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Edited by Margrit Hanbu¨cken, Pierre Mu¨ller, and Ralf B. Wehrspohn Mechanical Stress on the Nanoscale Related Titles Alkauskas, A.,Deák, P., Neugebauer,J., Zehetbauer,M. J.,Zhu, Y.T.(eds.) Pasquarello,A.,VandeWalle,C.G.(eds.) Bulk Nanostructured Materials Advanced Calculations 736pageswith366figuresand31tables for Defects in Materials 2009 ElectronicStructureMethods Hardcover ISBN:978-3-527-31524-6 402pageswith118figures 2011 Cazacu, O.(ed.) Hardcover ISBN:978-3-527-41024-8 Multiscale Modeling of Heterogenous Materials Jackson, K. A. FromMicrostructuretoMacro-Scale Kinetic Processes Properties CrystalGrowth,Diffusion,and 343pages PhaseTransitionsinMaterials 2008 453pageswith291figures Hardcover 2010 ISBN:978-1-84821-047-9 Hardcover ISBN:978-3-527-32736-2 Birkholz, M. Thin Film Analysis by Stallinga,P. X-Ray Scattering Electrical Characterization SharingthePlanet’sFreshwater of Organic Electronic Resources Materials and Devices 378pageswith175figuresand28tables 2006 316pages Hardcover 2009 Hardcover ISBN:978-3-527-31052-4 ISBN:978-0-470-75009-4 Edited by Margrit Hanbücken, Pierre Müller, and Ralf B. Wehrspohn Mechanical Stress on the Nanoscale Simulation, Material Systems and Characterization Techniques TheEditors AllbookspublishedbyWiley-VCHarecarefully produced.Nevertheless,authors,editors,and Dr.MargritHanbücken publisherdonotwarranttheinformationcontained CINaM-CNRS inthesebooks,includingthisbook,tobefreeof CampusLuminy errors.Readersareadvisedtokeepinmindthat Marseille,Frankreich statements,data,illustrations,proceduraldetailsor otheritemsmayinadvertentlybeinaccurate. Dr.PierreMüller LibraryofCongressCardNo.: appliedfor UniversitéPaulCézanne CampusSaint-Jérôme BritishLibraryCataloguing-in-PublicationData Marseille,Frankreich Acataloguerecordforthisbookisavailablefromthe BritishLibrary. Prof.Dr.RalfB.Wehrspohn FraunhoferInst.für Bibliographicinformationpublishedby WerkstoffmechanikHalle theDeutscheNationalbibliothek Halle,Germany TheDeutscheNationalbibliothekliststhispublica- tionintheDeutscheNationalbibliografie;detailed bibliographicdataareavailableontheInternetat http://dnb.d-nb.de. #2011Wiley-VCHVerlag&Co.KGaA, Boschstr.12,69469Weinheim,Germany Allrightsreserved(includingthoseoftranslation intootherlanguages).Nopartofthisbookmaybe reproducedinanyform–byphotoprinting, microfilm,oranyothermeans–nortransmittedor translatedintoamachinelanguagewithoutwritten permissionfromthepublishers.Registerednames, trademarks,etc.usedinthisbook,evenwhennot specificallymarkedassuch,arenottobeconsidered unprotectedbylaw. Typesetting ThomsonDigital,Noida,India Printing Binding CoverDesign Grafik-DesignSchulz,Fußgönheim PrintedinSingapore Printedonacid-freepaper PrintISBN: 978-3-527-41066-8 ePDFISBN:978-3-527-63956-4 oBookISBN: 978-3-527-63954-0 ePubISBN: 978-3-527-63955-7 V Contents Preface XV List of Contributors XVII PartOne FundamentalsofStressandStrainontheNanoscale 1 1 ElasticStrainRelaxation:ThermodynamicsandKinetics 3 FrankGlas 1.1 BasicsofElasticStrainRelaxation 3 1.1.1 Introduction 3 1.1.2 PrinciplesofCalculation 4 1.1.3 MethodsofCalculation:ABriefOverview 6 1.2 ElasticStrainRelaxationinInhomogeneousSubstitutionalAlloys 7 1.2.1 SpinodalDecompositionwithNoElasticEffects 8 1.2.2 ElasticStrainRelaxationinanAlloywithModulatedComposition 9 1.2.3 StrainStabilizationandtheEffectofElasticAnisotropy 11 1.2.4 ElasticRelaxationinthePresenceofaFreeSurface 11 1.3 Diffusion 12 1.3.1 DiffusionwithoutElasticEffects 12 1.3.2 DiffusionunderStressinanAlloy 13 1.4 StrainRelaxationinHomogeneousMismatchedEpitaxialLayers 14 1.4.1 Introduction 14 1.4.2 ElasticStrainRelaxation 15 1.4.3 CriticalThickness 16 1.5 MorphologicalRelaxationofaSolidunderNonhydrostaticStress 17 1.5.1 Introduction 17 1.5.2 CalculationoftheElasticRelaxationFields 18 1.5.3 ATGInstability 19 1.5.4 KineticsoftheATGInstability 21 1.5.5 CouplingbetweentheMorphologicalandCompositional Instabilities 21 1.6 ElasticRelaxationof0Dand1DEpitaxialNanostructures 22 1.6.1 QuantumDots 23 VI Contents 1.6.2 Nanowires 24 References 24 2 FundamentalsofStressandStrainattheNanoscaleLevel: TowardNanoelasticity 27 PierreMüller 2.1 Introduction 27 2.2 TheoreticalBackground 28 2.2.1 BulkElasticity:ARecall 28 2.2.1.1 StressandStrainDefinition 29 2.2.1.2 EquilibriumState 29 2.2.1.3 ElasticEnergy 30 2.2.1.4 ElasticConstants 30 2.2.2 HowtoDescribeSurfacesorInterfaces? 31 2.2.3 SurfacesandInterfacesDescribedfromExcessQuantities 34 2.2.3.1 TheSurfaceElasticEnergyasanExcessoftheBulk ElasticEnergy 34 2.2.3.2 TheSurfaceStressandSurfaceStrainConcepts 35 2.2.3.3 SurfaceElasticConstants 37 2.2.3.4 ConnectingSurfaceandBulkStresses 39 2.2.3.5 SurfaceStressandSurfaceTension 40 2.2.3.6 SurfaceStressandAdsorption 41 2.2.3.7 TheCaseofGlissileInterfaces 42 2.2.4 SurfacesandInterfacesDescribedasaForeignMaterial 42 2.2.4.1 TheSurfaceasaThinBulk-LikeFilm 43 2.2.4.2 TheSurfaceasanElasticMembrane 43 2.3 Applications:SizeEffectsDuetotheSurfaces 44 2.3.1 LatticeContractionofNanoparticles 44 2.3.2 EffectiveModulusofThinFreestandingPlaneFilms 46 2.3.3 Bending,Buckling,andFreeVibrationsofThinFilms 48 2.3.3.1 GeneralEquations 48 2.3.3.2 Discussion 50 2.3.4 StaticBendingofNanowires:AnAnalysisoftheRecent Literature 52 2.3.4.1 YoungModulusversusSize:Two-PhaseModel 52 2.3.4.2 YoungModulusversusSize:SurfaceStressModel 53 2.3.4.3 PrestressBulkDuetoSurfaceStresses 53 2.3.5 AShortOverviewofExperimentalDifficulties 54 2.4 Conclusion 55 References 56 3 OnsetofPlasticityinCrystallineNanomaterials 61 LaurentPizzagalli,SandrineBrochard,andJulienGodet 3.1 Introduction 61 3.2 TheRoleofDislocations 63 Contents VII 3.3 DrivingForcesforDislocations 63 3.3.1 Stress 64 3.3.2 ThermalActivation 64 3.3.3 CombinationofStressandThermal Activation 64 3.4 DislocationandSurfaces:BasicConcepts 65 3.4.1 ForcesRelatedtoSurface 65 3.4.2 BalanceofForcesforNucleation 66 3.4.3 ForcesDuetoLatticeFriction 66 3.4.4 SurfaceModificationsDuetoDislocations 68 3.5 ElasticModeling 68 3.5.1 ElasticModel 68 3.5.2 PredictedActivationParameters 70 3.5.3 WhatisMissing? 70 3.5.4 Peierls–NabarroApproaches 72 3.6 AtomisticModeling 72 3.6.1 ExamplesofSimulations 73 3.6.2 DeterminationofActivationParameters 74 3.6.3 ComparisonwithExperiments 75 3.6.4 InfluenceofSurfaceStructure,Orientation,and Chemistry 76 3.7 ExtensiontoDifferentGeometries 78 3.8 Discussion 79 References 80 4 RelaxationsontheNanoscale:AnAtomistic ViewbyNumericalSimulations 83 ChristineMottet 4.1 Introduction 84 4.2 TheoreticalModelsandNumericalSimulations 85 4.2.1 EnergeticModels 85 4.2.2 NumericalSimulations 87 4.2.3 DefinitionsofPhysicalQuantities 89 4.3 RelaxationsinSurfacesandInterfaces 91 4.3.1 SurfaceReconstructions 92 4.3.2 SurfaceAlloys:aSimpleCaseofHeteroatomic Adsorption 94 4.3.3 HeteroepitaxialThinFilms 96 4.4 RelaxationsinNanoclusters 98 4.4.1 FreeNanoclusters 99 4.4.2 SupportedNanoclusters 100 4.4.3 Nanoalloys 101 4.5 Conclusions 103 References 104 VIII Contents PartTwo ModelSystemswithStress-EngineeredProperties 107 5 AccommodationofLatticeMisfitinSemiconductor HeterostructureNanowires 109 VolkerSchmidtandJoergV.Wittemann 5.1 Introduction 109 5.2 DislocationsinAxialHeterostructureNanowires 111 5.3 DislocationsinCore–ShellHeterostructure Nanowires 113 5.4 RougheningofCore–ShellHeterostructure Nanowires 115 5.4.1 Zeroth-OrderStressandStrain 117 5.4.2 First-OrderContributiontoStressandStrain 120 5.4.3 LinearStabilityAnalysis 122 5.4.4 ResultsandDiscussion 124 5.5 Conclusion 127 References 127 6 StrainedSiliconNanodevices 131 ManfredReiche,OussamaMoutanabbir,JanHoentschel,AngelikaHähnel, StefanFlachowsky,UlrichGösele,andManfredHorstmann 6.1 Introduction 131 6.2 ImpactofStrainontheElectronicProperties ofSilicon 132 6.3 MethodstoGenerateStraininSiliconDevices 135 6.3.1 SubstratesforNanoscaleCMOSTechnologies 135 6.3.2 LocalStrain 136 6.3.3 GlobalStrain 139 6.3.3.1 BiaxiallyStrainedLayers 139 6.3.3.2 UniaxiallyStrainedLayers 142 6.4 StrainEngineeringfor22nmCMOSTechnologies andBelow 142 6.5 Conclusions 146 References 146 7 Stress-DrivenNanopatterninginMetallicSystems 151 VincentRepain,SylvieRousset,andShobhanaNarasimhan 7.1 Introduction 151 7.2 SurfaceStressasaDrivingForceforPatterningatNanometer LengthScales 152 7.2.1 SurfaceStress 152 7.2.2 SurfaceReconstructionandMisfitDislocations 153 7.2.2.1 HomoepitaxialSurfaces 153 7.2.2.2 HeteroepitaxialSystems 155 7.2.3 StressDomains 156 Contents IX 7.2.4 VicinalSurfaces 157 7.3 NanopatternedSurfacesasTemplatesfortheOrdered GrowthofFunctionalizedNanostructures 158 7.3.1 MetallicOrderedGrowthonNanopatterned Surface 158 7.3.1.1 Introduction 158 7.3.1.2 NucleationandGrowthConcepts 159 7.3.1.3 HeterogeneousGrowth 160 7.4 StressRelaxationbytheFormationofSurface-Confined Alloys 162 7.4.1 Two-ComponentSystems 162 7.4.2 Three-ComponentSystems 162 7.5 Conclusion 164 References 165 8 SemiconductorTemplatesfortheFabricationofNano-Objects 169 JoëlEymery,LaurenceMasson,HoudaSahaf, andMargritHanbücken 8.1 Introduction 169 8.2 SemiconductorTemplateFabrication 170 8.2.1 ArtificiallyPrepatternedSubstrates 170 8.2.1.1 MorphologicalPatterning 170 8.2.1.2 SiliconEtchedStripes:ExampleoftheUseofStrainto ControlNanostructureFormationandPhysical Properties 171 8.2.1.3 UseofBuriedStressors 171 8.2.2 PatterningthroughVicinalSurfaces 173 8.2.2.1 Generalities 173 8.2.2.2 VicinalSi(111) 173 8.2.2.3 VicinalSi(100) 173 8.3 OrderedGrowthofNano-Objects 175 8.3.1 GrowthModesandSelf-Organization 175 8.3.2 QuantumDotsandNanoparticlesSelf-OrganizationwithControl inSizeandPosition 176 8.3.2.1 Stranski–KrastanovGrowthMode 176 8.3.2.2 Au/Si(111)System 177 8.3.2.3 Ge/Si(001)System 179 8.3.3 Wires:CatalyticandCatalyst-FreeGrowthswithControl inSizeandPosition 179 8.3.3.1 StraininBottom-UpWireHeterostructures:Longitudinaland RadialHeterostructures 181 8.3.3.2 WiresasaPositionControlledTemplate 183 8.4 Conclusions 184 References 184 X Contents PartThree CharacterizationTechniquesofMeasuringStresseson theNanoscale 189 9 StrainAnalysisinTransmissionElectronMicroscopy: HowFarCanWeGo? 191 AnnePonchet,ChristopheGatel,ChristianRoucau, andMarie-JoséCasanove 9.1 Introduction:HowtoGetQuantitativeInformationon StrainfromTEM 192 9.1.1 Displacement,Strain,andStressinElasticityTheory 192 9.1.2 PrinciplesofTEMandApplicationtoStrained Nanosystems 192 9.1.3 AMajorIssueforStrainedNanostructureAnalysis: TheThinFoilEffect 193 9.2 BendingEffectsinNanometricStrainedLayers:ATool forProbingStress 194 9.2.1 Bending:ARelaxationMechanism 194 9.2.2 RelationbetweenCurvatureandInternalStress 195 9.2.3 UsingtheBendingasaProbeoftheEpitaxialStress: TheTEMCurvatureMethod 196 9.2.4 OccurrenceofLargeDisplacementsinTEMThinned Samples 197 9.2.5 AdvantagesandLimitsofBendingasaProbeofStress inTEM 199 9.3 StrainAnalysisandSurfaceRelaxationinElectron Diffraction 199 9.3.1 CBED:PrincipleandApplicationtoDeterminationof LatticeParameters 199 9.3.2 StrainDeterminationinCBED 201 9.3.3 UseandLimitationsofCBEDinStrainDetermination 202 9.3.4 NanobeamElectronDiffraction 203 9.4 StrainAnalysisfromHREMImageAnalysis:Problematic ofVeryThinFoils 203 9.4.1 Principle 203 9.4.2 WhatDoWeReallyMeasureinanHREMImage? 205 9.4.2.1 ImageFormation 205 9.4.2.2 Reconstructionofthe3DStrainFieldfroma2DProjection 205 9.4.3 ModelingtheSurfaceRelaxationinanHREMExperiment 206 9.4.3.1 FullRelaxation(UniaxialStress) 206 9.4.3.2 IntermediateSituations:UsefulnessofFiniteElementModeling 207 9.4.3.3 ThinFoilEffect:ASourceofIncertitudeinHREM 207 9.4.4 Conclusion:HREMisaPowerfulbutDelicateMethod ofStrainAnalysis 208 9.5 Conclusions 209 References 210