Reflection high-energy electron diffraction

366 Pages·2004·6.693 MB·English

by  Ichimiya A., Cohen P.I.

REFLECTION HIGH-ENERGY ELECTRON DIFFRACTION
Reflection high-energy electron diffraction (RHEED) is the analytical tool of choice for
characterizingthinfilmsduringgrowthbymolecularbeamepitaxy,sinceitisverysensitive
to surface structure and morphology. However, there has been a need for a book which
explainshowtoanalyzeRHEEDpatterns.
ThisbookservesasanintroductiontoRHEEDforbeginnersanddescribesdetailedex-
perimentalandtheoreticaltreatmentsforexperts.Firsttheprinciplesofelectrondiffraction
andmanyexamplesoftheinterpretationofRHEEDpatternsaredescribedforbeginners.
The second part contains detailed descriptions of RHEED theory. The third part applies
RHEED to the determination of surface structures, gives detailed descriptions of the ef-
fects of disorder and critically reviews the mechanisms contributing to RHEED intensity
oscillations.
Thisunifiedandcoherentaccountwillappealtobothgraduatestudentsandresearchers
inthestudyofmolecularbeamepitaxialgrowth.
Ayahiko Ichimiya isProfessorintheDepartmentofQuantumEngineering,Nagoya
University.Hisspecificareasofresearchinterestarereflectionhigh-eneryelectrondiffrac-
tion,crystalgrowth,surfacecharacterization,positrondiffractionandscanningtunneling
microscopy.
Philip I. Cohen isProfessorintheDepartmentofElectricalandComputerEngineer-
ing,UniversityofMinnesota.Hisresearchinterestsaremainlyinmolecularbeamepitaxy,
electrondiffraction,light-assistedfilmgrowthandion-assistedfilmgrowth.

REFLECTION HIGH-ENERGY
ELECTRON DIFFRACTION
AYAHIKO ICHIMIYA AND PHILIP I. COHEN
publishedbythepresssyndicateoftheuniversityofcambridge
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(cid:1)C CambridgeUniversityPress2004
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noreproductionofanypartmaytakeplacewithout
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Firstpublished2004
PrintedintheUnitedKingdomattheUniversityPress,Cambridge
TypefaceTimes10/13pt. SystemLATEX2ε [tb]
AcatalogrecordforthisbookisavailablefromtheBritishLibrary
LibraryofCongressCataloginginPublicationdata
Ichimiya,Ayahiko,1940–
Reflectionhigh-energyelectrondiffraction/AyahikoIchimiyaandPhilipI.Cohen.
p. cm.
Includesbibliographicalreferencesandindex.
ISBN0521453739
1.Reflectionhighenergyelectrondiffraction. 2.Thinfilms–Surfaces–Analysis.
I.Cohen,PhilipI. II.Title.
QC176.84.S931242004
530.4(cid:2)275–dc22 2004045180
ISBN0521453739hardback
ThepublisherhasuseditsbestendeavorstoensurethattheURLsforexternalwebsitesreferredtointhisbook
arecorrectandactiveatthetimeofgoingtopress.However,thepublisherhasnoresponsibilityforthewebsites
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Toourfamilies,especiallyourwives,AoiandMary.

Contents
Preface pagexi
1 Introduction 1
2 Historicalsurvey 3
2.1 Earlyexperiments 3
2.2 Molecularbeamepitaxy 4
2.3 Surfacestudies 7
2.4 Theoriesofsurface-structuredetermination 10
3 Instrumentation 12
3.1 Introduction 12
3.2 Designofapparatus 13
3.3 Electrongundesign 16
3.4 Energyfiltering 17
4 Wavepropertiesofelectrons 19
4.1 Introduction 19
4.2 Wavelengthandwavevector 19
4.3 Tangentialcontinuityofthewavevector:refraction 20
4.4 Plane-waveboundaryconditions 23
4.5 Absorptionoftheelectronbeam 25
5 Thediffractionconditions 28
5.1 Crystallattices 28
5.2 Keyideaofthediffraction 29
5.3 Millerindicesandreciprocallattices 31
5.4 Surfacelattices 33
5.5 TheEwaldconstruction 37
5.6 ThezerothLauezone:diffractionfromrows 40
5.7 Latticewithabasis 41
6 Geometricalfeaturesofthepattern 43
6.1 Finitetwo-dimensionalsheet:RHEEDstreaks 43
6.2 Incoherentscattering 45
vii
viii Contents
6.3 Latticeparameter 46
6.4 Vicinalsurfaces 49
6.5 Preferredislandsize 58
7 Kikuchiandresonancepatterns 62
7.1 Kikuchilines 62
7.2 Surface-waveresonances(Kikuchienvelopes) 66
8 Realdiffractionpatterns 77
8.1 Perfectlow-indexsurfaces 77
8.2 Streakpatterns 84
8.3 Orderedislands 88
8.4 Transmissionpatterns 89
8.5 Rotationallydisorderedsurfaces 97
8.6 Pseudo-one-dimensionalcrystals 103
8.7 Theroleoftheinstrument 107
9 Electronscatteringbyatoms 113
9.1 Introduction 113
9.2 Elasticscattering:adiabaticapproximation 113
9.3 Elasticscattering:Bornapproximation 114
9.4 Inelasticscatteringbyatoms 122
10 Kinematicelectrondiffraction 130
10.1 Introduction 130
10.2 Bornapproximation 131
10.3 Theeffectoftemperature 148
10.4 Kinematicpredictions 150
10.5 Crystalstructurefactorofathree-dimensionalperiodiclattice 151
11 Fouriercomponentsofthecrystalpotential 154
11.1 Introduction 154
11.2 Doyle–Turnerparametrization 154
11.3 Effectofthermalvibrations 156
11.4 Scatteringfactorsforionicmaterials 159
12 Dynamicaltheory–transfermatrixmethod 161
12.1 PlanofChapters12–14 161
12.2 Introduction 161
12.3 Generaltheory 162
12.4 Thetransfermatrix 163
12.5 Thetransfermatrixforasingleslice 165
12.6 Multi-slicemethod 168
12.7 Therecursion 169
12.8 Effectofabsorption 170
12.9 Relativisticcorrection 172
13 Dynamicaltheory–embeddedR-matrixmethod 173
13.1 Introduction 173
Contents ix
13.2 Fourierexpansion 174
13.3 Thewavefunctions 174
13.4 Multislicemethod 175
13.5 Therecursion 177
13.6 TheRHEEDintensity 178
13.7 Inelasticdamping 179
13.8 Examples 180
14 Dynamicaltheory–integralmethod 192
15 Structuralanalysisofcrystalsurfaces 195
15.1 Introduction 195
15.2 One-beamcondition 196
15.3 Examplesofstructuralanalysis 201
16 Inelasticscatteringinacrystal 211
16.1 Introduction 211
16.2 One-electronexcitation:Yoshioka’stheory 211
16.3 Evaluationoftheimaginarypotential 215
16.4 Plasmonscattering 218
16.5 Thermaldiffusescattering 221
16.6 Absorptioncoefficients 223
16.7 Analyticalformoftheimaginarypotential 224
16.8 Summary 230
17 Weaklydisorderedsurfaces 234
17.1 Introduction 234
17.2 Themainresult 238
17.3 Asurfacewithonlytwolayers 240
17.4 Markoviandistributionofsteps 244
17.5 GeneralMarkovresults 248
17.6 Vicinalsurfaces 248
17.7 Antiphasedisorder 253
17.8 Columnapproximation 257
18 Stronglydisorderedsurfaces 260
18.1 Introduction 260
18.2 Height–differencecorrelationfunction 260
18.3 Thediffractionprofile 262
18.4 Gaussiandisorder 266
19 RHEEDintensityoscillations 270
19.1 Experimentalobservations 270
19.2 Kinematictheory 284
19.3 Phenomenologicalstep-densitymodels 290
19.4 Stepdensitywithshadowing 293
19.5 Rate-equationmodelsofepitaxy 297
19.6 Phaseshiftandfrequencydoubling 301