SEMICONDUCTOR FABRICATION: TECHNOLOGY AND METROLOGY
CONTENTS PART THE APPLICATIONS 1 INTRODUCTION SCOPE OF X-RAY METROLOGY (XRM) SPECULAR X-RAY RE?ECTIVITY (XRR) DIFFUSE SCATTER X-RAY DIFFRACTION HIGH-RESOLUTION X-RAY DIFFRACTION DIFFRACTION IMAGING AND DEFECT MAPPING X-RAY FLUORESCENCE SUMMARY 2 THICKNESS METROLOGY INTRODUCTION DIELECTRICS AND METALS INTERFEROMETRIC METHODS INTENSITY METHODS MULTIPLE LAYERS EPITAXIAL LAYERS SMALL MEASUREMENT SPOTS COMPARISON OF XRR AND XRD FOR EPITAXIAL THICKNESS METROLOGY 3 COMPOSITION AND PHASE METROLOGY AMORPHOUS FILMS POLYCRYSTALLINE FILMS WAFERS AND EPITAXIAL FILMS VARIATION OF LATTICE PARAMETER WITH COMPOSITION: VEGARD’S LAW COHERENCY DISTORTION IN EPILAYERS ABSOLUTE LATTICE PARAMETER MEASUREMENTS RELATIVE LATTICE PARAMETER MEASUREMENTS REFERENCES 4 STRAIN AND STRESS METROLOGY STRAIN AND STRESS IN POLYCRYSTALLINE LAYERS SIN2? ANALYSIS GIIXD ANALYSIS RELAXATION OF EPITAXIAL LAYERS RELAXATION IN SIGE RELAXATION IN COMPOUND SEMICONDUCTORS RELAXATION IN COMPOUNDS BASED ON GAN THIN STRAINED SILICON LAYERS WHOLE WAFER DEFECT METROLOGY 5 MOSAIC METROLOGY GRAIN SIZE MEASUREMENT MOSAIC STRUCTURE IN SUBSTRATE WAFERS MOSAIC STRUCTURE IN EPILAYERS 6 INTERFACE ROUGHNESS METROLOGY INTERFACE WIDTH AND ROUGHNESS DISTINCTION OF ROUGHNESS AND GRADING MEASUREMENT BY GRAZING INCIDENCE ROCKING CURVES MEASUREMENT BY OFF-SPECULAR SPECIMEN DETECTOR SCANS ROUGHNESS DETERMINATION IN SEMICONDUCTORS ROUGHNESS DETERMINATION IN METALLIC FILMS ROUGHNESS DETERMINATION IN DIELECTRICS 7 POROSITY METROLOGY DETERMINATION OF POROSITY DETERMINATION OF PORE SIZE AND DISTRIBUTION PORES IN SINGLE CRYSTALS PART THE SCIENCE 8 SPECULAR X-RAY RE?ECTIVITY PRINCIPLES SPECULAR RE?ECTIVITY FROM A SINGLE IDEAL INTERFACE SPECULAR RE?ECTIVITY FROM A SINGLE GRADED OR ROUGH INTERFACE SPECULAR RE?ECTIVITY FROM A SINGLE THIN FILM ON A SUBSTRATE SPECULAR RE?ECTIVITY FROM MULTIPLE LAYERS ON A SUBSTRATE RE?ECTIVITY FROM A BILAYER RE?ECTIVITY FROM A PERIODIC MULTILAYER 9 X-RAY DIFFUSE SCATTERING ORIGIN OF DIFFUSE SCATTER FROM SURFACES AND INTERFACES THE BORN APPROXIMATION INTERFACE MODELING WITHIN THE BORN APPROXIMATION THE DISTORTED-WAVE BORN APPROXIMATION SEPARATION OF TOPOLOGICAL ROUGHNESS AND COMPOSITIONAL GRADING WITHIN THE DWBA EFFECT OF INTERFACE PARAMETERS ON DIFFUSE SCATTER MULTIPLE-LAYER STRUCTURES DIFFUSE SCATTER REPRESENTED IN RECIPROCAL SPACE SPECULAR SCAN OFF-SPECULAR COUPLED SCAN TRANSVERSE SCAN RADIAL SCAN TRANSFORMATION FROM ANGULAR COORDINATES TO RECIPROCAL SPACE UNITS 10 THEORY OF XRD ON POLYCRYSTALS 10 1 INTRODUCTION 10 1 1 MATHEMATICAL HEALTH WARNING 10 2 KINEMATICAL THEORY OF X-RAY DIFFRACTION 10 2 1 SCATTERING FROM A SMALL CRYSTAL 10 2 2 THE RECIPROCAL LATTICE 10 2 3 INTENSITY DIFFRACTED FROM A THIN CRYSTAL 10 3 DETERMINATION OF STRAIN 10 4 DETERMINATION OF GRAIN SIZE 10 5 TEXTURE 10 6 RECIPROCAL SPACE GEOMETRY 10 7 SUMMARY 11 HIGH-RESOLUTION XRD ON SINGLE CRYSTALS 11 1 INTRODUCTION 11 2 DYNAMICAL THEORY OF X-RAY DIFFRACTION 11 2 1 THE TAKAGI–TAUPIN GENERALIZED DIFFRACTION THEORY 11 2 2 THIN-LAYER AND SUBSTRATE SOLUTIONS 11 2 3 CALCULATION OF STRAINS AND MISMATCHES 11 3 THE DETERMINATION OF EPILAYER PARAMETERS 11 3 1 SELECTION OF EXPERIMENTAL CONDITIONS 11 3 2 MEASURING COMPOSITION 11 3 3 MEASURING THICKNESS 11 3 4 MEASURING TILT 11 3 5 MEASURING CURVATURE AND MOSAIC SPREAD 11 3 6 MEASURING DISLOCATION CONTENT 11 3 7 MEASURING RELAXATION 11 4 HIGH-RESOLUTION DIFFRACTION IN REAL AND RECIPROCAL SPACE 11 4 1 TRIPLE-AXIS SCATTERING 11 4 2 SETTING UP A TRIPLE-AXIS MEASUREMENT 11 4 3 SEPARATION OF LATTICE TILTS AND STRAINS 11 4 4 RECIPROCAL SPACE MAPPING 11 4 5 THE RELAXATION SCAN 11 4 6 GRAZING INCIDENCE IN-PLANE DIFFRACTION 11 5 SUMMARY 12 DIFFRACTION IMAGING AND DEFECT MAPPING 12 1 INTRODUCTION 12 2 CONTRAST IN X-RAY DIFFRACTION IMAGING (XRDI) 12 2 1 IMAGES OF DISLOCATIONS 12 3 SPATIAL RESOLUTION IN XRDI 12 3 1 REAL-TIME IMAGE DETECTORS 12 4 X-RAY DEFECT IMAGING METHODS 12 4 1 LANG PROJECTION TOPOGRAPHY 12 4 2 THE BEDESCAN METHOD 12 4 3 SECTION TOPOGRAPHY 12 5 EXAMPLE APPLICATIONS 12 6 SUMMARY THE TECHNOLOGY 13 MODELING AND ANALYSIS 13 1 WHAT HAS BEEN MEASURED? 13 2 DIRECT METHODS 13 3 DATA-FITTING METHODS 13 4 THE DIFFERENTIAL EVOLUTION METHOD 13 4 1 THE OBJECTIVE FUNCTION 13 4 2 PERFORMANCE AND EXAMPLES 13 5 REQUIREMENTS FOR AUTOMATED ANALYSIS 13 6 SUMMARY 14 INSTRUMENTATION 14 1 INTRODUCTION 14 2 X-RAY SOURCES 14 3 X-RAY OPTICS 14 4 MECHANICAL TECHNOLOGY 14 4 1 ANGLE MEASUREMENT AND CALIBRATION 14 5 DETECTORS 14 6 PRACTICAL REALIZATIONS 14 7 SUMMARY 15 ACCURACY AND PRECISION OF X-RAY METROLOGY 15 1 INTRODUCTION 15 2 DESIGN OF X-RAY METROLOGY 15 3 REPEATABILITY AND REPRODUCIBILITY 15 4 ACCURACY AND TRUENESS 15 4 1 X-RAY RE?ECTIVITY 15 4 2 HIGH-RESOLUTION X-RAY DIFFRACTION 15 5 REPEATABILITY AND THROUGHPUT 15 6 ABSOLUTE TOOL MATCHING 15 7 SPECIMEN-INDUCED LIMITATIONS 15 7 1 EFFECT OF LAYER DEFECTS 15 7 2 WHERE IS THE SURFACE? 15 7 3 COMPARISONS OF XRM WITH OTHER METROLOGIES 15 8 SUMMARY