In this chapter we deal with the experimental arrangement as a whole There are general aspects to consider in settingup an xray experiment The sample is illuminated by an incident beam striking the sample surface under a de64257nite angle of inciden ID: 27736
Download Pdf The PPT/PDF document "Diractometers and Reectometers In the pr..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
2DiractometersandReectometersInthepreviouschapterwedescribedthebasicelementsofx-rayequipment,namely,x-raysources,opticalelementstodenethebeampassandaproperbandpassofenergy,andvariousrecordingunitstodetectthex-rays.Inthischapterwedealwiththeexperimentalarrangementasawhole.Thereare 322DiractometersandReectometersonehastocompromisebetweenthedegreeofresolutionandthetimenec-essaryformeasurement.Inthischapterwewillshowthathighresolutionisnotrequiredingeneral.Sampleswithmosaicspread,heterostructureswithalargelatticemismatchorepilayerswithathicknessofafew100nmcanbeinvestigatedunderslightlyrelaxedconditionsofresolutionwithoutlossof2.1X-RayReectometersX-rayspecularreectometryisusedtomeasurethethicknessofindividualthinlayers,theverticalspacingofamultilayerstacking,thesurfaceandinterfaceroughnesses,andtheaveragedensityofalayeredsystem.AccordingtothelawofFresnelreectivity(Sects.5.2and6.4),theintensityleavingasmoothsurfacedecreasesveryrapidlyastheangleofincidenceincreases.Torecordthereectedintensityovermorethan6ordersofmagnitudeoneneedsahighlyintensiveincidentbeamand/oradetectorwithlownoise.Theapparativerequirementsshouldbedemonstratedbythefollowingexamples.Incaseoflayeredsamplesthelayerthicknessisdeterminedfromtheangulardistancebetweenthethicknessoscillations(Kiessigmaxima,seeSect.8.1).Therequiredangularresolutiondependsonthetotalthicknessoflm.Filmthicknessesofabout50nmprovideanangulardistancebetweenKiessigmaximaofabout0.1.Suchalmcanbeinvestigatedusingthe-doubletofasealedtubecollimatedbytwospatiallyseparatedlocatedslitsbeforethesampleandandanadditionalslitplacedbeforethedetector. Fig.2.1.Generalsetupofahigh-resolutionx-rayreectometer. 2.1X-RayReectometers33Theprecisedeterminationofthecriticalangleoftotalexternalreection,,whichisnecessaryforelectrondensityanalysis,demandsamuchbetterangularresolution.Oftenitissucienttomatchapproximatelywiththeangularpositionofhalf-intensitycomparedwiththeprimarybeam(Sect.8.1).Theaveragedensityisobtainedwithanaccuracyof5%ifismeasuredtoanaccuracyof2.3%.ItrequirespreciseangleadjustmentontheorderofItfollowsfromthesepreviousestimatesthatareectivityexperimentneedshighuxatthesamplesite,moderateangularresolutioninmostcases,butaccurateangleadjustmentbetweensampleanddetectorcircle.Athome-laboratoriesanangle-dispersivereectometer(Fig.2.1)shouldconsistofthesourceattachedtoaphoton-collectingsystemasG¨obel-mirror(completedbybeamcompressor),horizontalandverticalslitstodenethebeamsize,andadetectorwithalargedynamicalrange.Theslitscanbeinsertedeitherbeforeorafterthesample.Theangularresolutionoftheexperimentisadditionallycontrolledbyaknife-edgeattachedclosetothecenterofgoniometer.Boththesamplecircle,denotedby,andthedetectorcircle,2,movewithanaccuracyofThespecularreectivityisrecordedbyrunninganscan,wherecorrespondstothetrueangleofincidenceand2istheangularpositionofthedetectormeasuredwithrespecttotheincidentbeamdirection.Bothandtheexitanglearemovingsimultaneouslybythesameamount.Withso-calledreectometers,wherethesamplestaysxed,varydirectlyinsteadofand2whichisthecasewithatequipment,wherethex-raytubeisxed.ThepropertiesofthescanandotherswithdierentangularratioswillbedescribedinSect.3.2inThefunctionoftheknife-edge,showninFig.2.1,canbeexplainedasfollows.Forgeometricalandintensityreasons,bothcannotbereducedtoomuch.Becausetheincidentbeamdivergenceandthedetectoracceptancearelarge,theirradiatedsampleareamustbereducedtoachievesucientangularresolution.Thisisachievedbysinkingtheknife-edgeveryclosetotheaxisofgoniometerrotation,whichadditionallyhelpstobringthesamplesurfacetotherotationcenter(seebelow).Undertheseconditions,onlythosepartsofthebeamreachthedetector,whichareescapingthesamplestraightbeneaththeknife-edge.Theextremelimitationofthescatteringareareducesthedetectableintensitybyseveralordersofmagnitude.Thisdisadvantagecanbecompensatedforbyinsertionofaphotoncollectorinfrontofthesample(seeFig1.9).AnalternativesetupisshowninFig.2.2.TherstG¨obel-mirrorissuf-cienttosuppresstheline.Highresolutionstillcanbeachievedbyre-placingthebeamcompressorinFig.2.1byaBartelsmonochromator(Sect.1.2andFig.1.8).Relaxedresolutionbuthigheruxisachievedbyremov-ingthebeamcompressorbutsettingasecondG¨obelmirrorinfrontofthe 342DiractometersandReectometers Fig.2.2.Schemeofapowderdiractometerappliedforx-rayreectometrywithrelaxedangularresolution.detector.Thegainofdetectedintensityisduetothefactthatthesecondobelmirrorincreasesthebeamcrosssection.Specularlyandnon-specularlyscatteringphotonsaredeectedtowardthecenterofapointdetector.Thisset-upcorrespondstothatofapowderdiractometer[167].Atsynchrotronfacilitiestheincidentbeamisparallelenough.Thereec-tometerhastobeequippedverticallyinordertomakeuseoftheextremecollimationoftheincidentbeaminthisdirection(seeSect1.1).Forangulardispersiveexperimentsonehastoinsertanopticalelementformonochro-mazingtheincidentx-rayspectrum.Thiscanbedoneeitherbeforeorafterthesample.Acompletelydierentarrangementisnecessarytoperformanenergy-dispersiveexperiment(Fig.2.3)[57].Herethewhitebeamstrikesthesamplesurfaceunderaxedandthereectedbeamisrecordedbyanenergy dispersivedetectorataxedangle2.Inthiscasetheonlyrequirementisanapproximatelyparallelincidentbeamprovidedatasynchrotronfacilitywithoutopticalelementsexceptslits.Inahomelabo-ratoryasucientlyparallelbeamispreparedbypassingthebeamthroughtwoslitsxedatbothendsofanabout1-meter-longtube,whichshouldbeevacuatedtoreduceairscatteringandabsorptionbyair.Onlylowairabsorbancesuppliesthewholewhitespectrumofanx-raytube[238].Theresolutionofanenergy-dispersivescatteringexperimentisdeterminedbytheenergyresolutionofthedetector.Itamountsto(E/E2.5%),whichissucientforthinlmanalysis.Theadvantageofthisset-upisthepossibilitytorecordtime-dependentprocesses.Thescatteringspectrumalwaysisavail-ableandcanbecontrolleddirectlybytheuser.Theappearanceofintenselinesintheincidentspectrumofasealedtube,theenergydependenceof 2.1X-RayReectometers35sampleabsorbance,andthedetectorresponse(seeSect.1.3)makeitdiculttointerpretthespectrumquantitatively.ForquantitativeanalysisonehastoremovetheKandKlinesfromthebremsstrahlungspectrumaswellasseveraluorescencelinesexcitedintheequipmentbytheincidentphotons.Thereforetheenergy-dispersiveset-upisrecommendedformeasurementsonarelativescale,thanforabsolutemeasurements.However,usinglaboratorysourcesandchoosing,about5minutessucedtocollectaspectrumofanorganicmultilayersamplewithsatisfyingcountingstatistics[229]. BESSYII 30m Air2m Slits0.1x1mm2 GID Fig.2.3.Setupoftheenergy-dispersivereectometerinstalledattheEDRbeam-lineatBESSYII.Itisequippedtomeasuresimultaneouslythereectivityandgrazing-incidencediractionofasample.AttheEDRbeamlineofBESSYIIthesamesamplewasmeasuredinabout10secondswithmuchbetterstatistics[57].Hereenergy-dispersivereectometryisveryecientforrapidsampleanalysisandevenforroutinemeasurements.Samplealignmentisacrucialproblemforaccuratereectivitymeasure-ments.Inparticular,themainerrorofdensitydeterminationviameasure-mentofthecriticalangleoftotalexternalreectionistheinaccuratesamplealignment.Alsoatruespecularscancanberecordedonlywhen2isex-actlytwice.Theprocedureofalignmentissameforanangle-andenergy-dispersiveset-upandwillbeexplainedinthefollowing.Inordertomeasuretheanglescorrectly,therotationalaxisofthesamplecircle(-circle)hastobealignedexactlywiththesamplesurface(Fig.2.4).Additionally,onehastomakesurethatthepositionoftherotationaxesofbothcirclescoincideswiththecenteroftheincidentbeam;thatmeansthatthesamplehastoshadowhalfoftheincidentbeam.Withcommercial 362DiractometersandReectometers X-raysource Fig.2.4.Proceduretoalignthesamplesurfacenormalwiththerotationaxisofthereectometer.Thisprocedureisgeneralforalltypesofreectometersanddiractometersitisaguaranteethattherotationaxesofsampleanddetectorcoincide.However,theproceduretoadjustthesamplesurfaceconsistsofaniterativemovementandrockingofthesampleacrosstheincidentbeam(scan).Bothscanshavetorepeatuntilthepeakintensityofthe scanishalfoftheintensityoftheincidentbeam,measuredwithoutsample.Inthiscase-axisliesexactlyinthesamplesurfaceandthissurfaceisparalleltotheincident-beamdirection.Afterthisadjustmenttheangularpositionofthesample,however,maynotcoincidewiththezeromarkofthe-circle.Thismightbecausedbysurfacedamageorbyamiscutofthesurfacewithrespecttothebottomplaneofthesample.AdditionaltestsarenecessarytoredenetheTodothiswithsucientaccuracyonehastochooseanincidenceangleintherange0andndtheangularpositionofspecularlyreectedbeamatanangle2.If2doesnotcoincidewith2,thezeropointofthe-circleneedstobere-scaledby(2).Repetitionoftheprocedureatvariousvaluesofimprovestheprecisionofsamplealignment.ThereectivityexperimentsshouldbeoptimizedinsuchawaythatthespecularreectivitycanbemeasuredoverawiderangeofThisisnecessarytoshowtypicalfeaturesasBraggpeaksandKiessigfringescharacterizingthesample.DuetothedependenceofFresnelreectivitytheintensitydropsover6to8ordersofmagnitude.Sometimesitishelpfultorecordpartsofasinglereectivitycurveatdierentconditionsofangularresolutionandcountingtime.Sotheangularrangeclosetocanbedetectedwiththehighestresolutionavailable,butthewideanglerangeshouldberecordedusingarelaxedresolution.Underhomelaboratoryconditionsoneneedstochangetheangularresolution,i.e.,toincreaseordecreaseWhensynchrotronradiationisused,separatedetectionofthelow-angleandwide-anglerangeisnecessaryduetothelimitationofdetectorsensitivity. 2.2High-ResolutionDiractometer372.2High-ResolutionDiractometerInthesemiconductorindustry,inparticular,thenecessitytoanalyzeepitaxi-allygrownhighlyperfectmultilayermaterialsencouragedthedevelopmentofnewtypesofdiractometers.Theyarewelladaptedtomeasurelayerthick-ness,latticemismatchesandlatticestrainsofheterostructures.Theinvestiga-tionofquantumwellstructures,i.e.,thinlayerswiththicknessesoflessthan10nmembeddedwithinmuchthickercladdinglayers,requiresmeasurementofrockingcurvesoverawideangularrangeleftandrightwithrespecttotheBraggpeakofthesubstrate.Themethodofreciprocal-spacemappingmakesitnecessarytohavegoodresolutionintwodirectionsofreciprocalspace.Allthisrequiresahighlyintensebutparallelincidentbeamandalowback-groundassociatedwithagoodaspossibleangularresolution.Theseneedsshouldbesatisedbyahigh-resolutionset-upatasynchrotronbeamline.Unfortunately,duetothelimitedaccess,suchexperimentalstationscannotbeusedforroutinecharacterization.Thus,mostofmeasurementshavetobeperformedathomelaboratories.Modernhigh-resolutiondiractometersareequippedwithafour-bouncemonochromator(Fig.2.5).Theintensityofthex-raytubeisincreasedbyattachingaG¨obelmirror.Maximumresolulution,thatisnecessaryforreciprocal-spacemapping,isachievedbyuseofachannel-cutanalyzerbeforethedetector.Asforreectometers,thediractometermakesmotor-controlledangularstepsonbothsampleanddetectorcircle.Theequipmentissuitedtorecordreciprocal-spacemapsinthevicinityofapar-ticularBraggpeakofthesampleinseveralhours. Fig.2.5.High-resolutiondiractometer. 382DiractometersandReectometersTheequipmentshowninFig.2.5shouldbesimpliedifthesampleisnothighlyperfect.InthiscasetheBartelsmonochromatorcanbereplacedbyasingle-ordouble-crystalarrangement.Theanalyzercrystalmaybereplacedbyaslitsystemforsimplerockingcurveanalysis.TheachievableangularandenergyresolutioncanbeestimatedusingtheDuMonddiagramsshowninSect.1.2.Using(+)set-up,thedispersionenlargementofeachpeakoftherockingcurvesfollowsfromEq.(1.10)identifyingbytheangulardevia-tionfromthediractionmaximumofthemonochromatorandofsample,respectively.Thebroadeningofthediractioncurvecanreachseveralhundredsecondsofarcifthemonochromator/analyzerandsampleBragganglesdier.Inastrictsense,highresolutionisachievedonlyifmonochro-mator,sample,andanalyzeraremadefromsamematerialandscatteratexactlythesameBraggangles.Theuseofafour-bouncemonochromatorovercomesthisproblem.AsdemonstratedinSect.1.2,itcombinesthe+and++set-upandallowsonetomeasurealwaystheintrinsicrockingcurveofsample.Becausetheapparativebroadeningisverysmall,thetheexploitableintensityissmallcomparedwiththeusageofadouble-crystalarrangement. absorber- mator if Fig.2.6.Generalset-upofahigh-resolutiondiractometerequippedatabeamlineofastorageringfacility.Allpartsoftheequipmenthavetobemechanicallystableonatimescaleofseveralhoursordayssothatreciprocal-spacemapscanberecordedunderconstantconditions(seeSect.3.2).Reciprocal-spacemapsareobtained-scansfordierent2orrunning(scansfordierento-setanglesandplottingtherecordedintensitiesina2Dframe.Torunaparticularscanacrossthereciprocalspace,thesampleandthedetectorcircleshavetomoveinanarbitraryratiowhichdiersfrom1:2.Thesescansmustbesupportedbythediractometersoftware.Infact,com-putersoftwareisanessentialcomponentofmoderndiractometers.Fast 2.3LimitsoftheUseofPowderDiractometers39accesstoacodeofrockingcurvesimulationenablesinterpretationoftheexperimentalcurvesstraightafterthemeasurementandinteractiveaction.However,theuserhastomakesurebeforehandthatthebasicassumptionsofthesimulationsoftwareagreeswiththoseoftheactualexperiment.Finallyweproposeanoptimumarrangementforhigh-resolutiondirac-tionwhichcanbeinstalledatabeamlineatasynchrotronradiationfacility.Aschematicset-upisshowning.2.6.Becausethedemandforintensityisnotashigh(about8ordersofmagnititudearesucient)thehighphotonuxdeliveredbyanundulatorcanbeusedtodesignasetupwithverygoodangularresolution.Aheavyweightgoniometercanhelptoguaranteerepro-duciblestepsoflessthan0.Thesmalldivergenceofthesynchrotronradiationinverticaldirectionshouldnotbeenlargedbybentmirrors.Planemonochromatorcrystalsperformedbyadouble-crystalarrangementsupplyanenergybandpasswitharesolutionontheorderof10.Acollimationlinedenedbytwopairsofslits,aguidingslitpairstraightafterthemonochro-matorandadeningslitpairclosebeforethesample,reducethedivergenceoftheincidentbeam.Supposingasourceheightof100mandalengthofthebeamlineof20m,theslitheightof1mmprovidesadivergenceoflessthanonesecondofarc,whichismuchsmallerthantheintrinsichalf-widthofthesiliconmonochromatorcrystal(seeFig.1.5).Despitetheseconstrainstheuxatthesamplesitewillexceed10photons/secifwechooseatypi-calundulatorbeamlineofESRF.Finallyaplanemonochromatorshouldbeattachedclosebeforethepointdetectortoguaranteehigh-resolutionoftheexitangle,aswell.2.3LimitsoftheUseofPowderDiractometersSeveralproblemsofx-raycharacterizationcanbesolvedbyusinglow-resolutiondiractometers,i.e.,apowderdiractometer.Ifthelayeredmate-rialisdamaged,theBraggpeaksbecomebroadandlowinintensity.FollowingEq.(1.8),thedivergenceoftheincidentbeamshouldnotbemuchsmallerthantheangularwidthofthediractioncurveofthesampleunderinvestiga-tion.Inthecaseofpoly-crystallinematerialormaterialwithamosaicspreadtheintrinsiccurvewidthmayincreasetoseveralminutesofarc.Herefocusingbeamarrangementsarepreferred.Abentcrystal-monochromatororanalyzerinfrontofthesampleorthedetector,respectively,providesincreasedinten-sityandarelaxedangularresolution.AdisadvantageofthisarrangementisthesimultaneousappearanceoftheKdoubletintherockingcurve,whichhastobetakenintoaccountforthesimulationofthediractioncurves.Figure2.7showsthe(422)diractioncurvesofapartiallyrelaxed40pe-riodInAs/GaAsmultilayerrecorded,rst,withagraphite-analyzer-equippedpowderdiractometer,similartothatshowninFig.2.2and,second,underhigh-resolutionconditions(seeFig.2.5)usingafour-bouncemonochro-matorwithoutG¨obelmirror.Thetimetakentorecordthehigh-resolution 402DiractometersandReectometers33,033,5 highresolutionlowresolutionintensity[a.u.] Fig.2.7.RockingcurveofanInAs/GaAsmultilayerrecordedwithapow-derdiractometer,similartothatshowninFig.2.2,andwithhigh-resolutioncon-ditions,usingafour-bouncemonochromator.curvewasaboutvetimeslongerthanthatforthepowderdiractometer.ThemaindierencebetweenbothcurvesistheappearanceoftheKatthepowdercurve.Exceptintheregionclosetothesubstratepeak,thesu-perlatticepeaksareclearlyvisible.Here,theyaresmearedoutbecauseofthelowerangularresolutioncomparedwiththehigh-resolutioncurve.Becausethemeasuredangularwidthofsuperlatticepeaksisdeterminedbythemo-saicity,thestructureparametersofthemultilayersamplecanbeestimatedonthebasisofthispowdercurve[290].2.4Grazing-IncidenceDiractionAschematicillustrationoftheset-upofagrazing-incidencediraction(GID)experimentisshowninFig.2.8[89,281].Hereonehastodistinguishbetweenplaneofincidencecontainingandthesurfacenormalandthescatteringplanelyingapproximatelyperpendiculartotheplaneofincidenceandcontainingtheangles.Thelatteronesaremeasuredwithrespecttothediractinglatticeplane.Themethoduniesin-planeBraggdiractionandout-of-planereectivitycombinedwiththefeasibilityfordepthresolu-Theexperimentalset-upisthefollowing:amonochromaticandparallelx-raybeamasdenedinFig.2.6strikesthesamplesurfaceatanangle 2.4Grazing-IncidenceDiraction41 latticeplane Fig.2.8.Schematicset-upofagrazing-incidencediractionexperiment.tothecriticalangle.ThesampleisrotatedaroundthesurfacenormallyuntilaparticularlatticeplanelyingperpendiculartothesurfacefulllstheBraggconditionunderanin-planeBraggangle2(seeSect.3.3).Owingtorefractionoftheincomingbeamattheair sampleinterfacethepenetrationdepthoftheprobingx-raycanbecontrolledbychoosingbesmallerorlargerthan(Fig.2.9).Intherstcasetheincomingbeambecomesevanescentandpropagatesparalleltoandclosebelowthesurface.Theminimumpenetrationdepthisontheorderof4 10nm,dependingonthedensityofmaterial.Onincreasing,thepenetrationdepthwithinthesampleincreasesuptoabout400 600nm.TheGIDgeometryrequirescollimationinbothdirections,perpendicularandparalleltotheplaneofincidence.Ingeneral,aset-uplikethatshowninFig.2.6canbeusedbutwithadditionaleortstogainthein-planeres-olution.Infact,oneneedsasecondmonochromatorinstalledperpendiculartotherstone;thisreducesthephotonuxatthesamplesiteagain.Forpracticalreasonsthedivergencewithrespecttoshouldbeoneorderofmagnitudesmallerthanthatwithrespectto2.Ontheotherhand,amoderatedivergenceregarding2isnecessarytoexcitethecrystaltrun-cationrod(CTR)(seeSect.3.2).Theintensitydistributionalongthecrystaltruncationrodcanberecordedsimultaneouslyasafunctionofusingaposition-sensitivedetector(Sect.1.3).Themeasurementofreciprocal-spacemapsrequirestheinsertionofananalyzercrystal.Becausethereectivityofthetruncationrodisontheorderof10,theintensityofasealedtubeisnotenoughtorecordin planescatteringcurves.Theintensityofarotational- 422DiractometersandReectometers0,00,20,40,60,81,01,21,4 =0.1°=0.34° =0.5°penetrationdepth[nm]]Fig.2.9.TheeectivepenetrationdepthbelowaGaAssurfaceforaGIDexperi-ment,calculatedfordierentincidenceanglesandexitangleanodeissucientforthedetectionofin-planerockingcurvesintegratedoverthewholerange,i.e.,withawideopendetectorwindow.Themeasurement-resolvedcurveswithgoodangularresolutionisonlypossiblewithuseofsynchrotronradiation.integratedmeasurementcanalsobeperformedusingtheenergy-dispersivearrangementshowninFig.2.3.