Spectroscopic Ellipsometry Principles and

Spectroscopic ellipsometry has established its position as a high-precision optical-characterization technique - nevertheless, the principles of ellipsometry are often said to be difficult to understand, so the objective of this highly-illustrated book is to provide a fundamental insight into the technique by providing general descriptions for measurement and data analysis methods employed widely in spectroscopic ellipsometry.

Dr Hiroyuki Fujiwara is based at the National Institute of Advanced Industrial Science and Technology, Ibaraki, Japan. He received his PhD at the Tokyo Institute of Technology in 1996 and carried out post-doctoral research with Professor R.W. Collins at Penn State University. From 1998 to present he has been working as a senior research scientist at the Research Center for Photovoltaics at NIAIST. He received the 'Most Promising Young Scientist Award' from the Japan Society of Applied Physics and the 'Young Researcher Award' at the World Conference on Photovoltaic Energy Conversion in 2003.

Foreword	p. xiii
Preface	p. xv
Acknowledgments	p. xvii
Introduction to Spectroscopic Ellipsometry	p. 1
Features of Spectroscopic Ellipsometry	p. 1
Applications of Spectroscopic Ellipsometry	p. 3
Data Analysis	p. 5
History of Development	p. 7
Future Prospects	p. 9
References	p. 10
Principles of Optics	p. 13
Propagation of Light	p. 13
Propagation of One-Dimensional Waves	p. 13
Electromagnetic Waves	p. 18
Refractive Index	p. 19
Dielectrics	p. 24
Dielectric Polarization	p. 24
Dielectric Constant	p. 25
Dielectric Function	p. 29
Reflection and Transmission of Light	p. 32
Refraction of Light	p. 32
p- and s-Polarized Light Waves	p. 33
Reflectance and Transmittance	p. 39
Brewster Angle	p. 40
Total Reflection	p. 42
Optical Interference	p. 43
Optical Interference in Thin Films	p. 43
Multilayers	p. 46
References	p. 48
Polarization of Light	p. 49
Representation of Polarized Light	p. 49
Phase of Light	p. 49
Polarization States of Light Waves	p. 50
Optical Elements	p. 52
Polarizer (Analyzer)	p. 53
Compensator (Retarder)	p. 57
Photoelastic Modulator	p. 58
Depolarizer	p. 59
Jones Matrix	p. 60
Jones Vector	p. 60
Transformation of Coordinate Systems	p. 62
Jones Matrices of Optical Elements	p. 66
Representation of Optical Measurement	p. 68
Stokes Parameters	p. 70
Definition of Stokes Parameters	p. 70
Poincare Sphere	p. 72
Partially Polarized Light	p. 75
Mueller Matrix	p. 77
References	p. 78
Principles of Spectroscopic Ellipsometry	p. 81
Principles of Ellipsometry Measurement	p. 81
Measured Values in Ellipsometry	p. 81
Coordinate System in Ellipsometry	p. 84
Jones and Mueller Matrices of Samples	p. 86
Ellipsometry Measurement	p. 87
Measurement Methods of Ellipsometry	p. 87
Rotating-Analyzer Ellipsometry (RAE)	p. 93
Rotating-Analyzer Ellipsometry with Compensator	p. 97
Rotating-Compensator Ellipsometry (RCE)	p. 99
Phase-Modulation Ellipsometry (PME)	p. 104
Infrared Spectroscopic Ellipsometry	p. 106
Mueller Matrix Ellipsometry	p. 111
Null Ellipsometry and Imaging Ellipsometry	p. 113
Instrumentation for Ellipsometry	p. 117
Installation of Ellipsometry System	p. 117
Fourier Analysis	p. 120
Calibration of Optical Elements	p. 122
Correction of Measurement Errors	p. 127
Precision and Error of Measurement	p. 130
Variation of Precision and Error with Measurement Method	p. 131
Precision of ([psi], [Delta])	p. 135
Precision of Film Thickness and Absorption Coefficient	p. 137
Depolarization Effect of Samples	p. 139
References	p. 141
Data Analysis	p. 147
Interpretation of ([psi], [Delta])	p. 147
Variations of ([psi], [Delta]) with Optical Constants	p. 147
Variations of ([psi], [Delta]) in Transparent Films	p. 150
Variations of ([psi], [Delta]) in Absorbing Films	p. 155
Dielectric Function Models	p. 158
Lorentz Model	p. 160
Interpretation of the Lorentz Model	p. 162
Sellmeier and Cauchy Models	p. 170
Tauc-Lorentz Model	p. 170
Drude Model	p. 173
Kramers-Kronig Relations	p. 176
Effective Medium Approximation	p. 177
Effective Medium Theories	p. 177
Modeling of Surface Roughness	p. 181
Limitations of Effective Medium Theories	p. 184
Optical Models	p. 187
Construction of Optical Models	p. 187
Pseudo-Dielectric Function	p. 189
Optimization of Sample Structures	p. 191
Optical Models for Depolarizing Samples	p. 191
Data Analysis Procedure	p. 196
Linear Regression Analysis	p. 196
Fitting Error Function	p. 199
Mathematical Inversion	p. 200
References	p. 204
Ellipsometry of Anisotropic Materials	p. 209
Reflection and Transmission of Light by Anisotropic Materials	p. 209
Light Propagation in Anisotropic Media	p. 209
Index Ellipsoid	p. 213
Dielectric Tensor	p. 215
Jones Matrix of Anisotropic Samples	p. 217
Fresnel Equations for Anisotropic Materials	p. 222
Anisotropic Substrate	p. 222
Anisotropic Thin Film on Isotropic Substrate	p. 224
4 x 4 Matrix Method	p. 226
Principles of the 4 x 4 Matrix Method	p. 226
Calculation Method of Partial Transfer Matrix	p. 232
Calculation Methods of Incident and Exit Matrices	p. 233
Calculation Procedure of the 4 x 4 Matrix Method	p. 236
Interpretation of ([psi], [Delta]) for Anisotropic Materials	p. 237
Variations of ([psi], [Delta]) in Anisotropic Substrates	p. 237
Variations of ([psi], [Delta]) in Anisotropic Thin Films	p. 241
Measurement and Data Analysis of Anisotropic Materials	p. 243
Measurement Methods	p. 243
Data Analysis Methods	p. 245
References	p. 246
Data Analysis Examples	p. 249
Insulators	p. 249
Analysis Examples	p. 249
Advanced Analysis	p. 252
Semiconductors	p. 256
Optical Transitions in Semiconductors	p. 256
Modeling of Dielectric Functions	p. 258
Analysis Examples	p. 262
Analysis of Dielectric Functions	p. 268
Metals/Semiconductors	p. 276
Dielectric Function of Metals	p. 276
Analysis of Free-Carrier Absorption	p. 281
Advanced Analysis	p. 286
Organic Materials/Biomaterials	p. 287
Analysis of Organic Materials	p. 287
Analysis of Biomaterials	p. 292
Anisotropic Materials	p. 294
Analysis of Anisotropic Insulators	p. 295
Analysis of Anisotropic Semiconductors	p. 296
Analysis of Anisotropic Organic Materials	p. 299
References	p. 303
Real-Time Monitoring by Spectroscopic Ellipsometry	p. 311
Data Analysis in Real-Time Monitoring	p. 311
Procedures for Real-Time Data Analysis	p. 312
Linear Regression Analysis (LRA)	p. 313
Global Error Minimization (GEM)	p. 317
Virtual Substrate Approximation (VSA)	p. 323
Observation of Thin-Film Growth by Real-Time Monitoring	p. 328
Analysis Examples	p. 328
Advanced Analysis	p. 331
Process Control by Real-Time Monitoring	p. 333
Data Analysis in Process Control	p. 334
Process Control by Linear Regression Analysis (LRA)	p. 334
Process Control by Virtual Substrate Approximation (VSA)	p. 340
References	p. 342
Appendices
Trigonometric Functions	p. 345
Definitions of Optical Constants	p. 347
Maxwell's Equations for Conductors	p. 349
Jones-Mueller Matrix Conversion	p. 353
Kramers-Kronig Relations	p. 357
Index	p. 361
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Spectroscopic Ellipsometry Principles and Applications

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