RHEED

ReflectionHighEnergyElectronDiffractionWei-LiChen11/15/2007RHEED•ReflectionHighEnergyElectronDiffraction,RHEED,isanimportantrealtimeanalyticaltooltomonitorgrowthfrontcondition.•Thesmallincidentanglemakesitsensitivetothestructureoftopmonolayers.SubstratethermalcleaningmonitoringControllinginitialgrowthstageMonitoringsurfacestructureandgrowthdynamicsGrowthratemeasurementBravaisLattice•ABravaislatticeisaninfinitearraysofdiscretepointswithanarrangementandorientationthatappearsexactlythesame,fromwhicheverofthepointsthearrayisviewed.•ABravaislatticeconsistsofallpointswithpositionvectorsRoftheformintegers.aresandplane,sameintheallnotvectorsantthreeare,,where321332211inaaaanananRCrystalStructure•Theatomgroup,whichbuildscompletecrystalstructurebytranslationaloperationsiscalledcrystallographicunitcell•Crystalstructure=Lattice+BasisInGeneral:a≠b≠candα≠ß≠γ[010][100][001][010][110][111][110]­a­yaxy[111][111][111][111][111][111][111][111]Familyof111directionscxycbbaaOUnitCellGeometryzabczxyyoxoPzo[121]UnitcellFig.1.39FromPrinciplesofElectronicMaterialsandDevices,SecondEdition,S.O.Kasap(©McGraw-Hill,2002)(a)Aparallelepipedischosentodescribegeometryofaunitcell.Welinethex,yandzaxeswiththeedgesoftheparallelepipedtakinglower-leftrearcornerastheorigin(b)Identificationofadirectioninacrystal(c)DirectionsincubiccrystalsystemLatticeBasisCrystalUnitcellUnitcellaa(a)(b)(c)90xyBasisplacementinunitcell(0,0)(1/2,1/2)(d)Fig.1.70:(a)Asimplesquarelattice.Theunitcellisasquarewithasidea.(b)Basishastwoatoms.(c)Crystal=Lattice+Basis.Theunitcellisasimplesquarewithtwoatoms.(d)Placementofbasisatomsinthecrystalunitcell.FromPrinciplesofElectronicMaterialsandDevices,SecondEdition,S.O.Kasap(©McGraw-Hill,2002)(unitcellgeometries)andfourteenBravaislattices.CUBICSYSTEMa=b=c90°Manymetals,Al,Cu,Fe,Pb.Manyceramicsandsemiconductors,NaCl,CsCl,LiF,Si,GaAsTETRAGONALSYSTEMa=b­c===90°In,Sn,BariumTitanate,TiO2ORTHORHOMBICSYSTEMa­b­c===90°S,U,Pl,Ga(30°C),Iodine,Cementite(Fe3C),SodiumSulfateHEXAGONALSYSTEMa=b­c==90°;=120°Cadmium,Magnesium,Zinc,GraphiteRHOMBOHEDRALSYSTEMa=b=c==­90°Arsenic,Boron,Bismuth,Antimony,Mercury(­39°C)TRICLINICSYSTEMa­b­c­­­90°PotassiumdicromateMONOCLINICSYSTEMa­b­c==90°;­90°Selenium,PhosphorusLithiumSulfateTinFluorideFromPrinciplesofElectronicMaterialsandDevices,SecondEdition,S.O.Kasap(©McGraw-Hill,2002)3212133211323213212;2;2:spacereciprocaltheofvectorsprimitivethreeThe1lattice.reciprocalitsasknownislatticeBravaisgivenaofyperiodicitwiththewavesplaneyieldthatvectorswaveallofsetTheaaaaaπbaaaaaπbaaaaaπbeeeKRKirKiRrKiMillerIndicesPlaneVectorinBravaislatticeCrystalsymmetryequivalentplanesetsCrystalsymmetryequivalentvectorsetslkhlkhlkhlkh3213211:1:1::scoordinatethreeofintersecsplaneare,,xxxlkhxxxlkhlkhvectorreciprocalplaneFromPrinciplesofElectronicMaterialsandDevices,SecondEdition,S.O.Kasap(©McGraw-Hill,2002)(hk):11/2111(210)zinterceptatabcxyxinterceptata/2yinterceptatbUnitcellz(a)Identificationofaplaneinacrystal(111)­zyxzx(110)z­yyyz(010)(010)(010)(010)x(100)(001)(110)(010)xzy(111)(b)VariousplanesinthecubiclatticeFig.1.40:LabellingofcrystalplanesandtypicalexamplesinthecubiclatticeBragg’sandvonLaue’sFormulabooksKittel'inasrepresentisoflengththehalfbemustvectorlatticereciprocalthealongvectoraveincidentwtheofcomponentThe21ˆely,Alternativspace.reciprocalinvectorlatticeais1vectorlatticereciprocaltheofkdefinitiontheRecall1or2'vectorlatticetheis2'ˆˆ'ˆˆ'coscosn2dsinconditionBraggGKKKkKKkKkkK'k-keemkkRRmkkdmnndddRKiR'k-kiTheEdwaldConstructionGkTheGeometryofRHEED•ThegeometryofRHEEDisquitesimple,Fig.1.Anacceleratedelectronbeam(5–100keV)isincidentonthesurfacewithaglancingangle(3deg)andisreflected.Thehighenergyoftheelectronswouldresultinhighpenetrationdepth.However,becauseoftheglancingangleofincidence,afewatomiclayersareonlyprobed.ThisisthereasonofthehighsurfacesensitivityofRHEED.Uponreflection,electronsdiffract,formingadiffractionpatternthatdependsonthestructureandthemorphologyoftheprobedsurface.o3ansmallerthusuallyspace.reciprocaltheinntdisplacemediscretewithmatcheskwheredirectionatthehappensceinterferenveConstructispace.crystalrealtheofansformfouriertraisThisvectors.aveincidentwanddiffractedareandectorpositionvtheis])(exp[)(2)(scatteringofamplitudeThe20iViekkrrdrkkirhemsfcbabaccbaacbcbacbah,k,lwhereclbkahG2,2,2andintegersarek-kkonconstructisEdwald'i“MolecularBeamEpitaxy“editedbyR.F.C.FarrowFourierTransformKGskkssdrsisfrrdrsirsfsin4si