Table of Contents

Cover

Title

Preface

1 Uncertainties

1.1. Introduction
1.2. The reliability based design approach
1.3. The design of experiments method
1.4. The set approach
1.5. Principal component analysis
1.6. Conclusions

2 Reliability-based Design Optimization

2.1. Introduction
2.2. Deterministic design optimization
2.3. Reliability analysis
2.4. Reliability-based design optimization
2.5. Application: optimization of materials of an electronic circuit board
2.6. Conclusions

3 The Wave–Particle Nature of Light

3.1. Introduction
3.2. The optical wave theory of light according to Huyghens and Fresnel
3.3. The electromagnetic wave according to Maxwell’s theory
3.4. The quantum theory of light

4 The Polarization States of Light

4.1. Introduction
4.2. The polarization of light by the matrix method
4.3. Other methods to represent polarization
4.4. Conclusions

5 Interaction of Light and Matter

5.1. Introduction
5.2. Classical models
5.3. Quantum models for light and matter
5.4. Semiclassical models
5.5. Conclusions

6 Experimentation and Theoretical Models

6.1. Introduction
6.2. The laser source of polarized light
6.3. Laser-induced fluorescence
6.4. The DR method
6.5. Theoretical model for the analysis of the experimental results
6.6. Conclusions

7 Defects in a Heterogeneous Medium

7.1. Introduction
7.2. Experimental setup
7.3. Application to a model system
7.4. Analysis by means of theoretical models
7.5. Conclusions

8 Defects at the Interfaces

8.1. Measurement techniques by ellipsometry
8.2. Analysis of results by inverse method
8.3. Characterization of encapsulating material interfaces of mechatronic assemblies
8.4. Conclusions

9 Application to Nanomaterials

9.1. Introduction
9.2. Mechanical properties of SWCNT structures by MEF
9.3. Characterization of the elastic properties of SWCNT thin films
9.4. Bilinear model of thin film SWCNT structure
9.5. Conclusions

Bibliography

Index

End User License Agreement

List of Tables

1 Uncertainties

Table 1.1. Parameters of the mass–spring–damper system model

2 Reliability-based Design Optimization

Table 2.1. Parameters used for the numerical simulations
Table 2.2. Parameters used in the genetic algorithm
Table 2.3. The optimal values of PCB design variables

3 The Wave–Particle Nature of Light

Table 3.1. Electromagnetic waves and their associated uses and frequency range

7 Defects in a Heterogeneous Medium

Table 7.1. Lennard–Jones parameters of rare gases and oxygen, nitrogen and carbon atoms
Table 7.2. Diameters of possible trapping sites in rare gases
Table 7.3. Parameters of the rigid molecule: r₀ bond length (Å) ß bond angle (degree), µ dipolar moment (Debye) and Q_ii quadrupolar moment along the i axis of the molecule (Debye Å)
Table 7.4. Radiative transition frequencies observed in argon matrix and temporal characteristics (2,279.1 cm⁻¹ (stable site) and 2,273.4 cm⁻¹(unstable site) ¹³CO₂/Ar = 1/2,000, T = 5 K)
Table 7.5. Minimum population inversion estimation ΔN_T for the onset of the stimulated emission in a 180 µm thick sample (ΔN_T/N₀ ≤ 50 %); (a) matrix values; (b) gas phase; (c) derived from (a) and (b); (d) experimental; (e) deduced from (c) and (d)
Table 7.6. Parameters used in numerical simulations (concentration 1/200)

8 Defects at the Interfaces

Table 8.1. Characteristics of the silicone gels and epoxy samples
Table 8.2. Substrate characteristics
Table 8.3. Characteristics of the thin layers of the Cu-Ni substrate

9 Application to Nanomaterials

Table 9.1. The measurement parameters in the indentation procedure
Table 9.2. Results of nanoindentation
Table 9.3. Simulation results by finite element

List of Illustrations

1 Uncertainties

Figure 1.1. Biembedded beam
Figure 1.2. Mean of the displacement of the beam midpoint
Figure 1.3. Standard deviation of the displacement of the beam midpoint
Figure 1.4. Histogram of the stress on the solder joint
Figure 1.5. Density of the stress on the solder joint
Figure 1.6. Density of the initial stress (red) and optimized constraint (blue). For a color version of this figure, see www.iste.co.uk/dahoo/nanometer.zip
Figure 1.7. Mass–spring–damper system
Figure 1.8. Mean value of the displacement xu(t) for the intervals method (blue) and deterministic method (red)
Figure 1.9. Two-dimensional cross-beam
Figure 1.10. Average value of the displacement as a function of time
Figure 1.11. Standard deviation of the displacement as a function of time

2 Reliability-based Design Optimization

Figure 2.1. Deterministic design optimization based on the safety factor
Figure 2.2. Normal physical space
Figure 2.3. Evaluation process of the reliability index
Figure 2.4. Comparison of the RBDO and DDO approach
Figure 2.5. Total, failure and initial costs
Figure 2.6. Diagram of a printed circuit board with six layers of copper
Figure 2.7. Architecture of the PCB’s fiber reinforcement: a) overview; b) detail of fiber fabrics
Figure 2.8. a) Constitution of a laminate; b) designation of a laminate
Figure 2.9. Comprehensive approach of PCB optimization
Figure 2.10. Cross-section and EF mesh of PCB
Figure 2.11. Mapping of the fiber's volume and orientation effects on the eigenfrequencies f₁ a), f₂ b), f₃ c) and f₄ d) of the PCB
Figure 2.12. Evolution of the orientation angle; a) and the fiber volume; b) as a function of the number of iterations
Figure 2.13. Evolution of the ratio between the thickness of the copper and FR4 layer as a function of the number of iterations

4 The Polarization States of Light

Figure 4.1. Relations between the parameters in the frame Oxy in the plane normal to the wave vector k and the ellipse axes Oab of the components of the electric field
Figure 4.2. Linear, circular and elliptic polarizing states [WIK 38]. For a color version of this figure, see www.iste.co.uk/dahoo/nanometer.zip
Figure 4.3. The Poincaré sphere defined by the Stokes parameters and examples of the fundamental polarization states
Figure 4.4. Bloch sphere and pure states (pseudo-spin) of a two-level system

5 Interaction of Light and Matter

Figure 5.1. Interaction of light and matter
Figure 5.2. a) Positive and negative charges centers are superposed; b) polarization of matter from the displacement of centroids
Figure 5.3. Variation of the real part ε′ and the imaginary part ε′ of the dielectric function about the oscillation at resonance frequency ω₀
Figure 5.4. Discrete electronic energy levels: a) atom and b) diatomic molecule
Figure 5.5. Normal vibrations of molecules of a) CO₂ and b) O₃ (Q₁ symmetrical stretch, Q₂ bending mode, Q₃ antisymmetrical stretch)
Figure 5.6. Energies E of electrons as a function of the distance r between the atom in a solid material: BC, conduction band; BV, valence band; E_V, top of the valence band; E_C, minimum of the conduction band; Eg = E_C − E_V, energy gap or bandgap; E_f, Fermi level
Figure 5.7. BS and HS states of the ion: Fe(II) and Fe(III)

6 Experimentation and Theoretical Models

Figure 6.1. Typical laser mounting: back and forth standing wave
Figure 6.2. Divergence of a beam from a source in terms of areas ∑ of sources in phase (spatial coherence) and solid angle ΔΩ
Figure 6.3. Vibrational levels of ¹³C¹⁶O₂: pump (ν₃) and transitions of fluorescence at 16 μm (1, 2, 3) and 10 μm
Figure 6.4. Diagram of the experimental setup for spectroscopy by laser-induced fluorescence
Figure 6.5. IR-IR double resonance signal of the fundamental band
Figure 6.6. IR-IR double resonance signal of the hot band
Figure 6.7. Diagram of the experimental setup with two beams of the pump-probe spectroscopy by reflection or transmission. (A and B) The possibility of having crystal doublers/triplers or a parametric amplifier and polarization optics or any device with a second laser on path B
Figure 6.8. The possible pathways of relaxation of an excited molecule in the solid phase (vj mode): D*: donors; D and A: acceptor; M: matrix: (a) V-V intra- and intermolecular transfers (1, 2, 3); (b) transfer to lattice modes: intrinsic relaxation (4.5); (c) radiative relaxation: fluorescence emission (6)
Figure 6.9. Stimulated emission between two excited levels

7 Defects in a Heterogeneous Medium

Figure 7.1. Experimental setup for laser spectroscopy: induced fluorescence and double IR–IR resonance
Figure 7.2. Shape of the pulsed laser signals (5 ns) based on the detection system: (a) GeCu; (b) MCT
Figure 7.3. Shape of the pulsed laser signals (5 ns) based on the detection system: a) with preamplifier; b) without preamplifier
Figure 7.4. Diagram of the cryostat for sample preparation
Figure 7.5. Interaction potential for different rare gas atoms
Figure 7.6. Possible trapping sites in a fcc lattice
Figure 7.7. Possible trapping sites of CO₂ in a fcc lattice. For a color version of this figure see www.iste.co.uk/dahoo/nanometer.zip
Figure 7.8. O₃ trapping sites in a fcc lattice and atomic distortions of the noble gas Ar
Figure 7.9. Time characteristics of a signal: t₀, delay;τ_R, rise; τ_M, maximum; τ₁ and (τ₂), decay
Figure 7.10. Envelope of the fluorescence signals and the laser pump as a function of the trigger level (O₃/Kr = 1/200, width 130 µm); a) 1.5 V; b) 4.1 V
Figure 7.11. Spectral analysis of the fluorescence for the two trapping sites (sample: O₃ / Xe = 1/200; thickness, 85 µm; T = 5 K)
Figure 7.12. Vibrational energy levels of ¹⁶O₃ in Xe (single-site HF and double-site LF): pump (ν_{1 +}ν₃), fluorescence transition at 10 µm (2ν₃ → ν₃) and probe transitions (Cold and Hot band)
Figure 7.13. Three fluorescence signals: a) stable site; b) unstable site, Ar/¹³CO₂ = 2,000; T = 5 K
Figure 7.14. Global fluorescence: a) stable site; b) unstable site, Ar/¹³CO₂ = 2,000, T = 5 K
Figure 7.15. Fluorescence: a) delay b) envelope, Ar/N₂O = 2,000, T = 5 K
Figure 7.16. Fluorescence at 10 µm as a function of the pump energy: Ar/N₂O = 2,000, T = 5 K; (square) 260 µm; (rhombus) 180 µm; (triangle) 90 µm
Figure 7.17. Fluorescence at 10 µm as a function of the pump energy (unstable site Ar/¹³CO₂ = 520, T = 5 K)
Figure 7.18. Fluorescence at 16 µm as a function of the pump energy: a) stable site; b) unstable site (Ar/¹³CO₂ = 2,000, T = 5 K)
Figure 7.19. Double resonance signals: a) carried by the line P₂₆ (A: 4.2 µs) and the line P₄₂ (B: 4.1 µs) of the CO₂ laser (O₃/Ar = 1/2,000, width :110 mm); b) the probe(P₂₆) and pump superposed (A) and the probe (P₂₆) and pump laterally displaced (B)
Figure 7.20. Decay time constant of the DR signal as a function of the concentration at 5 K: a) O₃/Ar; b) O₃/Kr
Figure 7.21. Repopulation time constant of the ground state in xenon
Figure 7.22. Rise times of DR signals carried by the lines P-42-negative and P26-positive (O3/Ar = 1/2,000; thickness: 130 mm, MCT detector)
Figure 7.23. Simulation of the fluorescence signal as a function of time for different values of the energy of the pump laser (O₃/Xe = 1/200, thickness 85 µm)
Figure 7.24. Intrinsic relaxation constant of the studied polyatomic molecules in noble gas matrices depending on the momentum mismatch (between 5 and 9 K depending on the molecules)

8 Defects at the Interfaces

Figure 8.1. Elements of an ellipsometer: Source S; polarizer P; λ/4 quarter wave plate; compensator C; phase modulator PM; sample E; analyzer A; detector D
Figure 8.2. Stack of N isotropic layers of thickness D_i and index n_i of the sample of total thickness D on a substrate
Figure 8.3. Rough surface modeled by an effective medium
Figure 8.4. Maxima and minima of a function
Figure 8.5. Geometric transformations of a simplex
Figure 8.6. Schematic of IML module before and after the potting operation
Figure 8.7. Optical model “Gen Osc” of the software WVASE
Figure 8.8. a) Ellipsometric parameters of the B1 silicon gel; b) the real part n and imaginary part k of the complex refractive index and dielectric constant ε' and ε'' of the B1 silicon gel
Figure 8.9. Comparison of absorption coefficients of the B2 silicon gel: ATR, S.E
Figure 8.10. Comparison of absorption spectra of polymers B1, M1 and E1
Figure 8.11. Comparison of cos (Δ) spectra of polymer interfaces B1, B2 on Al before and after humidity and heat stresses. For a color version of this figure, see www.iste.co.uk/dahoo/nanometer.zip
Figure 8.12. Comparison of cos (Δ) spectra of polymer interfaces B3, B4 on Al before and after humidity and heat stresses. For a color version of this figure, see www.iste.co.uk/dahoo/nanometer.zip
Figure 8.13. Comparison of cos (Δ) spectra of polymer interfaces M1, M3 on Al before and after humidity and heat stresses. For a color version of this figure, see www.iste.co.uk/dahoo/nanometer.zip
Figure 8.14. Comparison of cos (Δ) spectra of polymer interfaces B1, B2 on CuNi before and after humidity and heat stresses. For a color version of this figure, see www.iste.co.uk/dahoo/nanometer.zip
Figure 8.15. Comparison of cos (Δ) spectra of polymer interfaces B3, B4 on CuNi before and after humidity and heat stresses. For a color version of this figure, see www.iste.co.uk/dahoo/nanometer.zip
Figure 8.16. Comparison of cos (Δ) spectra of polymer interfaces M1, M3 on CuNi before and after humidity and heat stresses. For a color version of this figure, see www.iste.co.uk/dahoo/nanometer.zip
Figure 8.17. Comparison of spectra cos (Δ) of polymer interfaces B1 (left) and B2 (right) on quartz and Al. For a color version of this figure, see www.iste.co.uk/dahoo/nanometer.zip
Figure 8.18. Comparison of spectra cos (Δ) of polymer interfaces B3 (left) and B4 (right) on quartz and Al. For a color version of this figure, see www.iste.co.uk/dahoo/nanometer.zip
Figure 8.19. Comparison of spectra cos (Δ) of polymer interfaces M1 (left), M2 (center) and M3 (right) on quartz and Al. For a color version of this figure, see www.iste.co.uk/dahoo/nanometer.zip
Figure 8.20. Comparison of spectra cos (Δ) of polymer interfaces B1 (left) and B2 (right) on quartz and CuNi. For a color version of this figure, see www.iste.co.uk/dahoo/nanometer.zip
Figure 8.21. Comparison of spectra cos (Δ) of polymer interfaces B3 (left) and B4 (right) on quartz and CuNi. For a color version of this figure, see www.iste.co.uk/dahoo/nanometer.zip
Figure 8.22. Comparison of spectra cos (Δ) of polymer interfaces M1 (left) and M3 (right) on quartz and CuNi. For a color version of this figure, see www.iste.co.uk/dahoo/nanometer.zip
Figure 8.23. Comparison of cos (Δ) spectra of polymer interfaces B1 and B2 on quartz and Si. For a color version of this figure, see www.iste.co.uk/dahoo/nanometer.zip
Figure 8.24. Comparison of cos (Δ) spectra of polymer interfaces B3 and B4 on quartz and Si. For a color version of this figure, see www.iste.co.uk/dahoo/nanometer.zip
Figure 8.25. Comparison of cos (Δ) spectra of polymer interfaces M1, M2 and M3 on quartz and Si. For a color version of this figure, see www.iste.co.uk/dahoo/nanometer.zip
Figure 8.26. Comparison of cos (Δ) spectra of polymer interfaces M3 and E1 on quartz and Si. For a color version of this figure, see www.iste.co.uk/dahoo/nanometer.zip
Figure 8.27. Absorption spectra by ATR of silicon gels B (1–4) and M (1–3). For a color version of this figure, see www.iste.co.uk/dahoo/nanometer.zip

9 Application to Nanomaterials

Figure 9.1. Variation of Young’s moduli of SWCNT structures of armchair, zigzag and chiral forms as a function of the radius
Figure 9.2. Young’s moduli of SWCNT structures of armchair, zigzag and chiral forms as a function of length
Figure 9.3. Shear moduli of SWCNT structures of armchair, zigzag and chiral forms as a function of the radius
Figure 9.4. The process of centrifugal induction for thin SWCNT films; a) static distribution process; b) stages of centrifugal induction
Figure 9.5. Optical microscope image of nanotubes distributed on silicon substrates
Figure 9.6. System to measure hardness by nanoindentation
Figure 9.7. Load–displacement experimental results
Figure 9.8. Load versus displacement: test and modeling results. For a color version of this figure see www.iste.co.uk/dahoo/nanometer.zip
Figure 9.9. Load on a SWCNT film structure as a function of the displacement of the indenter while measuring nanoindentation
Figure 9.10. Model by finite elements of the indenter-film system
Figure 9.11. Results of testing and modeling of the load of a thin film SWCNT structure as a function of the displacement. For a color version of this figure see www.iste.co.uk/dahoo/nanometer.zip
Figure 9.12. Distribution of deformations and stresses of the SWCNT film substrate system. For a color version of this figure see www.iste.co.uk/dahoo/nanometer.zip
Figure 9.13. Curves of load–displacement from testing and modeling. For a color version of this figure see www.iste.co.uk/dahoo/nanometer.zip
Figure 9.14. Effects on the load–displacement curve of different indentor forms. For a color version of this figure see www.iste.co.uk/dahoo/nanometer.zip
Figure 9.15. Effect of the thickness of the SWCNT structure on the load–displacement curve. For a color version of this figure see www.iste.co.uk/dahoo/nanometer.zip
Figure 9.16. Effect of the substrate's Young's modulus on the load–displacement curve. For a color version of this figure see www.iste.co.uk/dahoo/nanometer.zip
Figure 9.17. Experimental and simulated discharge curves. For a color version of this figure see www.iste.co.uk/dahoo/nanometer.zip

First published 2016 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

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The rights of Pierre Richard Dahoo, Philippe Pougnet and Abdelkhalak El Hami to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2016943672

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN 978-1-84821-936-6

Preface

The various actions decided on at a global level to stimulate sustainable development and to respond to climate issues bring forth increasingly stringent regulations in terms of greenhouse gas emissions and hazardous substances. In the automotive sector these regulations drive industrial companies to develop new mechatronic systems using electricity to replace the various mechanical functions of vehicles. International competition and constant pressure to improve the performance of innovative products compel the companies supplying embedded mechatronic devices to innovate in increasingly shorter lead times to remain competitive.

To improve the performance of embedded systems in terms of volume or mass reduction, or to reduce energy losses, the mechatronic industry implements new packaging methods (such as those based on multimaterials) or incorporates new materials (for instance, carbon nanotubes). Modeling and simulation are used to limit cost, increase durability and reduce lead time to market. The Physics of failure provides the knowledge to predict and reduce potential failures in application and optimize design before activating serial production. In this respect, Reliability Based Design Optimization (RBDO) is a numerical tool used to optimize design and reduce industrial fabrication risks. This approach can only be applied efficiently when the underlying physical phenomena are thoroughly understood and when the models used accurately represent the conditions under which the device operates.

To model a dynamic system consisting of interacting sub-parts, a simplified system behavior model based on realistic hypotheses and key parameters is first used. Dynamic behavior is controlled by Partial Differential Equations (PDE) based on the characteristics of the system. By incorporating elements or parameters that were initially not included and by improving the PDE (for instance by taking into account non linearities or novel coupling schemes …) this model is extended and improved leading to an increasingly precise simulation of the real functioning behavior, as used in the process like approach.

Theoretical models are usually built following an analysis of the complex system which leads to equations based on fundamental laws from the bottom-up. Consequences are deduced from realistic hypotheses and known physical laws. Either analytical or digital methods are applied to solve the equations. Whenever possible, experiments are conducted to compare expected results and real data. A top-down approach can also be applied using experimental methods. This approach is based on data obtained by applying specific stresses or external constraints, and from the study of the system response. Data from these tests are compared to simulation results from theoretical or empirical models. Both bottom-up and top-down approaches can lead to some uncertainties in data analysis. This can be evaluated through statistical analysis which provides predictions and margins of error. The objective is to reduce the margin of error in order to obtain realistic predictions and to better understand the properties of active materials.

This book describes experimental and theoretical methods which are developed in fundamental research to better understand the physical chemistry and physical processes in complex systems and which, on the nanometric scale, are the root cause of the outstanding properties of the materials used in innovative technological devices. It presents optical techniques based on polarized light which can be applied to detect material or interface defects which have an impact on their performance. It also describes how to measure the mechanical properties of nanomaterials and how to analyze experimental data taking into account the range of uncertainties using theoretical models.

This book is written for students at Master and Doctoral levels, teaching academics and researchers in Materials Science and Experimental Studies, as well as engineers and technical staff from industrial sectors involved in systems where embedded electronics, mechatronics and electronic and optical materials are employed.

Chapter 1 describes various approaches which take into account uncertainties and are applied to analyze the static and dynamic behavior of systems and structures. Chapter 2 presents an approach to optimizing the design of a system which matches design cost with the guarantee of functioning without failure in the planned use conditions. This approach is based on taking into account uncertainties and on simultaneously solving two problems: optimizing the production cost of the structures performing the expected functions and ensuring an acceptable probability to fulfill its function. Chapters 3 and 4 give an overview of the classical and quantum theories of light as well as the various methods established to describe the polarization state of light.

Chapter 5 reviews theories on the interaction of light and matter and various condensed phase materials used in industrial applications. The notion of incomplete information about a quantum system is presented using the density matrix to take into account the problem of the interaction of the quantum system with the environment. Chapter 6 describes lasers, sources of polarized light and the experimental methods based on lasers to study either bulk materials using Laser Induced Fluorescence and IR-IR Double Resonance techniques, or the surface of materials using techniques to analyze the reflexion of a probe over the ultrasonic waves created by a pump laser. These methods make it possible to discriminate the different paths through which energy dissipates in materials when defects are present. This approach is used to build theoretical models to understand and analyze the thermal effects in composite materials.

Chapter 7 describes how to apply these methods to model systems before describing the apparatus used to prepare the systems composed of molecules which are trapped at low temperature in a solid matrix (rare gases or nitrogen). The various lasers and infrared detectors used in Laser Induced Fluorescence and Double Resonance techniques are presented. The results obtained on O₃-GR, CO₂-GR, and N₂O-GR systems are analyzed using theoretical models developed to determine the energy relaxation rate constants according to the various paths through which a system may transfer energy. Predictions and extrapolations applying the results of the highlighted transfer mechanisms to other sytems are proposed.

Chapter 8 describes the study of the interfaces of assembled materials using the IR spectroscopic ellipsometry technique. This technique is summarized as well as the necessary equipment and the analysis process, which is based on an inverse method applied to the models describing the interaction of light and matter through optimization algorithms. The results obtained on various types of interfaces found in the assembly of mechatronic power devices are presented and discussed. The ellipsometry technique is used to determine the possible modifications that occur in the properties of the materials when they come into contact as a result of physical or physical-chemical processes, as well as to follow the evolution of interfaces as a function of temperature in a dry or humid atmosphere.

Chapter 9 describes how to determine the properties of carbon nanotubes by applying the RBDO approach which correlates theoretical models and statistical methods to characterization and fabrication methods.

Pierre Richard DAHOO
Philippe POUGNET
Abdelkhalak EL HAMI
June 2016