS TableC.1:pSAMTemperatureSensorCalibrationData. LakeshoreSensorModelLakeshoreSensorModel CX-1050-AA-1.4LCX-1050-CU-HT-1.4L SerialNumberX103297SerialNumberX134596 indexTemperature(K)Resistance( )Temperature(K)Resistance( ) 11.2001239214.81.1995138225.6 21.3014531724.51.2996530841.4 31.3999226474.81.3997125538.2 41.6017619376.01.5997218609.2 51.8041815067.71.8000914413.5 62.0001012310.31.9964311712.5 72.2003710330.42.201659746.46 82.400888876.432.401508352.72 92.599477783.342.598737312.47 102.800346919.272.796976493.96 113.000216233.212.995415841.74 123.200605674.013.198145300.68 133.402465207.053.396564863.22 143.600854821.023.599624487.47 153.801214488.853.799744172.93 163.993404213.273.996123907.02 174.182793975.404.202703663.44 184.533763608.254.589713288.94 194.944293261.714.999232973.78 205.458702921.395.511912663.31 216.180862562.036.235002334.03 227.001122261.007.057402058.36 238.031541984.028.086551804.01 249.061551777.809.125501613.42 2510.09141617.5510.15861466.64 2611.12031488.9911.19131348.73 2712.14101383.9212.21291252.61 2813.15161296.2813.22691172.19 2914.15461221.5714.22521104.24 3015.15241156.8815.21541045.55 3116.13701100.5816.1977994.256 3217.11901050.5517.1724948.751 3318.09781005.6818.1427908.072 3419.0774964.97919.1070871.505 3520.0548928.01220.0794837.787 3621.1348890.72421.1446804.163 3722.7142841.94122.7274759.469 3824.3140798.21124.3316719.454 3925.9307758.83325.9412683.751 4027.5459723.52127.5634651.468 4129.1683691.45029.1927622.167 4230.9802659.09331.0123592.643 126 TableC.2:pSAMTemperatureSensorCalibrationData. LakeshoreSensorModelLakeshoreSensorModel CX-1050-AA-1.4LCX-1050-CU-HT-1.4L SerialNumberX103297SerialNumberX134596 IndexTemperature(K)Resistance( )Temperature(K)Resistance( ) 4333.0928625.19833.1275561.912 4436.0913582.96336.1363523.563 4539.0904546.38039.1473490.353 4642.0924514.28442.1561461.428 4745.0860485.98445.1528435.888 4848.0842460.75648.1527413.159 4950.0821445.36850.1462399.419 5055.0777411.22755.1320368.824 5160.0722382.10660.1248342.742 5265.0623356.96565.1148320.212 5370.0568334.97870.1060300.580 5475.0535315.54975.0924283.259 5580.0447298.32080.0806267.876 5685.0496282.82685.0833254.075 5790.0475268.88190.0775241.622 5895.0448256.23195.0758230.358 59100.044244.702100.072220.100 60110.039224.459110.059202.063 61120.035207.222120.057186.701 62130.038192.360130.062173.486 63140.039179.429140.061161.979 64150.036168.074150.056151.893 65160.030158.021160.052142.949 66170.023149.085170.048134.984 67180.016141.076180.038127.854 68190.023133.852190.043121.422 69200.026127.329200.048115.603 70210.027121.415210.047110.319 71220.020116.019220.036105.507 72230.024111.086230.044101.105 73240.031106.568240.04297.0637 74250.022102.415250.03293.3474 75260.03498.5810260.04589.9072 76270.03295.0404270.03986.7346 77280.04391.7438280.04683.7939 78290.03588.6792290.04081.0603 79300.05285.8434300.04078.5092 80310.03883.2023310.01576.1460 81315.04981.9444315.02475.0136 82320.05780.7260320.02473.9221 83326.05879.3161326.01272.6612 84330.07378.4051330.02171.8414 127 APPENDIXD LINEARSHIFTMECHANISM(LSM)COMMANDS TableD.1:CommonlyusedLSMcommands.RefertoMcLennanPM1000MotionController manualformoreinformation.The'1'beginningeachcommandreferstotheaxisofmotion,of whichthereisonlyoneinthecaseofpSAM,butcouldbehigherifmultiplelinearmotion mechanismsareeverimplemented. CommandDescription 1qaQueryall.Returnsallofthecurrentsettingsandmodesofthecontrolleralongwiththecurrentpositions inasinglepageformat. 1qsQueryspeeds.Querythecurrentsettingsforthespeedsandaccelerations. 1qpQueryposition.Querythecurrentpositioninformation.ReturnsvaluesforCommandPosition(CP, steps),ActualPosition(AP, m),InputPosition(IP),AuxiliaryPosition(TP),andDatumPosition(OD, steps).CPisthesteppermotorposition,andAPisthepositionreadbythelinearencoder.IP,TP,are reservedforadditionallinearencodersandarenotused.ODisareferencepositionandisnotused. 1maMoveabsolute.Movethemotortothepositiongivenintheargument.Thepositionisrelativetothe CommandPositionofzero. 1mrMoverelative.MovethemotortothepositiongivenintheargumentrelativetothecurrentCommand Position. 1svSetvelocity.SetstheSlew(maximum)velocityforallfollowingmoves(steps/second,rangefrom1to 1,200,000.15,000typical.) 1abCommandabort.Sendingwillabortthecurrentmotion.Motioncontrolwillbedisabledaftercommand abortuntilresetwiththeRScommand. 1rsCommandReset.Resetsanabortcondition,enablingmotioncontrol. 128 BIBLIOGRAPHY 129 BIBLIOGRAPHY [1] JackEkin. 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