Thin Film Analysis by X-Ray Scattering

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.

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

• Preface ixSymbols xv1 Principles of X-ray Diffraction 11.1 The Basic Phenomenon 11.2 The θ/2θ Scan 111.3 Intensity of Bragg Ref lections 141.3.1 Atomic Form Factors 171.3.2 Structure Factor 191.3.3 Multiplicity 241.3.4 Geometry Factor 251.3.5 Preferred Orientation (Texture) 251.3.6 Polarization Factor 261.3.7 Absorption Factor 261.3.8 Integration of the Interference Function 291.4 Applications 37Exercises 39References 412 Identification of Chemical Phases 432.1 Histogram-Based Techniques 432.2 Linear Attenuation Coefficient µ 552.3 Determination and Interpretation of the µt Product 602.4 Analysis of Phase Mixtures 662.5 Amorphous Thin Films 702.6 Accurate Determination of Lattice Parameter 742.7 Applications 80Exercises 81References 833 Line Profile Analysis 853.1 Model Functions and Peak Parameters 863.2 Instrumental Line Profile 973.3 Deconvolution by Fourier Techniques 1013.4 Ref lection Broadening by Small Crystallite Size Only 1073.4.1 Scherrer Equation 1083.4.2 Column Height Distribution 1113.4.3 Crystallite Shapes Other Than Cubes 1123.4.4 Determination of the Column Height Distribution Function 1153.4.5 Determination of the Crystallite Size Distribution Function 1183.5 Concomitant Occurrence of Size and Strain Broadening 1203.5.1 Analysis According to Williamson and Hall 1223.5.2 Method of Warren and Averbach 1263.5.3 Single-Line Analysis 1293.5.4 Techniques of Whole-Pattern Fitting 1303.6 Applications 134Exercises 136References 1384 Grazing Incidence Configurations 1434.1 Grazing Incidence X-ray Diffraction (GIXRD) 1484.2 Penetration Depth and Information Depth 1554.3 Depth-Dependent Properties 1584.4 Refractive Index for X-rays 1604.5 Total External Ref lection and Critical Angle 1614.6 X-ray Ref lectivity (XRR) 1654.6.1 Ref lectivity of a Substrate 1664.6.2 Ref lectivity of a Single Layer 1684.6.3 Ref lectivity of Multilayers and Superlattices 1714.7 Grazing Incidence Diffraction (GID) 1754.8 Applications 177Exercises 179References 1815 Texture and Preferred Orientation 1835.1 Texture Factors 1885.2 Pole Figures 1915.3 Measurement of Pole Figures 1955.4 Directions, Orientations and Inverse Pole Figures 2005.5 Fiber Textures or Layer Textures 2045.5.1 Harmonic Method 2045.5.2 Whole Pattern Techniques 2075.5.3 Rocking Curves (ω Scans) 2115.6 Biaxial and Fully General Textures 2165.6.1 Azimuthal Scans (φ Scans) 2185.6.2 General Orientation Distribution 2205.6.3 Determination of Fully General Texture 2255.7 Depth Dependence of Thin-Film Textures 2285.8 Applications 230Exercises 234References 2356 Residual Stress Analysis 239Mario Birkholz and Christoph Genzel6.1 Ceiiinnosssttuv 2416.2 Fundamental Equation of XSA 2466.3 Measurement of d ψ Distributions 2496.4 Diffraction Elastic Constants (DECs) s 1 and 1/2s 2 2586.5 Grain Interaction Models 2616.6 The Effect of Texture 2656.7 Classification of Stresses 2686.7.1 Classification by Dimension 2686.7.2 Residual Stresses in Multiphase Materials 2696.7.3 Origin of Residual Stresses: Extrinsic and Intrinsic Stresses 2716.8 Effect of Residual Stress Gradients 2736.8.1 General Considerations 2736.8.2 The Biaxial Stress State 2746.9 Detection of Residual Stress Gradients in Thin Films 2766.9.1 Basic Relations 2766.9.2 X-ray Penetration Depth for the General Case of Asymmetric Diffraction 2786.9.3 Special Methods for X-ray Stress Gradient Analysis 2816.9.4 Grazing-Incidence Diffraction (GID) 2826.9.5 The Scattering Vector Method 2846.9.6 Realization of H Mode on a Four-Circle Diffractometer 2866.10 Applications 289Exercises 291References 2917 High-Resolution X-ray Diffraction 297Mario Birkholz and Paul F. Fewster7.1 Strain, Strain Relaxation and Composition in Epitaxial Layers 3037.2 High-Resolution Rocking Curves 3067.3 Mosaicity and Extinction 3147.4 Dynamical Theory of Ewald and Extensions 3197.5 High-Resolution Rocking Curves and Profiles from Layer Structures 3247.6 Reciprocal Space Mapping 3327.7 Diffuse Scattering 3377.8 Extensions to High-Resolution Diffraction 338Exercises 339References 340