Spectroscopic ellipsometry : principles and applications

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File Name: Fujiwara H. Spectroscopic ellipsometry (Wiley, 2007)(ISBN 0470016086)(O)(388s)_PEo_.pdf
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Uploaded: 03/20/2016

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Author: Hiroyuki Fujiwara
Year: 2007
Edition:
Publisher: John Wiley & Sons
City: Chichester, England ; Hoboken, NJ
Pages: 388
PagesInFile: 388
Language: English
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Library: Kolxo3
Library issue: 10

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Searchable: 1

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ISBN: 9780470016084,0470016086
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CRC32: B8373E48
SHA1: HLC67AHOTTJQYDCHTINC3GWVF5V6ZGFY
SHA256: 055650D3697F625C02230E89C53EDC77599F32B40969394716A2E07E1FC9E515
MD5: 844a76d50efaebb00153e8cab6dd0342

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Bridging the gap between laser physics and applied mathematics, this book offers a new perspective on laser dynamics. Combining fresh treatments of classic problems with up-to-date research, asymptotic techniques appropriate for nonlinear dynamical systems are shown to offer a powerful alternative to numerical simulations. The combined analytical and experimental description of dynamical instabilities provides a clear derivation of physical formulae and an evaluation of their significance. Starting with the observation of different time scales of an operating laser, the book develops approximation techniques to systematically explore their effects. Laser dynamical regimes are introduced at different levels of complexity, from standard turn-on experiments to stiff, chaotic, spontaneous or driven pulsations. Particular attention is given to quantitative comparisons between experiments and theory. The book broadens the range of analytical tools available to laser physicists and provides applied mathematicians with problems of practical interest, making it invaluable for graduate students and researchers 1.1 Features of Spectroscopic Ellipsometry 1 -- 1.2 Applications of Spectroscopic Ellipsometry 3 -- 1.3 Data Analysis 5 -- 1.4 History of Development 7 -- 1.5 Future Prospects 9 -- 2 Principles of Optics 13 -- 2.1 Propagation of Light 13 -- 2.1.1 Propagation of One-Dimensional Waves 13 -- 2.1.2 Electromagnetic Waves 18 -- 2.1.3 Refractive Index 19 -- 2.2 Dielectrics 24 -- 2.2.1 Dielectric Polarization 24 -- 2.2.2 Dielectric Constant 25 -- 2.2.3 Dielectric Function 29 -- 2.3 Reflection and Transmission of Light 32 -- 2.3.1 Refraction of Light 32 -- 2.3.2 p- and s-Polarized Light Waves 33 -- 2.3.3 Reflectance and Transmittance 39 -- 2.3.4 Brewster Angle 40 -- 2.3.5 Total Reflection 42 -- 2.4 Optical Interference 43 -- 2.4.1 Optical Interference in Thin Films 43 -- 2.4.2 Multilayers 46 -- 3 Polarization of Light 49 -- 3.1 Representation of Polarized Light 49 -- 3.1.1 Phase of Light 49 -- 3.1.2 Polarization States of Light Waves 50 -- 3.2 Optical Elements 52 -- 3.2.1 Polarizer (Analyzer) 53 -- 3.2.2 Compensator (Retarder) 57 -- 3.2.3 Photoelastic Modulator 58 -- 3.2.4 Depolarizer 59 -- 3.3 Jones Matrix 60 -- 3.3.1 Jones Vector 60 -- 3.3.2 Transformation of Coordinate Systems 62 -- 3.3.3 Jones Matrices of Optical Elements 66 -- 3.3.4 Representation of Optical Measurement / Jones Matrices 68 -- 3.4 Stokes Parameters 70 -- 3.4.1 Definition of Stokes Parameters 70 -- 3.4.2 Poincare Sphere 72 -- 3.4.3 Partially Polarized Light 75 -- 3.4.4 Mueller Matrix 77 -- 4 Principles of Spectroscopic Ellipsometry 81 -- 4.1 Principles of Ellipsometry Measurement 81 -- 4.1.1 Measured Values in Ellipsometry 81 -- 4.1.2 Coordinate System in Ellipsometry 84 -- 4.1.3 Jones and Mueller Matrices of Samples 86 -- 4.2 Ellipsometry Measurement 87 -- 4.2.1 Measurement Methods of Ellipsometry 87 -- 4.2.2 Rotating-Analyzer Ellipsometry (RAE) 93 -- 4.2.3 Rotating-Analyzer Ellipsometry with Compensator 97 -- 4.2.4 Rotating-Compensator Ellipsometry (RCE) 99 -- 4.2.5 Phase-Modulation Ellipsometry (PME) 104 -- 4.2.6 Infrared Spectroscopic Ellipsometry 106 -- 4.2.7 Mueller Matrix Ellipsometry 111 -- 4.2.8 Null Ellipsometry and Imaging Ellipsometry 113 -- 4.3 Instrumentation for Ellipsometry 117 -- 4.3.1 Installation of Ellipsometry System 117 -- 4.3.2 Fourier Analysis 120 -- 4.3.3 Calibration of Optical Elements 122 -- 4.3.4 Correction of Measurement Errors 127 -- 4.4 Precision and Error of Measurement 130 -- 4.4.1 Variation of Precision and Error with Measurement Method 131 -- 4.4.2 Precision of ([psi], [Delta]) 135 -- 4.4.3 Precision of Film Thickness and Absorption Coefficient 137 -- 4.4.4 Depolarization Effect of Samples 139 -- 5 Data Analysis 147 -- 5.1 Interpretation of ([psi], [Delta]) 147 -- 5.1.1 Variations of ([psi], [Delta]) with Optical Constants 147 -- 5.1.2 Variations of ([psi], [Delta]) in Transparent Films 150 -- 5.1.3 Variations of ([psi], [Delta]) in Absorbing Films 155 -- 5.2 Dielectric Function Models 158 -- 5.2.1 Lorentz Model 160 -- 5.2.2 Interpretation of the Lorentz Model 162 -- 5.2.3 Sellmeier and Cauchy Models 170 -- 5.2.4 Tauc-Lorentz Model 170 -- 5.2.5 Drude Model 173 -- 5.2.6 Kramers-Kronig Relations 176 -- 5.3 Effective Medium Approximation 177 -- 5.3.1 Effective Medium Theories 177 -- 5.3.2 Modeling of Surface Roughness 181 -- 5.3.3 Limitations of Effective Medium Theories 184 -- 5.4 Optical Models 187 -- 5.4.1 Construction of Optical Models 187 -- 5.4.2 Pseudo-Dielectric Function 189 -- 5.4.3 Optimization of Sample Structures 191 -- 5.4.4 Optical Models for Depolarizing Samples 191 -- 5.5 Data Analysis Procedure 196 -- 5.5.1 Linear Regression Analysis 196 -- 5.5.2 Fitting Error Function 199 -- 5.5.3 Mathematical Inversion 200 -- 6 Ellipsometry of Anisotropic Materials 209 -- 6.1 Reflection and Transmission of Light by Anisotropic Materials 209 -- 6.1.1 Light Propagation in Anisotropic Media 209 -- 6.1.2 Index Ellipsoid 213 -- 6.1.3 Dielectric Tensor 215 -- 6.1.4 Jones Matrix of Anisotropic Samples 217 -- 6.2 Fresnel Equations for Anisotropic Materials 222 -- 6.2.1 Anisotropic Substrate 222 -- 6.2.2 Anisotropic Thin Film on Isotropic Substrate 224 -- 6.3 4 x 4 Matrix Method 226 -- 6.3.1 Principles of the 4 x 4 Matrix Method 226 -- 6.3.2 Calculation Method of Partial Transfer Matrix 232 -- 6.3.3 Calculation Methods of Incident and Exit Matrices 233 -- 6.3.4 Calculation Procedure of the 4 x 4 Matrix Method 236 -- 6.4 Interpretation of ([psi], [Delta]) for Anisotropic Materials 237 -- 6.4.1 Variations of ([psi], [Delta]) in Anisotropic Substrates 237 -- 6.4.2 Variations of ([psi], [Delta]) in Anisotropic Thin Films 241 -- 6.5 Measurement and Data Analysis of Anisotropic Materials 243 -- 6.5.1 Measurement Methods 243 -- 6.5.2 Data Analysis Methods 245 -- 7 Data Analysis Examples 249 -- 7.1 Insulators 249 -- 7.1.1 Analysis Examples 249 -- 7.1.2 Advanced Analysis 252 -- 7.2 Semiconductors 256 -- 7.2.1 Optical Transitions in Semiconductors 256 -- 7.2.2 Modeling of Dielectric Functions 258 -- 7.2.3 Analysis Examples 262 -- 7.2.4 Analysis of Dielectric Functions 268 -- 7.3 Metals/Semiconductors 276 -- 7.3.1 Dielectric Function of Metals 276 -- 7.3.2 Analysis of Free-Carrier Absorption 281 -- 7.3.3 Advanced Analysis 286 -- 7.4 Organic Materials/Biomaterials 287 -- 7.4.1 Analysis of Organic Materials 287 -- 7.4.2 Analysis of Biomaterials 292 -- 7.5 Anisotropic Materials 294 -- 7.5.1 Analysis of Anisotropic Insulators 295 -- 7.5.2 Analysis of Anisotropic Semiconductors 296 -- 7.5.3 Analysis of Anisotropic Organic Materials 299 -- 8 Real-Time Monitoring by Spectroscopic Ellipsometry 311 -- 8.1 Data Analysis in Real-Time Monitoring 311 -- 8.1.1 Procedures for Real-Time Data Analysis 312 -- 8.1.2 Linear Regression Analysis (LRA) 313 -- 8.1.3 Global Error Minimization (GEM) 317 -- 8.1.4 Virtual Substrate Approximation (VSA) 323 -- 8.2 Observation of Thin-Film Growth by Real-Time Monitoring 328 -- 8.2.1 Analysis Examples 328 -- 8.2.2 Advanced Analysis 331 -- 8.3 Process Control by Real-Time Monitoring 333 -- 8.3.1 Data Analysis in Process Control 334 -- 8.3.2 Process Control by Linear Regression Analysis (LRA) 334 -- 8.3.3 Process Control by Virtual Substrate Approximation (VSA) 340 -- 1 Trigonometric Functions 345 -- 2 Definitions of Optical Constants 347 -- 3 Maxwell's Equations for Conductors 349 -- 4 Jones-Mueller Matrix Conversion 353 -- 5 Kramers-Kronig Relations 357

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