Applications and Metrology at Nanometer Scale 1 - Abdelkhalak El Hami

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in order to obtain a model that closely represents the reality of operating systems and provides pertinent simulation results.

      The theoretical models that are based on the fundamental laws of physics use a bottom-up approach. These models can be studied using analytical or numerical methods. When experiments can be implemented, simulation results are compared to experimental results. It is also possible to use experimental methods and a top-down approach to build a database of the response of the system to applied stresses. These data are then analyzed by comparing them to the response of theoretical or empirical models. In all the cases, there is a degree of uncertainty in the statistical analysis of the data, which leads to predictions with a margin of error. The lower the margin of error, the closer the predictions are to reality, leading to a sound understanding of the functionalities of working materials.

      As Book 9 of the “Reliability of Multiphysical Systems Set”, this book is designed to provide applications for Book 2 in the set, entitled Nanometer-scale Defect Detection Using Polarized Light. This is achieved by describing the experimental and theoretical methods developed in fundamental research laboratories to understand the physics or chemical processes, which at the nanometer scale are at the origin of the remarkable properties of the materials introduced in innovative technological devices. It presents optical techniques based on polarized light, which are used to characterize interface and bulk material defects that have an impact on the performance of nanodevices. It also describes how mechanical properties of nanomaterials can be determined using theoretical models and by the analysis of experimental results and their uncertainties.

      This book is intended for students at master and doctoral levels, teaching academics and researchers in materials science, physics engineering and experimental study, as well as R&D and manufacturing engineers of large groups and SMEs in the field of electronics, mechatronics, or optical or electronic materials.

      Chapter 2 describes how to manage system variable uncertainties in the design process. The objective is to obtain a design that meets the performance requirements, has a stable response when design parameters vary randomly and respects a threshold of minimal performance for a given confidence level. Several methods for analyzing the effect on the output of uncertainties in the system input parameters are presented with practical applications: a probabilistic approach, interval analysis, a fuzzy logic method, designs of experiments and principal component analysis.

      Chapter 3 is dedicated to various applications of electromagnetic waves. After a quick summary of the main characteristics of electromagnetic waves and microwave antenna theory, the following applications are studied: energy of a monochromatic plane wave, properties of a rectangular waveguide, performance of a wire antenna and antenna networks. These applications facilitate the understanding of the operation of antennas for the fifth generation (5G) of mobile telecommunication systems.

      Chapter 4 deals with functional materials employed in intelligent systems. The main characteristic of these intelligent materials is the coupling of their various physical properties. Thermodynamic coupling and multiphysics coupling are studied for piezoelectric, magnetostrictive and shape memory materials. Application exercises are provided for the deformations of a plate-like thin layer, a piezoelectric accelerometer, a piezoelectric transducer and a piezoelectric sensor.

      Pierre Richard DAHOO

      Philippe POUGNET

      Abdelkhalak EL HAMI

      October 2020

      Introduction

      The scientific study of measurement is known as metrology. Any measure is based on a universally accepted standard and any measuring process is prone to uncertainty. In engineering science, measurement concerns various types of parameters. Legal metrology is imposed by a regulatory framework that the manufactured product must respect. Technical or scientific metrology involves the methods used to measure the technical characteristics of the manufactured product. In engineering sciences, measurement concerns various types of parameters. In a more general context of a systemic approach, metrology should also be considered in connection with other indicators of the production system. These measures enable the follow-up and development of the processes implemented for ensuring and optimizing product quality or reducing failure so that it meets client expectations. The ability of a product to meet quality and reliability expectations can be addressed in the design stage, according to a RBDO (Reliability-Based Design Optimization) approach described in the “Reliability of Multiphysical Systems Set Book 2”, entitled Nanometer-scale Defect Detection Using Polarized Light. More generally, RBDO makes it possible to consider the uncertain parameters of manufacturing processes, measurement and operational conditions in order to optimize the manufacturing process, the design parameters and the overall quality of the product.

      Reliability of Multiphysical Systems Set Book 2 focused on three levels of design for manufacturing an industrial product:

       – Numerical methods developed in engineering from mathematical models and theories in order to optimize product quality from its design according to RBDO. This methodology is a source of applications in engineering science intended to address optimization problems in the industrial field.

       – Experimental methods developed in fundamental research relying on the light–matter interaction and on simulation-based analysis using theoretical models in order to make nanometer-scale measurements and conduct the analysis. These methods are used in nanosciences for the elaboration of knowledge leading to nanotechnologies.

       – Finally, the application of these two approaches in the example presented in Chapter 9 of Reliability of Multiphysical Systems Set Book 2 (Nanometer-scale Defect Detection Using Polarized Light) to the measurement of the physical properties of a nanomaterial, carbon nanotube.

      In sciences, there are various ways to measure a dimension. The measuring instruments or methods employed depend on the scale at which metrology is approached. In order to describe the issues at stake for measurement at a given scale, we present the methods employed for the measurement processes at two scales of interest for scientists, namely the infinitely small, which corresponds to the Planck length of 1.6 x 10–35 m, and the infinitely large, which corresponds to the diameter of the Universe evaluated at 8.8 x 1026 m. This is to help the reader understand that, even though becoming an expert in a scientific field or in a given subject is not the objective, it is necessary to understand some basic tenets in order to master the methods used for successful metrology at a given scale.

      In 1899, Planck determined a unit of length lP=√(Gh/2πc3)≈ 1.6 x 10–35 m, referred to as Planck length, based on fundamental constants: G, gravitational constant (6.6 x 10–11 Nm2 Kg–2), h, Planck’s constant (6.64 x 10–34 Js) and c, the speed of light (2.99,729,458 x 108 ms–1). This length cannot be measured with the measurement technologies available on Earth. Indeed, the smallest length measurable at the LHC (Large Hadron Collider) of CERN, the particle accelerator in which two protons are made to frontally collide in a ring of 26,659 km, which led to the discovery in 2012 of the Higgs boson, is approximately 10–16 m, which is 19 orders of magnitude higher than the Planck length. CMS and ATLAS detectors were used in the observation of the Higgs boson, the latest prediction of the standard model not yet observed. The measurement at the scale

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