Mechanical stress on the nanoscale: simulation, material systems and characterization techniques (Weinheim, 2011). - ОГЛАВЛЕНИЕ / CONTENTS
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ОбложкаMechanical stress on the nanoscale: simulation, material systems and characterization techniques / ed. by M.Hanbücken, P.Müller, R.B Wehrspohn. - Weinheim: Wiley-VCH, 2011. - xxi, 358 p.: ill. - Incl. bibl. ref. - Ind.: p.357-358. - ISBN 978-3-527-41066-8
 

Оглавление / Contents
 
        Preface ................................................ XV
        List of Contributors ................................. XVII

Part One. Fundamentals of Stress and Strain on the
Nanoscale ....................................................... 2

1  Elastic Strain Relaxation: Thermodynamics and Kinetics ....... 3
   Frank Clas
   1.1  Basics of Elastic Strain Relaxation ..................... 3
        1.1.1  Introduction ..................................... 3
        1.1.2  Principles of Calculation ........................ 4
        1.1.3  Methods of Calculation: A Brief Overview ......... 6
   1.2  Elastic Strain Relaxation in Inhomogeneous
        Substitutional Alloys ................................... 7
        1.2.1  Spinodal Decomposition with No Elastic Effects ... 8
        1.2.2  Elastic Strain Relaxation in an Alloy with
               Modulated Composition ............................ 9
        1.2.3  Strain Stabilization and the Effect of Elastic
               Anisotropy ...................................... 11
        1.2.4  Elastic Relaxation in the Presence of a Free
               Surface ......................................... 11
   1.3  Diffusion .............................................. 12
        1.3.1  Diffusion without Elastic Effects ............... 12
        1.3.2  Diffusion under Stress in an Alloy .............. 13
   1.4  Strain Relaxation in Homogeneous Mismatched Epitaxial
        Layers ................................................. 14
        1.4.1  Introduction .................................... 14
        1.4.2  Elastic Strain Relaxation ....................... 15
        1.4.3  Critical Thickness .............................. 16
   1.5  Morphological Relaxation of a Solid under
        Nonhydrostatic Stress .................................. 17
        1.5.1  Introduction .................................... 17
        1.5.2  Calculation of the Elastic Relaxation Fields
               ................................................. 18
        1.5.3  ATG Instability ................................. 19
        1.5.4  Kinetics of the ATG Instability ................. 21
        1.5.5  Coupling between the Morphological and
               Compositional Instabilities ..................... 21
   1.6  Elastic Relaxation of 0D and 1D Epitaxial
        Nanostructures ......................................... 22
        1.6.1  Quantum Dots .................................... 23
        1.6.2  Nanowires ....................................... 24
               References ...................................... 24
2  Fundamentals of Stress and Strain at the Nanoscale Level:
   Toward Nanoelasticity ....................................... 27
   Pierre Müller
   2.1  Introduction ........................................... 27
   2.2  Theoretical Background ................................. 28
        2.2.1  Bulk Elasticity: A Recall ....................... 28
               2.2.1.1  Stress and Strain Definition ........... 29
               2.2.1.2  Equilibrium State ...................... 29
               2.2.1.3  Elastic Energy ......................... 30
               2.2.1.4  Elastic Constants ...................... 30
        2.2.2  How to Describe Surfaces or Interfaces? ......... 31
        2.2.3  Surfaces and Interfaces Described from Excess
               Quantities ...................................... 34
               2.2.3.1  The Surface Elastic Energy as an
                        Excess of the Bulk Elastic Energy ...... 34
               2.2.3.2  The Surface Stress and Surface Strain
                        Concepts ............................... 35
               2.2.3.3  Surface Elastic Constants .............. 37
               2.2.3.4  Connecting Surface and Bulk Stresses ... 39
               2.2.3.5  Surface Stress and Surface Tension ..... 40
               2.2.3.6  Surface Stress and Adsorption .......... 41
               2.2.3.7  The Case of Glissile Interfaces ........ 42
        2.2.4  Surfaces and Interfaces Described as a Foreign
               Material ........................................ 42
               2.2.4.1  The Surface as a Thin Bulk-Like Film ... 43
               2.2.4.2  The Surface as an Elastic Membrane ..... 43
   2.3  Applications: Size Effects Due to the Surfaces ......... 44
        2.3.1  Lattice Contraction of Nanoparticles ............ 44
        2.3.2  Effective Modulus of Thin Freestanding Plane
               Films ........................................... 46
        2.3.3  Bending, Buckling, and Free Vibrations of Thin
               Films ........................................... 48
               2.3.3.1  General Equations ...................... 48
               2.3.3.2  Discussion ............................. 50
        2.3.4  Static Bending of Nanowires: An Analysis of
               the Recent Literature ........................... 52
               2.3.4.1  Young Modulus versus Size: Two-Phase
                        Model .................................. 52
               2.3.4.2  Young Modulus versus Size: Surface
                        Stress Model ........................... 53
               2.3.4.3  Prestress Bulk Due to Surface
                        Stresses ............................... 53
        2.3.5  A Short Overview of Experimental Difficulties ... 54
   2.4  Conclusion ............................................. 55
        References ............................................. 56
3  Onset of Plasticity in Crystalline Nanomaterials ............ 62
   Laurent Pizzagalli, Sandrine Brochard, and Julien Codet
   3.1  Introduction ........................................... 62
   3.2  The Role of Dislocations ............................... 63
   3.3  Driving Forces for Dislocations ........................ 63
        3.3.1  Stress .......................................... 64
        3.3.2  Thermal Activation .............................. 64
        3.3.3  Combination of Stress and Thermal Activation .... 64
   3.4  Dislocation and Surfaces: Basic Concepts ............... 65
        3.4.1  Forces Related to Surface ....................... 65
        3.4.2  Balance of Forces for Nucleation ................ 66
        3.4.3  Forces Due to Lattice Friction .................. 66
        3.4.4  Surface Modifications Due to Dislocations ....... 68
   3.5  Elastic Modeling ....................................... 68
        3.5.1  Elastic Model ................................... 68
        3.5.2  Predicted Activation Parameters ................. 70
        3.5.3  What is Missing? ................................ 70
        3.5.4  Peierls-Nabarro Approaches ...................... 72
   3.6  Atomistic Modeling ..................................... 72
        3.6.1  Examples of Simulations ......................... 73
        3.6.2  Determination of Activation Parameters .......... 74
        3.6.3  Comparison with Experiments ..................... 75
        3.6.4  Influence of Surface Structure, Orientation,
               and Chemistry ................................... 76
   3.7  Extension to Different Geometries ...................... 78
   3.8  Discussion ............................................. 79
        References ............................................. 80
4  Relaxations on the Nanoscale: An Atomistic View by
   Numerical Simulations ....................................... 83
   Christine Mottet
   4.1  Introduction ........................................... 84
   4.2  Theoretical Models and Numerical Simulations ........... 85
        4.2.1  Energetic Models ................................ 85
        4.2.2  Numerical Simulations ........................... 87
        4.2.3  Definitions of Physical Quantities .............. 89
   4.3  Relaxations in Surfaces and Interfaces ................. 92
        4.3.1  Surface Reconstructions ......................... 92
        4.3.2  Surface Alloys: a Simple Case of Heteroatomic
               Adsorption ...................................... 94
        4.3.3  Heteroepitaxial Thin Films ...................... 96
   4.4  Relaxations in Nanoclusters ............................ 98
        4.4.1  Free Nanoclusters ............................... 99
        4.4.2  Supported Nanoclusters ......................... 100
        4.4.3  Nanoalloys ..................................... 101
   4.5  Conclusions ........................................... 103
        Reference ............................................. 204

Part Two. Model Systems with Stress-Engineered Properties ..... 107

5  Accommodation of Lattice Misfit in Semiconductor
   Heterostructure Nanowires .................................. 109
   Volker Schmidt and Joerg V. Wittemann
   5.1  Introduction .......................................... 109
   5.2  Dislocations in Axial Heterostructure Nanowires ....... 111
   5.3  Dislocations in Core-Shell Heterostructure
        Nanowires ............................................. 113
   5.4  Roughening of Core-Shell Heterostructure Nanowires .... 115
        5.4.1  Zeroth-Order Stress and Strain ................. 117
        5.4.2  First-Order Contribution to Stress and
               Strain ......................................... 120
        5.4.3  Linear Stability Analysis ...................... 122
        5.4.4  Results and Discussion ......................... 124
   5.5  Conclusion ............................................ 127
        Reference ............................................. 127
6  Strained Silicon Nanodevices ............................... 131
   Manfred Reiche, Oussama Moutanabbir, Jan Hoentschel,
   Angelika Hähnel, Stefan Flachowsky, Ulrich Cösele, and
   Manfred Horstmann
   6.1  Introduction .......................................... 131
   6.2  Impact of Strain on the Electronic Properties of
        Silicon ............................................... 132
   6.3  Methods to Generate Strain in Silicon Devices ......... 135
        6.3.1  Substrates for Nanoscale CMOS Technologies ..... 135
        6.3.2  Local Strain ................................... 136
        6.3.3  Global Strain .................................. 139
               6.3.3.1  Biaxially Strained Layers ............. 139
               6.3.3.2  Uniaxially Strained Layers ............ 142
   6.4  Strain Engineering for 22 nm CMOS Technologies and
        Below ................................................. 142
   6.5  Conclusions ........................................... 146
        Reference ............................................. 146
7  Stress-Driven Nanopatterning in Metallic Systems ........... 151
   Vincent Repain, Sylvie Rousset, and Shobhana Narasimhan
   7.1  Introduction .......................................... 151
   7.2  Surface Stress as a Driving Force for Patterning at
        Nanometer Length Scales ............................... 152
        7.2.1  Surface Stress ................................. 152
        7.2.2  Surface Reconstruction and Misfit
               Dislocations ................................... 153
               7.2.2.1  Homoepitaxial Surfaces ................ 153
               7.2.2.2  Heteroepitaxial Systems ............... 155
        7.2.3  Stress Domains ................................. 156
        7.2.4  Vicinal Surfaces ............................... 257
   7.3  Nanopatterned Surfaces as Templates for the Ordered
        Growth of Functionalized Nanostructures ............... 158
        7.3.1  Metallic Ordered Growth on Nanopatterned
               Surface ........................................ 158
               7.3.1.1  Introduction .......................... 158
               7.3.1.2  Nucleation and Growth Concepts ........ 159
               7.3.1.3  Heterogeneous Growth .................. 360
   7.4  Stress Relaxation by the Formation of Surface-
        Confined Alloys ....................................... 162
        7.4.1  Two-Component Systems .......................... 162
        7.4.2  Three-Component Systems ........................ 162
   7.5  Conclusion ............................................ 164
        Reference ............................................. 265
8  Semiconductor Templates for the Fabrication of Nano-
   Objects .................................................... 269
   Joël Eymery, Laurence Masson, Houda Sahaf, and Margrit
   Hanbücken
   8.1  Introduction .......................................... 269
   8.2  Semiconductor Template Fabrication .................... 270
        8.2.1  Artificially Prepatterned Substrates ........... 270
               8.2.1.1  Morphological Patterning .............. 270
               8.2.1.2  Silicon Etched Stripes: Example of
                        the Use of Strain to Control
                        Nanostructure Formation and Physical
                        Properties ............................ 172
               8.2.1.3  Use of Buried Stressors ............... 272
        8.2.2  Patterning through Vicinal Surfaces ............ 273
               8.2.2.1  Generalities .......................... 173
               8.2.2.2  Vicinal Si(111) ....................... 173
               8.2.2.3  Vicinal Si(100) ....................... 173
   8.3  Ordered Growth of Nano-Objects ........................ 175
        8.3.1  Growth Modes and Self-Organization ............. 175
        8.3.2  Quantum Dots and Nanoparticles Self-
               Organization with Control in Size and
               Position ....................................... 176
               8.3.2.1  Stranski-Krastanov Growth Mode ........ 176
               8.3.2.2  Au/Si(111) System ..................... 177
               8.3.2.3  Ge/Si(001) System ..................... 179
        8.3.3  Wires: Catalytic and Catalyst-Free Growths
               with Control in Size and Position .............. 179
               8.3.3.1  Strain in Bottom-Up Wire
                        Heterostructures: Longitudinal and
                        Radial Heterostructures ............... 181
               8.3.3.2  Wires as a Position Controlled
                        Template .............................. 183
   8.4  Conclusions ........................................... 184
        Reference ............................................. 184

Part Three. Characterization Techniques of Measuring
Stresses on the Nanoscale ..................................... 189

9  Strain Analysis in Transmission Electron Microscopy:
   How Far Can We Go? ......................................... 191
   Anne Ponchet, Christophe Gatel, Christian Roucau, and
   Marie-José Casanove
   9.1  Introduction: How to Get Quantitative Information on
        Strain from ТЕМ ....................................... 192
        9.1.1  Displacement, Strain, and Stress in
               Elasticity Theory .............................. 192
        9.1.2  Principles of ТЕМ and Application to Strained
               Nanosystems .................................... 192
        9.1.3  A Major Issue for Strained Nanostructure
               Analysis: The Thin Foil Effect ................. 193
   9.2  Bending Effects in Nanometric Strained Layers:
        A Tool for Probing Stress ............................. 194
        9.2.1  Bending: A Relaxation Mechanism ................ 194
        9.2.2  Relation between Curvature and Internal
               Stress ......................................... 195
        9.2.3  Using the Bending as a Probe of the Epitaxial
               Stress: The ТЕМ Curvature Method ............... 296
        9.2.4  Occurrence of Large Displacements in ТЕМ
               Thinned Samples ................................ 197
        9.2.5  Advantages and Limits of Bending as a Probe
               of Stress in ТЕМ ............................... 199
   9.3  Strain Analysis and Surface Relaxation in Electron
        Diffraction ........................................... 199
        9.3.1  CBED: Principle and Application to
               Determination of Lattice Parameters ............ 199
        9.3.2  Strain Determination in CBED ................... 201
        9.3.3  Use and Limitations of CBED in Strain
               Determination .................................. 202
        9.3.4  Nanobeam Electron Diffraction .................. 203
   9.4  Strain Analysis from HREM Image Analysis:
        Problematic of Very Thin Foils ........................ 203
        9.4.1  Principle ...................................... 203
        9.4.2  What Do We Really Measure in an HREM Image? .... 205
               9.4.2.1  Image Formation ....................... 205
               9.4.2.2  Reconstruction of the 3D Strain
                        Field from a 2D Projection ............ 205
        9.4.3  Modeling the Surface Relaxation in an HREM
               Experiment ..................................... 206
               9.4.3.1  Full Relaxation (Uniaxial Stress) ..... 206
               9.4.3.2  Intermediate Situations: Usefulness
                        of Finite Element Modeling ............ 207
               9.4.3.3  Thin Foil Effect: A Source of
                        Incertitude in HREM ................... 207
        9.4.4  Conclusion: HREM is a Powerful but Delicate
               Method of Strain Analysis ...................... 208
   9.5  Conclusions ........................................... 209
        Reference ............................................. 210
10 Determination of Elastic Strains Using Electron
   Backscatter Diffraction in the Scanning Electron
   Microscope ................................................. 213
   Michael Krause, Matthias Petzold, and Ralf В. Wehrspohn
   10.1 Introduction .......................................... 213
   10.2 Generation of Electron Backscatter Diffraction
        Patterns .............................................. 214
   10.3 Strain Determination Through Lattice Parameter
        Measurement ........................................... 215
   10.4 Strain Determination Through Pattern Shift
        Measurement ........................................... 216
        10.4.1 Linking Pattern Shifts to Strain ............... 226
        10.4.2 Measurement of Pattern Shifts .................. 229
   10.5 Sampling Strategies: Sources of Errors ................ 221
   10.6 Resolution Considerations ............................. 222
   10.7 Illustrative Application .............................. 225
   10.8 Conclusions ........................................... 229
        Reference ............................................. 230
11 X-Ray Diffraction Analysis of Elastic Strains at the
   Nanoscale .................................................. 233
   Olivier Thomas, Odile Robach, Stéphanie Escoubas, Jean-
   Sébastien Micha, Nicolas Vaxelaire, and Olivier Perroud
   11.1 Introduction .......................................... 233
   11.2 Strain Field from Intensity Maps around Bragg Peaks ... 234
   11.3 Average Strains from Diffraction Peak Shift ........... 236
   11.4 Local Strains Using Submicrometer Beams and Scanning
        XRD ................................................... 240
        11.4.1 Introduction ................................... 240
        11.4.2 High-Energy Monochromatic Beam: 3DXRD .......... 241
        11.4.3 White Beam: Laue Microdiffraction .............. 243
   11.5 Local Strains Derived from the Intensity
        Distribution in Reciprocal Space ...................... 248
        11.5.1 Periodic Assemblies of Identical Objects with
               Coherence Length > Few Periods ................. 248
               11.5.1.1 Introduction .......................... 248
               11.5.1.2 Reciprocal Space Mapping .............. 249
               11.5.1.3 Applications .......................... 251
        11.5.2 Single-Object Coherent Diffraction ............. 252
   11.6 Phase Retrieval from Strained Crystals ................ 254
   11.7 Conclusions and Perspectives .......................... 255
        Reference ............................................. 256
12 Diffuse X-Ray Scattering at Low-Dimensional Structures in
   the System SiGe/Si ......................................... 259
   Michael Hanke
   12.1 Introduction .......................................... 259
   12.2 Self-Organized Growth of Mesoscopic Structures ........ 259
        12.2.1 The Stranski-Krastanow Process ................. 260
        12.2.2 LPE-Grown Si1-xGex/Si(001) Islands ............. 261
   12.3 X-Ray Scattering Techniques ........................... 262
        12.3.1 High-Resolution X-Ray Diffraction .............. 262
        12.3.2 Grazing Incidence Diffraction .................. 263
        12.3.3 Grazing Incidence Small-Angle X-Ray
               Scattering ..................................... 264
   12.4 Data Evaluation ....................................... 265
   12.5 Results ............................................... 266
        12.5.1 The Influence of Shape and Size on the GISAXS
               Signal ......................................... 266
        12.5.2 HRXRD Measurement of Strain and Composition .... 269
        12.5.3 Positional Correlation Effects in HRXRD ........ 270
        12.5.4 Iso-Strain Scattering .......................... 272
   12.6 Summary ............................................... 273
        Reference ............................................. 274
13 Direct Measurement of Elastic Displacement Modes by
   Crazing Incidence X-Ray Diffraction ......................... 275
   Geoffrey Prévot
   13.1 Introduction .......................................... 275
   13.2 Elastic Displacement Modes: Analysis and GIXD
        Observation ........................................... 276
        13.2.1 Fundamentals of Linear Elasticity in Direct
               Space .......................................... 276
               13.2.1.1 Basic Equations ....................... 276
               13.2.1.2 Atomic Displacements and Elastic
                        Interactions .......................... 277
        13.2.2 Green's Tensor in Reciprocal Space ............. 279
        13.2.3 Grazing Incidence X-Ray Diffraction of
               Elastic Modes .................................. 280
               13.2.3.1 Diffraction by a Surface .............. 280
               13.2.3.2 Contribution of the Elastic Modes ..... 280
               13.2.3.3 Procedure for Analyzing the Systems ... 282
   13.3 Self-Organized Surfaces ............................... 282
        13.3.1 Force Distribution and Interaction Energy for
               Self-Organized Surfaces ........................ 282
        13.3.2 A 1D Case: OCu(110) ............................ 283
        13.3.3 A 2D Case: NCu(00l) ............................ 286
   13.4 Vicinal Surfaces ...................................... 289
        13.4.1 Force Distribution and Interaction Energy for
               Steps .......................................... 289
        13.4.2 Experimental Results for Vicinal Surfaces of
               Transition Metals .............................. 292
   13.5 Conclusion ............................................ 294
        Reference ............................................. 295
14 Submicrometer-Scale Characterization of Solar Silicon
   by Raman Spectroscopy ...................................... 299
   Michael Becker, George Sarau, and Silke Christiansen
   14.1 Introduction .......................................... 299
   14.2 Crystal Orientation ................................... 300
        14.2.1 Qualitative Maps ............................... 300
        14.2.2 Quantitative Analysis .......................... 302
        14.2.3 Comparison with Other Orientation Measurement
               Methods ........................................ 306
   14.3 Analysis of Stress and Strain States .................. 307
        14.3.1 General Theoretical Description ................ 307
        14.3.2 Quantitative Strain/Stress Analysis in
               Polycrystalline Silicon Wafers ................. 309
               14.3.2.1 Assumptions ........................... 309
               14.3.2.2 Numerical Determination of Stress
                        Components ............................ 310
        14.3.3 Experimental Procedure to Determine Phonon
               Frequency Shifts ............................... 311
        14.3.4 Additional Influences on the Phonon Frequency
               Shifts ......................................... 311
               14.3.4.1 Temperature ........................... 311
               14.3.4.2 Drift of the Spectrometer Grating ..... 313
        14.3.5 Applications ................................... 313
               14.3.5.1 Mechanical Stresses at the Backside
                        of Silicon Solar Cells ................ 313
               14.3.5.2 Stress Fields at Microcracks in
                        Polycrystalline Silicon Wafers ........ 315
               14.3.5.3 Stress States at Grain Boundaries in
                        Polycrystalline Silicon Solar Cell
                        Material and the Relation to the
                        Grain Boundary Microstructure and
                        Electrical Activity ................... 316
        14.3.6 Comparison with other Stress/Strain
               Measurement Methods ............................ 318
   14.4 Measurement of Free Carrier Concentrations ............ 318
        14.4.1 Theoretical Description ........................ 319
        14.4.2 Experimental Details ........................... 321
               14.4.2.1 Small-Angle Beveling and Nomarski
                        Differential Interference Contrast
                        Micrographs ........................... 321
               14.4.2.2 Evaluation of the Raman Data .......... 322
               14.4.2.3 Calibration Measurements .............. 324
        14.4.3 Experimental Results ........................... 324
        14.4.4 Comparison with other Dopant Measurement
               Methods ........................................ 328
   14.5 Concluding Remarks .................................... 328
        Reference ............................................. 329
15 Strain-Induced Nonlinear Optics in Silicon ................. 333
   Clemens Schriever, Christian Bohley, and Ralf В.
   Wehrspohn
   15.1 Introduction .......................................... 333
   15.2 Fundamentals of Second Harmonic Generation in
        Nonlinear Optical Materials ........................... 334
   15.3 Second Harmonic Generation and Its Relation to
        Structural Symmetry ................................... 336
        15.3.1 Sources of Second Harmonic Signals ............. 337
        15.3.2 Bulk Contribution to Second Harmonic
               Generation ..................................... 338
        15.3.3 Surface Contribution to Second Harmonic
               Generation ..................................... 341
   15.4 Strain-Induced Modification of Second-Order
        Nonlinear Susceptibility in Silicon ................... 343
   15.5 Strained Silicon in Integrated Optics ................. 348
        15.5.1 Strain-Induced Electro-Optical Effect .......... 348
        15.5.2 Strain-Induced Photoelastic Effect ............. 350
   15.6 Conclusions ........................................... 352
        Reference ............................................. 353

        Index ................................................. 357


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