Bowen D.K. X-Ray metrology in semiconductor manufacturing (Boca Raton, 2006). - ОГЛАВЛЕНИЕ / CONTENTS
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ОбложкаBowen D.K. X-Ray metrology in semiconductor manufacturing / Bowen D.K., Tanner B.K. - Boca Raton: CRC Press, 2006. - 279 p. - ISBN 0-8493-3928-6
 

Оглавление / Contents
 
Part 1  The Applications

1. Introduction ................................................. 3
   1.1 Scope of X-ray Metrology (XRM) ........................... 3
   1.2 Specular X-ray Reflectivity (XRR) ........................ 7
   1.3 Diffuse Scatter ......................................... 11
   1.4 X-ray Diffraction ....................................... 16
   1.5 High-Resolution X-ray Diffraction ....................... 21
   1.6 Diffraction Imaging and Defect Mapping .................. 24
   1.7 X-ray Fluorescence ...................................... 27
   1.8 Summary ................................................. 29

2. Thickness Metrology ......................................... 31
   2.1 Introduction ............................................ 31
   2.2 Dielectrics and Metals .................................. 32
       2.2.1 Interferometric Methods ........................... 32
       2.2.2 Intensity Methods ................................. 35
   2.3 Multiple Layers ......................................... 39
   2.4 Epitaxial Layers ........................................ 42
       2.4.1 Interferometric Methods ........................... 42
       2.4.2 Intensity Methods ................................. 44
       2.4.3 Small Measurement Spots ........................... 44
       2.4.4 Comparison of XRR and XRD for Epitaxial
             Thickness Metrology ............................... 45
   2.5 Summary ................................................. 46

3. Composition and Phase Metrology ............................. 47
   3.1 Introduction ............................................ 47
   3.2 Amorphous Films ......................................... 48
   3.3 Polycrystalline Films ................................... 52
   3.4 Wafers and Epitaxial Films .............................. 53
       3.4.1 Variation of Lattice Parameter with Composition:
             Vegard's Law ...................................... 53
       3.4.2 Coherency Distortion in Epilayers ................. 54
       3.4.3 Absolute Lattice Parameter Measurements ........... 55
       3.4.4 Relative Lattice Parameter Measurements ........... 57
   3.5 Summary ................................................. 59
   References .................................................. 60

4. Strain and Stress Metrology ................................. 61
   4.1 Introduction ............................................ 61
   4.2 Strain and Stress in Polycrystalline Layers ............. 62
       4.2.1 sin2ψ Analysis .................................... 62
       4.2.2 GIIXD Analysis .................................... 62
   4.3 Relaxation of Epitaxial Layers .......................... 67
       4.3.1 Relaxation in SiGe ................................ 70
       4.3.2 Relaxation in Compound Semiconductors ............. 71
       4.3.3 Relaxation in Compounds Based on GaN .............. 72
   4.4 Thin Strained Silicon Layers ............................ 73
   4.5 Whole Wafer Defect Metrology ............................ 75
   4.6 Summary ................................................. 76
   References .................................................. 77

5. Mosaic Metrology ............................................ 79
   5.1 Grain Size Measurement .................................. 79
   5.2 Mosaic Structure in Substrate Wafers .................... 81
   5.3 Mosaic Structure in Epilayers ........................... 82
   5.4 Summary ................................................. 86
   References .................................................. 86

6. Interface Roughness Metrology ............................... 87
   6.1 Interface Width and Roughness ........................... 87
   6.2 Distinction of Roughness and Grading .................... 90
       6.2.1 Measurement by Grazing Incidence Rocking Curves ... 90
       6.2.2 Measurement by Off-Specular Specimen Detector
             Scans ............................................. 92
   6.3 Roughness Determination in Semiconductors ............... 92
   6.4 Roughness Determination in Metallic Films ............... 94
   6.5 Roughness Determination in Dielectrics .................. 96
   6.6 Summary ................................................. 97
   References .................................................. 97

7. Porosity Metrology .......................................... 99
   7.1 Determination of Porosity ............................... 99
   7.2 Determination of Pore Size and Distribution ............ 100
   7.3 Pores in Single Crystals ............................... 106
   7.4 Summary ................................................ 106
   References ................................................. 107


Part 2  The Science

8. Specular X-ray Reflectivity ................................ 111
   8.1 Principles ............................................. 111
   8.2 Specular Reflectivity from a Single Ideal Interface .... 115
   8.3 Specular Reflectivity from a Single Graded or Rough
       Interface .............................................. 116
   8.4 Specular Reflectivity from a Single Thin Film on a
       Substrate .............................................. 119
   8.5 Specular Reflectivity from Multiple Layers on a
       Substrate .............................................. 122
       8.5.1 Reflectivity from a Bilayer ...................... 124
       8.5.2 Reflectivity from a Periodic Multilayer .......... 125
   8.6 Summary ................................................ 127
   References ................................................. 127

9. X-ray Diffuse Scattering ................................... 129
   9.1 Origin of Diffuse Scatter from Surfaces and
       Interfaces ............................................. 129
   9.2 The Born Approximation ................................. 130
       9.2.1 Interface Modeling within the Born
             Approximation .................................... 133
   9.3 The Distorted-Wave Born Approximation .................. 135
       9.3.1 Separation of Topological Roughness and
       Compositional Grading within the DWBA .................. 137
   9.4 Effect of Interface Parameters on Diffuse Scatter ...... 140
   9.5 Multiple-Layer Structures .............................. 141
   9.6 Diffuse Scatter Represented in Reciprocal Space ........ 145
       9.6.1 Specular Scan .................................... 146
       9.6.2 Off-Specular Coupled Scan ........................ 147
       9.6.3 Transverse Scan .................................. 148
       9.6.4 Radial Scan ...................................... 148
       9.6.5 Transformation from Angular Coordinates to
             Reciprocal Space Units ........................... 149
   9.7 Summary ................................................ 150
   References ................................................. 150

10. Theory of XRD on Polycrystals ............................. 151
    10.1 Introduction ......................................... 151
         10.1.1 Mathematical Health Warning ................... 152
    10.2 Kinematical Theory of X-ray Diffraction .............. 152
         10.2.1 Scattering from a Small Crystal ............... 155
         10.2.2 The Reciprocal Lattice ........................ 158
         10.2.3 Intensity Diffracted from a Thin Crystal ...... 159
    10.3 Determination of Strain .............................. 162
    10.4 Determination of Grain Size .......................... 164
    10.3 Texture .............................................. 166
    10.6 Reciprocal Space Geometry ............................ 167
    10.7 Summary .............................................. 170
    References	............................................... 171

11. High-Resolution XRD on Single Crystals .................... 173
    11.1 Introduction ......................................... 173
    11.2 Dynamical Theory of X-ray Diffraction ................ 174
         11.2.1	The Takagi-Taupin Generalized Diffraction
                Theory ........................................ 176
         11.2.2	Thin-Layer and Substrate Solutions ............ 178
         11.2.3	Calculation of Strains and Mismatches ......... 179
    11.3 The Determination of Epilayer Parameters ............. 181
         11.3.1	Selection of Experimental Conditions .......... 181
         11.3.2	Measuring Composition ......................... 183
         11.3.3	Measuring Thickness ........................... 185
         11.3.4	Measuring Tilt ................................ 187
         11.3.5	Measuring Curvature and Mosaic Spread ......... 187
         11.3.6	Measuring Dislocation Content ................. 189
         11.3.7	Measuring Relaxation .......................... 190
    11.4 High-Resolution Diffraction in Real and Reciprocal
         Space ................................................ 193
         11.4.1	Triple-Axis Scattering ........................ 193
         11.4.2	Setting up a Triple-Axis Measurement .......... 194
         11.4.3	Separation of Lattice Tilts and Strains ....... 194
         11.4.4	Reciprocal Space Mapping ...................... 197
         11.4.5	The Relaxation Scan ........................... 201
         11.4.6	Grazing Incidence In-Plane Diffraction ........ 204
    11.5 Summary .............................................. 207
    References ................................................ 207

12. Diffraction Imaging and Defect Mapping .................... 209
    12.1 Introduction ......................................... 209
    12.2 Contrast in X-ray Diffraction Imaging (XRDI) ......... 209
         12.2.1 Images of Dislocations ........................ 212
    12.3 Spatial Resolution in XRDI ........................... 216
         12.3.1 Real-Time Image Detectors ..................... 217
    12.4 X-ray Defect Imaging Methods ......................... 219
         12.4.1 Lang Projection Topography .................... 219
         12.4.2 The BedeScan Method ........................... 220
         12.4.3 Section Topography ............................ 223
    12.5 Example Applications ................................. 224
    12.6 Summary .............................................. 228
    References ................................................ 229


Part 3  The Technology

13. Modeling and Analysis ..................................... 233
    13.1 What Has Been Measured? .............................. 233
    13.2 Direct Methods ....................................... 234
    13.3 Data-Fitting Methods ................................. 236
    13.4 The Differential Evolution Method .................... 238
         13.4.1	The Objective Function ........................ 241
         13.4.2	Performance and Examples ...................... 242
    13.5 Requirements for Automated Analysis .................. 246
    13.6 Summary .............................................. 246
    References ................................................ 247

14. Instrumentation ........................................... 249
    14.1 Introduction ......................................... 249
    14.2 X-ray Sources ........................................ 249
    14.3 X-ray Optics ......................................... 251
    14.4 Mechanical Technology ................................ 254
         14.4.1 Angle Measurement and Calibration ............. 254
    14.5 Detectors ............................................ 254
    14.6 Practical Realizations ............................... 255
    14.7 Summary .............................................. 255
    References ................................................ 257

15. Accuracy and Precision of X-ray Metrology ................. 259
    15.1 Introduction ......................................... 259
    15.2 Design of X-ray Metrology ............................ 260
    15.3 Repeatability and Reproducibility .................... 260
    15.4 Accuracy and Trueness ................................ 261
         15.4.1 X-ray Reflectivity ............................ 262
         15.4.2 High-Resolution X-ray Diffraction ............. 262
    15.5 Repeatability and Throughput ......................... 263
    15.6 Absolute Tool Matching ............................... 265
    15.7 Specimen-Induced Limitations ......................... 266
         15.7.1 Effect of Layer Defects ....................... 266
         15.7.2 Where Is the Surface? ......................... 266
         15.7.3 Comparisons of XRM with Other Metrologies ..... 268
    15.8 Summary .............................................. 269
    References ................................................ 270

Index ......................................................... 271


 
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