Nanometer-scale Defect Detection Using Polarized Light

This book describes the methods used to detect material defects at the nanoscale. The authors present different theories, polarization states and interactions of light with matter, in particular optical techniques using polarized light. Combining experimental techniques of polarized light analysis with techniques based on theoretical or statistical models to study faults or buried interfaces of mechatronic systems, the authors define the range of validity of measurements of carbon nanotube properties. The combination of theory and pratical methods presented throughout this book provide the reader with an insight into the current understanding of physicochemical processes affecting the properties of materials at the nanoscale.

Table of Contents:
Preface xi Chapter 1. Uncertainties 1 1.1. Introduction  1 1.2. The reliability based design approach 2 1.2.1. The MC method 2 1.2.2. The perturbation method  3 1.2.3. The polynomial chaos method 7 1.3. The design of experiments method  9 1.3.1. Principle  9 1.3.2. The Taguchi method 10 1.4. The set approach 14 1.4.1. The method of intervals 15 1.4.2. Fuzzy logic based method 18 1.5. Principal component analysis  20 1.5.1. Description of the process 21 1.5.2. Mathematical roots 22 1.5.3. Interpretation of results 22 1.6. Conclusions  23 Chapter 2. Reliability-based Design Optimization 25 2.1. Introduction  25 2.2. Deterministic design optimization 26 2.3. Reliability analysis  27 2.3.1. Optimal conditions  30 2.4. Reliability-based design optimization 31 2.4.1. The objective function  31 2.4.2. Total cost consideration 32 2.4.3. The design variables 33 2.4.4. Response of a system by RBDO  33 2.4.5. Limit states 33 2.4.6. Solution techniques  33 2.5. Application: optimization of materials of an electronic circuit board 34 2.5.1. Optimization problem  36 2.5.2. Optimization and uncertainties 39 2.5.3. Results analysis  43 2.6. Conclusions 44 Chapter 3. The Wave–Particle Nature of Light 47 3.1. Introduction 48 3.2. The optical wave theory of light according to Huyghens and Fresnel 49 3.2.1. The three postulates of wave optics  49 3.2.2. Luminous power and energy  51 3.2.3. The monochromatic wave  51 3.3. The electromagnetic wave according to Maxwell’s theory  52 3.3.1. The Maxwell equations 52 3.3.2. The wave equation according to the Coulomb’s gauge 56 3.3.3. The wave equation according to the Lorenz’s gauge  57 3.4. The quantum theory of light 57 3.4.1. The annihilation and creation operators of the harmonic oscillator  57 3.4.2. The quantization of the electromagnetic field and the potential vector  61 3.4.3. Field modes in the second quantization  66 Chapter 4. The Polarization States of Light  71 4.1. Introduction 71 4.2. The polarization of light by the matrix method  73 4.2.1. The Jones representation of polarization 76 4.2.2. The Stokes and Muller representation of polarization 81 4.3. Other methods to represent polarization 86 4.3.1. The Poincaré description of polarization 86 4.3.2. The quantum description of polarization 88 4.4. Conclusions  93 Chapter 5. Interaction of Light and Matter 95 5.1. Introduction  95 5.2. Classical models 97 5.2.1. The Drude model  103 5.2.2. The Sellmeir and Lorentz models 105 5.3. Quantum models for light and matter 111 5.3.1. The quantum description of matter  111 5.3.2. Jaynes–Cummings model  118 5.4. Semiclassical models 123 5.4.1. Tauc–Lorentz model 127 5.4.2. Cody–Lorentz model  130 5.5. Conclusions  130 Chapter 6. Experimentation and Theoretical Models 133 6.1. Introduction  134 6.2. The laser source of polarized light 135 6.2.1. Principle of operation of a laser  136 6.2.2. The specificities of light from a laser 141 6.3. Laser-induced fluorescence 143 6.3.1. Principle of the method 143 6.3.2. Description of the experimental setup  145 6.4. The DR method  145 6.4.1. Principle of the method 146 6.4.2. Description of the experimental setup  148 6.5. Theoretical model for the analysis of the experimental results  149 6.5.1. Radiative relaxation 152 6.5.2. Non-radiative relaxation  153 6.5.3. The theoretical model of induced fluorescence 160 6.5.4. The theoretical model of the thermal energy transfer 163 6.6. Conclusions  170 Chapter 7. Defects in a Heterogeneous Medium  173 7.1. Introduction 173 7.2. Experimental setup  175 7.2.1. Pump laser 176 7.2.2. Probe laser 176 7.2.3. Detection system 177 7.2.4. Sample preparation setup  180 7.3. Application to a model system  182 7.3.1. Inert noble gas matrix  182 7.3.2. Molecular system trapped in an inert matrix 184 7.3.3. Experimental results for the induced fluorescence 188 7.3.4. Experimental results for the double resonance  198 7.4. Analysis by means of theoretical models 203 7.4.1. Determination of experimental time constants  203 7.4.2. Theoretical model for the induced fluorescence 209 7.4.3. Theoretical model for the DR  214 7.5. Conclusions 216 Chapter 8. Defects at the Interfaces  219 8.1. Measurement techniques by ellipsometry 219 8.1.1. The extinction measurement technique  222 8.1.2. The measurement by rotating optical component technique 223 8.1.3. The PM measurement technique  224 8.2. Analysis of results by inverse method 225 8.2.1. The simplex method 232 8.2.2. The LM method  234 8.2.3. The quasi-Newton BFGS method 237 8.3. Characterization of encapsulating material interfaces of mechatronic assemblies  237 8.3.1. Coating materials studied and experimental protocol  239 8.3.2. Study of bulk coatings  241 8.3.3. Study of defects at the interfaces  244 8.3.4. Results analysis  251 8.4. Conclusions 253 Chapter 9. Application to Nanomaterials  255 9.1. Introduction 255 9.2. Mechanical properties of SWCNT structures by MEF 256 9.2.1. Young's modulus of SWCNT structures 258 9.2.2. Shear modulus of SWCNT structures  259 9.2.3. Conclusion on the modeling results  260 9.3. Characterization of the elastic properties of SWCNT thin films 260 9.3.1. Preparation of SWCNT structures 261 9.3.2. Nanoindentation 262 9.3.3. Experimental results 263 9.4. Bilinear model of thin film SWCNT structure  265 9.4.1. SWCNT thin film structure 266 9.4.2. Numerical models of thin film SWCNT structures 268 9.4.3. Numerical results  269 9.5. Conclusions  274 Bibliography 275 Index 293