Optical Characterization of Thin Solid Films (eBook)

Olaf Stenzel finished his diploma thesis in laser spectroscopy at the physics department of Moscow State University, Russia, in 1986. He received his PhD from Chemnitz University of Technology, Germany, in 1990 and habilitated there in 1999 in the field of optical properties of heterogeneous optical coatings. From 2001, he has worked at the Optical Coating Department of Fraunhofer Institute for Applied Optics and Precision Engineering IOF in Jena, Germany. There he worked for several years as  the group manager for optical coating characterization. He is the author of The Physics of Thin Film Optical Spectra: An Introduction, (Springer 2005, 2015) and Optical Coatings: Material Aspects in Theory and Practice, (Springer 2014). Currently his focus is on teaching at the Abbe School of Photonics at Friedrich Schiller Universität Jena, Germany, where he reads lectures on "Structure of Matter" and "Thin Film Optics" for master of photonics students. He is a member of OSA - The Optical Society.Miloslav Ohlídal is a Professor of Applied Physics at the Brno University of Technology, Czech Republic. He was educated at the Masaryk University Brno, Czech Republic, where he received his RNDr. (1975) and Ph.D. (1989) degrees in Physics. From 1977-1981 he was a research worker at the Military Institute 060, where he dealt with military applications of lasers. Since 1981 he is engaged in the optical research at the Institute of Physical Engineering, Brno University of Technology. He directs the Laboratory of Coherent Optics. His research spans the various aspects of optics of thin films, laser light scattering, study of surface topography by optical methods, and optical instruments designing. Over the several past years his group has developed the technique of imaging spectroscopic reflectometry for optical characterization of thin films. He cooperates closely with industry. Prof. M. Ohlídal is a member of SPIE - The International Society for Optical Engineering, OSA-The Optical Society, and The Union of Czech Mathematicians and Physicists.

Foreword 7
Preface 9
Contents 11
Contributors 19
Symbols and Abbreviations 21
Introduction and Modelling 25
1 Introduction 26
1.1 First Considerations 26
1.2 Coating Characterization and Quality Control 31
1.3 Organisation of the Book 31
2 Characterization of Porous Zirconia Samples as an Example of the Interplay Between Optical and Non-optical Characterization Methods 34
2.1 Optical and Non-optical Coating Characterization 34
2.2 Optical Characterization Based on Intensity Measurements 37
2.3 Characterization Example: Interplay Between Optical and Non-optical Methods 39
2.3.1 Optical Constants 39
2.3.2 Relation of Optical Constants to Porosity: Mixing Models 41
2.3.3 Application to a Porous Film 42
2.4 Conclusions 51
References 52
3 Universal Dispersion Model for Characterization of Thin Films Over Wide Spectral Range 53
3.1 Introduction 53
3.2 Theoretical Background 55
3.2.1 Classical Model 55
3.2.2 Models Based on Quantum Mechanics 57
3.2.3 Broadening 62
3.3 Dispersion Models of Elementary Excitations 66
3.3.1 Phonon Absorption 67
3.3.2 Valence Electron Excitations 82
3.3.3 Electronic Transitions Involving Localized States 95
3.3.4 Free Carrier Contributions 97
3.3.5 Core Electron Excitations 99
3.4 Conclusion 101
References 102
4 Predicting Optical Properties from Ab Initio Calculations 105
4.1 Introduction 105
4.2 Band Structure Calculations 106
4.2.1 Wave Function Quantum Mechanics 106
4.2.2 Density Functional Theory 108
4.2.3 Exchange-Correlation Functionals 109
4.2.4 Beyond the DFT 111
4.3 Optical Properties 115
4.3.1 Bethe--Salpeter Equation 116
4.3.2 Usual Workflow 118
4.4 Modeling of Complex Systems 119
4.4.1 Special Quasi-random Structures 119
4.4.2 Simulated Annealing 120
4.4.3 Example: Refractive Index of TixSi1-xO2 121
4.5 Few Notes on Interpretation of the Results 122
4.5.1 Predictions Versus Experiment 122
4.5.2 Electronic Versus Optical Band Gap 123
4.6 Conclusions 123
References 124
Spectrophotometry and Spectral Ellipsometry 127
5 Optical Characterization of Thin Films by Means of Imaging Spectroscopic Reflectometry 128
5.1 Introduction 129
5.2 Motivation for Development and Exploitation of Imaging Spectroscopic Reflectometry 129
5.3 Brief Specification of Non-microscopic Imaging Spectroscopic Reflectometry at Normal Incidence of Light 131
5.4 Experimental Set Up of ISR Technique 133
5.5 Imaging Spectroscopic Reflectometers 134
5.5.1 Imaging Spectroscopic Reflectometer with Wide Spectral Range 134
5.5.2 Imaging Spectroscopic Reflectometer with Enhanced Spatial Resolution 136
5.6 Data Acquisition 138
5.7 Key Features of Imaging Spectroscopic Reflectometry 140
5.8 Methods of Imaging Spectroscopic Reflectometry 140
5.8.1 Single-Pixel ISR Method as the Stand-Alone Method 142
5.8.2 Single-Pixel ISR Method as the Complementary Method 143
5.8.3 Manual Multi-pixel ISR Method 146
5.8.4 Global Method 148
5.9 Precision and Accuracy of ISR 152
5.10 Another Application of ISR 155
5.11 Conclusion 158
References 160
6 Data Processing Methods for Imaging Spectrophotometry 163
6.1 The Challenges 164
6.2 Single-Spectrum Models 168
6.2.1 Thickness 169
6.2.2 Optical Constants 170
6.2.3 Non-uniformity 172
6.2.4 Spectral and Angular Averaging 176
6.2.5 Roughness 178
6.2.6 Thick Layers, Mixing and Incoherent Models 183
6.3 Multi-spectra Processing 184
6.3.1 Manual Multi-pixel 184
6.3.2 Zonal Multi-pixel 185
6.3.3 Timeline Multi-sample 186
6.4 Global Data Processing 186
6.4.1 Alternate Global and Local Fitting 187
6.4.2 Sparse Levenberg–Marquardt Algorithm 189
6.4.3 Direct Solution 192
6.5 Concluding Remarks 192
References 194
7 In Situ and Ex Situ Spectrophotometric Characterization of Single- and Multilayer-Coatings I: Basics 196
7.1 Introduction 196
7.2 Theory 198
7.2.1 Basics 198
7.2.2 Elaboration of Film Thickness and Optical Constants from Single Thin Film Spectra 200
7.2.3 Multilayer Spectra Evaluation 205
7.3 Further Information Gained from Optical Constants 208
7.3.1 Basic Classical Dispersion Models and Analytic Properties of the Dielectric Function 208
7.3.2 Often Used Other Dispersion Models 211
7.3.3 Optical Properties of Material Mixtures 214
7.3.4 An Empirical Extension of the Multi-oscillator Model: The Beta Distributed Oscillator (?_do) Model 215
7.4 Conclusions 219
References 220
8 In Situ and Ex Situ Spectrophotometric Characterization of Single- and Multilayer-Coatings II: Experimental Technique and Application Examples 222
8.1 Experimental Techniques in Spectrophotometry 222
8.1.1 Spectral Resolution 223
8.1.2 Sample Illumination 226
8.1.3 Transmission and Reflection Measurements 226
8.1.4 Pre-processing of Spectra 229
8.1.5 Specifics of In Situ Spectrophotometry 231
8.1.6 Shift Measurement 235
8.2 Examples 238
8.2.1 Basics 238
8.2.2 Ex Situ Characterization of Substrates 239
8.2.3 Ex Situ Characterization of Single Layer Coatings 240
8.2.4 Interplay of Ex Situ and In Situ Spectroscopy: Preparation and Characterization of a V-Coating 246
8.3 Conclusions 249
References 250
9 Ellipsometry of Layered Systems 252
9.1 Introduction 252
9.2 Matrix Formalisms 253
9.2.1 Jones Formalism 253
9.2.2 Stokes–Mueller Formalism 255
9.2.3 Matrix Formalism for Isotropic Layered Systems 259
9.2.4 Matrix Formalism for Anisotropic Layered Systems 263
9.3 Theory of Ellipsometric Measurements 268
9.3.1 Conventional Ellipsometry 268
9.3.2 Generalized Ellipsometry 269
9.3.3 Mueller-Matrix Ellipsometry 270
9.3.4 Techniques for Conventional and Generalized Ellipsometry 271
9.3.5 Techniques for Mueller-Matrix Ellipsometry 273
9.3.6 Imaging Ellipsometry 274
9.4 Applications 276
9.4.1 Approximation of Reflection Coefficients of Inhomogeneous Layers 276
9.4.2 Uniaxial Anisotropic Layer 279
9.4.3 Reflection and Transmission of Light by Transparent Slabs Covered with Layered Systems 282
9.5 Conclusion 284
References 285
Characterization of Defective and Corrugated Coatings 287
10 Optical Characterization of Thin Films Exhibiting Defects 288
10.1 Introduction 288
10.2 Quantities for the Optical Characterization 289
10.3 Random Roughness of Thin Film Boundaries 290
10.3.1 Effective Medium Approximation 290
10.3.2 Rayleigh–Rice Theory 294
10.3.3 Scalar Diffraction Theory 296
10.4 Area Non-uniformity of Thin Films 300
10.5 Inhomogeneity of Thin Films Represented by Refractive Index Profiles 306
10.5.1 Exact Solutions 306
10.5.2 WKBJ Approximation 308
10.5.3 Approximation by Multilayer Systems 309
10.5.4 Approximation Based on Recursive Formulae 309
10.5.5 Runge–Kutta Methods 310
10.6 Overlayers and Transition Layers 311
10.7 Numerical Examples 312
10.8 Experimental Examples 315
10.8.1 Slightly Randomly Rough Surface Covered with Very Thin Overlayer 315
10.8.2 Thin Film with Thickness Non-uniformity, Boundary Roughness and Overlayer 318
10.8.3 Inhomogeneous Thin Film 320
10.8.4 Transition Layers 322
10.9 Closing Remarks 325
10.10 Conclusion 326
References 326
11 Scanning Probe Microscopy Characterization of Optical Thin Films 331
11.1 Introduction 331
11.2 Instrumentation 333
11.2.1 Probe and Feedback Mechanism 334
11.2.2 Scanners 336
11.3 Metrological Traceability 338
11.3.1 Scanning System Calibration 339
11.3.2 Cantilever Stiffness Calibration 339
11.3.3 Apex Radius Calibration 340
11.4 Data Processing 343
11.4.1 Basic Tasks 343
11.4.2 Roughness Analysis 344
11.4.3 Step Height Analysis 349
11.5 Tip Sample Convolution Effect on Statistical Properties 350
11.6 Perspectives 351
11.7 Conclusion 354
References 354
12 Resonant Waveguide Grating Structures 356
12.1 Introduction 357
12.2 Characterization of Mechanical Loss in Optical Coating Materials and Implications for Waveguide Gratings in Precision Metrology 358
12.3 Functionality of Waveguide Gratings as High Reflectivity Mirrors 361
12.4 Fabrication of Monolithic Waveguide Gratings 363
12.5 Dimensional Characterization of Waveguide Gratings 365
12.6 Optical Characterization of Waveguide Gratings 365
12.6.1 Reflectance Measurements in a Cavity 365
12.6.2 Spectral and Angular Dependent Reflectance and Transmittance Measurements 367
12.6.3 Temperature Dependent Transmittance Measurements 368
12.7 Outlook 370
References 370
13 Polarization Control by Deep Ultra Violet Wire Grid Polarizers 374
13.1 Introduction 375
13.2 Polarization of Light 376
13.3 Characterization of Polarizing Elements 377
13.4 Common Elements for Polarization Control 377
13.5 Wire Grid Polarizers 379
13.6 Fabrication of Wire Grid Polarizers 383
13.7 Design and Characterization of Titania Wire Grid Polarizers 384
13.8 Application Ranges for Different Materials 387
13.9 Outlook 387
References 388
Scatter and Absorption 390
14 Roughness and Scatter in Optical Coatings 391
14.1 Definitions and Standards 392
14.1.1 Angle Resolved Scattering 392
14.1.2 Total Scattering 394
14.2 Theoretical Background 395
14.2.1 Light Scattering from a Single Rough Surface 396
14.2.2 Light Scattering from Thin Film Coatings 398
14.2.3 Roughness Evolution of Multilayer Coatings 399
14.3 Instruments for Light Scattering Measurements 401
14.3.1 Total Scattering Measurements 401
14.3.2 Angle Resolved Scattering Measurements 401
14.3.3 Compact Scattering Sensors 404
14.4 Application Examples 406
14.4.1 Light Scattering and Roughness of Substrates 406
14.4.2 Light Scattering from Multilayer Coatings 408
References 416
15 Absorption and Fluorescence Measurements in Optical Coatings 420
15.1 Overview of Absorption Measurement Techniques and Absolute Calibration 421
15.1.1 Calorimetry 422
15.1.2 Photo-Thermal Techniques 423
15.1.3 Photo-Acoustic Technique 426
15.2 Laser Induced Deflection (LID) Technique 428
15.2.1 Absolute Calibration, Measurement Procedure and Absorption Calculation 429
15.2.2 LID Measurement Concepts 431
15.2.3 Experimental Results 434
References 443
16 Cavity Ring-Down Technique for Optical Coating Characterization 445
16.1 Introduction 445
16.2 The CRD Technique for Detecting Reflectivities 447
16.2.1 The General CRD Concept and Physical Basics 447
16.2.2 Fundamentals of Optical Resonators 448
16.2.3 CRD Using Pulsed Light Sources 450
16.2.4 CRD Using Continuous Sources 452
16.2.5 Calculating the Mirror Reflectivity 455
16.3 Making It Run! A Guide Towards a CRD System 456
16.3.1 The Light Source 456
16.3.2 The Detection Unit 458
16.3.3 Broad Band Measurements 459
16.3.4 The Cavity Design 460
16.3.5 Coupling of Cavity and Light Source 461
16.3.6 Accuracies 463
16.4 Limits of the Technique 465
16.5 Summary 467
References 467
Index 469