Table of Contents

Preface ix

Symbols xv

1 Principles of X-ray Diffraction 1

1.1 The Basic Phenomenon 1

1.2 The θ/2θ Scan 11

1.3 Intensity of Bragg Ref lections 14

1.3.1 Atomic Form Factors 17

1.3.2 Structure Factor 19

1.3.3 Multiplicity 24

1.3.4 Geometry Factor 25

1.3.5 Preferred Orientation (Texture) 25

1.3.6 Polarization Factor 26

1.3.7 Absorption Factor 26

1.3.8 Integration of the Interference Function 29

1.4 Applications 37

Exercises 39

References 41

2 Identification of Chemical Phases 43

2.1 Histogram-Based Techniques 43

2.2 Linear Attenuation Coefficient µ 55

2.3 Determination and Interpretation of the µt Product 60

2.4 Analysis of Phase Mixtures 66

2.5 Amorphous Thin Films 70

2.6 Accurate Determination of Lattice Parameter 74

2.7 Applications 80

Exercises 81

References 83

3 Line Profile Analysis 85

3.1 Model Functions and Peak Parameters 86

3.2 Instrumental Line Profile 97

3.3 Deconvolution by Fourier Techniques 101

3.4 Ref lection Broadening by Small Crystallite Size Only 107

3.4.1 Scherrer Equation 108

3.4.2 Column Height Distribution 111

3.4.3 Crystallite Shapes Other Than Cubes 112

3.4.4 Determination of the Column Height Distribution Function 115

3.4.5 Determination of the Crystallite Size Distribution Function 118

3.5 Concomitant Occurrence of Size and Strain Broadening 120

3.5.1 Analysis According to Williamson and Hall 122

3.5.2 Method of Warren and Averbach 126

3.5.3 Single-Line Analysis 129

3.5.4 Techniques of Whole-Pattern Fitting 130

3.6 Applications 134

Exercises 136

References 138

4 Grazing Incidence Configurations 143

4.1 Grazing Incidence X-ray Diffraction (GIXRD) 148

4.2 Penetration Depth and Information Depth 155

4.3 Depth-Dependent Properties 158

4.4 Refractive Index for X-rays 160

4.5 Total External Ref lection and Critical Angle 161

4.6 X-ray Ref lectivity (XRR) 165

4.6.1 Ref lectivity of a Substrate 166

4.6.2 Ref lectivity of a Single Layer 168

4.6.3 Ref lectivity of Multilayers and Superlattices 171

4.7 Grazing Incidence Diffraction (GID) 175

4.8 Applications 177

Exercises 179

References 181

5 Texture and Preferred Orientation 183

5.1 Texture Factors 188

5.2 Pole Figures 191

5.3 Measurement of Pole Figures 195

5.4 Directions, Orientations and Inverse Pole Figures 200

5.5 Fiber Textures or Layer Textures 204

5.5.1 Harmonic Method 204

5.5.2 Whole Pattern Techniques 207

5.5.3 Rocking Curves (ω Scans) 211

5.6 Biaxial and Fully General Textures 216

5.6.1 Azimuthal Scans (φ Scans) 218

5.6.2 General Orientation Distribution 220

5.6.3 Determination of Fully General Texture 225

5.7 Depth Dependence of Thin-Film Textures 228

5.8 Applications 230

Exercises 234

References 235

6 Residual Stress Analysis 239
Mario Birkholz and Christoph Genzel

6.1 Ceiiinnosssttuv 241

6.2 Fundamental Equation of XSA 246

6.3 Measurement of d ψ Distributions 249

6.4 Diffraction Elastic Constants (DECs) s 1 and 1/2s 2 258

6.5 Grain Interaction Models 261

6.6 The Effect of Texture 265

6.7 Classification of Stresses 268

6.7.1 Classification by Dimension 268

6.7.2 Residual Stresses in Multiphase Materials 269

6.7.3 Origin of Residual Stresses: Extrinsic and Intrinsic Stresses 271

6.8 Effect of Residual Stress Gradients 273

6.8.1 General Considerations 273

6.8.2 The Biaxial Stress State 274

6.9 Detection of Residual Stress Gradients in Thin Films 276

6.9.1 Basic Relations 276

6.9.2 X-ray Penetration Depth for the General Case of Asymmetric Diffraction 278

6.9.3 Special Methods for X-ray Stress Gradient Analysis 281

6.9.4 Grazing-Incidence Diffraction (GID) 282

6.9.5 The Scattering Vector Method 284

6.9.6 Realization of H Mode on a Four-Circle Diffractometer 286

6.10 Applications 289

Exercises 291

References 291

7 High-Resolution X-ray Diffraction 297
Mario Birkholz and Paul F. Fewster

7.1 Strain, Strain Relaxation and Composition in Epitaxial Layers 303

7.2 High-Resolution Rocking Curves 306

7.3 Mosaicity and Extinction 314

7.4 Dynamical Theory of Ewald and Extensions 319

7.5 High-Resolution Rocking Curves and Profiles from Layer Structures 324

7.6 Reciprocal Space Mapping 332

7.7 Diffuse Scattering 337

7.8 Extensions to High-Resolution Diffraction 338

Exercises 339

References 340

About the Author

Dr. Mario Birkholz was born 1958 in Hamburg, Germany. He studied physics at the Free University of Berlin and completed his diploma thesis on structural investigations of biological membranes in 1986, and obtained his Ph.D. on the structure of stoichiometry deviations in iron-pyrite in 1990. Research positions at Hahn-Meitner-Institut Berlin, at Fraunhofer Institute for Thin Film and Surface Technology, Braunschweig, and at IHP Microelectronics, Frankfurt (Oder), followed.
He is involved in the development of thin film systems for applications in photovoltaics, sensor technology and as protective coatings. His main scientific interest is focused on the structure and morphology of thin films, their investigation by x-ray scattering techniques and the relation between structure and function.

Reviews

"... this book should prove very useful to anyone..."
Material Characterization