Renée El

Melhem Bat

Blaise Pascal

R Gourdon

M Jean

Marc Lancelin

M Gérard Scorletti
email: gerard.scorletti@ec-lyon.fr

Isabelle Mme

Von Bueltzingloewen

Marco Cantoni

Dr M Smaïl Chalal

Prof Marc Nicolas Legros

Thierry Menguy

Fabrice Martinez

Frank Bauer

Jéôme Payen

Mike Millar

Pavel Nowakowski

Mickaël Philippe Masseron

Matthieu Champagne

Guillaume Colas

Prof Jérôme Chevalier

Thierry Douillard

Annie Malchère

Sophie Cattzottes

Claude Esnouf

Mihai Apreutesei

Lucian Roiban

Philippe Steyer

Kevin Lepinay

Mohamed-Hedi Jomaa

Juan Xiao

Karine Masenelli-Varlot

Lucile Joly-Pottuz

Florent Dalmas

Emilie Berangère

Sergieu Wael Yang

Emmanuel Sandrine

Jaqueline Claude

Antonia Jalila

Hui Yuan Metz

Keywords: 3D morphological and crystallographic analysis of materials with a Focused Ion Beam (FIB) Focused ion beam (FIB), Electron backscatter diffraction (EBSD), crystal orientation mapping, electron tomography, FIB-SEM, drifts, alignment by cross-correlation, surface topography, 3D EBSD, spatial resolution, channelling

The aim of the present work is to optimize the serial-sectioning based tomography in a dual-beam focused ion beam (FIB) microscope, either by imaging in scanning electron microscopy (so-called FIB-SEM tomography), or by electron backscatter diffraction (3D-EBSD tomography). In both cases, successive layers of the sample are eroded with the help of the ion beam, and sequentially acquired SEM or EBSD images are used to reconstruct its volume. Because of different uncontrolled perturbations, drifts are generally present during the FIB-SEM acquisition. We have thus developed a live drift correction procedure to keep automatically the region of interest (ROI) in the field of view. For the reconstruction of the investigated volume, an accurate post-mortem alignment of the image series is further required. Current methods using cross-correlation routines, expected to be robust, show limitations because it is difficult and sometimes impossible to rely on an absolute reference. This was demonstrated by dedicated experiments; we suggest therefore two alternative methods which allow good-quality alignments. As for 3D-EBSD tomography, technical problems, linked to the accuracy of the ion beam nanomachining and to the geometrical repositioning of the sample between milling and EBSD positions, lead to an important limitation of the spatial resolution when using commercial softwares (~ 50 nm) 3 . Moreover, 3D EBSD suffers from theoretical limits (large electron-solid interaction volume for EBSD and FIB milling effects), and requires a very long acquisition time. A new approach, coupling SEM imaging (with a good resolution of a few nanometres in both X and Y directions) at low SEM voltage, and crystal orientation mapping with EBSD at high SEM voltage, is proposed. Computer scripts have then be developed, which allow to control the milling, the acquisition of SEM and EBSD data. The interest and feasibility of this approach are demonstrated with a practical case (nickel super-alloy). Finally, regarding crystal orientation mapping, an alternative way to EBSD has been tested. It consists in taking advantage of channelling effects (ions or electrons) on the imaging contrast of secondary electrons. This method correlates simulations with the intensity variation of each grain within an experimental image series obtained by tilting and/or rotating the sample under the primary beam. This routine is applied again on a real case (polycrystal TiN), and shows a maximal misorientation of about 4° for Euler angles, as compared to a reference EBSD map. The application perspectives of this approach, potentially faster than EBSD, are also evoked.

In memory of dear colleagues and friends -Couple Van iii Résumé L'objectif principal de ce travail est d'optimise la tomographie par coupe sériée dans un microscope 'FIB', en utilisant soit l'imagerie électronique du microscope à balayage (tomographie FIB-MEB), soit la diffraction des électrons rétrodiffusés (tomographie dite EBSD 3D). Dans les 2 cas, des couches successives de l'objet d'étude sont abrasées à l'aide du faisceau ionique, et les images MEB ou EBSD ainsi acquises séquentiellement sont utilisées pour reconstruire le volume du matériau.

En raison de différentes sources de perturbation incontrôlées, des dérives sont généralement présentes durant l'acquisition en tomographie FIB-MEB. Nous avons développé une procédure in situ de correction des dérives afin de garder automatiquement la zone d'intérêt (ROI) dans le champ de vue. Afin de reconstruire le volume exploré, un alignement post-mortem aussi précis que possible est ensuite requis. Les méthodes actuelles utilisant la corrélation-croisée, pour robuste que soit cette technique numérique, présente de sévères limitations car il est difficile, sinon parfois impossible de se fier à une référence absolue. Ceci a été démontré par des expériences spécifiques ; nous proposons ainsi 2 méthodes alternatives qui permettent un bon alignement. Concernant la tomographie EBSD 3D, les difficultés techniques liées au pilotage de la sonde ionique pour l'abrasion précise, et au repositionnement géométrique correct de l'échantillon entre les positions d'abrasion et d'EBSD, conduisent à une limitation importante de la résolution spatiale avec les systèmes commerciaux (environ 50 nm) 3 . L'EBSD 3D souffre par ailleurs de limites théoriques (grand volume d'interaction électrons-solide et effets d'abrasion). Une nouvelle approche, qui couple l'imagerie MEB de bonne résolution en basse tension, et la cartographie d'orientation cristalline en EBSD avec des tensions élevées est proposée. Elle a nécessité le développement de scripts informatiques permettant de piloter à la fois les opérations d'abrasion par FIB et l'acquisition des images MEB et des cartes EBSD. L'intérêt et la faisabilité de notre approche est démontrée sur un cas concret (superalliage de nickel).

En dernier lieu, s'agissant de cartographie d'orientation cristalline, une méthode alternative à l'EBSD a été testée, qui repose sur l'influence des effets de canalisation (ions ou électrons) sur les contrastes en imagerie d'électrons secondaires. Cette méthode corrèle à des simulations la variation d'intensité de chaque grain dans une série d'images expérimentales obtenues en inclinant et/ou tournant l'échantillon sous le faisceau primaire. Là encore, la méthode est testée sur un cas réel (polycritsal de TiN) et montre, par comparaison avec une cartographie EBSD, une désorientation maximale d'environ 4° pour les angles d'Euler. Les perspectives d'application de cette approche, potentiellement beaucoup plus rapide que l'EBSD, sont évoquées.

Titre: Analyse 3D morphologique et cristallographique des matériaux par microscopie FIB Mots-clés: Sonde ionique focalisée (FIB), Diffraction des électrons rétrodiffusés (EBSD), cartographie d'orientation cristalline, tomographie électronique, FIB-MEB, dérives, alignement par corrélation croisée, topographie de surface, EBSD 3D, résolution spatiale, canalisation.

Contents viii 1

General introduction

The aim of this introduction is to position the subject of this thesis in the context of the use of a recent Focused Ion Beam (FIB) system for its potential application in the field of Materials Sciences. As it will be described all along this manuscript, modern double columns FIB are wonderful 'nano-knifes' allowing significant advances in the characterization of materials at the nanometric level. The FIB permits to cut the matter at a nanometric resolution, providing the way to perform a nano-manipulation and in situ testing of nano-object, to study buried details in a microstructure, extract localised thin foils for Transmission Electron Microscopy (TEM) of acquire stacks of 2D images for 3D analysis. The association of an electron column (Scanning Electron Microscope, SEM) with an ionic column allows both the imaging and the nano-machining of the sample. In the following section (I.1), we will briefly survey the applications of the FIB mainly regarding the 3D study of microstructures, which did constitute the starting point of this thesis. Then we will shortly present the instrument available at the CLYM and used during this work (II.2). The motivations and the outline of this document will constitute the two last sections (I.3 and I.4 respectively).

I.1. 3D characterization in materials science

The characterisation of microstructures is a key point in Materials Sciences to understand the properties of materials and further improve their performances. Therefore, microscopy techniques, from optical to electron microscopy play a great role in these micro-and nanostructural investigations. If we focus here on Scanning Electron Microscopy, the observation is most of the time performed in two-dimensions (2D): either the surface of the sample is intentionally cut (and generally polished or prepared in a certain way regarding the observation technique), or a fresh surface is produced by fracture. This basic approach suffers two main limitations:

-On the one hand, the surface has to be representative of the distribution and parameters of the features of interest (precipitates, pores, fractures, grain size,…), which is not the case especially if those features are not distributed in an isotropic way. -On the other hand, the feature of interest may be invisible on the produced surface and no characterization can be performed (typical cases are interfaces or grain-boundaries, or inclusions embedded in the bulk of the sample).

For these naïve reasons, three-dimensional (3D) volumetric investigations of microstructures, often referred as 'tomography', is more and more required for a complete, quantitative and representative analysis of materials.

In its principle, the 3D microstructure is virtually generated from a large series of 2D images after digital geometry processing, including alignment, segmentation, reconstruction and visualisation.

The tomography began X-rays in the early 1900s and has been extensively developed as Computer Tomography (CT) nowadays, applied in both Materials and Medical Sciences. Here the set of 3D imageshas to be proceed with the volume reconstruction. TEM tilting tomography has further been developed on the same principle and is also largely used today in all domains, from nanotechnology to biological applications.

Another tomography method is achieved by serial sectioning and has been applied in materials science since the 1920s. Here the 3D microstructure can be directly reconstructed from the serial images obtained from freshly sectioned layers: this is actually real tomography in the etymologic sense. This can be performed with an optical microscope, a Scanning Electron Microscope on polished or ultramicrotome-cut sections, or on the same basis with an Atom Probe (although the specimen does have a specific needle geometry, and the slicing (and in the best cases the reconstruction) is performed at the atomic level). In this context, the FIB is an ideal tool to perform such tomography since nanometric slices can be accurately removed with the ion beam, allowing the stack of 2D images from the fresh surfaces to be acquires with any signal available in a SEM.

According to the possibility of mounting analytical tools on the SEM such as Energy-Dispersive Xray (EDX) analysers or EBSD (Electron BackScattered Diffraction) cameras, tomography can be performed in a 4D space, where the chemical and/or the crystallographic dimensions (respectively for EDX and EBSD) can be added to the 'conventional' volume information.

I.2. The FIB instrument at CLYM

As illustrated in figure I.1, a Carl ZEISS Nvision 40 dual-beam FIB workstation has been installed at Microscope Centre of Lyon (CLYM1 ) since 2010. CLYM is a federation of numerous laboratories around Lyon, not only for convergent scientific researches on materials, but also for individual specified research needs. As already evoked in section I.1, the FIB is a versatile tool for widespread materials science applications, from integrated circuit editing and transmission electron microscopy (TEM) sample preparation to microstructural analysis and prototype nano-machining.

This thesis was prepared in the context of the common interest of two partners of the CLYM platform, the MATEIS (University of Lyon, INSA) and LGL-TPE (University of Lyon, ENS). MATEIS is working on all classes of materials: metals, polymers, ceramics and their composite associations from the point of view of their mechanical and multi-functional properties. LGL is a specialised in geology and interested in studying the microstructure of minerals and especially meteorites in the perspective of understanding geologic phenomena, such as the earth formation or earthquakes of volcano activity. The FIB represents a great interest for these two components: on the one hand, TEM thin foils preparations and 3D analysis are the main potential applications for MATEIS2 ; on the other hand, 3D analysis, and the ability to work on very small pieces of matter (in the case of meteorites, which are rare, and even objects) constitute the principal motivation to use the FIB at LGL. Other CLYM partners are also mostly interested in practicing the FIB, especially in the field of nano-Sciences and Nanotechnology at INL and ILM laboratories at University of Lyon (mainly for nano-machining and nano-patterning applications).

I.3. Motivations of the present study

Watching the literature or the scientific and commercial communications about using a FIB, one might think this is an instrument which can be driven, easily. This is not really true: as for the SEM which has undergone many improvements in a recent past, regarding its performances and the development of a large variety of detectors, the signals of which can be mixed in a complex way, the FIB is actually a complex instruments with a lot of possibilities but which demands great skills to obtains good results. In this context, we aimed at learning how to use this instrument in practice, and improve some of the operations that are possible, and which might not be well developed on a manufacturer side.

According to this, the present thesis is a contribution to the improvement, of new development of methods mainly in 3D approaches as permitted in a FIB.

As presented in section I.1, the acquisition of stacks of 2D images is the current way to acquire 3D information on materials. The success of such FIB-SEM tomography relies on the quality of the acquisition, and especially its stability in time since the acquisition can take several hours, even days according to the volume to be investigated. This is where the problem is: different kinds of perturbations occur, due to the sample, the microscope of its environment, degrade the quality of the acquisition up to the point that the Region Of Interest (ROI) can even be lost during the experiment. Although manual correction is very simple, it imposes the permanent presence of the user, which is rather tedious and not efficient. We thus decided in a first step to work on this problem and develop a routine allowing an automatic live correction, which was not specifically documented in the literature at the time of our contribution on this subject (this routine is presented in details in an Appendix at the end of the text). Another important issue, although largely underestimated (or even ignored) in the literature is the accuracy of the required post-mortem alignment of the 2D image stack before realizing the 3D reconstruction. We have prepared specific experiments to demonstrate that the commonly used alignment procedure, based on cross-correlation calculations between successive images, can be significantly flawed even if they imply dedicated markers machined on the ROI in order to serve as 'fixed' references for the alignment. On this point, we have developed a robust method based on the surface topography of the sample itself which can be reconstructed independently and used as a good reference for the stack alignment. All this constitutes the third chapter of this thesis, which is preceded by a classical bibliographic survey in Chapter II.

Beyond basic SEM imaging to provide morphological 3D information in FIB-SEM experiments, the EDX and EBSD analytical tools are often added to the FIB system to get more information from the sample. 3D EDX in FIB was significantly developed, according to its relatively simple experimental setup which does not requires any movements of the sample on its stage (rotation or tilt): it has been studied in several PhD thesis, like M. Schaffer at Graz University of Technology (with an application to porous ceramic materials) [Schaffer 2008], F. Lasagni at Vienna University of Technology (Albased alloys) [Lasagni 2006], and P. Burdet at EPFL Lausanne (NiTi-stainless steel wires) [Burdet 2012]. This is not the case with 3D-EBSD which was little developed (PhD thesis of Groeber M. at the Ohio State University [Groeber 2007]) because of the main experimental difficulties: o the EBSD technique is very sensitive to the quality of the sample surface (roughness, collecting geometry…) and this requires a long time for preparing the working area, and a controlled procedure when slicing the material with the ion beam o contrary to 3D-EDX, 3D EBSD in a FIB requires (at least, in the ZEISS NVision 40) a systematic 180° rotation to change form the SEM-FIB to the EBSD positions, which is very time-consuming and a great source of instabilities and loss of the ROI.

In this context, there was no robust and efficient commercial solution provided by the manufacturer when we installed the microscope. All these disadvantages encouraged us to develop a novel approach to perform 3D-EBSD mapping together with conventional FIB-SEM tomography, which means improving the process by mixing the crystallographic and morphological information in a 3D FIB-SEM-EBSD procedure. One of the further ideas was also to improve the resolution of the approach by using the better imaging resolution (as compared to the EBSD resolution) in the final reconstructed volume, going for typically 50 nm 3 in 'classical' 3D-EBSD to a few nm 3 . This is the concern of Chapter IV.

As a complement to EBSD, which is the most-well adapted technique to characterize crystallographic orientations of grains in a SEM, we have been interested in the possible application of contrast channelling (with primary electrons of ion-induced electrons) as a simple, robust and rapid alternative to EBSD. After having presented some theoretical aspects of contrast channelling, a preliminary approach is presented of a methodology and software to address this question in 2D (as a first step). As in Chapter IV, the feasibility is demonstrated on a test system. All this constitute Chapter V.

Moreover, the classical 2D EBSD is limited for its spatial resolution and acquiring speed for a large area mapping. However, the channelling contrast is linked closely to the crystal orientation, and has a better spatial resolution comparing to EBSD with its backscattered mechanism. Therefore, a new routine is developed to determine the Euler's angle.

I.4. Structure of the manuscript

To summarize, this dissertation includes 5 chapters: o Chapter II introduces the state of art of FIB instrument and EBSD technique. Including a basic presentation of the Carl ZEISS NVision 40 instrument and the main concepts regarding the different parts (ion -electron sources and column optics). The principles of the interactions of ions and electrons with solids are then surveyed in order to explain the ability of milling by ion beam, and reminded the performances in terms of high resolution imaging with the electron column. Last, the general theory and the indexing process of EBSD patterns, as well as the EBSD setup in the FIB are reviewed. o Chapter III describes firstly the current acquiring process and post-mortem alignment for a stack of images acquired during a 3D FIB-SEM tomographic experiment. A dedicated experiment has been performed to show a classical alignment issue arising from a basic application of cross-correlation routines. New methods are then proposed and critically discussed and quantitatively compared in terms of accuracy. o Chapter IV is dedicated to 3D-EBSD. It first describes the geometrical set-up, the current available acquiring process and post-mortem software provided as a commercial solution from manufacturers. Then a new strategy for 3D EBSD acquisition is proposed, and the required steps are presented, together with a feasibility test demonstrating the interest of a mixed FIB-SEM-EBSD tri-dimensional approach. o Chapter V is a preliminary work on the use of channelling contrast in a FIB-SEM microscope, and its connection to crystal orientation. A method is proposed, and tested on a study case, which can constitute a fast alternative to EBSD when the required information is mainly the knowledge of the grain orientation in a polycristal. o Chapter VI constitutes the usual Conclusion and Perspectives part of the work. It is followed by an Appendix explaining exhaustively the 'live drift correction' and 'auto-focusing' developed in Chapter III for FIB-SEM tomography experiments3 .

State-of-the-art: FIB microscope and EBSD technique

Resume of chapter

The working principle of two widely applied ion sources (liquid metal ion sources -LMIS and gas field ion sources -GFIS) is described. Especially for LMIS, a detailed presentation is proposed to understand the role of different parameters. The field-assisted electron sources, which are typically used in a dual-beam FIB for high resolution imaging, are presented and compared to ion sources. Then, the ion and electron columns setup are described. The interactions between ions or electrons and matter are also reviewed to show why ion beam can mill away materials, and how electron beam can give different imaging signals.

According to these performances, FIB/SEM tomography is now becoming more and more popular to get 3D information on morphology. For further 3D information on crystallography, an EBSD camera can be added to the FIB system. The general theory and operating conditions of EBSD are reviewed. Recent works in the literature will be surveyed, which intend to rule out the two mains limits of this technique, currently the longtime of acquisition and its limited spatial resolution.

Résumé de chapitre

Le principe de deux sources ioniques très utilisées (sources d'ions à métal liquide -LMIS et sources d'ions de champ de gaz -GFIS) par émission de champ est décrite. Dans le cas des LIMS, une présentation plus détaillée est proposée pour comprendre les différents paramètres qui en contrôlent l'émission. Les sources d'électrons assistées par effet champ, qui sont généralement utilisées dans la sonde ionique focalisé 'double faisceau' pour l'imagerie en haute résolution, sont présentées et comparées aux sources d'ions. Les configurations des colonnes ioniques et électroniques colonne sont décrites. Les interactions ions -ou électrons -matière sont également revues, qui montrent pourquoi un faisceau d'ions peut usiner les matériaux, et comment le faisceau d'électrons peut donner lieux aux différents signaux détectés.

Ces performances expliquent le succès grandissant des approches tomographiques en FIB/SEM pour obtenir des informations morphologiques en 3D. L'ajout d'une caméra EBSD au système FIB permet d'étendre l'information 3D aux aspects cristallographiques. La théorie et les conditions d'exploitation générales de l'EBSD sont revues. Nous évoquerons les travaux en cours pour contourner les limites essentielles de cette technique: la durée des acquisitions et la résolution spatiale limitée.

II.1. Introduction

II.1.1. General introduction

The EBSD technique and FIB instrument are today two well-developed microscopy approaches for a microstructural investigation in Materials Science.

The EBSD technique started to develop quickly in the 90s, when the Hough or Burns algorithm was applied to realise fully automatic procedure. Then, with the enormous progress in microelectronic science, the greater working speed of newest EBSD system has attended around 1000 Hz 4, 5,6 (collecting and indexing patterns for 1000 points per second).

Commercialised FIB instruments appeared firstly in 1980s within the semi-conductor industry for repairing or modifying integrated circuits and micro-electronic devices. Up to now, the FIB microscope has become a standard micro-operating tool in research institutions for Materials through to Life Sciences owing to its extensive applications: micro-preparation of sample for other techniques (such as TEM, atom probe), prototype micro-machining, serial sectioning tomography, etc.

Coupling EBSD and FIB to get 3D crystallographic related information becomes possible with the modern dual-beam FIB/SEM instrument equipped with very sensitive EBSD detector. 3D EBSD extends broadly the capacity of classical 2D EBSD to analyse the volume of materials. It is equipped with a SII Zeta ion gun (Ga LMIS), a ZEISS Gemini ® FEG, a SII Gas inject system (W, SiO x , C, H 2 O, XeF 2 ), a flood gun, multi-detectors (SESI, Inlens, EsB, STEM), an Oxford Instruments 50mm 2 SDD EDX detector, an Oxford Instruments Nordlys F + EBSD camera, two KlockeNanotechnik micromanipulators and a Fibics external scan generator.

II.1.2. NVision 40 FIB instrument at CLYM

II.1.2.1. Configuration unit

The NVision 40 FIB-SEM system was developed by Carl ZEISS SMT7 and SII NanoTechnology Inc. 8 , and commercialised since 2006. The unit available at CLYM has been installed and became operated in mid-2010. As illustrated in figure II.1, this FIB microscope consists in a ZEISS GEMINI ® (Schottky field emission gun based) electron column (vertical), a SII Zeta (Ga + liquid metal ion source based) ion column (inclined 54° to electron column) and a SII Gas injection system (W and C for deposition, SiO x , H 2 O and XeF 2 for enhanced etching) to provide FIB's basic functions of milling, imaging and deposition, respectively. In addition, the NVison is equipped with two analytic tools, including an Oxford Instruments 50 mm 2 SDD EDX detector for chemical analysis and an Oxford Instruments Nordlys F + EBSD detector for crystallographic investigation. Two KlockeNanotechnik micro-manipulators are also available for micro-operations, especially the preparation of TEM lamella. A flood gun is present for charge neutralization during the FIB process and the SEM imaging on nonconductive specimens. More recently (2013), an external scan generator from the Fibics Company was added; it allows to scan very large fields of view or drive both ion and electron beams in a very automatized way. Evidently, for attaining high performances, the ion and electron columns and the microscope chamber are under high vacuum condition.

The basic concept of the FIB-SEM configuration is that the ion column and electron column are aligned so that they arrive at a common point -the coincidence point (typically 5 mm below the pole piece of electron column in the NVision 40) -; a specimen, placed at this coincidence point can be locally modified by ion beam with a high positioning accuracy (4 nm at 30 keV for SII Zeta ion column), and imaged at the same time with the electron beam in high resolution (1.7 nm at 1 keV for ZEISS GEMINI ® electron column). The ion probe and energy is changed by selecting prefixed current/voltage couples in the system, while the electron probe can be modified in successive accelerating voltages and prefixed currents. The probe geometry is controlled electronically by changing the aperture with different diameters, adapting the optic lenses and setting the accelerating voltage at the ion/electron source.

Several detectors are available for acquiring images in different modes: so-called SESI (secondary electrons and secondary ions), InLens (secondary electrons -positioned in the electron column lenses), BSD (backscattered electrons), EsB (energy selective backscattered electrons), and STEM (transmitted electrons -positioned below the sample -) detectors. Some of these devices are removable for easy dfaily operations (i.e. BSD and STEM detectors).

The Nordlys F + EBSD detector is installed in the sample plane of ion and electron column, under the electron column. Its maximum working speed is about 600 Hz.

Main parameters defining the working conditions of the NVision system are summarized in table II.1 and table II.2.

II.1.2.2. Controlling unit

All the operation processes concerning the FIB-SEM part are performed via the ZEISS controlling software -SmartSEM ® . Moreover, the open Application Programming Interface (ZEISS API9 ) allows access to almost any microscope parameter (electron and ion optics, stage, vacuum system, detectors, scanning and image acquisition). This application may simplify some more or less basic operations process as compared to traditional manual operations in the case of repetitive procedures. As a result, it has been widely used in the present work (see section IV.3.2, V.3.1 and Appendix), and principally programmed in the Visual Basic 6 (VB6) environment for this study.

The 3D EBSD acquiring process is performed through the 'HKL Fast Acquisition' software (option '3D EBSD') provided by the Oxford Instruments company.

II.2. FIB instrument

The FIB instrument was firstly applied in nanotechnology sciences with an initial designing idea. This initial goal was then extended with the development of optimized stable, highly-bright and longlife timed ion sources: liquid metal ion sources (LMIS) and gas filed ionization sources (GFIS). Their basic working principles will be introduced and compared to the Field Emission Gun (FEG) type electrons sources. Further comparisons on the physical gun column set-up and the interactions between charged particles (ions and electrons) and solid will also be presented.

II.2.1. Brief History of FIB

In 1959, Richard Feynman, who later was awarded with Nobel Prize in Physics in 1965, asked for the first time [Feynman 1960] the question on the limits of miniaturization and further manipulation in a small dimension during a well-known speech. This titled "There's plenty room at the bottom" talk sketches out the base of a research area, which is known today as 'nanotechnology'. The main question he asked is how to write in a very small dimension. Concerning the method, he proposed to send a source of ions in reverse direction through the microscope lenses, which is focused to a very small spot. This describes exactly the principle of nowadays focused ion beam columns: the idea of nano-manipulation, as can be done at the large 'human scale' as illustrated in figure II.2, was thus initiated.

With this first idea, people started to look for suitable ion sources, which have a sufficient high brightness, which produce ion beam to be refocused in a spot with a certain current density. Early inspiring domains for developing the future FIB ion source were field ion microscopy (FIM) [Müller 1951] [Müller 1956] [Müller 1969], and secondary ion mass spectroscopy (SIMS) [Castaing 1962] [Liebl 1967[START_REF][END_REF]] using a gas field ionization source (developed later for further, chemical analysis).

II.2.2. Ion sources versus electron sources

As indicated by N. Yao [Yao 2007], the ion beam and electron beam are based on the same principle. They both consist of a stream of charged particles that is focused by a series of lenses and apertures onto a sample and both employ similar methods to produce and accelerate the particles emitted from their sources. It is meaningful to describe the main sources of ions and electrons.

II.2.2.1. Liquid Metal Ion Sources (LMIS)

LMIS (usually the low-drag blunt-needle LMIS, so called normal LMIS [Forbes 2009a]) is the most widely used source for commercial FIB instruments, owing to its reliability and simplicity [Knuffman 2013]. Its principle is shown in figure II.3: a metal is heated to the liquid state and provided at the end of a needle (usually in tungsten with an end apex radius of a few micrometers); then, a Taylor cone 10 is 10 Gilbert found first time the formation of a cone by applying a high electrostatic field to a fluid in 1600 [Gilbert 1600]. In 1914, Zeleny [Zeleny 1914] [Zeleny 1917] observed and filmed firstly the cones and jets from the formed under the application of a very high electric field (typically 10 V/nm or more) by a nearby electrode (the "extraction" electrode, shown in figure II.6). As the cone's tip gets sharper, the electric filed becomes stronger, until ions are produced from the emitter by field evaporation. At the emission currents (about 2 !A) normally used in FIB instruments, the jet apex of cone has a radius of about 1 to 2 nm [Kingham 1984]. However, the apparent optical beam size is of the order of 50 nm, which is mainly caused by space-charge effects 11 occurring due to high current densities (of order 10 11 A/m 2 ) [Kruit 2009] above the jet apex [Orloff 2003] [Forbes 2009a]. Therefore, electro hydro dynamic (EHD) effects 12 on the liquid ionizant supply, ion emission and space-charge effects are the main points to understand the behaviour of LMIS. The early research on LMIS originally attempts to develop charged-metal-droplet thrusters by EHD colloid for spacecraft propulsion in the 60's showed that liquid metals can generate large numbers of ions. In mid 70s, Krohn [Krohn 1974] [Krohn 1975] produced a high brightness (0.9"10 5 Acm -2 sr -1 at 21 kV with an energy spread of 12 eV at 10 !A current) with a small effective diameter (0.2 !m) by using a liquid gallium (Ga) from an EHD source. Seliger [START_REF] Seliger | [END_REF]] and Swanson [Swanson 1983] also proved that this liquid Ga + source can have a high brightness and produce a small spot size. In all these early devices, the liquid metals were supplied via a capillary cube, which was the standard EHD source procedure. Although it gives a higher emission current, this source is less steady than the normal LMIS, especially at low emission currents. According to [Forbes 2009a], the blunt-needle LMIS was found out accidentally by Ventakesh, a student who raised the voltage extremely high and blew the end of the sharp needle. Her supervisor [Clampitt 1975] discovered that the emission currents were much higher and had been attained successfully for several metals, including Ga. It was soon established (and later confirmed) that this was due to the formation of liquid cone-jet at the emitter apex [Benassayag 1985] [Driesel 1996], and liquid supply was improved by grooves or roughness meniscus of very dilute hydrochloric acid and Ethyl alcohol suspended from a capillary tube in air. Until 1964, Taylor proposed firstly the exactly conical solution to equations [Taylor 1964] of Electro Hydro Dyamics (EHD). High voltage TEM micrographs (figure II.4) [Wagner 1981[START_REF] Gaubi | [END_REF] show the formation of Taylor cone, and also the real shape of cone -a large jet like protrusion at high currents [Benassayag 1985] [Driesel 1996]. 11 It means the interactions of the ions among themselves, known as 'Boersch effet' [Kruit 2009]. It is this effect that cause the large energy spread of the ion beam formed by LMIS [Orloff 2003]. 12 See the reference 7 for Taylor cone.

a)

b) [Wagner 1979] [Bell 1986] [Swanson 1988] on the needle surface, which reduces certain electrical and viscous flow problems, allowing low-drag liquid flow. As to the ion source species, different single component source (for example, In, Bi, Al, Sn, Cs and Au) or several elements as alloys (for example, Au-Si, Au-Ge, Pt-B, Pd-B and Pd-As) have been fabricated for LMIS [Orloff 2003]. Ga is the most popular element in commercial FIB instruments (including our ZEISS Nvision 40 workstation) not only for many intrinsic metallurgical proprieties [START_REF] Bozack | Materials considerations in liquid metal ion source development[END_REF]] (listed in table II.3), but also because the heavy Ga + is effective for ion milling. Along with regularly increasing applied voltage -V e , the Ga LMIS works at different regimes (listed in table II.4) in different emission current -I e , which were demonstrated by high voltage in-situ TEM experiment [Benassayag 1985] [Driesel 1996]: 1) Onset regime: the pseudo-spherical meniscus elongates progressively to wet the tip apex towards a more ellipsoidal shape. When a critical voltage is achieved, the meniscus starts to oscillate (shown in figure II.4a). The extreme positions of this oscillation correspond to the meniscus without field and the 'Taylor cone' which is going to appear, respectively. This could be considered as the result of dynamic balance between the surface tension and the electrostatic stresses. 2) Intermediate regime: the Taylor cone becomes stable (figure II.4b), but it is difficult to confirm if a jet apex of 'Taylor cone' exists, although it is predicted by theory as a fine wire of about 1 nm in diameter [Kingham 1984] at low ion emission currents. 3) Most-steady regime: the shape of the Taylor cone becomes more and more concave (figure II.4c,d) with increasing current. Moreover, the angle at the extremity of cone decreases towards the apex, giving rise to a cuspidal rather than conical shape, with a liquid-jet-like protrusion (figure figure II.5a). Driesel [Driesel 1996] confirmed not only the increasing of the jet length l and the jet diameter d, but also the decreasing of the cone half-angle α in this range. 4) Upper unsteady regime: It is featured by rapidly increasing current noise, which is usually linked to droplet emission [Mair 1996]. By the TEM micrographs, the increasing of the jet length l, the jet diameter d and the decreasing of the cone half-angle α continues. An oscillation of the cone appears at 70-80 µA [START_REF] Gaubi | [END_REF]] [Benassayag 1985]. At 100 µA, the cone submitted to strong vibrations.

Its apex explodes and emission spreads over a large area of the cone, giving to the system the aspect of a flame jet. Moreover, an intense thermal evaporation from the extracting plate loads to W needle being heated at temperatures higher than 1000°C, which is observed from the facetted W tip extremity(figure II.4g-i).

All these features, including the I e -V e characteristics [Mair 1984] [Mair 1986], have been well described in the literature [Forbes 2009a]. According to the above, the 'most-steady regime' (i.e. the emission current between 0.45 !A and ~25 !A) seems to be the most suitable state of Ga LMIS for producing a stable and relatively noise-free ion flux. Furthermore, for the practical application of Ga LMIS in a focusing column, the energy distribution determines the final current density of the focused spot; to some extent, it will however be limited by the chromatic aberration of the optical system. This is the main reason for which the operating current of modern FIB instruments is limited to around 2 !A (as shown in figure II.6).

It should be mentioned that the vacuum has to be very good not only for the LMIS source and the ion column (of the order of 10 -8 mbar) in order to avoid any contamination of the source and to prevent electrical discharge in the high voltage ion column. This is also true for the sample chamber (vacuum of the order of 10 -6 mbar) to reduce the interaction of the ion beam with gas molecules, which would decrease the ion mean free path in the FIB column. Another important point is the LMIS lifetime. It obviously depends on the nature and amount of material in the reservoir; it is measured in terms of !A-hours per mg (or !A-hours per cm 3 ) of matter. Typical source lifetimes for Ga are ~ 383 !A-hours/mg (or 2260 !A-hours/cm 3 , with the Ga density around 5.9 g/cm 3 ) [Orloff 2003]. 13 The width of the ion energy distribution, which is assessed by full width at half maximum (FWHM), and associated mainly with the chromatic aberration for ion optics. Another action in practice is to heat the source when the combination of the suppressor and extraction voltages do not allow to produce a suitable working beam current. Although the Ga + LMIS of FIB instrument is operated at its 'most-steady regime', the emission current and the applied voltage is not completely linear. The extraction voltage is typically set to a constant value and the suppressor voltage is gradually increased to maintain a constant beam current [Giannuzzi 2005] [Cho 2011]. Sometimes a larger extraction voltage (remaining always in the 'most-steady regime' of Ga + LMIS) may be used to start the source, which is then reduced as soon as emission starts.

Figure II.6a is a geometrical illustration of Ga + LMIS for the SII gun ion in ZEISS Nvision 40 FIB workstation. A suppressor electrode is added like other modern FIB instruments to minimize the secondary electron component, which may be included sometimes in the measured emission current possibly leading to an overestimate of the true emission current by a factor of up to 2 [START_REF] Forbes | The Theory of Bright Field Electron and Field Ion Emission Sources[END_REF]]. Figure II.6b shows the dialog window to operate the ion beam in the SmartSEM ® software.

II.2.2.2. Gas Field Ionization Sources (GFIS)

Another type of ion sources is called GFIS. Contrarily to LMIS, the ionizing atoms are initially free in a gas phase just above a solid surface, rather than strongly bounded to a liquid surface, and the ions are formed by surface field ionization slightly above the emitter surface, rather than by field evaporation at the surface.

Their principle is shown in figure II.7: a sharpened needle (typically W) is placed in front of an extractor. A neutral gas (often noble) is introduced near the needle's tip, which is polarized by applying a voltage between the emitter and the extractor. The supplying gas particles are trapped to the needle-shaped field emitter by polarization forces, captured by thermal accommodation, and funnelled toward the needle tip by the polarization potential-energy well. In a thin ionization layer (~10 pm) just outside a critical surface slightly above the needle's tip (~ 500 pm above the edge of the metal atom for the helium-on-tungsten system) the bounced about gas atoms can be field ionized by quantum mechanical tunnelling of the electron into the metal, when a nucleus enters an ionization zone [Forbes 2009b],. There are strong variations across the surface for the generated ion current density in the ionization layer, which are related to the existence of disc-like zones of relatively intense ionization above the protruding atoms, which produces narrow ion beams. Furthermore, the emitter is often cryogenically cooled to increase the density of available atoms for ionization. This GFI emitter was invented by Müller [Müller 1951] in 1951 and applied it to the well-known field ion microscope (FIM). Using different operating and focusing conditions, Levi-Setti [Levi-Setti 1974], Escovitz [START_REF] Escovitz | [END_REF]] and Orloff [Orloff 1975] demonstrated the possibility of applying GFIS to produce a FIB in the early 1970's.

In contrast to a (110)-oriented W tip (diameter ~100nm) used in the FIM, pyramidal (111)-oriented W tip are used in GFIS [Fink 1986] [Fink 1988]. Because the (111) planes have a relatively high surface free energy, the apex of the tip is smaller in size as compared to the case of (110)-oriented tips (these (110) planes being the denser planes in the c.c. structure); it is thus easier to obtain a sharper and more stable tip. What is important here is that the fixed imaging gases supply is no more interacting with hundreds of atoms but with a single atom. Consequently, the emission per atom is increased, which means a high brightness and monochromatic source. However, such tips have a limited working period once the apex atom leaves its bounding site. From that, ALIS corporation (part of Carl ZEISS company now) invented a computer controlled in-situ process (probably chemically assisted) to restore the damaged emitter to its original state. In their design, the rounded (111) oriented W emitter tip ends as a three-sided pyramid, or trimer (the most stable form of the pyramid apex consisting of a set of three atoms). With this shape, the electric field is concentrated at the apex of the pyramid; therefore the field ionization takes place mainly at the topmost atoms like the tip introduced by Fink [Fink 1986] [Fink 1988]. Using these techniques, a helium ion microscopy have been successfully commercialised14 since 2007. The source size could reach approximately 3 angstroms with a brightness of 4×10 9 Acm -2 sr -1 . The He microscope presents the advantage to minimize any chemical, electrical, or optical alteration of the sample, providing a negligible sputtering and rapid diffusion out of it.

The total emission current in GFIS depends on the ionizing gas 'background' pressure15 (typically ~10 -5 torr) P bk and the emitter temperature T e [Souton 1963]. Normally, a GFIS is operated at a fixed voltage (named 'the best source voltage'16 , in the range 40 to 45 V/nm for the ZEISS He ion microscope) like the Ga LMIS in a conventional FIB instrument. Thus, the probe-current should be adjusted17 by changing the background gas pressure P bk . Another important parameter of the He + GFIS is its energy spread which is affected by several factors: apex field, gas temperature, tip radius, and the local environment. With a "safe" pressure range at the best source field cooled to near 80 K, the ZEISS He + GFIS gives an energy spread around 0.5 eV [Ward 2006].

These two LMIS and GFIS ion sources are the main commercialized sources in modern FIB systems. Typically, LMIS-base FIB instruments are principally used for the nanofabrication with their heavy energized ions, while the GFIS-based FIB instruments are more devoted to scanning ion microscopes [Castaldo 2012]: the ion beam is also the imaging beam. This cannot be adequately performed with a LMIS source, since in this case the heavy ions (such as Ga + ) lead to a significant erosion during imaging; in addition the emission droplets can introduce an undesired contamination. This could partly explain the development of dual-beam FIB instruments, where an imaging electron column is added to the ion column. Then the ion beam is principally used as milling tool. All the work performed in this thesis was done using a Ga + LMIS-based FIB (figure II.1).

There are also some other type of sources, which are currently the subject of academic researches, like a cold atomic beam ion source with both high brightness and low emittance [Claessens 2007[START_REF] Hanssen | [END_REF]] [Steele 2010] [Knuffman 2013], plasma ion sources for high probe current and further micromachining in high speed [START_REF] Smith | [END_REF]] [Menon 2013], solid electrolyte ion sources for avoiding the implantation of Ga [Escher 2006], ionic liquid ion sources for the possibility of producing very diverse molecular ions in terms of mass, composition and properties [START_REF] Zorzos | [END_REF][START_REF] Takeuchi | [END_REF]].

II.2.2.3. Electron sources

The field-assisted electron sources are based on the above mentioned Müller emitter used in the FIM. There are 3 mainly types of such sources (table II.5): the room-temperature W emitter (usually called a 'cold field emitter'); the heated W emitter (generally called a 'thermal field emitter', or described as a 'built-up W Schottky emitter'); and zirconiated W Schottky emitter (often called 'ZrO/W Schottky emitter'). The sharp W tip has here a (100) orientation which appears to be more appropriate for producing a good field electron emission than the classical (110) orientation. The source consists in a W emitter with a sharp tip, an extraction electrode and an acceleration electrode. When a negative voltage is applied, the electric field concentrates on the end of the tip, which gives rise to the emission of electrons by tunnelling effect.

Good optical performances, i.e. high brightness and low energy spread, can be obtained with a cold field emission. However, it requires very good vacuum conditions (< 10 -10 torr) and regular 'flashheating' to desorb contaminations, restore and smooth the W surface. For the thermal field emission, the emitter works beyond 1200°C. This reduces the problem of contamination but degrades the energy spread. For ZrO/W Schottky emission, the emitter tip is protruded after the suppressor voltage, which restrains the Richardson-type field emission from the shank and prevents the shank out of bombardment of ionized contaminants. Furthermore, continuous Zr atoms to the tip are supplied by surface diffusion from a ZrO reservoir upon the shank. This ZrO layer inhibits ion bombardment and thus limits the heating of the tip. Accordingly this source is very stable during operation.

As for the ion sources, other types of electron sources are currently investigated: carbide-based sources [Kang 2013], metallic emitters ending with in a single atom [Ishikawa 2007], carbon naotubes [Saito 2010]. These researches aim at optimizing the operating conditions, such as the ability to work under poor vacuum conditions, the generation of an adequate angular intensity on axis, lower energyspread, less susceptible to stochastic coulomb particle-particle interactions (SCPPI) effects.

II.2.2.4. Summary of field emission sources in FIB instrument

Since we have presented shortly the principle of usual charged source (ions and sources) by field emission in modern FIB instrument, it is meaningful to summarise their main optical properties together (see table II.6).

II.2.3. Ion column versus electron column

a) b)

As illustrated in figure II.8, a FIB column is similar to a SEM column; it is typically composed by the ion/electron source, two lenses (condenser lens and objective lens), a deflection/astigmatism unit and a series of apertures. Generally, the divergent beam, produced by ion/electron source, is demagnified by the condenser lens to a small probe, then focused by the objective lens as a fine spot on the specimen, and repositioned by deflection coils. Due to the great difference of mass for ions and electrons, the design is however not completely same. More details will be given below in the case of SII Zeta ion and ZEISS GEMINI ® I electron columns which are the main elements of the ZEISS NVision 40 unit used in this work.

II.2.3.1. Ion beam column

The electrostatic lenses are generally employed for focusing an ion beam. The force (𝐹 !"! ) on a charged particle, due to an electric field 𝐸 is expressed as 𝐹 !"! = 𝑞 • 𝐸, whereas the force produced by a magnetic field 𝐵 is: 𝐹 !"# = 𝑞 • 𝑣×𝐵; they both depend directly on the velocity of the moving particle. A particle accelerated by a potential ΔV will gain a speed 2𝑞∆𝑉 𝑚, where qΔV is the energy and m is the mass of particle. With the higher mass of ions ( 𝑚 !" ! 𝑚 ! ! = 1.3×10 ! ), their velocity is 0.0028 times that of electrons accelerated by the identical potential, while their momentum is 370 times higher. Therefore, the magnetic optics should be impractically huge to supply the capacity of focusing an ion beam. In the contrast, electrostatic lenses can be greatly small, and more quickly reacting for beam deflection, as required during ion beam blanking for example. However, the aberrations (principally spherical aberration and chromatic aberration) of electrostatic lenses are quite severe.

A first octopoles ('upper octopole' in figure II.8a) is available under the condenser lenses to adjust the beam stigmatism. In order to raster scanning ion beam over the user defined area, a second octopole ('lower octopole' in figure II.8a) is used over the objective lenses.

II.2.3.2. Electron beam column

Electromagnetic lenses are known to be well-adapted to the electron beam because of their low aberrations. The ZEISS GEMINI ® electron column further features a 'beam booster', which maintains a high positive potential (8 keV) throughout the whole column almost regardless the electron accelerating voltage by the user (up to 21 kV in fact). The primary beam is then decelerated by the electrostatic lens, located in the pole piece, before landing on the specimen. This design has many advantages: i) the traverse chromatic aberration (scaled as α•ΔE/E, where α •is the convergence angle and ΔE is energy spread) has a minimal effect on the imaging resolution, especially at low voltages, because the beam energy E is kept at a high value; ii) the electrostatic/electromagnetic lens minimizes the magnetic effects at the sample; iii) the beam broadening resulting from Coulomb electron-electron interactions in the crossover, referred to as Boersch effect [Kruit 2009], is reduced; iv) the electric field of electrostatic lens can remove the possible streaking, locally charging electrons from the sample surface, and can at the same time accelerate SEs to the Inlens detector (see below).

Besides this beam booster, an electromagnetic multi-hole aperture similar to the 'spray aperture' in the ion column (see figure II.9) is mounted close to the extractor of the electron source; it rejects excess electrons which do not enter into the illuminating beam aperture angle of the objective lens. This insures a minimal loss in the beam brightness, even at low electron accelerating voltages. As mentioned in sub-section II.1.2.1, the SEM image is produced by collecting different signals (see section II.2.4) using different detectors: EsB, SESI, and InLens (shown in figure II.9) which will be briefly described below.

• EsB

The EsB, or Energy Selective Backscatter detector is located after a filtering grid excited at a selective voltage (between -1.5 kV and 0 V), which repels any secondary (low energy) electrons and thus enhances the chemical contrast due to the BackScattered Electrons. This detector is very useful for high resolution imaging at low voltage, because a very narrow energy window can be chosen to collect electrons generated very near the sample surface; this point will be re-discussed in sub-section II.2.5.

• SESI

The so-called SESI detector is actually a conventional Everhart-Thornley (E-T) type detector for collecting the Secondary Electrons (SE); its grid bias can however generate a negative potential (-1500 to 0 V) to collect secondary ions, in addition to the usual positive potential (0 to 700 V) for SE. As the SESI detector is mounted laterally to the typical working position of the specimen in the FIB-SEM instrument (i.e. at the coincidence point), it provides a good topographic contrast with a large depth of field, and allows large fields of view.

• InLens

The so-called InLens detector is placed axially above the objective lens and under the filter grid for SE collection. The retarding field for primary electrons produced by the electrostatic lens as discussed above, accelerates the secondary electrons emitted by the sample towards the InLens detector, so that the detection efficiency at low accelerating voltages is excellent: this electric field mainly attracts lowenergy SE like a low-pass filter, and in consequence the SE with higher energy are gathered by outlens detector (E-T detector here). In contrary to the SESI detector, it permits little topographic contrast because of its upper position. The InLens detector also allows to operate the microscope at a small working distance (WD) with a small probe size.

II.2.4. Beam interactions with solid

The Ga + LMIS -based FIB system has more applications than a conventional imaging instrument, because of the large mass of ions compared to electrons, which gives rise to different interaction types with condensed matter.

II.2.4.1. Ion-solid interactions

Energetic ion impinging on solid materials leads to kinetic energy losses of the ions through interactions (elastic and inelastic) between the ions and the target. Basically, these interactions are distinguished according to the type of energy conservation: elastic scattering events (so-called nuclear interactions) result in the displacement of lattice atoms, surface sputtering, and formation of defects; inelastic scattering events (so-called electronic losses) cause the production of secondary electrons (SE), X-rays and phonons. As illustrated in figure II.10, there are many possible effects due to these interactions: i) Ion reflection and backscattering: impinging ions can be deflected by target atoms in a backscattering process, following the transfer of energy from the ion to the solid, which depends on the mass of each and the energy of the primary ion beam. As for crystalline materials, this process may be used under suitable conditions to produce 'ion channelling' (ions travel far into the crystal along low index directions), which leads to darker contrast in image and links closely to crystallographic orientation on polycrystalline sample. A further review and application of this ion channelling contrast will be performed in chapter V of this thesis. ii) Ionic Emission: Secondary ion emission occurs when surface atoms are ionized and sufficiently energized to be ejected from the surface. They can be used to form an image, or can be collected and mass separated to perform SIMS. Secondary electrons (often referred as ion-induced secondary electrons, ISE) are emitted from the top few atomic layers where the primary ion impacts the solid, simultaneously with backscattered electrons or sputtered particles exiting the sample; the low energy electrons are usually collected for imaging. Accordingly, the signal is enhanced when the surface is sputter-cleaned, otherwise loss of contrast can occur due to surface oxidation and/or contamination. iii) Atomic sputtering: Physical sputtering, also referred as knock-on sputtering, occurs if the incident ions transfer sufficient momentum to surface (or near-surface) atoms. This constitutes the basis of the 'micro-machining' or 'milling' processes used to remove material with a great precision in the FIB instrument. The sputtering depends on the material, crystal orientation, ion beam incidence angle and extent of redeposition. Redeposition is a severe drawback of the FIB machining operation, although it is not an intrinsic effect; it however reduces the effective sputter efficiency simply because the redeposited material lands in the area being sputtered, and thus must be removed a second time. During sputtering, surface roughening and shadowing effects are common, such as the so-called 'curtain effect' (described later), a typical example of shadowing the topography for cross-sectioning. Surface roughening, particularly ripple formation, is the result of a competition between a smoothing effect by surface diffusion or viscous flow, and a roughening through curvature-dependent sputter yields (the sputter yield depends on local curvature for the incidence angle). Finally, chemical sputtering can occur if the incident ions form new compounds with surface atoms, which obviously modifies the nature of the target and of the ejected species as well. iv) Sample damage: Sample surface rearrangement, point defect creation and dislocation formation occur due to momentum transfer, during which atoms or groups of atoms can be moved from weakly bound surface binding sites to more strongly bound surface binding sites. These ions with sufficient energy can go into the solid, leading to internal dislocation and point defect in the bulk material. The atomic rearrangement causes amorphization in crystals. If the impinging ions lose all their energy and get trapped in solid, ion implantation occurs. Besides these events, some additional and unusual types of damage have been reported although not fully understood. They include surface grains reorientation in some bcc [Spolenak 2005] and fcc [START_REF] Giannuzzi | [END_REF][START_REF] Olliges | [END_REF]] metals, formation of new Ga-containing phases [START_REF] Giannuzzi | [END_REF]] [Casey 2002] and grain growth [START_REF] Park | [END_REF]]. v) Sample heating: During ion bombardment, nearly all the ion kinetic energy is converted to heat, while only a small part is stored as defects in the sample or emitted as energetic particles or radiations. This heating effect depends strongly on the time of ion implantation; it strictly locates at the region defined by collision cascade. For a typical FIB milling operation, the dwell-times of ion beam are of the order of micro-seconds, so the thermal effect can be negligible unless the material has a low thermal conductivity, such as polymer-based [Liu 2013] or biological specimens [Marko 2006]. Solutions consist in decreasing the experiment duration, or depositing a thin conductive film on the sample surface; the use of a complementary cryogenic stage and/or a cryo-transfer system can also significantly reduce both heating effect and surface damage [Hayles 2007] [Holzer 2007[START_REF] Neuber | [END_REF]].

Figure II.10. Schematic illustration of interaction between incident Ga + beam and the matter (adapted from [Giannuzzi 2005]).

• Milling

As mentioned above, milling (with medium or high energies of a Ga + beam, i.e. 5-30 keV) depends principally on the sputtering yield, Y, which is defined conventionally as the number of ejected particles from a solid surface per incident particle. Sigmund [Sigmund 1981] introduced the linear collision cascade model to describe the sputtering process. In his theory, energy and momentum are transferred from the primary ions to target atoms either by 'cascades' of binary collision between incident ions and target atoms, or by recoiling atoms and stationary atoms. When a cascade intersects the surface and transfers sufficient energy to its atoms (or to the near-surface) to overcome the surface blinding energy (SBE), sputtering of atoms on or near the surface occurs. With an energy exceeding some arbitrary minimum energy E 0 , the sputtering yield according to Sigmund's theory can be expressed as:

! ! ! ! ! ! ! ! !"! ! !!!!! ! ! ! (II.1)
where # is a dimensionless function incorporating the ion beam incidence angle, the mass ratio M 2 /M 1 and the ion energy E, and $x 0 is the depth interval for which the atoms set in motion have an energy > E 0 . More recent models were proposed by Matsunami [Matsunami 1984], Bohdansky [Bohdansky 1984] and Yamamura [Yamamura 1996].

According to Sigmund model, the dependence of the sputter yield versus the incidence angle for homogeneous, isotropic and planar surfaced polycrystalline targets can be given by

𝑌 𝜃 ! = 𝑌 0 𝑐𝑜𝑠 !! (𝜃 ! ) (II.2)
where f is a constant and depends mainly on mass ratio of target/ion -M 2 /M 1 . As illustrated in figure II.11a, Sigmund model agrees well with the experimental measurement [Kaito 1999[START_REF] Fu | Process modeling and simulation of focused ion beam milling of water ice in a cryogenic environment[END_REF]] at low incidence angle, but it should be corrected for high angles [Sigmund 1981] [Bohdansky 1984] [Yamamura 1996]. It is shown also that there is a maximum sputtering yield between 75° and 85°; this odes not however correspond to the most current case of normal incidence (~ 90°) during computerassisted specimen preparation in modern FIBs. It was further demonstrated that the largest sputtering angles produce a large topography on sample surface [Barna 1990]; in contrast, the best TEM sample were obtained around 89° at the lowest energy possible. At the normal incidence, increasing the primary energy of ion beam increases the number of collision cascades with enough energy to overcome SBE; however, it causes a deeper projected range of ion (R p in figure IV.14).

The dependence of sputter yield on primary energy and mass is often estimated by supposing ideal surface conditions, from the integration of the number per energy distribution dN/dE over a solid angle of 2π

!" !" = ! !! ! !! ! ! ! ! ! ! !!! ! ! (II.3)
where E p , E and U s are the primary, secondary and surface blinding energies, respectively. A universal curve (figure II.12) for the energy distribution of sputtered atoms is obtained by normalizing the energy scale to the intensity maximum, E m . The figure II.12 shows also that heavier ion sources or lower surface binding energies of target materials can produce higher sputter yields [Tseng 2007] (Atomic weights: 39.95 for Ar, 69.72 for Ga; binding energies: 3.80 for Au and 4.69 for Si in eV/atoms).

The ion probe current (in amperes, equivalent to units of charge per unit time or coulombs/sec) is a quantitative parameter of the time rate flow of energy, i.e. number of ions delivered per unit time.

The collision cascade model presented above can be well simulated with Monte-Carlo based calculations (see figure II.11a and figure II.12) which consider ion-solid interactions including electronic stopping and elastic collisions. The most widely used Monte-Carlo based simulation is the program TRIM or SRIM18 (Transport or Stopping Range of Ions in Matter), which do contain some simplifications for estimating the effects of ion-solid interactions [START_REF] Volkert | [END_REF]] [Ziegler 2012]. A detailed application on SRIM will be performed in section IV.2.2.

To conclude this introduction on milling with a FIB, it can be summarized that a great number of parameters have a significant influence of the process. On he one-hand, one can list intrinsic materialdependent parameters such as the sample nature, the orientation of crystalline materials causing 'ion channelling' and the surface roughness. On the other hand, extrinsic FIB factors are important; some of these factors can be chosen by the user (incidence angle, primary energy, probe current), some others are predefined for a routinely use (dwell time, scanning strategy) or simply imposed by the manufacturer (convergence of the ion beam, the type of ions -which has be accounted as a relative parameter through the mass ratio of target/ion -) [Latif 2000] [Mulders 2007[START_REF] Knipling | [END_REF]] [Urbanek 2010]. The situation is thus rather complex and each milling experiment required, to a large extend, a case-by-case approach.

• Deposition

Modern FIB instruments are generally equipped with a Gas Injection System (GIS). This device allows a local deposition of conducting material (Pt, W, or C) or insulating material (SiO 2 ) to be achieved. The principle is to crack an hydrocarbon precursor using the incident ion beam, or the electron beam in a dual-beam system like in a physical vapour deposition process (PVD). Furthermore, with specific injected gas (XeF 2 or H 2 O), local chemical vapour deposition (CVD) occurs with chemical sputtering which enhances the etching rate of the ion beam. Classically C (or W or Pt) is used to 'welder' the thin lamellae onto dedicated copper half-grids for further TEM studies.

• Imaging

The ISE are typically collected with low primary ion beam energy and current in order to avoid an artificial degradation of sample surface.

II.2.4.2. Electron-solid interactions a) b)

A primary electron beam entering a solid sample, leads to different interactions between electrons and the target solid: elastic large-angle scattering, principally with the nucleus of target solid atoms, which includes the backscattering; inelastic scattering, which causes Plasmon excitation, electronelectron binary collisions and ionization. Figure II.13a is a schematic cross section in the X-Z plane of interaction volume produced under the impact of the electron probe on a bulk specimen; it shows the main signals available for imaging and microanalysis, and their positions in this interaction volume. • Backscattered electrons Backscattered electrons (BSE), with high energy (near E 0 ), are generated mostly through elastic interactions between incident electrons and the nucleus of target atoms. The backscattering coefficient ( (defined as ! ! ! ! !"# !! ! and always < 1, where n B is the number of incident electrons and n BSE is the number of backscattered electrons) is strongly dependent on the target atomic number(s), the energy and the incident angle of primary electrons. The topography and chemical composition of the sample also influence the emission of BSE. Because of multi-scattering events, BSE are generally spread out in energy (as shown in figure II.13b), angular distribution, lateral spatial distribution and sampling depth during their emission. As shown in figure II.13a, the lateral resolution in BSE imaging is dependent on the position of BSEs escaping from a depth in a typical 0.1 -0.5 !m range.

• Secondary electrons

Secondary electrons (SE), with low energy (typically ~ 10 eV), are generated in 3 ways: type I, inelastic interaction between primary incident electrons and orbital electrons (especially valence electrons) or inner-shell electrons (below 50 eV by convention); type II, target atom electrons of the specimen; type III, spurious signals arising for example from the interactions between BSE and the pole piece above the sample. The SE yield ) (defined as

! ! ! ! !" !! ! , thus possibly > 1, where n B is a) b) c)
the number of incident electrons and n SE is the number of secondary electrons) is then used to quantify the SE, which is sensible to the primary incident energy, the sample tilted angle, the topography of sample surface, shadowing effects, collection geometry. The typical depth resolution (' in figure II.13c) of SE imaging is between 5 and 50 nm.

• Auger electrons and Characteristics X-rays

As mentioned above, the ionization produced by the inelastic interaction between a primary incident electron and the nucleus of target atom, create an inner-shell electron vacancy which will be filled with an electron from an upper shell. The de-excitation energy produced during this process is either transferred directly to an atomic electron without radiation, which causes the emission of an Auger electron (AE), or converted to a radiative transition, which results in the emission of a characteristic X-ray (photon). This emission serves as the basis for elemental chemical analysis (Energy-Dispersive X-ray -EDX -spectroscopy).

II.2.5. High resolution imaging in SEM

The highest resolution is often obtained at high voltage minimizing negative effects (chromatic aberration, aperture diffraction and Boersch effect, etc.) related to the size of the electron probe. However, the corresponding large volume of interaction results in a large number of generated electrons, which can accumulate onto the sample surface. This effect may lead to the distortion of the images and strong charge effects for insulating samples. As a result, low voltage electron microscopy is more and more adapted to high resolution imaging not only for the obvious reduction of electronsolid interaction volume (cf. figure II.14), but also for reducing charging effects on non-conductive samples. Furthermore, the EsB detector is well adapted for the collection of BSE in low voltage for high resolution imaging. Firstly, the SE with low energy are repelled by the grid filter, which can improve the signal-to-noise ratio for BSE imaging. Then, as illustrated in figure II.15, by adapting the potential of the grid filter, low-angle BSE escape from only the top few nanaometres of the sample surface are collected, although they are emitted throughout the entire interaction volume.

II.2.6. Summary for FIB-SEM instruments

The modern ion beam column in a dual-beam FIB instrument, typically using a Ga + LMIS source with an energy-spread of around 5 eV, a brightness of about 5 " 10 9 A m -2 sr -1 and a final probe size of about 3 nm, allows to perform etching (nano-machining) with a spatial accuracy of about 3 nm, which is far from the high resolution performance offered by field assisted electrons sources or GFIS.

The modern SEM column in a dual-beam FIB instrument, most frequently equipped with a ZrO/W Schottky emitter with an energy-spread of around 0.5 eV, a brightness of about 10 12 A m -2 sr -1 and a final probe size of about 1 nm is well adapted to high resolution imaging especially at low voltage (a few nanometres, depending upon the features to be resolved and the nature of the sample).

Thanks to these above technical parameters, the dual-beam FIB-SEM is a very powerful and versatile equipment of considerable interest in the field of Materials Science for the characterization of microstructures. It is especially more and more applied for serial sectioning tomography with a spatial 3D resolution of about a few nanometres.

When equipped with an EBSD system, the FIB-SEM can even provide crystallographic information, and in principle in 3D. This point will be tackled in the present work; since the EBSD technique is in itself also a specific research domain, we will first present a bibliographic survey on this technique in the next section II.3.

II.3. Electron Backscatter Diffraction

Electron Backscatter Diffraction (EBSD), also known as Backscatter Kikuchi Diffraction (BKD), Backscatter Electron Kikuchi Diffraction (BEKD) and Orientation Imaging Microscopy (OIM), is a technique used to study the micro-texture of materials. In the literature, Electron Backscatter Diffraction Patterns (EBSP), Backscatter Kikuchi Patterns (BKP) and Backscatter Electron Kikuchi Patterns (BEKP) refer specifically to the image formed by the diffraction. Crystal orientation (crystallographic) analysis, crystal structure analysis (phase identification) and assessment of lattice strain are three main applications of EBSD.

The EBSD analysis is dedicated to SEM samples placed in a highly tilted sample (for high backscattering efficient, see figure II.16); the crystallographic information is then deduced by the diffraction pseudo-Kikuchi patterns produced by electrons backscattered by the tilted specimen under the impact of the primary beam [Schwarzer 2009] [Randle 2010]. The philosophy of producing orientation maps in electron microscopy has been greatly developed in TEM [Zaefferer 2000] [Randle 2010] through the interpretation of Transmission Kikuchi Patterns (TKP) [START_REF] Zaefferer | [END_REF]] [Schwarzer 1998] providing high angular (0.1 -0.01°) and spatial resolutions (~ 10 nm) [Dey 2006] [Zaefferer 2011], or using spot diffraction patterns possibly coupled with electron beam precession [Engler 1996[START_REF] Rauch | [END_REF]]. The angular resolution in EBSD is its ability to differentiate two crystallographic orientations very close one to each other; from recent improvements by carrying out cross-correlation on directly BKP [Brough 2006], it was claimed that the angular resolution can be as low as 0.006° [Wilkinson 2006].

A variant of conventional SEM-EBSD is to perform it on a TEM sample in the transmission mode within the SEM [START_REF] Geiss | [END_REF]] [Keller 2012] [Trimby 2012] [Brodusch 2013a] [Suzuki 2013] [Robert 2013]. This method, named Transmission-EBSD (t-EBSD), can provide a spatial resolution comparable to the TKP technique in a TEM (< 10 nm). Nishikawa and Kikuchi discovered firstly [Nishikawa 1928] these diffraction patterns in the backscattering mode; Kikuchi lines consist in pairs of parallel black and white lines similar to their existing homologues in the transmission electron microscope [Kikuchi 1928]. They were first described as "black and white lines in pairs due to multiple scattering and selective reflection". Still today, the formation mechanism of these Kikuchi patterns is not fully understood from a quantitative point of view. We will present rapidly the kinematic (geometrical) theory and its extension to the dynamical theory allowing the intensity distribution of Kikuchi patterns to be calculated. Kikuchi diffraction patterns are the gnomonic projections (figure II.17a, b) of the geometry of lattice planes in a crystal. This process consists of two steps [Schwarzer 1997]. Firstly, the primary beam electrons are scattered incoherently in the sample, which leads to electron trajectories distributed with a wide range of angles above point S in figure II.17). These electrons may be considered to Where d hkl is the inter-planar spacing for a family of planes, θ B is the Bragg angle, n is the order of reflection (integer value, n=1 for EBSD) λ e is the electron wavelength.

II.3.1. Kikuchi diffraction patterns

II.3.1.1. General basic theory

These diffractions result in two cones (named Kikuchi or Kossel cones) of electron radiation generated from a single set of planes, which extend about the normal of the reflecting atomic planes, with a large opening angle of 180°-2θ B (indicated in figure II.17c) [Zaefferer 2007]. These cones cut an observation plan (phosphor screen) which is placed tangential to the propagation sphere of the electrons. Typically, the Bragg angle is about 0.5°, which leads to a very large apex angle of the reflected cones (close to 180°): as a consequence, the section of these cones appears as a parallel pair of almost straight lines, so-called Kikuchi (or Kossel) lines. Their spacing is proportional to an angular distance 2θ B (distances on the pattern are equivalent to angles). Hence, each pair of straight lines represents a plane in crystal, the actual trace of the plane lying equidistant between the pair. Low index crystallographic directions, called zone axes, lead to EBSD patterns with a high density of Kikuchi lines as shown in figure II.17d. The Kikuchi pattern is a map of angular relationships in crystal, it thus respects crystalline symmetry and thus allows crystallographic indexing. The total angular range of Kikuchi pattern depends on the distance between the specimen and the camera: a large distance results in a more magnified pattern with a smaller angular coverage, and vice versa.

The quality of the EBSD pattern is governed by several factors, among which the surface roughness which rapidly degrades the contrast up to the point it makes it simply impossible to record Kikuchi lines. The signal-to-noise ratio is linked to the diffuse continuous background arisen from the impact of inelastically scattered electrons. Other main 'imperfections' in the Kikuchi lines include contrast asymmetry due to misorientation effects (sharp Kikuchi line pairs are obtained only from high-index lattice planes and thin samples [Zaefferer 2007]).

Concerning the intensity of Kikuchi lines: in the kinematical theory, the diffracted intensity I hkl of a specific reflection (hkl) is classically proportional to the square of the structure factor F hkl :

2 hkl hkl F I ∝ (II.5)
the structure factor is defined as the sum of scattering from all atoms of the unit cell:

)] ( 2 exp[ ) ( 1 , j j j N j j e hkl lz ky hx i f F + + = ∑ = π θ (II.6)
where j is the j th atom in the unit cell and f e,j (θ) is the corresponding atomic scattering factor for a given diffraction angle θ. The exponential function describes the phase shift of waves diffracted by the atom j, for which the position in the unit cell is defined by the coordinates x j , y j , z j . The electron scattering factor can be derived for a particular element from the X-ray atomic scattering factor f x, j (θ) using the Mott formula:

( )

) ( ) 2 ( sin 4 ) ( , 2 0 2 2 2 0 , θ θ ε λ π θ j x j e f Z h e m f - = (II.7)
With the electron rest mass m 0 , the electron charge e, the wavelength ', Planck's constant h, the permittivity of vacuum + 0 and the atomic number Z.

Interestingly, resolution tests [Humphrey 1999] have shown that the main part of the EBSD signal originates from a volume much smaller than the interaction volume shown in Figure II.13a; it consists in electrons which have mostly suffered only one diffraction event.

II.3.1.2. Dynamic theory

Like in TEM (see for example [Reimer 1986]), since electrons interact much stronger with matter than X-rays, multiple diffractions occur in the scattering processes involved in EBSD. Therefore the above simple geometric model and kinematical approximation presented above cannot describe properly the exact intensity distribution in a Kikuchi pattern. Kikuchi patterns from backscattered electrons in SEM now can be calculated successfully [Winkelmann 2007] [Winkelemann 2008] using the Bloch wave approach that is usually applied for convergent beam electron diffraction (CBED) in the TEM. With this theoretical frame, an excellent agreement [Winkelmann 2010] can be obtained between experimental patterns and simulations (see figure II.18). In the calculation, a total of 1200 reflections were considered; on average 150 reflections were treated exactly, the others were included by perturbation. A lattice constant equal to 3.147 Å was used [Winkelmann 2010].

In the case of TKP, CBED patterns are formed by an external convergent probe sampling the same Bragg interference cones as the internal sources. That is why the CBED patterns show line patterns with a geometry similar to EBSD and other Kikuchi patterns. However, the intensity distribution in CBED patterns is related only to those electrons which retain a fixed phase with respect to incident beam. A nice compilation of simulation and of appropriate references could be found in the work of Tanaka [Tanaka 2002] [Omoto 2002] on Kikuchi diffraction patterns obtained in the TEM with high energy electrons. In their work, thermal diffuse scattering (TDS) is mentioned as the process leading to incoherent scattering of primary Bloch wave field.

II.3.2. System set-up in a SEM

a) b)

An automated SEM-based EBSD system is typically composed by three main parts: the SEM, the pattern acquisition device (or camera) and the software, which are showed in figure II.19. The spatial resolution is defined as the overlapping distance between two diffraction patterns and is influenced by these parameters below.

i) Microscope parameters

By comparison of modern field emissions guns and traditional thermionic emitters, field emission guns have a brightness of about 3 orders of magnitude higher, and are superior in producing high beam current in small probes of 0.02 µm and less; they further enable high currents of several tens of nA in beam spots of a few nm diameter. Hence, FEG SEMs are the first choice for high speed and highresolution orientation microscopy. Another important advantage of FE guns is their much smaller beam aperture and therefore their larger depth of focus.

ii) Nature of the sample

The backscattered signal increases with atomic number. As a result, frequently, there is more detail and greater clarity in patterns from high-atomic-number elements than low atomic numbers.

iii) Specimen/microscope geometry

There are four main parameters which are very important in EBSD setup: a) the specimen tilt (the angle of incidence between the primary electron beam and the specimen normal), which must be at least 45° to form the pattern; the optimum contrast is found for a tilt between 70° and 80°. b) the working distance (the specimen height), which should be as short as possible to minimize focusing distortions (the most common value is 15-25mm). c) the specimen-to-screen distance, which remains fixed in the process of data collection. d) the pattern center, which is defined as the point of intersection on the EBSD camera and an electron beam perpendicular to both the primary electron beam and the horizontal. An Accurate identification of the specimen-to-screen distance and the pattern centre is an important part of the EBSD calibration.

a) b) iv) Accelerating voltage

There is a linear relationship between accelerating voltage and interaction volume for a specific element. Therefore, a low accelerating voltage is chosen if a good spatial resolution is required. Figure II.20 describes the relationship between the accelerating voltage and average lateral spatial resolution in nickel with a standard tungsten-filament SEM. At the same time, the size of the interaction volume is correlated with the atomic number of the element: generally, a high accelerating voltage can be chosen for high atomic number specimens. A good compromise to optimize the resolution is to use an accelerating voltage of 20 kV for conducting materials and about 8 kV for non-conductive materials.

Inverse to resolution, using higher accelerating voltage presents several advantages: e) a high accelerating voltage (30-40 kV) increase the efficiency of the phosphor screen under the impact of electrons, which results in a brighter diffraction pattern. f)

there is less interference from stray electromagnetic fields and the experiment can be conducted in a more stable way. g) the electron beam penetrates further and, thus, the diffraction pattern originates from a region deeper below the surface so that surface contamination or surface damage effects are minimized. However the resolution is I counterpart degraded. It should be noted that changing the accelerating voltage changes the electron wavelength, which in turn changes the spacing of the Kikuchi bands according to Bragg's law (equation II.1).

v) Probe current

The probe current is adjusted according to the sensitivity of the camera and the contrast of the recorded patterns; it is generally fixed in the normal operating range of 0.1-50 nA. One can accept to degrade the signal-to-noise ratio of the Kikuchi lines when using image enhancement post mortem numeric methods.

II.3.3. Indexing procedure

Indexing of BKP is a two steps operation [Vonlanthen 2007]: (1) the detection of the diffraction bands; (2) the identification of the diffracting phase associated with the detected bands.

Intuitively it may seem simple to identify Kikuchi lines in step (1) by usual line filtering, gradient, or contour tracing methods using a basic computer. But Kikuchi pairs are diffuse broad bands with non-uniform intensity distributions, rather than sharp straight lines, and they generally lie over a high background level. In other words, the usual routines are not well suited. Therefore, specific transformations -the Radon transform [START_REF] Radon | Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten[END_REF]] [Deans 1983] or Hough transform [Hough 1962] [Lassen 1992] [Wright 1992] [ [START_REF] Kunze | [END_REF]], which is a special case of the more general Radon transform [Deans 1981] have been applied and developed over the past.

Basically, a straight line can be described by a polar equation like:

! ! sin cos y x r + = (II.8)
Where r is the distance from the origin, and * is the angle between r and the horizontal (x axis) in (x, y) space. In a gray-tone image, let f(x, y) be a 2-dimensional function. Then, the mathematical definition of the Radon transformation of f(x, y) is:

( ) ( ) ! ! " " # " " # $ # $ # $ = dxdy y x y x f R ) sin cos ( , , % % & ' % & (II.9) The Radon transform R(,, *) is a 2-dimensional integral transformation with the kernel ) sin cos ( ! ! " # $ % $ % y x
. If we consider only a discrete Radon transform (i.e. applied to a numeric array of pixels (x r , y s ) arranged as rows and columns), the integrals in Equation II.3 are replaced by sums. When stepping through the Radon space from one cell (x,y) to the next, the intensity values of all points(x, y) on the corresponding Kikuchi line, i, in the patterns are extracted, accumulated, and then stored in this cell (cf. figure II.21). A stripe of uniform intensity is transformed to a butterflyshaped peak in Radon space. Lines embedded in the stripe are mapped to cells of constant high intensity, while lines intersecting the stripe are mapped to cells of reduced intensity according to the section length. If the line or the stripe is fragmented, the accumulated peak intensity is reduced according to the missing sections, but all co-linear image points are still taken into account correctly. number of image points in the initial diffraction pattern is reduced after a binning operation before carrying out the transformation. The separation into a high and a low intensity Radon space, R + and R -, reduces the interference between dark and bright Kikuchi lines [Schwarzer 1998]; this is particularly efficient in the case of transmission patterns. The Hough Transform [Hough 1962] is similar to the Radon transform, while the Radon transform first accumulates the pixel intensities along a line in the image and then attributes this value to a single cell in Radon space, the Hough transform maps each individual pixel (x r , y s ) separately from the image onto a sinusoidal curve of constant intensity in the Hough space, that represents all possible lines through this pixel (see figure II.22a,b). Spurious single high-intensity sinusoidal curves in the image lead to single high intensity sinusoidal curves. The sinusoidal curves are then overlaid. For co-linear pixels in the image, their sinusoidal curves intersect in a common Hough cell (, 1 , * 1 ) and give rise to a spot whose intensity equals the accumulated intensities along the line in the image. The detection of a line in the image comes again to the much easier detection of a single spot in the Hough space. As the Hough transformation is applied on a gray scale image, the cross points representing bright Kikuchi lines will also be bright. Thus, detecting a peak of high intensity in the Hough space identify a band in the diffraction pattern (see figure II.22c,d).

a) b) c) d)
In modern EBSD systems, the automated extraction of band positions from digitized Kikuchi patterns has replaced interactive measurement of band position by the operator, except for system calibration or in case of superimposed patterns.

For step (2), in order to identify the reflecting planes associated with the detected bands (see figure II.23), the inter-planar angles between the bands are compared with the angles calculated from a theoretical crystallographic data set of material, calculated and stored in a so-called 'material file'. A wide choice of such material files is available in commercial EBSD software databases. Typically, the positions of the 5 to 10 smallest and most intense bands are passed to the indexing routine. Consideration of first 3 to 4 families of {hkl} planes is usually sufficient for solving a backscatter Kikuchi pattern in the case of high crystal symmetry such as cubic and hcp (hexagonal close-packed). Increasing the number of banks and of {hkl} families is required in the case of low crystal symmetry. The large angular range of backscatter Kikuchi patterns favors correct indexing. Reference directions in the specimen space are finally indexed, and the crystallographic orientation of the grain is given either in (hkl)[uvw] notation, by three Euler angles, (-1 , ., -2 ), or by the rotation matrix, g, which transforms the specimen coordinate system under consideration into the crystal-fixed coordinate system. The maximum number of indexed bands versus the number of bands that have been considered for indexing a pattern can be used as a measure a probability that a correct solution has been found.

The less perfect of the diffracting crystal volume, the more diffuse the corresponding Kikuchi pattern, see figure II.24. The blur indicates a high density of point defects or dislocations, lattice strain, thermal lattice vibrations due to the Debye-Waller factor, micro-fragmentation of the lattice, or the superposition of diffraction patterns from several grains sampled at a time by the primary beam spot. The cause of a diffuse pattern as shown in figure II.24 a) may be an unexpected surface layer, such as carbon, of excessive thickness, a contamination layer due to poor vacuum conditions, a deformation layer from inadequate sample preparation, or a defocused electron beam or EBSD detector. The blur can be expressed by a quantity, named "pattern quality", PQ, (or Image Quality, IQ) by measuring the sharpness of some band edges (profile analysis), of the height of peaks in Hough space, or by performing a Fast Fourier Transform (FFT) of either the original diffraction pattern or the Radon transformation [Schwarzer 2003]. Pattern quality maps of coarse grain materials clearly display grain a)

b)

boundaries and surface scratches, and often show features which look like a dislocation network.

Pattern quality can be used to discriminate between deformed and recovered or recrystallized grains in a microstructure [Schwazer 2009]. Maurice and Fortunier [Maurice 2008] designed a three-dimension Hough transform for the detection of conic curves of EBSD and XRD patterns. With this new 3D Hough transform 20 , the EBSD elastic strain analysis gives an absolute accuracy of order 5"10 -4 for local strain measurements, XRD pattern could be indexed automatically.

II.3.4. Recent developments in EBSD technique

Although the EBSD technique has been largely improved from many software and hardware aspects since the pioneer works almost 50 years ago, it remains still limited by two important factors: the indexing speed and the spatial resolution. As a consequence, many attempts were undertaken and are sometimes still currently developed in order to improve these two points.

II.3.4.1. Fast EBSD

A high speed of measurement improves not only the sample throughput of the SEM, but is also indispensable for dynamic experiments.

The high sensitivity of the detector is of key importance for high speed. Because of the introduction of digital cameras, the speed of on-line acquisition may exceed 750 patterns per second on suitable samples [S/fferud 2008], and one may consider that hardware is yet not the limiting factor. More important factors are the acquisition step itself and the software improvement. 20 the main difference of this 3D method with the 2D Hough transform is that for each cell (p1, p2) of 2D base plane in Hough space, the intensity of pixel (x, y) is added to the 3D voxel (p1, p2, sin*), where * is the Bragg angle.

a) b)

Adaptive orientation imaging microscopy [Yang 1999], also called Mesh refinement [Schwarzer 2009] is an effective means to increase speed during acquisition. Firstly, an overview of the microstructure is obtained by scanning on a coarse raster grid with a step size slightly smaller than the diameter of the smallest grains. If intra-granular structure is not concerned, it is principle sufficient to measure the orientation of each grain only once. As a result, a refined mesh is overlaid of half the step size in the second, and of quarter step size in third loop; but patterns that will be acquired (and evaluated) on the intermediate grid positions are those where orientation between neighboring nodal points on the preceding grid differ by more than a preset value. Therefore, measurements on the refined meshes in the following passes automatically concentrate along grain boundaries. Those grid points which would be skipped from measurement are assigned the average orientations of their neighbors. So the limitations of this approach are typically small twins bands that might easily be overlooked in their matrix grains; problems also arise when the microstructure consists in a wide distribution of grain sizes since the starting mesh grid has to be rather fine in order to observe smallest grains. In these cases, ignored features, such as for example grain boundaries or tripe points, may in principle be extracted from SE or BSE images of the microscopy by automated pattern recognition methods. They may then be used to choose the locations for orientation measurement. If grain boundaries or phases can be recognized by their relief after a slight etch, the relief contrast in a SE or BSE image can additionally be used to located features in the microstructure.

Improving the software is also a major step. Of course, the speed at which a band can be localized in the pattern scales linearly with the number of pixels in the pattern and the number of (ρ, θ) points in the discrete Radon transformation. Typically, the calculation and evaluation of a Radon transformation of 100 by 100 points takes averagely about 10 times longer than indexing the detected bands. Therefore, the speed can be quadrupled by simply coarsening the backscatter diffraction patterns when the size of transformation is reduced to one fourth. However, an unwanted side-effect is produced: a much-reduced angular resolution. If a single band can be initially located in a pattern of 100 by 100 pixels at a typical deviation accuracy of Δα = 1.5-2°, it will be twice as large or worse after coarsening. Then, the error limits in the indexing routine have to be widened to account for this inaccurate band location. Nevertheless, and as a consequence of this inaccuracy, fewer detected bands are indexed unambiguously. Sometimes, this leads to wrong orientation being found, and the fraction of points indexed with high confidence may decrease significantly.

The process of separate acquisition and storing of pattern sequences as raw, unprocessed bitmap images is significantly faster than simultaneous acquisition and online pattern solving. Additionally, offline pattern solution has many advantages over online orientation microscopy, in particular, because pattern interpretation can be repeated anytime (to refine it or screen new structures for example) by using the original backscatter Kikuchi sequences [Sϕfferud 2008].

II.3.4.2. Energy-filtered

As mentioned in subsection II.3.1.1, the BKP is generally constructed by the contributions of backscattered electrons, which are Bragg reflected and have energies close to the incident beam energy. However, not all electrons contribute equally to the contrast of the Kikuchi patterns. Only the 'low-loss electrons', whose energies are within 90% of incident beam energy, are considered as major contributor to EBSD patterns. In contrast, the 'high-loss electrons', which suffer a significant energy loss due to inelastic collisions contribute the Kikuchi contrast with a higher diffuse background (i.e. with a lower contrast). Although this 'high-loss electrons' are much less numerous that elastic or pseudo-elastic electrons, filtering the EBSD patterns will not only improve their contrast (see figure II.25) but also reduce both the depth and lateral extent of the region contributing to them, which hence improves the spatial resolution [Eades 2009]. This mechanism is a somewhat similar to the EsB detector discussed in subsection II.2.5.

II.3.4.3. t-EBSD

The t-EBSD, firstly named by Keller [Keller 2012] is actually based on the large-angle forward scattering of electrons in transmission; it is thus also called t-EFSD [Brodusch 2013]. In contrast to the conventional EBSD geometry where the specimen is tilted towards the EBSD detector by 70°, the sample in t-EBSD experiments is tilted -20° in the opposite direction as shown in figure II.26. As it is a transmission mode, a thin foil is required. This set-up collects a lot more signal (see figure II.27), i.e. transmitted electrons (TE), than in conventional EBSD on thin foils, i.e. BSE. Because the BSE contribution decreases with specimen thickness while TE yield increase [Reimer 1998]. Concerning the WD, it should be adapted according to usual recommendations with the atomic number Z in conventional EBSD (low WD for lighter elements and high WD for heavier elements in order to increase the number of high-angle scattered electrons). Especially, as the significant reduced volume of interaction (cf. figure II.28), the spatial resolution of t-EBSD is improved to a few nanometres below 10 nm.

Recently, with the easiest access to FIB instrument, it is easier to prepare a thin sample and this transmitted mode EBSD is certainly of increasing interest and applicability; this is particularly true if the EBSD system is installed in a FIB.

II.4. Remarks and requirements for 3D-EBSD

In general, conventional EBSD usually applies to a plane view of a two-dimensional section, where the sample of interest has been mechanically cut and polished. However, as for morphology or any microstructural feature, this approach essentially produces a 2D information which may be insufficient, or even inaccurate for characterizing properly the material of interest. A typical example is grain boundaries. Grain boundaries are represented by 5 macroscopic parameters (3 parameters about the

a) b) c) d)
disorientation across the boundary and 2 parameters about the plane normal of the boundary) [Randle 1997]. In a 2D measurement, only the disorientation can be determined certainly, while only one parameter of the plane normal is reachable. There might be considerations helping to deduce the missing parameter (such as, in a state close to thermodynamic equilibrium, the theory of the lowest energy [Rohrer 2004] which may be applied to predict grain boundary planes), but in the most general case a 3D approach will be needed. Using stereology [Adams 1986[START_REF] Saylor | [END_REF]] [Randle 2008] or other methods, 3D statistics could measured.

X Y

A true 3D characterization can then be performed by serial sectioning, easy to undertake in its principle but with the advantage of being destructive. According to this simpel statement, the dualbeam FIB-SEM microscope is an ideal tool which appears very pertinent when compared to other possible techniques, such as mechanical polishing, chemical polishing and laser or electrical discharge ablation: all these methods present inherent difficulties and in all cases a much worst resolution as compared to what can be performed in the FIB-SEM. The main difficulties are [Zaefferer 2009] the control of the sectioning depth, the achievement of flat and parallel surfaces, the correct alignment of the ROI, the inadequation or non-quantitative contrast of the microscopy techniques used (in the case of photonic microscopy) which may prevent the reconstruction, and the time required to produce a reasonable stack of images. It could however be noted that, despite of these above difficulties, some powerful 3D orientation maps based on serial sectioning with mechanical polishing in conjunction with optical microscopy have been successfully produced [START_REF] Lewis | [END_REF]] [Rowenhorst 2006].

In principle, and according to the computer-aided softwares proposed by manufacturers (such as Oxford Instruments on the ZEISS unit available at CLYM), the acquisition process of 3D-EBSD in a FIB can be completely automatic once the working area is prepared, This perspective is all the more attractive that EBSD is largely used and has become more and more popular in Materials Sciences as illustrated by the evolutions plotted in figure II.30a, b). Nevertheless, an internet search with the key words '3D EBSD' or 'FIB-EBSD' in science citation index (SCI) gives still yet little results as compared to classical EBSD (see figure II.30 b, d). Indeed efficient 3D EBSD does not only require a FIB instrument: it suffers from severe limitations in terms of spatial resolution (~50 nm for x, y and z direction) as compared to tomography in the imaging modes, very long acquisition time (from dozens of hours up to a few days for a volume of about 1000 !m 3 -9000 !m 3 ).

Therefore, this merits some efforts to optimize this approach and we will discuss this point in some more details, from both theoretical and technical points of view, in chapter IV in order to define a strategy allowing the 3D-EBSD practice to be optimized and improved.

II.5. Conclusions from the literature review

This chapter intended to provide a general presentation of the techniques and theories related to the FIB instrument; to conclude this survey, we can summarize some stringent features and raise some marking points which could be relevant in the context of the present work: 1) Modern LMIS-based dual-beam FIB/SEM microscopes are versatile tools for nano-operation. One interesting application is 3D nano-tomography by serial nano-etching, which looks accurate, reproducible and robust. However, if the experiment intends to reconstruct large volumes, it will take a long time and can suffer from instabilities during the acquisition: shall we be confident with the accuracy of automatic procedures and if not, how can we improve it? 2) Conventional 2D EBSD is a well-known and widely used technique in Materials Science for its simple setup. This 'success' invites to the development of 3D approach: how can the limitation in resolution and the time-consuming constraints be overcome? 3) Using heavy ions make it tempting to extract information from the ion-induced channeling effects in crystalline materials: is this information useful and if yes how can we treat it?

According to the motivations listed in section I.3 of this document, we ambition that this thesis contributes to the developments of methodologies especially in the context of 3D studies, and we thus will try to bring solutions, or at least partial solutions to these points during our investigation.

[ Post-mortem alignment for serial sectioning FIB-SEM tomography

Resume of chapter

The tomography via a dual beam FIB/SEM is a new powerful tool to get 3D information of a relatively large volume of matter (a few hundreds of cubic micrometers) with a good resolution (~ 5 nm). The principle of nano-tomography in FIB/SEM consists in acquiring successive images after FIB milling. The experimental details for the acquisition step are firstly presented in this chapter. In a second step, post-mortem alignments are necessary for the image series, even if live drift corrections have been performed during the acquisition. Indeed live drift corrections are generally performed just to keep the Region of Interest (ROI) in the field of view; moreover, the control of the exact thickness removed between the successive slices cannot be made (or is hard to achieve) during the acquisition and has to be determined if possible, post-mortem. Accurate alignments in the X, Y viewing plane is also required. According to the literature, cross-correlation alignment is usually performed. We will focus on the limitations of this procedure, and demonstrate its dangers by comparing the obtained results with more accurate results from dedicated experiments, where proper references the topography of the sample surface or the machining of a FIB drilled hole are used.

Résumé de chapitre

La tomographie par la double sonde de la sonde ionique focalisée et de la microscopie à balayage (FIB/SEM) est un nouvel outil puissant pour acquérir des informations tridimensionnels (3D) sur un volume relativement grand (jusqu'à quelques centaines de microns cube) avec une bonne résolution spatiale (autour de 5 nm). Le principe de nano-tomographie dans un FIB/SEM consiste à acquérir des images successives après l'abrasion de FIB. Les détails de l'acquisition 3D de manipulation sont d'abord dans ce chapitre. Deuxièmement, des alignements post-mortem nécessitent sur les images de série de la tomographie par le FIB/SEM même si la correction des dérives in-situ était effectuée pendant l'acquisition. En effet, les corrections de dérive in-situ sont effectuées généralement juste pour garder la zone d'intérêt sous champs de vue ; de plus, le contrôle d'épaisseur exacte enlevée entre les images successives ne peut pas être réalisée (ou est difficile à réagir) et doit être déterminée si possible post-mortem. Des alignements précis dans le plane de vue X-Y. Selon les littératures, l'algorithme de corrélation croisée est utilisé habituellement. On va focaliser sur les limitations de la procédure, et montrer les risques par la comparaison ces résultats obtenus avec les résultats plus précises d'après des expériences délicates où des références propres (la topographie de la surface de l'échantillon ou un trou percé par l'abrasion de FIB sont appliqués.

III.1. Introduction

3D FIB/SEM slice-and-view tomography in a dual-beam (DB) FIB is a modern powerful method to get three-dimensional (3D) information of a moderate analysed volume (10~1000 µm 3 ) at resolution of a few nanometres [Uchic 2007] [Mobus 2007] [Holzer 2012] [Cantoni 2014]. As illustrated by figure III.1, this scale bridges perfectly the gap between X-ray tomography at a resolution of a fraction of micrometre [Salvo 2003] and Transmission Electron Microscopy (TEM) tilting nano-tomography, typically down to one nanometre [Midgley 2003] and even at atomic resolution in some favourable cases [START_REF] Goris | [END_REF]] [Scott 2012]. However, high resolution 3D techniques like TEM tilting or atom probe tomography are generally limited to very small analysed volumes, and they generally require a long and accurate sample preparation. Thus, they are not always perfectly adapted to the problem of interest, especially in terms of size of the analysed volume. In this respect, 3D FIB/SEM is a very good compromise between resolution and volume size. One of the main drawback of 3D FIB/SEM experiments is the time of the acquisition step, which concerns both the quality of acquired data (regarding possible damage, uncorrected drift, loss of focus,…) and the user's presence in the case of manual or semi-automatic acquisitions. Apart from the constraints imposed by the sample itself, the acquisition time is also dependent of some hardware limitations, such as the sensitivity and position of different detectors (SESI, Inlens, EsB detectors in the ZEISS Nvision40 FIB), the electron column technology (for example, GEMINI II SEM column comparing to GEMINI I column of ZEISS instruments). As a result, a compromise should always be made between analysed volume of material and spatial resolution according to the pertinent scale for studying the microstructure of the material of interest.

III.2. History of serial sectioning tomography

The word tomography is originated from the Greek words tom1 ("cut") or tomos ("part" or "section") and graphein ("to write") 21 [START_REF] Principe | High-density FIB-SEM 3D nanotomography: with application of realtime imaging during FIB milling[END_REF]]. The serial sectioning tomography [DeHoff 1983] agrees well with this literal definition to acquire raw 3D data at the macro-to the micro-scale: the sample is 'sectioned' with a given tool and the results or data are 'written' under a certain form, iteratively, during the process. In most cases, a planar surface should be prepared before the experiment via mechanical sectioning, mechanical grinding and polishing, or ion milling.

This methodology has been applied to investigate the microstructure of structural metals [Forsman 1918] about 100 years ago. Manual procedures were then employed throughout the 1960s up to the early 2000s [Kral 2000] [Simmons 2009]. The sectioning methods (based on etching, sputtering and grinding, etc.) always assume that the material is removed at a constant rate [Patkin 1982[START_REF] Hutter | [END_REF][START_REF] Li | Serial sectioning method in the construction of 3D microstructures for particle-reinforced MMCs[END_REF]]. The accuracy of these above manual sectioning technique should be assessed. Recently developed robotic devices (figure III.2), based on microtome [Wolfsdorf 1997] [START_REF] Alkemper | Quantitative serial sectioning analysis[END_REF]] and precision mechanical polishing systems [Spowart 2003[Spowart , 2006]], reduce obviously this problem. With further automatic stage and optical microscope, they are suitable for a microstructural characterization of millimetre scale volumes with a micron-level resolution and accuracy. The 2D written data during a serial sectioning experiment can include different types and/or quantities of information for different levels of spatial resolution. For example, optical microscope [START_REF] Li | Serial sectioning method in the construction of 3D microstructures for particle-reinforced MMCs[END_REF]] [Kral 1999] and SEM based techniques are frequently combined to characterize the grain microstructure. FIB-based 3D-like experiments were firstly reported by using a combination of FIB and SIMS [Sakamoto 1998] [Tomiyasu 1998] [Dunn 1999] at a lateral spatial resolution of about 50 nm. The ion information coming out from the use of induced secondary electrons can however lead to a better spatial resolution [Inkson 2001a] [Inkson 2001b]. The first generation of FIB instruments consisted in a single ionic column, which induced severe constraints in terms of sample geometry and imaging/machining sequence (see figure III.3c,e).

The first 3D serial sectioning tomographic experiments by a dual beam system (ion beam for sample etching and electron beam for electron-induced secondary electron images) were performed on an Al wire of an integrated circuit [Cheng 1998] [Sakamoto 1998]. However, their ion and electron beams were perpendicular, which induced limitations regarding the working area and the sample preparation.

8 !m 8 !m 5 !m 10 !m b) a) d) c) f) e)
From about 2004, modern commercial dual-beam systems appeared, the geometrical set-up of which greatly facilitating the serial sectioning tomography: the sample remains fixed during the data collection, the ion beam permits a sectioning accuracy in the nanometre range. Main features of the dual-beam FIB will be presented below.

III.3. Details of dual-beam FIB/SEM serial sectioning tomography

The FIB/SEM sectioning tomography typically consists in at least two main steps: data collection and post-mortem treatment. The data collection or acquisition is a repetitive process of imaging (generally using the electron beam of the SEM column) and milling by the ion beam, once the working area has been conveniently prepared. The post-mortem treatment concerns alignment, filtering, reconstruction and visualisation of collected data; this constitutes an important process to produce interpretable, quantitative and reliable 3D results. These different operations will be exhibited below.

III.3.1. Preparation of the working area

Firstly, the sample is mounted on a stub as in conventional SEM, and positioned at the coincidence point were both ionic and electron beam converge. It is highly recommended that this position is also adjusted on the eucentric position, since, in practice, any 3D experiment will require frequent tilting of the stage of the microscope during the preparation step.

The preparation of the working area can then begin; it will essentially consist in preparing a flat surface of material, free of any possible shadowing with respect to both the ion and electron beams. The first operation concerns the protection of the top surface which will be exposed to the ion beam. Typically, the deposition of a thin layer (usually carbon) is performed on the surface, with a size adequate to cover the future region of interest for the 3D analysis. This protective layer is shown in figure III.4). It can noted that this protective layer minimizes the undesirable damages of the milled surface due to the incident energetic ions, and known as the 'waterfall' or 'curtain' effects as shown in figure III.5. The curtain effect qualifies essentially all heterogeneities produced during the ion bombardment, leading to vertical regions which are more or less milled depending upon their constitution (orientation of crystalline grains, phases made of different atomic species, materials made of soft and hard regions [START_REF] Fu | Process modeling and simulation of focused ion beam milling of water ice in a cryogenic environment[END_REF]] [Hazekamp 2011]…). To produce the protective layer, a flux of carbon-based gas (usually phenanthrene -C 14 H 10 ) is sent by a dedicated Gas Injection System (GIS) made of a fine nozzle approaching the surface of the sample at about 4 hundred micrometers (figure III.6). This gas is then decomposed by the effect of the electron or ion beam: both can indeed be used, which lead to the deposition of carbon atoms on the surface below. It's beyond the scope of this section to discuss in details the reasons for using either the electron beam or the ion beam (see however [Utke 2008]), but in the case of 3D experiments, it is generally admitted that using the gallium ions is more rapid and efficient. To give a short explanation, the use of Ga + ions produces damage during etching as illustrated by figure III.7. In this figure, the effect of the incident energy of the ion beam is clearly evidenced by the width of the amorphized region (case of crystalline material). This undesirable effect obviously exist during the milling process of the 3D experiment, but also during the carbon deposition process when assisted by the Ga + ions; however, the width of the affected layer (about 50 nanometres at maximum as shown in figure III.7) is not relevant with respect to the much larger size of the milled depth in 3D experiments, so the possible damage produced during the carbon deposition when assisted by the ion beam has no practical consequence on the quality of the 3D results. With its protective layer, the sample is ready to prepare the ROI for the 3D experiment. The main idea is to prepare a flat (X, Y) surface, or wall, free of any shadowing, which will be successively milled to reveal new fresh surfaces in the depth of the material. To do so, a main trench is made in front and on both sides of this surface as shown schematically in figure III.8a). This etching is like the 'stair-case' used in the case of the FIB preparation of thin foils for TEM in the 'lift-out' procedure (figure III.8b). Removing the material in front of the working area serves to prevent any shadowing effect for subsequent SEM observation. In practice, it is also very useful to remove material on both lateral sides of the ROI (leading thus to a 'U-shape' geometry) in order to avoid the undesirable re-deposition of removed matter on the ROI.

Although significant shadowing is prevented by this 'U-shape' geometry, some undesirable contrast variation generally subsists from the top to the bottom of the viewing area, as illustrated by figure III.9. This effect is essentially visible on SE images, and is due to the absorption of emitted secondary electrons within the trench wall, which consequently cannot reach the detector [Matthijs de Winter 2009]. As illustrated in figure III.10, an alternative oblique sectioning geometry [Matthijs de Winter 2009] [Hazekamp 2011] has been proposed to improve this situation. This geometry presents another advantage: possible less 'curtain effect' for the freshly etched cross section [Montoya 2007] [Lepinay 2013]. However, the efficiency of the further subsequent slicing is reduced owing to a worse incidence geometry: according to simulations, the sputtering rate at an incidence angle of 90° is (figure III. Because there is always the constraint of analysed time and our FIB system is adapted to standard geometry (figure III.17), all the FIB/SEM tomographic experiment presented here are executed with standard geometry.

III.3.2. Parameters for the acquisition of 3D FIB/SEM tomography

III.3.2.1. SEM imaging parameters

Before starting the tomographic experiment, it is worth defining the image conditions regarding spatial resolution and size of the target volume since all parameters are interrelated. For example, achieving a spatial resolution of 5 nm/pixel requires typically an image size of 2048 " 1536 pixels if the field of view to be acquired is 10 !m.

The question of the depth or 'Z' resolution during a 3D experiment is slightly more complex. Modern instruments provide several options regarding both the choice of imaging detectors (secondary electron detectors: ETD or In-lens for the ZEISS machines, and back-scattered detectors: classical BSE, EsB and the way to mix them).

To give general ideas, we will consider here the respective cases of Secondary Electron (SE) imaging and Back-scattered Electron (BSE) imaging.

As a main explanation, the SE contrast is generally attributed to surface topography and, in conventional SEM imaging, is therefore very sensitive to roughness and contamination. In a FIB during a 'slice-and-view' acquisition, we may emphasize that relatively smooth surfaces, with limited topography, are produced by the ion beam sectioning. So we could expect a very small contrast in SE images of FIB cross-sections. This is clearly not true, as demonstrated by figure III.11), which compares a SE image (on the left) to a BSE one (right). Collected SE are produced near the surface (figure II.13), and carry a structural information through the difference in escape energy, depending upon the probed phases (figure III.12) [Cazaux 2008] [Reimer 1998]. In addition, so-called SE2 and SE3 electrons can be generated by back-scattered electrons and bring an additional contribution to the image contrast. Since they carry information for deeper regions in the sample, they participate to the degradation of the 'Z' resolution. In a ZEISS instrument, the In-lens detector essentially collects 'normal' SE electrons, and so the 'Z' resolution can be simply equal to sectioned layer thickness. Nowadays, thicknesses as small as 2-3 nm seem to be reasonably attainable by FIB sectioning, and this may represent in most cases the optimal resolution that one can obtain in 3D.

!m

In the case of BSE imaging, a worse resolution is expected on the basis of usual arguments like in classical SEM Imaging. However, filtering BSE, as permitted by EsB detector in the ZEISS Gemini column greatly improves the usual spatial (X,Y) resolution (see sub-section II.2.5) [Reimer 1998] With conventional BSE detectors, BS electrons produced deeper in the sample can be collected (typically around 10 nm -depending on the electron beam EHT and materials -, as illustrated in figure IV.11), so the tomographic 'Z' resolution is not necessarily improved by decreasing the sectioning thickness since information arises from deeper areas in the bulk. In this case, reducing the electron accelerating voltage improves obviously the depth resolution (figure III.13), although the lateral resolution is slightly decreased. This is further highly recommended in the case of non-conductive specimens in order to reduce and possibly avoid charging effects [Bell 2013]. Reducing the electron energy, down to typically 1 to 2 keV, simplifies the situation with respect to the asymmetric electron penetration (and thus resolution) due to the inclined surface as depicted in figure III.13.

Obviously the above considerations on the 'Z' resolution must be related to the size of the features of interest. As pointed out by Uchic [Uchic 2007], a general rule is that a minimum of 10 sections (which means 10 voxels) is needed per feature to accurately characterize feature size and shape. This may, or may not, be fulfilled depending upon the actual size of these features. As an example, a minimum depth resolution of 5 nm is needed for the sample presented in figure III.13, and this conclusion further implies to adjust the SEM acceleration voltage to at most 1 kV. The last point worth discussing concerns backscattered electrons in the case of a 3D EBSD experiment; this will be carried out later in section IV.1.1.

The previous considerations show that the situation may be complex, independently of other different imaging parameters to be chosen like in conventional 2D SEM (accelerating voltagealready discussed -, but also aperture, current, scanning speed, dwell time…). It is usually a case-bycase analysis in order to optimize the contrast of the acquired images according to the nature of the sample and the resolution needed to characterize its microstructure in 3D.

III.3.2.2. FIB milling parameters

The milling parameters, like essentially the FIB accelerating voltage and the milling current have to be adjusted in order to minimize the degradation of the sample (see the curtain effect discussed in section III.3.1) and speed up the slicing process. Regarding these two points, it seems very difficult to draw out universal strategies because it remains essentially sample dependant: this means, the degradation, the eroding speed will depend on the structural, crystallographic nature of the sample, the resolution needed (or desired), and it's again a case-by-case study. What can be summarized here in the case of the ZEISS Nvision system is as follows:

-Typical ion currents: between 300 pA and 1.5 nA (700 pA as a 'mean' value) -Ion beam energy: maximal value (30 kV for the ZEISS Nvision, leading to the fastest operations without any systematic stronger degradation or drawback compared to low energy beams: as an example, the curtain effect seems on the contrary to be minimized with high energies, shown in figure III.14). The question of the slicing step, partly discussed in relation to the 'Z' resolution and voxel size (see above), is also an important issue. We will discuss this point in the next sub-section, because it will be seen that the reproducibility and the accuracy of the slicing process is greatly influenced by the tomographic mode itself and many other external sources (like mechanical instabilities, external electro-magnetic fields, drifts,…). As far as the 'Z' resolution is concerned, it may be emphasized that minimizing the curtain effect is certainly benefit to produce 'flatter' surfaces, thus a better control the thickness of the removed material. An important point concerns the way the instrument allows the user to define the thickness of the successively removed slices. Firstly, this thickness (defined as a parameter called 'Inc Style' in the SmartSEM ® ZEISS user interface) must be an integer number of a FIB pixel size along the Z direction. Secondly, this pixel size cannot be freely chosen: for technical constraints regarding the numerical control of the ion beam in our microscope, its value is linked to the size, in pixels, of the milled area. This value is not necessarily equal to the pixel size of the SEM images, although it will be convenient to have a simple ratio (1:1, 1:2,…).

All these considerations make that it is the voxel size of a FIB-3D experiment is not necessarily isotropic, although the pixel is usually a square along the X and Y directions in the viewing plane. The final geometry is illustrated by figure III.15. As a concluding remark, it may be stated that all these parameters will also have a drastic influence on a final and very important point, which is the total time of a 3D FIB-SEM experiment. Regardless of any other limitations, like sample degradation or instabilities, the better the resolution and the volume size, the longer the experiment. Indeed, the situation can be rationalized in terms of (i) the a) b)

voxel size needed (controlling the expected, or at least, numerical resolution), (ii) the total volume to be explored, (iii) the lateral X,Y size (in pixels) of the series of images to be acquired. The last two parameters will impose the number of slices to be generated, which itself is directly linked to the total time of the experiment. Based on various experiments performed during the present work, we can give some general trends, which are shown in figure III.16. Finally, the acquisition can be launched. The prepared flat surface or cross-section is successively imaged and sliced by removing a thin layer with, ideally, a constant thickness () in figure III.17) in the Z direction, thanks to the ion beam. The image acquisition with the ZEISS SmartSEM ® system relies typically on 'Pause Mill for Imaging' procedure, which means that the ion beam is blanked while the SEM image is acquired. Then the ion beam is re-operating to prepare the next slice. This discontinuous operating mode may produce slice thickness variations which can be corrected during the post-mortem treatment (seeing section III.3.4 and section III.5.1).

It is instructive to explain how the microscope adjusts the specimen in focus during the successive milling operations. After each slice removal by the ion beam, a volume represented by the section AA' B'B in figure III.17 is eroded, and the imaging surface changes from AA' to BB'. Both the field of view and the focus have then be changed; to restore proper viewing conditions, the SEM column applies a beam shift )%cos2 in the Y direction (the SEM scanning direction) to maintain the same view; simultaneously, the working distance is adjusted by the quantity )%sin2. Owing to the software facilities within SMARTSEM ® , the values of the working distance and the beam shift(s) can be monitored during a 3D experiment, which confirms these adjustments, see figure III.18.

III.3.4. Bibliographical approaches of alignment

Independently of any live drift correction, further post-mortem alignment in both X, Y and Z directions are implicitly applied for the image stack to get a correct virtual volume reconstruction (see figure III.19). The correction in X-Y directions usually consists in operating translations according to cross-correlation of successive images in most softwares, like Amira, Avizo (Visualization Sciences Group22 , Burlington, MA, USA), Aphelion (ADCIS23 , Saint-Contest, France), IDL (Exelis24 , McLean, VA, USA), IMOD [Kremer 1996](, plugin 'StackReg' [Thevenaz 1998] or 'MultiStackReg' in the Fiji25 package. On the other hand, the drifts in the Z direction could be measured [Schaffer 2007] [Holzer 2004] from microstructural features or fiducial markers and corrected [START_REF] Ritter | [END_REF]] with one of the image processing softwares listed above. The cross-correlation algorithm (figure III.20) calculates the product of convolution between the 'current image' and the complex conjugate of a 'reference image':

𝐶𝐶𝐹 𝑟 = 𝐼 ! * 𝑅 ! 𝐼 ! 𝑅 ! + 𝑟 ! !!! (III.1)
Where * indicates the complex conjugate of functions values, 𝐼 ! 𝑅 ! are the point intensities in the reference image, 𝐼 ! 𝑅 ! + 𝑟 are the point intensities in the image to align, and N represents the number of pixels in each image. The position of the maximum intensity of the cross-correlation with respect to the centre of the image gives the required translations (in (X, Y) pixels values) that will align the current image with respect to the reference one (figure III.20). In the case of sequential images from serial sectioning experiment (including FIB/SEM tomography), the first image is typically considered as the reference image to align the succeeding images. After the application of all translations for the whole series, the original 3D morphology of structure can be reconstructed as the simple stacking of the aligned images (figure III.21). This is the simple concept mostly used for aligning a series of images from a 3D FIB-SEM experiment. However, the region of interest where the cross-correlation will be calculated remains to be selected (figure III.22). In principle, the use of reference markers will allow to measure the thickness of the removed slices of matter, and consequently, deduce the possible variation in those thicknesses. As already said, these markers are generally made on the top surface, but can also be milled on one of the side surface as shown in figure III.24) [Groeber 2007].

Indeed it has been shown that in most 3D FIB-SEM experiments, the thickness of layers eroded by the ion beam is not constant [Inkson 2001a] [Schaffer 2007] (figure III.25a). This can obviously be due to some undesirable drift in the Z direction, or possibly, some instabilities in the scan of the ion beam itself. To measure these thicknesses, one can for example acquire supplementary images of the ROI but with a large field of view in order to have a global view showing reference markers [Schaffer 2007], see figure III.23). This solution increase drastically the time of the experiment, then increase the risk of sample degradation or severe drifts, etc… An alternative way is to record only such global views [Kotula 2006], figure III.25b), but in this case the resolution is sacrificed.

Any of these methods appears to be time consuming or not really accurate; as a result, Holzer and co-workers [Holzer 2004] proposed to simply work with 2 images showing the same fiducial markers, one before and one after the 3D experiment, from which they can deduce the average thickness knowing the total number of slices and the total removed thickness. However, this calculation may leads to a very rough estimation especially if the markers are erased (for example in the case of a milling performed with a high ion beam current [Schaffer 2007]). Although the cross-correlation method or the alignment based on markers appear to be easy-to-use and apparently efficiency, we will show in the next sub-section that they are indeed not robust in general.

III.4. Complement on the alignment procedure

III.4.1. Issues of commonly used alignment methods

In practice, the post-mortem alignment methods described above may be efficient, but they can indeed be quite inaccurate in a lot of cases and this for several reasons which are all linked to the fact that the exact geometry of the sample is, essentially, unknown.

We can list here some of these reasons: (i) Any cross-correlation routine will align features which, in reality, should not be aligned: this can indeed create flawed microstructure with perfect alignments from a numerical point of view but not representative from a structural point of view. An illustration is given in figure III.26, where we can imagine a prominent unaligned feature of the real microstructure which will give rise to a perfect but false alignment. We will see later on practical examples that significant misalignments are easily produced by cross-correlation, although the 3D microstructure seems to be perfectly aligned by eye inspection. (ii) During milling, markers may be partially covered by undesirable re-deposition, and then they can lose their efficiency. Some sophisticated method can be used to prevent to 'erase' the alignment markers: for example, a dedicated alignment marker geometry (figure III.22f) has recently been proposed [Lepinay 2013] using an elaborated scheme of milling and deposition of TEOS / Pt TEOS, in order to conserve a good SEM contrast and avoid any visibility loss to contamination by FIB redeposition. This approach does not apply in the case of a non-flat or inclined surface as discussed in (iii).

a) b)

(iii) Alignment based on the top surface (or the intersection of the (X,Y) and (X,Z) planes) may be wrong if this surface is not flat and/or inclined -not parallel to the microscope stage -). According to the above, a dedicated test experiment has been carried out in order to demonstrate the difficulties in the alignment procedure based on the most common approach, which is based on crosscorrelations.

III.4.2. Demonstration of the inaccuracy of cross-correlation methods for aligning a series of images during a 3D FIB-SEM experiment

In order to test the accuracy of the cross-correlation alignment, we performed a dedicated experiment: a small volume was completely extracted from the bulk in order to access easily to lateral surfaces, where specific markers were FIB-prepared. The sample used here was a mineral (a serpentine) which is used in another context (high pressure and high temperatures experiments in situ during X-ray analysis). It is a rather delicate sample to prepare, and thus presents some topography on its top surface which will be used in a second step for the post-mortem alignment. Extraction a microvolume form a bulk sample is a long and tedious operation, but it offers the advantage to suppress any shadowing, and to minimize any possible re-deposition of sputtered material. Figure III.27a shows such a micro-volume of about 20 " 40 " 16 !m 3 extracted from the bulk sample by 'lift-out' method [Schaffer 2008] [Shearing 2009]. Once extracted, the small volume was glued on a standard copper support for TEM lamellae (figure III.27b-c). 4 linear markers are milled (figure III.27d) on the lateral side with a low ionic current, and further filled with deposited tungsten. These 4 lines are used for two purposes: the two parallel lower lines are intended to allow a good stack alignment along the Y direction, and the two intersecting upper lines will allow the thickness increment to be checked in the Z direction. As shown in the front image of figure III.28, the trace of these markers on the lateral side also allow the alignement in the X direction.

Then, a tomographic series of images is acquired according to the experimental parameters listed in table III.1. After the experiment, we did perform different cross-correlation based alignments on several reference areas: 1) central area of ROI, 2) the left border of ROI with fiducial markers, and 3-4) large and small areas respectively including the interface between the top-deposited carbon layer and the ROI. In parallel, a 'correct' alignment was performed by aligning manually the markers shown in figure III.27d. As conclusion, this test is really instructive. It firstly demonstrates that cross-correlation based alignments are not accurate. It must be recalled that in all cases shown in figure III.28, the eye inspection of the reconstructed volumes gives a good feeling of reasonably well-aligned volumes. It secondly demonstrates that arrays of parallel or intersecting lines on a side surface can be efficient in order to produce a correct alignment. However, the difficulty would then be to align properly these markers. In the present case, the alignment was performed manually, slice after slice. From a practical

!m

Alignment with two parallel line markers

X Y Z Y
point of view, this cannot be an efficient method, and aligning these markers by a cross-correlation will suffer the same limitations as indicated above.

According to these considerations, it must be concluded that cross-correlation alignments cannot be robust because the geometry of the sample is not 'robust': (i) any edge, or surface intersection may be misaligned in any kind of wavy way; (ii) the microstructure of the material is unknown by definition and cannot serve as a reference; (iii) the topography of the surface may influence the location, visibility of any marker and further induce inaccuracy.

This last point is the basis of a possible 'robust' alignment: the topography of the top surface is inherent to the sample, and the reconstruction should reproduce it after a correct alignment. We then just have to measure this topography by an independent mean, and use this as a reference for the alignment. This is the strategy which will be applied in the next sub-section.

III.5. Developed methods for alignment

From this extensive comparison of cross-correlation approaches using different references, we can conclude that lateral fiducial markers are helpful, if not necessary, to provide a correct alignment. Obviously, the preparation process of such a 'lift-out' block is a long step which cannot applied for routine work. It should moreover be indicated that imaging such a sample is rather delicate form a very practical point of view regarding the adjustment of the contrast brightness, due indeed to the very high contrast difference between the material itself and the 'voids' on each side owing to the absence of matter. An alternative method is to prepare a conventional excavation, like in figure III.15 or figure III.25b, but enlarging the lateral trench (like again on the right-hand part of figure III.25b, in order to realize FIB markers as seen in figure III.27d. This will however leads to the same contrast/brightness problem.

Another reason for which the lateral markers do not constitute an ideal solution is linked to the relatively poor accuracy in the 'X' alignment. Whereas the markers geometry is perfectly adapted the alignment along the y direction (see figure III.28), it is not very accurate for compensating possible drifts in the X direction, since the X direction corresponds to the small depth of milled lines (even refilled with tungsten deposition).

Accordingly, all these considerations have led us to adopt another and new strategy for a more accurate and universal alignment. For that, we need a robust reference, linked to the object, to perform such an accurate alignment. One such reference might be the surface of the sample itself, which can serve as a good reference if its topography can be reconstructed independently and without being dependent or affected by any possible drift during the 3D acquisition sequence. This new strategy will be developed in the following sub-sections.

III.5.1. Using the topography of sample surface for accurate alignment

III.5.1.1. Reconstructing the topography of the sample top surface

We already evoked that markers on the top surface can be good references for the alignment if one is certain that this surface has a known geometry, which means that it should essentially be flat. As discussed in section III.2, different methods were employed to obtain such a nominally planar, flat sample surface: for example ultramicrotome [Heymann 2006] [Villinger 2012] or vibratome [Knott 2008] sections for biological sample, or polishing techniques for ceramic or metal based materials [Wu 2003] [Keehan 2008]. However, this preparation is not always possible, neither accurate for all samples. As a typical example, the deformed serpentine used previously -figure III.25b -) exhibits a lot of porosities or grooving effects, brittleness and weak resistance to delamination during any preparation process, which cannot ascertain that the surface can be as flat as needed. But in general, whatever the topography of the surface, and especially if this top surface is not perfectly flat, it can serve as an intrinsic reference for a subsequent alignment of the 3D stack of images produces during the nano-tomography experiment.

It is difficult to have a well prepared flat surface for 3D experiment. To do so, we need to be able to characterize this surface in 3D before the slice-and-view sequence. This is indeed quite easy to perform by a stereoscopic approach [Boyde 1973 In this process, the magnification and scan condition are easily adapted to adjust the spatial resolution (in the present case, 10 nm/pixel). As stated above, this reconstructed surface will be used as the reference to align the stack of images produced during the 3D FIB-SDEM experiment. Since these images are acquired along the Z direction, we need to produce line profiles of the reconstructed surface as Y(X) curves for increasing Z. An illustration of such a line is given in figure III.30 (corresponding to the top surface of a sectioned plane AA' in figure III.17 Before proceeding, a final comment should be made about the fact that, during the 3D FIB-SEM experiment, redeposition of milled matter could affect the surface topography, which would then make the comparison of surface profiles obtained at each slicing step, with the prior reconstructed surface meaningless. To avoid this problem, the top surface will be covered by a thin layer of tungsten prior to the usual carbon deposition as a protective layer, thus exhibiting a strong contrast in SEM, and providing after an easy segmentation the 2D line references on which the alignment will be based on.

In addition, and again to compare all possible alignments strategies, we performed a classic 'U' shape of the ROI, with a lateral (right) widely enlarged in order to mill fiducial markers as was performed in the lift-out block discussed in section III.4.2. These markers are shown in figure III.31a.

After this preparation step, the tomography acquisition was launched according to the experimental parameters listed in table III.2. An important parameter here is the INC STYLE value, which should correspond to the removed thickness at each slice. Thanks to the strong contrast of the deposited tungsten layer (figure III.31b), the profile of the top surface for each FIB sliced plane (figure III.31c) is easily obtained. After the whole image stack has been acquired, the alignment procedure will consist in determining the X, Y shifts of each image compared to a fixed reference. Since the reference is the surface, we have to compare each FIB top surface profile, as shown in figure III.31c, to its correspondent profile among all so-called 'MEX' profiles as shown in figure III.30b. During this comparison, shifts along X and Y directions allowing the perfect one-to-one match will directly give the misalignment drifts for the image of interest. This is basically the principle of our analysis; however, it must be developed in details from a numerical point of view.

III.5.1.2. Comparing top surface profiles obtained by FIB and from the reconstructed topography

Let us first introduce notations for the top surfaces profiles measured from the image stack produced during the 3D FIB-SEM experiment: YFIB i (X), where i represent the rank of the i th profile. With this writing, we recall that the YFIB value (in pixel) is along the Y direction, and the X coordinate (in pixel) is along the X direction. Accordingly, we denote by YMEX j (X') the top surface profile deduced from the topography as measured by the MEX stereoscopic approach; in this second expression, it is important to note that:

-The scaling on the Y direction is the same for both profiles -The scaling on the X direction is also the same for both profiles, but the MEX profile is larger than the FIB one, which means that matching any FIB profile with a MEX one will require to 'translate' this FIB profile in the MEX referential. This is illustrated in figure III.32. -At the end of the matching procedure of all YFIB i (X) with all YMEX j (X') profiles, we obtain a series of MEX profiles matching the series of FIB profiles; we can then call BM(i) the index of the MEX profile matching the i th FIB profile. According to this convention, we have performed the FIB-MEX comparison using a homemade program written in the Python language using adequate existing Python subroutines. Both types of profiles were obtained from 2D images after a simple binarisation according to the high brightness of the tungsten layer. Then, for each FIB profile YFIB i (X), the best matching MEX profile MEX BM(i) (X') is determined according to the maximisation of the correlation coefficient when translating the FIB profile within the whole X' interval of the MEX profile as already illustrated in figure III.32.

"m

A typical match is illustrated in figure III.33. This shows an apparent inconsistency: two successive FIB profiles are matched by the same MEX profile. We can understand why this happens looking at the details of figure III.34: indeed, at the beginning of the sequence, the topography of the surface does not vary so much, which implies that the difference between successive FIB profiles, and similarly MEX profiles, is very small, and several resembling MEX profiles can be associated to a given FIB profile.

Figure III.34. Display of the best comparison of YFIB 1 (X) profile with several successive YMEX j (X') profiles, with j varying from 357 to 366; note that although the correlation coefficient presents a minimum for BM(1)=378, all MEX profiles, and more importantly, all values of shift along X and Y look very similar.

What is indeed important, and can be deduced from figure III.34, is that the shifts along X and Y remain very comparable in all these close matches. These shift values are indeed the essential parameters we need to refine in order to align correctly the whole stack of FIB images.

The complete analysis of the whole FIB series is illustrated by the diagram in figure III.35 where the rank of the successive matching MEX profiles is reported for all FIB profiles as a red curve in a first step. In this figure, it is seen than about the first 60 FIB profiles are matched by almost the same MEX profiles with an index close to 380. However, for the rest of the series, there is monotonous variation of BM(i) as a function of i. This is indeed what should occur if the removed thickness at each milling step during the FIB-SEM acquisition is constant, as expected. From a statistical point of view, it is then quite meaningful to re-analyse the data (that is, re-do the matching procedure of the whole FIB series) by adding the constraint that the interval between any set of {BM(i),BM-(i+1)} is constant. According to the fact that we know that fluctuations may occur during the fibbing experiment, we think that it is necessary to relax this constraint by allowing some scatter. The result of this second analysis is the green curve superimposed on figure III.35: this 'best match' has been obtained assuming an interval of 0.6 MEX profiles between successive FIB slices, as deduced from the slope of the linear interpolation plotted in figure III.35. Consequently the unknown interval BM(i)-BM-( i+1) is corresponds to 6 nm (according to the spatial resolution of the MEX images of 10 nm/pixel).

From this we can perform the volume reconstruction deduced from the analysis of the surface topography. It is interesting to check the lateral side of this volume where the line markers were produced before the slice-and-view acquisition. Figure III.36 shows the initial lateral side, with various measurements lines, among which those serving to measure the angle between the two intersecting lines at the bottom of the micrograph in a), which is almost equal to 30°. In b), the same side of the sample is shown after the reconstruction using the topographic alignment. Consistently, the same angle is measured at about 27 ± 3°; the accuracy of this measurement is not good because of the fluctuations observed at points C, D (see below). Last, we can compare this to the reconstruction performed assuming a cubic voxel during the 3D acquisition, as expected from the INC STYLE parameter chosen with a value equal to the (X,Y) pixel size, i.e. 10 nm (see table III.2). Clearly, this value does not correspond to the actual interval between successive slices which has been more correctly estimated around 6 nm in the present case. This remark is very important, since it means that this parameter has to be measured in order to allow accurate and relevant true dimensional measurements on the reconstructed volume. At this stage, we must comment the quality of the reconstruction of the markers lines after the alignment. It is easily seen in figure III.36b that whereas the top horizontal line is almost perfectly restored and linear, the reaming lines below (both horizontal one and intersecting ones) present significant noisy oscillations. At a first sight, these features might be considered as a consequence of a bad alignment. However, a closer inspection shows that this is not the case. Considering the yellow markers reproduced on figure III.36c, it is seen that the 'perturbation' (linearity default) is small at the top of the image (point A on the first horizontal marker line), but it increases towards the bottom part of the image (points B, C and D). This means that the 3D stack of micrographs that have been recorded, and which are seen on their edge in figure III.36, exhibit fluctuations in the scan process during acquisition, leading to some random stretching effect along the vertical direction of all micrographs.

This phenomenon has been encountered many times during numerous 3D acquisitions, whatever the type of samples (conducting or non-conducting, sensitive to the electron beam or not,…). At this stage, we cannot ascertain whether this stretching effect is due to some external perturbation, such as a stray field, or to internal problems, such as slight magnification changes caused by some lens hysteresis for example. It may be thought that a more sophisticated control of the electron beam scanning, as permitted for example by the external Fibics 27 device on a ZEISS microscope, could improve the situation.

To conclude on this part, we can say that the topographic alignment performed here gives very good results. It must be compared to alternative and more classical alignments methods as described in the section III.4. We have already demonstrated that cross-correlation based alignments on the microstructure are not accurate (see section III.4.2). Nevertheless, it is still worth comparing these methods with the topographic alignment described above. In the study case described by figure III.29-36, 3 supplementary alignments were also performed using different areas for cross-correlation (plugin 'MultiStackReg' in Fiji software): the two parallel upper lines (seen from the X direction, i.e. the (Y, Z) plane), the centre of the ROI and the interface between deposited layer and sample surface.

III.5.1.3. Comparing the 'topographic' alignment with other alignment methods

Figures III.37-41 provide the comparison between all approaches. In each case, the side view where the makers lines can be seen is shown, together with a 3D plot of the superimposed top surfaces reconstructed from the best aligned FIB slices (in red, background) and from the MEX software (in green, foreground). Visually, a perfect alignment would produce a perfect superimposition of both surfaces, and the display would then be totally green; this means that the more red parts, the worst the alignment quality. This is also measured by an overall error factor calculated as the Euclidian distance between both surfaces (expressed in pixels).

The main conclusion is that the topographic alignment (figure III.37) provides clearly the best result: figures III.37-40 are indeed sorted by figure of merit with error factors summarized in table III.3. These error factors represent the mismatch between the surfaces reconstructed by the MEX software and the aligned FIB sections; this difference can also be rendered graphically as reported on figure III.41, which further re-emphasizes that the topographic alignment provides the best result.

Table III.3. Quantitative comparison of alignment methods

Alignment method

Error factor (pixel unit) Topographic alignment 17182 Cross-correlation on markers 144461 Cross-correlation on interface 157261 Cross-correlation on centre of ROI 170145 Whereas it is obvious that the two last approaches (cross-correlation directly on the sample microstructure, even including the top surface intersection -figure III.39 -) do not provide correct alignments, it could be tempted to assign a good quality to the procedure using the lateral marker lines. This alignment is in fact the second best one. table III.3): this means that this alignment must not be correct in the X direction which cannot be properly accounted when aligning the stack in the (Y, Z) plane.

III.5.2. Drilled tube

The previous method, consisting in aligning the stack of images from the topography of the top surface is excellent in quality but rather time consuming. A final attempt can be made to provide an

f error = 170145 a) b) a) c) b) d)
easier alignment using another type of marker intentionally performed on the sample. We already stated that markers that are commonly machined on the surfaces of the samples may not be good references for the alignment, since depending on the surface topography, and/or partially erased or modified during the FIB process (degradation, re-deposition, see sections III.3 and III.4.1). We actually need a marker geometry which can serve as an absolute geometrical reference.

In figure III.26, we discussed the problem of aligning an inclined 'tube', which would be transformed as a horizontal one if no information is provided on its inclination. This constitutes the basis of a new marker type: we will FIB-drill a hole across the ROI, and knowing its angle of inclination and the distance between successive slices (FIB slicing step), a reasonable alignment route can be used. It must be recalled here that the idea of drilling holes to serve as alignment markers was already proposed [Uchic 2009], but with a different geometry.

From this idea, a hole across all slices to be cut has been performed as illustrated in figure III.42. Typically, the sample is tilted at 54° in the microscope to reach the FIB position (i.e. the ion beam arrives perpendicular to the sample surface). In order to drill a tube before the acquisition, the stage is tilted at 0°. Then FIB objective voltage is increased of 300V (about 36000V normally) and the current is increased to 700 pA (at 30 kV, instead of nominally 80 pA) in order to promote an efficient drilling. An important parameter is the defocusing of the beam, which is required to also allow an efficient drilling: if the beam is focussed (i.e. on the top surface), a large crater is created but no directional drilling as required for the purpose of the experiment. Then, the ion beam is set to the spot mode at a given position point on the sample surface (X-Z plane) closed to the working area for a sufficiently long time in order to drill a hole through a reasonable thickness, namely the thickness that will be removed during the forthcoming 3D acquisition. In our attempts, we found it reasonable to use about 8 minutes. According to this procedure, we expect that the angle between the hole axis and the top surface is equal to 36°. Indeed, this theoretical angle is not a good reference since it needs to assume a flat and horizontal surface (at zero tilt). The good reference is in fact the front view of the successive slices, since these surfaces are generated by the ion beam, and thus contain the inclined axis of the FIB at 54° (see figure III.42 b). Then, a tomographic series of images is acquired according to the experimental parameters listed in table III.4. The overall geometry of the sample is shown in figure III.42. The post-mortem alignment was performed according to 3 methods: 1) Alignment using the hole The image stack was first aligned through a cross-correlation method leading to an horizontal, linear hole axis (perpendicular to the milled surface -plane AA' in figure III.17 -), and the successive images were subsequently shifted along Y to reproduce the theoretical angle of 54°, as mentioned above. The resulting volume is shown in figure III.44, together with the comparison of the top surface topography reconstructed either by MEX or by the FIB tomography, as shown in figure III.37-40. 2) Alignment using the surface topography method This 'best' method (as discussed in the previous section) gives the resulting volume shown in figure III.45. The error factor, qualifying the agreement between the 'MEX' and 'FIB' reconstructed surfaces drops from 473176 in figure III.44 to 22443.

3) Aligned based on a cross-correlation of the ROI We used here the 'best' cross-correlation approach as suggested by the previous section, which includes the interface between the milled and the top surface of the ROI (figure III.46).

These results show that 'best' alignment method remains that using the surface topography. As for figure III.41, we report the 'colorized' differences between the reconstructed surface with different alignment references and the MEX reconstructed surface in figure III.47. Indeed, the alignment using the drilled hole gives the worst reconstruction, although the hole appears to be perfectly restored, then aligned, in figure III.44a). In fact, a major difficulty arises from several sources which have already been discussed throughout this chapter. First, the alignment of the successive sections of the drilled hole is performed by cross-correlation, which gives apparent good results but may fail, especially because these sections vary in size and shape from one slice to another. Second, the inclination of the hole (54° from the milled surfaces) is the most stringent parameter to be reconstructed, since it depends on the accuracy of the removed thickness at each milling step. In other words, the correct reconstruction relies on the accuracy of the point positions A, C, C',… in figure III.42, which themselves depend upon the milling thickness. In order to perform the alignment of the hole, we have to assume a constant milling thickness estimated to about 6 nm (the milling parameter was set to 5 nm as reported in table III.4). Doing so, the median section of the reconstructed hole is shown in figure III.48a) after reconstruction from the image series aligned using the hole sections: obviously, the mean inclination of the hole axis is perfectly 36°, but the surface topography is not well reconstructed as measured form figure III.47. Similarly, the reconstructed hole is shown in figure III.47b) and c) when deduced form the alignment using the surface topography and the cross-correlation method respectively. In the case of the surface alignment, the deduced inclination angle is very close to the expected value of 36°. In the last case of figure III.47c), we again have to assume a constant thickness of 6 nm for each of the milled slices. This alignment gives a rather inaccurate estimation of the inclination of the drilled hole, which remains however consistent with the expected value. Moreover, it is seen that the hole 'envelope' is not complete since it disappears at the right-hand side of the projection. This effect is a consequence of the cross-correlation method, which leads to strong shifts along the X direction as illustrated by the top (X,Z) of the reconstructed surface after the cross-correlation alignment, see figure III.49. According to this, it must be concluded that the relatively good error in figure III.47 (compared to the case of the 'hole' alignment) is fortuitous. This further emphasizes the lack of confident we may have in alignments based on cross-correlation methods applied in the X-Y planes, since in the present example, we have chosen the 'best' of such alignments (applied on a ROI including the intersection with the top surface of the sample).

III.6. Discussion and conclusions

FIB/SEM tomography has become a powerful tool to get very rich three-dimensional information of a moderate analysed volume (10~1000 !m 3 ) at resolution of a few nanometres in a relatively reasonable time (12h for a 15 3 !m 3 size at resolution of 10 nm). It is then all the most important to pay a great attention to the quality of the alignment method employed before the 3D reconstruction in order to preserve the relevance of the micro-and nanostructural features that are intended to be studied.

In this chapter, we have discussed the methods that can be used in order to produce a reasonable alignment of the image stack obtained after such a 3D FIB-SEM experiment. This task is generally considered as an easy one, since, in principle, only X and Y (small) shifts of the working area are expected. One origin of these shifts can be some instability during the experiment itself, and it is tempting to try to correct them in situ as was proposed in Appendix 1. Then, one may expect that a cross-correlation method can simply be used in order to align the image stack.

We have shown here that it is not true. Cross-correlation methods is a powerful method to align images from a numerical point of view, but since they do not rely on an accurate 'a priori' knowledge of the true 3D microstructure, they cannot give universally good results. Even when using fiducial markers pre-machined on the lateral surfaces of the working area, some undesirable misalignments can subsist, which are indeed undetectable if no universal reference is available (the majority of the cases).

We have then demonstrated that using the topography of the sample surface itself, easily reconstructed from a stereoscopic analysis (as, for example, permitted by commercial softwares such as MEX which was used in the present work), can be a good reference providing the mean of a correct alignment. To do so, we have developed a method consisting in aligning line profiles extracted from the SEM-FIB images stack with corresponding ones obtained from the 'MEX' surface reconstruction. This approach has also allowed us to provide a way to estimate more accurately the thickness of the Z X slices of matter removed during the 3D acquisition. Indeed, the method provides a good means for relatively correct alignments along the 3 directions X,Y and Z.

We have also tested an alternative method consisting to drill a hole across the ROI in order to constitute a good reference for a subsequent alignment of the image stack. It can be further improved especially to try to obtain a constant diameter of the hole, which appeared here to vary as a function of depth. These variations might explain why the results obtained with this method of alignment are not as good as expected. Nevertheless, the method is probably not very convenient since it suffers from two main drawbacks: firstly the hole is essentially in the middle of the area of interest, which implies a lack of information about the reconstructed microstructure, and possibly some damage in its vicinity. Secondly, drilling the hole, although quite rapidly machined (under the present conditions, where however its diameter is not constant), requires some skill in order to realize it in the adequate incidence and position.

Coupling contrast of 3D-EBSD and FIB/SEM tomography

Resume of chapter

3D-EBSD, realised by serial sectioning within a FIB, is a powerful approach to obtain 3D information of crystallography. However, its spatial resolution is limited to (50 nm) 3 for different reasons, which will be presented for theoretical and technique points. This resolution limits 3D EBSD for studying nano-materials. Another main drawback of 3D-EBSD is that it is time-consuming, thus heavily sensitive to any problem during a long acquisition. At the same time, the resolution of FIB-SEM tomography can achieve (2 nm) 3 ., and the method is significantly faster, although reasonably long, that 3D-EBSD. These simple statements lead to the conclusion that mixing both FIB-SEM and EBSD tomographies should in principle give better results. Consequently, we have developed a new automatic programme, coupling 3D EBSD and FIB-SEM tomography in a suitable parameterized way using the Carl ZEISS API capabilities. The method is thus explained, and a first result is reported on method on a test sample (Ni alloy) for investigating its microstructure from both morphological and crystallographic points of views.

Résumé de chapitre

La diffraction des électrons rétrodiffusés en 3D, réalisée de manière séquentielle par abrasion en série dans la sonde ionique focalisée, est une méthode puissante pour avoir des informations cristallographiques tridimensionnelles. Par contre, sa résolution spatiale est limitée à (50 nm) 3 pour différentes raisons qui seront présentées du point de vue technique et théorique. Cette résolution limite l'étude des nanomatériaux par EBSD 3D. De plus, cette approche est très coûteuse en temps d'acquisition, et peut donc facilement souffrir de problèmes liés à d'éventuelles instabilités durant la phase expérimentale. La tomographie FIB-SEM quant à elle peut atteindre (2 nm) 3 . Ces constats conduisent naturellement à l'idée de mixer les 2 approches afin d'obtenir de meilleurs résultats. Nous avons donc développé une nouvelle approche couplant l'EBSD 3D et la tomographie FIB-SEM, grâce à la mise au point d'un programme d'acquisition souple qui utilise les possibilités de l'API ZEISS. La méthode est décrite, et un premier résultat obtenu sur un alliage modèle de nickel en démontre la faisabilité.

IV.1. Introduction

As mentioned in section II.4, 3D EBSD tomography in a FIB microscope is a good way to characterize quantitatively bulk crystalline materials, owing to the high precision of FIB milling, comparing to other serial sectioning methods (see section III.2). Pioneering works in this perspective were performed about 10 years ago: Groeber et al. have used a FEI Strata DB235 FIB-SEM combined with an EDAX/TSL EBSD system [START_REF] Groeber | [END_REF]]; Mulders and Day worked with a FEI Nova600 FIB-SEM combined with a Channel 6 Oxfords/HKL EBSD system [Mulders 2005]; Zaefferer et al. did their experiments in a ZEISS Crossbeam XB1540 FIB-SEM and an EDAX-TSL EBSD system [Zaefferer 2005]. The overall crystallographic and 3D characterization of the microstructures include: five geometrical parameters for grain-boundaries [Dillon 2009] [Khorashadizadeh 2011], the real form of grains / lamellar structures with possible different atomic arrangements [Adachi 2008] [He 2012], the evolution of microbands [Quadir 2007] [Afrin 2011] [George 2013], the orientation gradients [Konrad 2006[START_REF] Calcagnotto | Orientation gradients and geometrically necessary dislocations in ultrafine grained dual-phase steels studied by 2D and 3D EBSD[END_REF]] and other microstructural features after plastic deformation [Xu 2007] [Korte 2011] and fatigue crack mechanism [Motoyashiki 2007] [Weiland 2009] with cyclic loading. All these works revealed well the capacity of this technique: real 3D description of microstructures from both morphological and crystallographic points of view.

However, 3D-EBSD suffers severe practical limitations. Resolution is a first one: the realistic optimum voxel resolution of 3D EBSD seems to be 50 × 50 × 50 nm 3 [Zaefferer 2009], although a better resolution is claimed to be about (20 nm) 3 [Mulders 2005]. This size is too limited to study nano-materials or nano-structures, such as for example, nano precipitates in alloys [Sarosi 2005], thin films [Alimadadi 2013], etc. The two main reasons for this limited spatial resolution are the mechanism of formation of backscatter Kikuchi patterns and FIB milling effects (contamination of Ga + , formation of point defects and dislocations, etc., see sub-section II.2.4.1) which affect the quality of diffraction patterns. Although certain strategies (like a deposited or coated layer on the sample surface, reducing milling current or tension [Saowadee 2012], supplementary low-angle incident ion beam milling [Liu 2012] [Saowadee 2013]) can be employed to minimize the milling effects, and thus improve the EBSD pattern quality, the resolution of this technique is still limited by the backscatter mechanism itself [Zaefferer 2008] [Keller 2012]. One way to improve the spatial resolution in (2D) EDSD is top minimize the volume of electron-solid interactions as performed in transmission Kikuchi patterns (TKP) based methods recently developed in a SEM (as discussed in sub-section II.3.4.3, see figure II.26,II.27 and II.28). However, this so-called t-EBSD requires a thin sample (around 100 nm) to get interpreted signals, thus is hardly convenient for a real 3D approach in Materials Science, where a relatively large volume, up to (30 µm) 3 is typically required form a statistical and representative point of view. Resolution can also be improved by decreasing the SEM voltage, which efficiently reduces the size of interaction volume [Steinmetz 2010]. One drawback of this is however that the contrast is much more sensitive to the ion damage effects at the surface or in the sub-surface region.

To overcome these problems, computer simulations have been developed [START_REF] Groeber | [END_REF]] [Konijnenberg 2012] in order to facilitate the identification oéf grains near grain boundaries, where overlap effects between grains make the determination of their crystallographic orientation more delicate (see figure IV.1).

Another severe limitation of 3D-EBSD, at least in a conventional FIB instrument equipped with a conventional EDSD acquisition system is the duration of any experiment. It will be described in the next section that the experimental setup requires numerous time-consuming operations, including stage displacements which themselves require calibration procedures. The run-time of different processes in a single cycle of a 3D-EBSD experiment is typically as follows: EBSD mapping, taking about 6 minutes (an indicative reasonable small time, obviously directly depending upon the size of the ROI and the step of the electron beam displacement), stage movements (2 times) -2 minutes -, recognition of the ROI (2 times) -2 minutes -and FIB milling -typically 2 minutes -. Thus, the total time is about 12 minutes for each EBSD map. As for conventional 3D nano-tomography in the FIB-SEM mode, we can aim at acquiring several hundreds of images in a stack, which ends up with a considerably long and, in practice, unrealistic experiment (as an example, 500 images represent about 4 days of continuous acquisition!). In the next subsections, we will successively describe: in IV.2, the commercial 3D-EBSD solution provided by the manufacturers; the problems and limitations of this approach (section IV.3) and the present work performed during this study in order to improve the experimental approach and, at the same time, improve the speed and 'quality' (i.e. spatial resolution) of the experiment (section IV.4).

IV.2. Current automatic 3D EBSD in a FIB

IV.2.1. Geometrical Set-up in a FIB-SEM

For a typical 3D FIB-EBSD system, the EBSD camera can be mounted either below the FIB column (so-called 'rotation set-up', see figure IV.2a) or opposite to it (so-called 'tilt set-up', see figure IV.2b).

Very recently, a third geometry (so-called 'static set-up', see figure IV.2c) was developed on the latest generation of instruments, where the EBSD camera is perpendicular to the plane of FIB-SEM columns, is being developed. Actually, these three geometries are named according to the sample behaviour during the acquisition [Zaefferer 2009]. At the time of this publication, the 'static set-up' configuration was essentially configuration was essentially a concept which has been commercialized 29 , or developed as a prototype since this date [Guyon 2014]. In this configuration, the investigated surface is placed parallel to the ion beam and tilted 70° away from an horizontal plane, so that no more sample movement is needed during the acquisition. However, this set-up requires a special position of the EBSD camera, which further requires a specific design of other components in the FIB chamber. In the case of the equipment available during this thesis, it was not possible to evolve towards this 'ideal' geometrical set-up. Indeed, there are a lot of installed systems where the sample has still to be rotated to allow the 3D-EBSD procedure, and in this context it remains interesting to spend some efforts in the optimisation of such experiments (as will be reported in section IV.4). In the rotation set-up, the sample has to be tilted in different ways: in the EBSD position, the investigated surface is usually tilted 70° away from the horizontal position; in the milling position, the investigated surface is tilted 54° away from the horizontal position, so that the ion beam is parallel to its surface to be eroded. The idea is then to adapt the geometry, i.e. the inclination of the specimen holder in order to minimize displacements when changing from EBSD to FIB positions, and viceversa. This intuitive strategy is obviously guided by the need to spare time during the experiment, and avoid any additional source for inaccuracies in positioning the sample in the two different working positions. Thus, a pre-tilt of the object is insured by a specific holder; its value is about 53° in the case of Oxford Instrument EBSD setup in a ZEISS NVision 40 FIB, see figure IV.3. Then, an additional tilt of 17° is performed with the microscope stage. This value is calculated in such a way that the sample becomes ready for the EBSD milling: 70°= 53° + 17. Then, a 180° rotation around the inclined axis (by 17°) brings the sample in the FIB position at 36° from the horizontal, as illustrated by figure IV.3. However, an adaptation of the working distance is required between the EBSD and FIB positions (respectively 10 and about 5 mm, see figure IV.4) [START_REF] Groeber | [END_REF]] [Mulders 2005].

In the tilt set-up, the sample has to be tilted about an axis perpendicular to the electron and ion beam in order to swap between the EBSD and FIB milling positions. Moreover, because of the angular limitation of the stage and EBSD camera during the experiment, a y movement of stage may be needed [Zaefferer 2005].

For the above mentioned geometries, two sectioning strategies are possible [Zaefferer 2009]. One, which is named the grazing-incidence 'Edge Milling' method, is given in figure IV.5a. After the mechanical grinding and polishing preparation to the sample, a sharp rectangular edge is produced. Then milling is performed at the grazing incidence to one surface of sample edge. This method presents the advantages of being easy to set up; it further allows investigation of large volumes. However, its main limitation is that the microstructure to be explored must be close to the sample edge, which may be difficult achieved. An alternative method is the low-incidence 'Surface Milling' approach (figure IV.5b). The sample is tilted so that the ion beam enters the surface at an angle of 10-20°. Clearly, the advantage of this method is its flexibility in analyzing any microstructural feature within the sample. The disadvantage is that the milling area must be larger than the imaged area in order to avoid shadowing effects on the EBSD detector. In any case however, it is important to check that the edges of the milled area do shade the outgoing EBSD signal [Mulders 2005]. Usually, it is required that the side walls bounding the milling area are inclined at angles higher than 45° on all sides for shadow-free diffraction patterns. Generally, these potential shadowing area are removed with a large ion beam current in order to spare time (only the investigated surface will be milled with a small ion current).

In this study, we are working in the rotation set-up, and the grazing-incidence 'Edge Milling' method, which is moreover suggested by Oxford Instruments, has been applied.

IV.2.2. Automatic 3D EBSD data collection

Similarly to classical FIB-SEM tomography (as discussed in chapter III), 3D EBSD tomography requires also successive and repetitive processes of FIB slicing and EBSD mapping. However, as already mentioned above, 3D EBSD requires a longer preparation step for the ROI to avoid any shadow effect on the Kikuchi diffraction patterns, and also to get a surface with good 'diffracting' quality. After this preparation, the acquisition can be run in a complete automatic mode, like performed by different authors [Mulders 2005] [Zaefferer 2008] who used the '3D EBSD' option in the 'HKL Fast Acquisition' software of Oxford Instruments. It is interesting to list here below the different tasks that are accomplished by this commercial procedure:

1) The sample is mounted on the dedicated holder, which is set to the "milling" geometry. Then, the user aligns the specimen and inserts the EBSD camera. 2) After selection of the region of interest, a protective W or C layer is deposited on the top of it.

Then, alignment markers are created on the specimen surface. 3) A rough cut generates the first area at the edge of the sample that will be mapped by EBSD. This is a cleaning/smooth step. 4) The actual 3D area of interest is then defined by its depth, length and width, all in relation to the dedicated alignment markers. 5) The sample is then set to "EBSD" geometry where it is checked that high-quality EBS Patterns can be produced. The user selects the phase for EBSD analysis and can fine-tune the EBSD parameters. The mapping area is defined according to the previous alignment markers (realized on the top surface), and new markers are defined which will be used for the EBSD alignment: a SEM reference image "1" is then recorded from these markers. 6) The sample is put back to the "milling" geometry and inspected with both beams. Possible residual areas masking the escape of the EBSD signal from deeper slices are milled away. A second reference image "2" is recorded on the 'FIB' alignment markers (this image is generally obtained in the ion-induced mode). Both reference images are illustrated form markers "1" and "2" in figure IV.6. 7) The automation now takes over full control of the dual-beam and EBSD system. 8) The specimen is moved to the "EBSD" geometry and aligned by pattern recognition to subpixel accuracy according to the above captured image "1" of alignment markers at EBSD position. 9) An EBSD map is created from the selected region of the specimen.

a) b)

10) The specimen is moved to the "milling" geometry and the specimen is accurately re-aligned according to the second reference image "2" in the milling position. Then, a slice of material is removed. 11) The previous three steps are repeated for remaining slices.

In the work of Mulders and Day, the (1)-( 6) operations are called the "set-up" phase, which are indeed the preparation steps, and ( 7)-( 11) are called the "Run" phase, in practice the acquisition phase.

IV.2.3. Software for 3D-EBSD data treatment

Besides some free softwares (DREAM3D work generally on the serial 2D EBSD data to provide the alignment of sliced sections, and allow segmentation of grains and noise reduction with different computer algorithms.

IV.3. Resolution limits and potential solution for 3D EBSD in a FIB

Although commercial software and hardware are mature to allow completely automatic acquisitions, 3D EBSD experiments suffers from a limitation in resolution, due to the physics of electron backscattering; in 3D, it can be estimated to about (50 nm) 3 . Roughly speaking, the lateral resolution, about 50 nm in both X and Y directions, is equivalent to the depth (Z) resolution, which is further related to the milling accuracy after repositioning the ROI as discussed in section .IV.2.2. (a reasonable value for the minimum eroded thickness permitted by the Zeiss / Oxford Instruments combination is then 50 nm). This limitation makes 3D EBSD inapplicable to the investigation of fine microstructures, as basically illustrated in figure IV.7.

In contrary, low voltage SE or BSE imaging in conventional SEM give access to a nanometric resolution (discussed in sub-section II.2.5 and III.1) of about 1.1 nm in X-Y direction and 2-3 nm in Z direction (depending on the nature of the sample, the accelerating voltage and the detector configuration). This basic statement suggests that there is some interest in try to 'mix' both 3D SEM-FIB tomography (as discussed in chapter III) and 3D EBSD. This will be the aim of the next section (IV.4). Before that, it seems worth giving more details on the reasons for the limitation of resolution in a 3D EBSD approach.

IV.3.1. Reasons for resolution limits

The spatial resolution accessible in a 3D EBSD experiment as permitted with the ZEISS / Oxford Instruments setup, is controlled by several factors: technically, the markers (cross-hairs shape) used as reference for accurately repositioning the ROI, are often imaged at low magnification (shown in figure

5 "m 1 1 2 2 3 3 a) b)
IV.6), which constitutes a first source of inaccuracy. After each stage movement for any position change, there is only one drift correction, which does not allow to access to any desired milling accuracy (i.e. in the 2-3 nm range for each slice). In addition, there are physical reasons limiting the resolution: the large electron-solid interaction volume and ion beam contamination effect after milling process are the two main reasons. These three points are further documented in the following three sub-sections.

IV.3.1.1. Single area recognization process for the ROI

As illustrated in figure IV.8a, the 'Drift correction' is run twice in an EBSD mapping cycle after the movement of stage: for ion beam at milling position and for electron beam at EBSD position. According to the recommendations of Oxford Instruments, and as tested many times, the cross-hairs should be captured (shown in figure IV.8 b and c) at a low magnification (pixel size around 100 -200 nm) for a continuous acquisition. It has been noted that even though these markers are well visible in the field of view, the system may sometimes fail in their identification. Although the cross-correlation alignment usually works correctly at a sub-pixel level, errors as large as the thickness slice (≥ 50 nm) are also been encountered in some other cases. As a result, the 'Drift correction' alignment is neither accurate, nor reproducible in a satisfactory way.

IV.3.1.2. Spatial resolution of EBSD

As discussed in section II.3, the sample for an EBSD experiment is tilted approximately by 70° relatively to the horizontal plane beam in order to generate Kikuchi patterns with a sufficient intensity (i.e. high backscatter coefficient, see figure II.16) owing to the steep forward scattering of electrons. As a result, the excitation volume (shaded part of figure IV.9), which means the fraction of the interaction volume of primary electrons with the sample from which electrons are backscattered and leave the crystal without further scattering to form the EBSD pattern is elongated in vertical direction.

Obviously, this volume size governs the inherent resolution of EBSD: therefore, the spatial resolution (table IV.1) in EBSD along the primary electron beam, δ y , is about three times (1/cos70°) worse than δ x (about 2 times of the beam spot size). The depth resolution δ z depends on the mean free penetration depth of backscattered electrons. The excitation volume increases for light materials and high electron accelerating voltage (discussed in sub-section II.3.2). The influence of the material nature is well demonstrated in the work of Chen [Chen 2013], which shows a higher resolution on high-atomic-number Ag in comparing to low-atomic-number Al with the same electron accelerating voltage of 10 keV.

Figure IV.9. Schematic illustration for the interaction volume (whole sphere-liked form), the elongated excited volume (shaded part) and the spatial resolution ) in a classical EBSD geometry (5 6 20°) [Schwarzer 1993]. Because of the highly tilted sample surface, the spatial resolution in y direction () y ) is worse than ) x .

Lowering the beam accelerating voltage, which will reduce the size of the interaction volume, seems to be an efficient and direct way to improve the EBSD spatial resolution in a real case, as shown in figure IV.10 [Steinmetz 2010]. Furthermore, table IV.1 reports several data from the literature; it can be noted that decreasing the SEM voltage from 30 keV to 10 keV leads to an improvement of the lateral resolution from 150 nm to 50 nm in a Ni sample (results from [Isabell 1997]).

As it might however be intuitively expected, lowering the electron accelerating voltage is unfortunately not an 'universally good' method to improve the resolution of (3D) EBSD. Improved EBSD spatial resolution on a TWIP steel obtained by lowering the SEM accelerating c)

A first point is that the EBSD pattern quality is rapidly degraded when lowering the accelerating voltage, as clearly demonstrated by figure IV.11a, despite the increase of the exposure time to counterbalance the weak brightness and sensitivity of the phosphor screen at low voltages (figure IV.11b). In any case increasing the acquisition time will rapidly limit the feasibility of a 3D experiment.

Secondly, decreasing the accelerating voltage is very critical for EBSD analysis grain boundaries, especially in the case of ion beam milled surfaces: even at 'high' SEM voltages, the superposed crystal lattices at grain boundaries result already in more 'channelling-in' electrons, which leads to bad contrasts in both SEM and EBSD images.

IV.3.1.3. FIB milling effect

Even though FIB is a powerful tool here to extend materials characterization from 2D to 3D, FIB milling is inherently destructive and may produce spectacular specimen surface degradation owing to the implantation of large mass ions, such as crystal structure damage [Pelaz 2004] and amorphization [Rubanov 2005] [Konrad 2006]. The depth of the damage layer is a function of incident angle of ion beam (typically fixed to 90° in the 3D EBSD case), the ion accelerating voltage (figure IV.12) and the nature of the milled material [START_REF] El-Awady | Effects of focused ion beam induced damage on the plasticity of micropillars[END_REF]. As a result, this damage can be reduced by low-kV FIB polishing during EBSD-FIB experiments [Saowadee 2013], as performed in the case of TEM sample preparation [Kato 2004] [Yabuuchi 2004] [Schaffer 2012]. As illustrated in figure IV.12, the intensity of Kikuchi patterns is decreased with increasing FIB voltage. More directly in figure IV.13, the EBSD map obtained after milling with the lowest FIB voltage shows much more small grains. Alternatively, an additional cleaning process with lower FIB current and voltage performed after a normal (relatively fast) milling process can be realized in order to remove significantly surface damages, and thus allow EBSD maps with a better quality to be acquired [Saowadee 2013].

kV 10 kV 20 kV 30 kV

In order to illustrate more clearly the damage of ion beam, we can perform indicative SRIM/TRIM simulations. Although run under simplified theoretical assumptions, this program gives a reasonable view of the depth penetration of ions in condensed matter.

Simulation in SRIM/TRIM

SRIM is a group of computer programs which calculate the interaction of ions with matter; the core of SRIM is a program named TRIM (TRansport of Ions in Matter). TRIM is based on the Monte Carlo method, and allows the final 3D spatial distribution of ions to be calculated in the targeted material. A limitation of these programs is that all targets are considered as amorphous materials, which neglects the potential contribution of channelling or other orientation dependent phenomena [Giannuzzi 2005]. Meanwhile, as indicated in the SRIM textbook [Ziegler 2008], a cylindrical symmetry in the final ion distributions is assumed in the program. The assumed cylindrical axis is perpendicular to the target surface. From the above assumption, the definitions of different output values (R p , Mean Projected Range; R y , Lateral Projected Range; R r , Radial Range) are as follows:

! ! ! ! ! ! ! ! ! (IV.1) ! ! ! ! ! ! ! ! ! (IV.2) ! ! ! ! ! ! ! ! ! ! !!! ! ! (IV.3)
Where X i is the projected range of ion "i" on the x-axis, i.e. the perpendicular distance from the surface to the end of an ion's track; 7 i x i sum of the ion projected ranges; 7 i x i / N the mean projected range of N ions; and <x> the mean projected range of all ions. For the assumed cylindrical symmetry of the ion distribution, the above lateral range definition averages the absolute values. To simplify the view of these parameters, a schematic representation is drawn in figure IV.14 with N = 1. As illustrated in figure IV.15, the ion penetration into the material increases with the ion energy, which corresponds to the results reported in figure IV.12 and figure IV.13. At the same time, the ion penetration increases in light materials as compared to heavier ones as which is shown in table IV.2.

From tha above discussion, lowering the ion beam energy can improve the EBSD map quality by reducing the ion damages. But in the persepctive of a 3D EBSD experiment, this will lead to much longer milling time and will considerably increase the total acquisition time (see figure II.13). More importantly, even with a low ion milling voltage and an averaging of EBSD signal, many features remain challenging for a correct EBSD analysis, like the grain boundaries as illustrated in figure IV.13.

Finally, just because of the existence of ion damage, the SEM voltage cannot either be lowered ultimately to improve the resolution. As discussed in sub-section II.3.4.2, backscattered electrons with a high escape energy contribute principally to Kikuchi patterns, while other electrons are more contributing to the background. As shown in figure IV.16 and figure IV.17 in projection, electrons with highest exit energy escaped mainly from shallower surfaces (< 10 nm; the blackest part in figure IV.16 and most central area in figure IV.17). Decreasing the SEM voltage may lead that these z y x y electrons come essentially from the ion damaged sub-surface, which cannot improve the EBSD spatial resolution as intuitievly expected owing to the smaller electron-solid interaction volume.

In order to illustrate simulateously these two factors limiting the spatial resolution in 3D EBSD, figure IV.18 reports simulated results. For materials of moderated atomic number like Cu, the Kikuchi patterns are generated from both within and below the Ga+ ion damaged layer, thereby generating good quality patterns. For materials of higher atomic number (Z>29), the damage layer is wider than the depth of electron penetration, but this is compensated by the greater BSE yield, which generates Kikuchi patterns of similar quality to copper. For materials of low atomic number, there is both a large Ga+ ion penetration depth (see table IV.2 for Al) and a low BSE yield, which collaboratively result in a low quality of Kikuchi patterns.

All these considerations indicate that acting only on the EBSD acquisition conditions (SEM and milling -FIB -voltages) will not allow to improve the spatial resolution of 3D EBSD, which remain controled intrinsically by the physcial limitations inherent to the EBSD technique. This simple conclusion shows that any possible improvement will require to use other signal(s) complementary to EBSD; this will be the subject of the following sub-section.

IV.3.2. Potential solution to improve the resolution limit

As discussed in section III.1, classical 3D FIB/SEM tomography permits a high spatial resolution, down to around 2 nm with a low SEM voltage. Mixing such 'high-res' SEM images with EBSD maps could then be an efficient way to improve the EBSD resolution in the X-Y plane. Figure IV.19 shows 4 images obtained from a Cu alloy sample in 15 kV (typical SEM voltage for EBSD) and 1.5 kV with the InLens and BSE detectors, respectively. As expected, the low voltage Images contain much richer information. Furthermore, whereas the slice 'resolution' is somewhat limited in the 3D-EBSD routines on the ZEISS / Oxford Instruments association (a sectioning limitation of about 50 nm -see section IV.3 -), it can easily be decreased to a few nanometres in classical FIB/SEM tomography. This is the first motivation for coupling classical FIB/SEM tomography with regular EBSD mapping.

Another point is the time taken by a systematic recording of EBSD maps at each slice of the 3D sequence. We can further ambition to correlate structural features as revealed by SEM imaging on a given slice, with crystallographic information obtained by EBSD on an adjacent or previous slice in the succession of slices within the 3D sequence. This means that we can spare a lot of EBSD maps by recording them only every 10 (as indicative number) slices, without losing too much (or ideally any) information.

The principle of this 'mixed FIB-SEM / 3D-EBSD' approach will be based on a classical FIB-SEM tomography: alternate sequence of acquisition of microstructural information (imaging by SE or BSE) and slice erosion (FIB milling), in which some EBSD maps acquisitions are intercalated at a frequency defined by the user.

Although this principle is trivial and apparently simple, it realization requires a lot of sub-processes because we will have to substitute home-made routines to commercial procedures which cannot be divided into the elementary bricks that we need to control properly the successive steps of the desired approach. These various operations will be presented subsequently.

IV.4. Dedicated coupling 3D EBSD with FIB-SEM tomography

IV.4.1. Difference with existed commercial 3D EBSD software of acquisition

In the existing commercial SmartSEM ® software of Carl ZEISS, and HKL Fast Acquisition (HKL FA) of Oxford Instruments, the strategy to realize 3D acquisitions is not identical. Figure IV.20 shows the experimental details of these two softwares.

For SmartSEM ® , the total milled width is fixed by adapting the FIB pixel size, and then the erosion thickness of each layer is defined. For HKL FA, the erosion thickness of each layer is fixed, so a certain desired milling width is achieved by repeating the erosion within a small height rectangle. These differences produce the experimental limitation of the Z resolution in 3D EBSD, as already mentioned in previous sections.

Experimentally, the erosion thickness during slice sectioning must be coherent with the FIB pixel size. For example, in figure IV.21, if an ultimate resolution of 50 nm is desired in the Z direction, the FIB pixel size should be adjusted to 100 nm because this parameter is predefined for a milling iùage size of 1024 x 768 pixels (see chapter 3). Then, a milling resolution of 2048 " 1536 will have to be selected in the present case, and the 'nudge' value of system should be set to 50 nm.

Figure IV.20. Two different ways to implement FIB sectioning: for FIB/SEM tomography, the total width (here chosen to be 0.1 !m -100 nm -) to be milled is fixed by the 'Height' parameter and the erosion thickness (here 25 nm) of each layer is defined by 'Inc Style' in a cycle. For 3D EBSD, the erosion thickness (here 12.5 nm) of each layer is fixed by the 'Nudge' parameter, which represents the depth eroded by the ion beam. However in the next cycle it is recommended to adjust the 'Height' parameter to typically 3 times the 'Nudge' value in order to suppress the polishing damage and redeposition effects). In the given example, to achieve the same milling volume, the elementary milling cycle in the HKL Fast Acquisition must be repeated 8 times (so that 8 x 12.5 nm = 100 nm = 0.1 !m). In addition, a further constraint is that both 'Inc Style' and 'Nudge' values have to be compatible with the FIB milling pixel size. To express more clearly the difference between the commercial 3D EBSD procedure and our developed coupling program, a synoptic diagram is shown in figure IV.22 and subsequent explanations are given below.

In 'commercial' 3D EBSD, the experimental process is governed by two FIB parameters: states of 'external control' and 'FIB milling'. At the EBSD position, after having operated a cross-correlation on the markers area, the 'external control' is set to 'on', so that the HKL FA software (Oxford Instruments) can control the electron beam to scan over the ROI and acquire EBSD map. Once the EBSD map is finished, SmartSEM ® (ZEISS) controls again the microscope to move the stage and perform the cross-correlation for the ion beam operation. Then the new task of milling defined by a rectangle (see figure IV.20b) is run. The state of 'FIB milling' will be watched this time. Once 'off', this means that a layer with the desired thickness has been removed. The stage is re-positioned at the EBSD position, and previous processes will be repeated according to the user preferences. It is important to note that the SEM voltage remains always the same for all acquiring processes.

In our newly developed program, the stage is at first positioned both at milling and EBSD positions to store the different SEM parameters (gun and aperture alignments, contrast and brightness for images, etc.). Contrarily to the 'Drift correction' option in the SmartSEM ® software, the markers are captured here at three magnification in the FIB and SEM modes at the milling position and in the SEM mode at the EBSD position. The first lower magnification images aim at correcting any possible large stage drift after each stage movement. The second and third images are used for a higher accuracy drift correction (up to a few nanometres according to the user's choice). Then, the milling task (represented as the large rectangle at left in figure IV.20a) is predefined for the classical FIB-SEM tomography. After defining the frequency of EBSD mapping during the sequence of FIB-SEM tomography, the program starts by acquiring an EBSD map. The stage is positioned in the milling position after mapping and the SEM voltage is lowered by recalling saved parameters. The cross-correlation for the electron beam is launched firstly to put the ROI in the field of view for SEM imaging by using the SEM beam shifts. Then the cross-correlation for the ion beam is performed to find again the markers, and resume the milling by applying 'nudge' both in X and Y directions. The step of 'nudge' happens almost at the same of resume milling, because this 'nudge' can only be used while the milling state is on (the nudge is adapted here because at this stage the beam shifts have no action on the position of the milling area -solid lines of rectangle in figure IV.20a). However, the FIB beam shift is also changed only for checking the alignment quality, and set back to its initial value. After all this, the FIB-SEM tomography is run in the 'slice-and-view' mode until the desired thickness has been removed. The milling is paused, and the stage is positioned again at the EBSD position. The SEM is set to the conditions for EBSD mapping. The cross-correlation is performed to find the surface on which the EBSD mapping has to be run. Then, above processes are repeated until the end of the milling task. The order of all these processes can be found in figure IV.23.

From the above description, the developed program has overcome the problems for spatial resolution both in X, Y and Z directions, indicated in section IV.3.1, principally by combining the high resolution FIB-SEM tomography with EBSD mapping.

It must be added that the EBSD acquisition is controlled by the commercial HKL Fast Acquisition software, which implies limitations for the user: once the procedure has started, it is not possible anymore to change settings such as focusing and stigmatism of electron beam, the contrast and brightness values, the EBSD mapping area, etc.). Even though the cross-correlations are indicated by confidence coefficient (see figure IV.8a), it is hard to check them after the destructive experiment; as discussed in chapter 3, it must be recalled that the alignment quality can drastically affect the reconstruction result. For these serial EBSD maps, it is also very challenging to perform an accurate alignment only on the basis of crystallographic information on the microstructure.

IV.4.2. Details of our program

The complete and detailed loop of operations to perform is presented in figure IV.23. In order to drive the successive elementary operations, a manager routine (named 'MAITRE') has been programmed (figure IV.24), which controls all processes for both ion and electron beams, the movements of the microscope, the acquisition of SEM images and that of the EBSD maps (with a dedicated command from an Oxford Instruments API).

This 'MAITRE' program has been written in Visual Basic 6. All sub-routines (executables .exe files written in VB, C or C++) are called by this main routine; for convenience, these sub-routines have been named as their equivalent in the command list of the SmartSEM ® API (when existing), such as: STARTEBSDMAP, MOVETOFIB, CLOSEFIBVALVE, etc. A number has been added when the subroutine is called several times (for example, LENSHYSTERESIS) to clearly identify when it is active in the whole process. All elementary steps of the whole loop will then be briefly explained.

IV.4.2.1. Recalling microscope stage at milling position and EBSD position

The displacements of the stage during the 3D EBSD experiment are very delicate because:

-the great volume of the support which is used for the 3D EBSD experiment (figure IV.25), -the proximity of 3D EBSD support to polar piece, -the permanent insertion of EBSD camera during complete experiment.

Figure IV.26 shows the interface window of the sub-routine 'saving and recalling positions', which is written to avoid any collision with the support, the EBSD camera or the polar piece during the displacement of stage. The principle of this sub-routine is to save the positions of the stage respectively for the EBSD mapping and the ion erosion, and to perform the displacements from one position to another. For both positions, the stage parameters are saved, including X, Y, Z, M, T, R; a safe distance along Z and an urgent stop are also considered in the routine. Figure IV.27 illustrates the various steps of the support movement from the EBSD to the milling position (the displacement from the milling to the EBSD position is completely inversed). During this operation, it is very import to performed a safe movement on -Y to avoid any collision and damge.

Moreover, because of the repetitive movements of the stage during the acquisition, a stage backlash (both for X-Y-Z-R-M) is typically performed for each position as suggested by Carl ZEISS.

IV.4.2.2. Multi-regional recognition

After all previously mentioned stage movements, the ROI is expected to come back properly in in the field of view. On our system, it is generally not the case, and error in the expected correct position as important as 10 !m can be observed as shown in figure IV.28. Then, a further drift correction has to be performed to reposition properly the ROI. Executing window for multi-regional recognition: manual mode permits user to define 3 different magnifications for precise location of the ROI and automatic mode uses 3 predefined magnifications. The manual mode is suggested to adapt the size of the ROI.

A new sub-routine for multi-regional recognization is thus written with a strategy similar to that of the live drift correction reported in Appendix 1; it mixes routines from the Carl Zeiss API and the 'MultiStackReg' and 'linear stack alignment with SIFT' plugins run in the Fiji software. Moreover, two cross-hairs are machined on deposited layer as fiducial markers (shown in figure IV.28) for step 8 and 18 in figure IV.23. Contrarily to the Zeiss 'drift correction' option where the alignment is performed at a single magnification (see figure IV.8b and c), we have used here 3 magnifications (MAG1 < MAG2 < MAG3): MAG1 intends to correct any possible large drifts (such as reported in figure IV.28), MAG2 is for an intermediary location with a rough accuracy (normally sufficient for EBSD), and MAG3 is the highest magnification allowing to re-position the ROI with a precision of about a few nanometres, which is suitable or even needed for achieving a final good resolution in FIB/SEM tomography.

This re-alignment procedure should in principle simple to apply: as discussed previously, the calculated shifts for a correct re-positioning should be directly realized with the ion, or the electron

40 !m b) a)
beamshifts depending upon when the procedure is applied: either before cutting a new slice or before acquiring the SEM image of the freshly milled surface. The constraint in the 'milling' position is that we need that the ion beam always mills the same area, which cannot be insured with the beamshifts and requires that the nudge value should be restored, according to the calculations for the sub-process 'FIB drift correction' (# 8) in figure IV.23. As for the acquisition of the SEM image, figure IV.30 shows an example of the procedure on a cross-section in the case of low-voltage SEM imaging; it can be seen that the program gives an excellent quality of alignment with accuracy of nanometres.

IV.4.2.3. Recalling different experimental conditions

As discussed previously, the illumination conditions for SEM imaging and EBSD mapping are different. SmartSEM ® permits to save most of experimental conditions (EHT, aperture size, detector, etc.) especially in a so-called 'recipe' format (figure IV.31). These recipes are actually text files with a given extension '.EMRCP', which can be recalled by macros written in SmartSEM ® , or more directly by commands of Carl ZEISS API (used in our sub-routines). During the programming of all sub-routines, we encountered two main, although minor problems but which we had to solve, regarding the efficiency of the response of the system to the injected command.

In several cases, we had to incorporate delays by a few seconds between two successive operations: for example, when varying the electron accelerating voltage, the parameter 'WD' is applied a few seconds later to avoid a system error caused by an apparent unsuitable WD value. Also, during switching from the tomography to the EBSD mapping condition, a discord error will be generated by the system if 'WD' and 'EHT' are performed at the same time because a large WD is believed to be applied during a voltage increase.

Also, hysteresis effects frequently perturbed the image or settings quality, for example when changing the WD and EHT parameters (and also various other parameters). We found that it was necessary to recall the recipe concerned by the current action, then correct the hysteresis and recall the recipe again to get good imaging conditions (see figure IV.32).

IV.5. Feasibility experiment IV.5.1. Material & details of experiment

A preliminary experiment was performed on a Ni super-alloy sample. This sample was selected because it is a model sample frequently used by Oxford Instruments to test the feasibility of 3D-EBSD in a ZEISS FIB; it provides high-quality diffraction patterns and presents a textured in the grain microstructure (which then we aim at identifying). It further involves different precipitates (size and crystallography), and the whole microstructure cover a large range of sizes, from the micrometre to the nanometre.

Ni-based super-alloys have great metallurgical properties, i.e. high temperature creep and fatigue resistance, good phase stability and oxidation or corrosion resistance, and it is largely used for industrial applications like gas turbines (hot zones) [Reed 2006] [Raisson 2008]. It is well known that with the addition of alloying elements such as aluminium and titanium, a two-phase equilibrium microstructure develops, consisting of a FCC matrix (known as γ, with a random distribution of the different species of atoms, see figure IV.33a) and hardening precipitates (known as γ' with the Ni 3 Al based L1 2 structure, in which the nickel atoms are the face-centres and the aluminium or titanium atoms are located at the cube corners, see figure IV.33b). The γ' is perfectly coherent with the γ matrix, with morphologies nearly spherical at the SEM resolution level (see these features in figure IV.34a,b). Obviously, the similarity between the γ and γ' make them indiscernible in EBSD as seen in figure IV.34 c, d). On the contrary, twins in the γ phase is not seen in SEM but easily identified by EBSD. We can then easily understand that 3D EBSD and 3D SEM-FIB approaches are fully complementary on such a system. 3D-EDX would then be also useful in order to identify the chemical nature of the secondary phases precipitating in this material (figure IV.34a,b). Indeed two new phases are identified: a first numerous population of small precipitates and a second one of coarser and less frequent particles, appearing with a white and dark contrasts in the Inlens images (figure IV.34b). This thorough investigation was beyond the objectives of the present work and we did not try to identify more clearly the nature of these precipitates. Generally speaking, chemical analyses in these systems involve deeper TEM characterization (for example EFTEM [Sarosi 2005] [Tiley 2010] and/or HAADF [Chen 2014]). In this preliminary experiment, we will mainly on the global crystallographic orientations of larger grains and the morphology of precipitates. In principle, there is no specific limitation that could prevent the crystallographic analysis of the two populations of precipitates, but we did not pay attention to this parameter simply because of their small size: it would have been required either to acquired very large images and EBSD maps to include these precipitates in the overall analysis, or acquire specific subsets in order to treat only a few of them (both approaches are possible but again beyond the scoop of the present experiment).

The parameters for the experiment are given in table IV.3. The SEM accelerating voltage and WD values for the EBSD mapping were set to get a low value of MAD (Mean Angular Deviation), the specific parameter of the Oxford-Instruments EBSD software qualifying the match between experimental patterns and theoretical patterns). According to the procedures presented in section IV.4.2 (see figure IV.24a), different conditions and microscope parameters for the FIB-SEM tomography and the EBSD acquisitions have been saved and then the experiment has been launched after the dedicated preparation of the work area, as described in the following sub-section.

IV.5.2. Working area preparation

The preparation begins by a rapid milling (with a large ionic current) of the sample to produce a 'coarse nose' shape as for a classical 3D EBSD experiment shown in figure IV.6.

As discussed in chapter III, the post-mortem alignment of the image series in a FIB-SEM 3D sequence can be delicate and in any case requires fixed details, such as markers, present in all images. For sake of simplicity, we did not use the 'topographic alignment' procedure, although this method appeared as the most efficient and accurate one. We have thus simply used standard markers on the top surface, but to increase the accuracy of our alignment, we choose to flatten this surface using the FIB.

The sample top-surface above the ROI was positioned parallel to the ion beam (see figure IV.35a), so that this surface could be cleaned delicately (shown in figure IV.35 b and c), as it is performed on the surface for EBSD mapping. After that, the surface is covered by a protective layer of C, where some markers are machined (three parallel lines in the middle for the future alignment of SEM sliced images in X and Y directions, and two other intersecting lines with a given angle in order to control the eroded thickness of each layer in the Z direction, shown in figure IV.35 b), and filled by W to provide a good contrast in SEM imaging. The markers are finally covered again by C to protect them under the effect of the ion beam during the acquisition. Finally, two cross-hairs on the newly deposited C layer are milled for allowing the repositioning steps by cross-correlation (see figure IV.35d).

Once above protective layers and markers are ready, the sample was positioned again to classical FIB-SEM tomography position. Progressively decreasing ion currents at 30 keV were applied to the ROI like in the surface preparation for 3D EBSD experiment, so that a surface can gives good EBSD diffraction patterns.

Once above protective layers and markers are ready, the sample was positioned again to classical FIB-SEM tomography position. Progressively decreasing ion currents at 30 keV were applied to the ROI like in the surface preparation for 3D EBSD experiment, so that a surface can gives good EBSD diffraction patterns.

IV.5.3. Preliminary results

Because of the instability of the FIB instrument, two repeated 'backlash' procedures were performed to stabilize well the microscope stage (a slow drift was observed after only one backlash); in the course of the acquisition, the recall of SEM conditions and hysteresis of the electron gun were also repeated twice in order to get SEM images of good quality.

In the perspective of performing only a test experiment, we decide to acquire only a small volume sliced into 100 micrographs (indeed, two times 100 SEM images acquired in EsB & InLens modes) and only 11 EBSD maps (one map every 10 FIB-SEM slices). These images were first aligned according to markers (three parallel lines in the middle of top surface, shown in figure IV.36) by the usual cross-correlation routine (plugin 'MultiStackReg' in Fiji software).

IV.5.3.1. Mean layer thickness

The first parameter to verify is the sectioned thickness of each layer during the tomography. By measuring the distance between the right marker and the central marker (see figure IV.36), the mean eroded layer thickness is prone to be 9.5 nm, which was defined to be about 10 nm. In comparison to classical FIB-SEM tomography (see subsection III.5.1.2) without stage movement and drift correction in Z direction, our program performs accurately the milling job even with numerous stage movements thanks to the multi-regional recognition routine that we developed (see sub-section IV.4.2.2). As a result, the voxel size of the image stack in FIB-SEM imaging is considered to be isotropic as 10 nm " 10 nm " 10 nm, while the nominal voxel size for the stack of EBSD maps is 50 nm " 50 nm " 100 nm.

From the resolution point of view, as discussed in subsection IV.3.1.2, these imaging conditions allow to access to all microstructural features we intended to capture in this test sample (like precipitates in this test sample) in three dimensions, as it will be reported in the following sub-section.

IV.5.3.2. Statistics of precipitates

In order to get the 3D morphology of both populations of precipitates (different from the #' family), our two stacks of images (EsB and Inlens) were treated and segmented according to different methods. They are then visualized in the Fiji software with the help of the 3D viewer module (see figure IV.37; family of precipitates 1 are shown in pink whereas family 2 is displayed in green colour).

!m

From this reconstruction, we find that most precipitates 2 seem to have nucleated closely to, or around precipitates 1; the size of precipitates 1 presents a relatively large scatter whereas the size of precipitates 2 is more homogeneous. These distributions can be extracted by 3D counting, and the results are shown in figure IV.38 a) and b). As these precipitates are sphere-like, they were thus treated as sphere to get an estimate of their radius (see figure IV.38 c and d). For precipitates 1, the mean radius is about 55 nm, thus most of them cannot be detected by EBSD or cannot be indexed (black points in EBSD maps); about 6 of them are larger than 150 nm (see circles A and B in figure IV.39), thus were indexed in the hypothesis of the # phase, the only phase declared in the identification procedure of the EBSD. Their EBSD patterns were however quite noisy and it is thus not possible to rely unambiguously on this indexing. Nevertheless, we can postulate at this stage that they could be large so-called secondary 8' precipitates [Sarosi 2005 More interesting, the combination of the morphological reconstruction with the EBSD results shows that the preferred crystal orientation of 8 matrix grains hosting precipitates 1 is <100> as shown in figure IV.40 (for the second family, we found the <110> orientation -not shown here -). For the larger precipitates which could be indexed in a cubic phase (let's call it #" for convenience), the orientation relationship we get form the EBSD analysis is {111}8" // {100}8 and {110}8" // {110}8 (see circle A & B in figure IV.39 and figure IV.41 for example). This is not consistent with the expected 'cube-cube' 8 / 8' orientation relationship (see for example [Dubiel 2009]), thuis the hypotheis of large secondary 8' precipitates is probably to be excluded. There are two ways to reconstruct the 3D volume. The first method consists in extracting all grain boundaries, numeration all grains in each complete SEM image (shown in figure IV.41e) and coloration all grains according to EBSD maps (shown in figure IV.41f). However, this method requires a 'super' image processing programme, which can manage all grains in 3D. Thus, we found it more efficient to treat each grain individually by cropping the complete volume of SEM images into different areas (for example, rectangle C and D in figure IV.41), drawing manually the grain boundary of each grain and grouping them into one volume. After that, all grains of this nickel super-alloy can be reconstructed in both FIB-SEM mode and EBSD mode.

As evoked above, the spatial resolution of FIB-SEM tomography is higher than 3D EBSD tomography, which was easily demonstrated in the previous sub-section concerning the precipitates. This high resolution is also useful for the reconstruction of grains. Figure IV.42 illustrates an example of grain reconstruction respectively from 3D EBSD data and FIB-SEM tomography. It is clearly shown that FIB-SEM tomography is more accurate to reproduce the shape of grains and especially their limits, which may be important for the determination of the exact position of intergranular precipitates. Obviously the reconstruction in FIB-SEM tomography is also better because it is based on 101 sliced images at a spatial resolution of (10 nm) 3 in FIB-SEM tomography, while 11 serial images at a resolution of 50 nm × 50 nm × 100 nm in 3D EBSD.

After the reconstruction step, grain statistics are compared (see figure IV.43) on the basis of the equivalent circular of spherical Ferret radius (respectively in 2D and 3D) for all particles from: 2D SEM, 2D EBSD ,3D SEM, and 3D EBSD data. It can be seen that both 2D and 3D sets of data are consistent between SEM and EBSD. The most important feature is however that the 2D results show larger size that the 3D results, although both histograms are very similar for the small sizes below typically 0.1 µm. We did not check in more detail whether this finding is the consequence of an anisotropic shape of the grains, or is simply due to the fact that the 2D data plotted in figure IV.43a and c are obtained from a single 2D projection.

IV.6. Discussion & conclusions

The 3D EBSD in dual beam FIB is an approach to get the 3D crystallographic information, such as true grain shape and size, connectivity. In the current commercial software for a 3D EBSD acquisition with our system, all processes are automatic, including required movements of the microscope stage between milling and EBSD position. However, because of some inherent technical difficulties, such as: driving the ion beam for accurate machining, repositioning accurately the ROI between the milling position and the EBSD position, and because of the theoretical physical limits (large electron-solid interaction volume for EBSD and FIB milling effects limiting the resolution to about (50 nm) 3 ), this approach is limited to the study of real nano-scaled microstructures. Thus, defining accurate grainboundaries need a computer-aided approach where a 'smoothing' procedure has to be applied in order to delimitate properly the grain edges. Finally, the main drawback (by far) of automatic approaches is that they are time-consuming and thus subjected to any perturbation or instability during the acquisition.

In this chapter, we have reported a new approach which couples 3D EBSD and FIB-SEM tomography. In this way, the resolution of 3D EBSD can be improved to about (10 nm) 3 and expected to be about (2 nm) 3 . This method relies on some programming using principally the ZEISS API and Fiji macro, in order to drive in a very parameterized way the EBSD acquisition during a conventional 3D FIB-SEM acquisition.

We have demonstrated the feasibility of this routine on a Ni super-alloy model system. The morphology and preferred orientation of the matrix host grains concerning nano-scaled precipitates have been measured in 3D; the true grain shapes have also been obtained, all data with a much better accuracy and statistical meaning than what could be obtained from a simple 3D FIB-SEM approach or a 3D EBSD mapping.

This work is then a first step for optimizing 3D EBSD in a FIB. As a preliminary study, it suffers a main limitation regarding the data treatment. Mixing the 3D FIB-SEM and 3D EBSD information leads to quite large data sets which is in itself a problem when handling them with a personal computer: firstly, adequate routines are probably not existing in order to merge properly volumes with different sizes and resolution; secondly, treating the whole information at once may be a problem form the point of view of computer memory and calculation time. We thus choose to adopt a different strategy, where the EBSD data are used to help the treatment of SEM images. It must be recalled here that the latter exhibits the best resolution in both (X,Y) and Z directions, which indicates that it is logical to mainly rely on them for the final reconstruction. When it seems intuitive that EBSD mapping can help the SEM imaging in delimitating the grain-boundaries, it is not that obvious to implement this in an automatic image treatment. We thus perform this grain segmentation manually. Such a manual approach is sometimes also needed for simple 3D-FIB-SEM or 3D-EBSD reconstructions.

Further work is then needed to develop a robust numerical approach to help and optimize the way both 2D/ 3D SEM and EBSD images can be mixed in order to make the post-mortem treatment more efficient, rapid and universal. Typically, the segmentation of all grains as discussed in sub-section IV.5.3.3. is the critical step.

A second perspective is to improve the 'live' acquisition. If the grain size could be estimated during the 3D acquisition, the parameters for acquiring EBSD maps (such as, in priority, their frequency), could be adapted in real time to better resolve small grains for example, or minimize the acquisition time when large grains are encountered, which does not require any EBSD map during several slicing steps.

Channelling contrast for orientation mapping

Resume of chapter

The EBSD is clearly the standard technique to measure crystal orientations in a SEM. However, it suffers from some limitations: it requires an additional attachment to the microscope (EBSD camera and acquiring hardware and software), delicate sample surface preparation, its spatial resolution is limited typically to 10 nm in the best case, and the acquisition of orientation maps can be time consuming.

This chapter presents an alternative way to get crystal orientations from SE image series with induced channelling effects (either by an ion or electron beam). The electron channelling contrast has been employed for a long time to study microstructures in deformed materials, while the ion channelling contrast has started to be used recently for studying thin films. The theory for channelling was established in the 60s', and can be used quantitatively to describe the SE contrast evolution as a function of the orientation of grains under the primary incoming beam. This has been used in the present work to develop a method allowing the crystallographic orientations to be determined through the evolution of the channelling contrast versus a tilt or an in-plane rotation of the sample.

This new method for crystal orientation correlates the experimental SE intensity variation profiles during image acquisition to a database of calculated theoretical profiles. A preliminary experiment has been performed and the results have been successfully compared to EBSD maps, with a max disorientation of about 4° for Euler angles.

Résumé de chapitre

L'EBSD est devenue la technique standard pour mesurer l'orientation cristalline des grains d'un polycristal dans un MEB. Cependant, cette technique nécessite un détecteur d'EBSD, un système hardware et software, une préparation délicate de la surface de l'échantillon, et présente, comme autre inconvénient, une résolution spatiale limitée généralement à 10 nm dans les meilleurs cas, et des temps d'acquisition très longs.

Ce chapitre propose une autre façon d'obtenir des cartographies d'orientation cristalline à partir d'une série d'images obtenues en électrons secondaires en mettant à profit les effets de canalisation induits soit par un faisceau primaire ionique ou électronique. Le contraste électronique de canalisation a été utilisé depuis longtemps pour l'étude des microstructures dans les matériaux déformés, tandis que le contraste ionique de canalisation a été récemment utilisé pour caractériser des films minces. La théorie de la canalisation a été établie depuis les années 1960, et peut être utilisé pour décrire quantitativement l'évolution du contraste des images en fonction de l'orientation des grains par rapport au faisceau primaire.

La nouvelle méthode que nous proposons consiste à quantifier l'évolution du contraste de canalisation en fonction d'une inclinaison de l'échantillon, ou d'une (rotation dans son plan) par rapport au faisceau incident. Elle repose sur une comparaison des profils expérimentaux de variation de l'intensité expérimentale des images expérimentales en électrons secondaires avec une base de données de profils théoriques calculés. Une expérience préliminaire de faisabilité montre un très bon accord entre les cartes d'orientation obtenues par cette méthode et la 'référence' EBSD, avec une désorientation maximale d'environ 4° pour les angles d'Euler.

V.1. Introduction

As reviewed in section II.3, the EBSD technique is exponentially employed in material science [Schwarzer 2009] to get crystallographic information and microstructural parameters (grain size, grain form, grain boundary, etc.) for its relatively simple configuration in a SEM comparing to other approaches, like X-rays and TEM. However, it suffers its inherent problems like all other techniques: i) the limited spatial resolution: because of the backscattered mechanism to form diffraction pattern, its spatial resolution is about 10 × 30 × 20 nm (in X, Y and Z direction, see figure IV.9 and table IV.1) even for a heavy element; ii) possible long time of acquisition: for representativeness of microstructure and accuracy of measurement [Humphreys 2001], the EBSD step size could be very small, which leads to a long acquisition time (even extended to ten hours or more); iii) an additional EBSD camera and a computer with special algorithm is needed.

Although the SE contrast of a single image induced by electrons or ions has a much better spatial resolution for its low escape depth and short acquiring time even after some integrating process, it can't offer directly the crystallographic information. On the other hand, the SE contrast evolves with different tilted angle of the sample (shown in figure V.1), and is considered to be in relation with the channelling effect [START_REF] Levisetti | Ion Channeling Effects in Scanning Ion Microscopy with a 60 Kev Ga+ Probe[END_REF]] [Franklin 1988] [Phaneuf 1999]. Both the secondary electron and the secondary ion images exhibit the channelling contrast, while the one in figure V.1 shows the Ga + ion induced SE contrast. As indicated by Giannuzzi [Giannuzzi 2013], 'the channelling of any charged particle depends on its size and incidence angle with respect to the crystallographic atomic spacing of the target'. Thus, this effect can be used potentially to identify the crystal orientation like EBSD with a good spatial resolution [Silk 2010] [Veligura 2012].

In this part, two different programs were written for the acquisition of image series (either ion or electron introduced SE contrast) and post-mortem crystal orientation identification from the intensity evolution in acquired image series. This work is in collaboration with Cyril Langlois, who proposed this subject as his scientific activity for his candidate for assistant professor on FIB instrument at Mateis laboratory of INSA Lyon.

In the next subsections, we will successively describe: in V.2, the theory and current main applications of channelling contrast in materials science; the existing works for linking the channelling and the crystallographic orientation and our work of extracting crystal orientation from the channelling contrast in image series in V.3. Evolutional intensity (grey level) in FIB secondary electron contrast of 4 grains, which is a function of variation from the normal incidence as the specimen (aluminium alloy) is tilted with respect to gallium ion beam [Phaneuf 1999].

V.2. Theory and current applications of channelling contrast V.2.1. The case of electron beam V.2.1.1. Theory

The two-beam Bloch wave model is typically used to simulate the electron channelling [Joy 1982] (see figure V.2). Electron channelling contrast is linked directly to the backscattering at the sample surface. A lattice-coherent electron wave is formed by these Bragg coherently scattered electrons. Bloch wave I has maxima along the channels and is weakly scattered, and Bloch wave II has maxima aligned with atom planes and is strongly scattered. The ratio of Bloch wave II to Bloch wave I depends on the angle between incident primary beam and the crystal lattice. As illustrated in figure V.2b, when an electron beam is scanned over a flat crystal surface, the emitted backscattered electrons vary with the angle of incident angle of primary beam according to crystal lattice. If * < * B , there will be enhanced backscattering. If * > * B , there will be decreased backscattered signal. The angular width for electron channelling is 2Wg, expressed as:

!! ! ! ! ! ! ! (V.1)
where 9 g is the extinction distance for reflection g and ! !!" ! ! ! !!" . The orientation contribution to the total backscatter intensity can be written as:

!! ! !! ! !! ! ! ! ! !!! ! ! ! ! ! !!! ! ! ! ! ! ! ! ! ! ! ! !!! ! ! !!! ! ! ! ! ! ! ! (V.2)
where N is the number of atoms per unit volume, : B is the cross section for backscattering, ; = s 9 g with s being the excitation error that indicates the angular deviation of the primary electron beam wave vector, k 0 , from the exact Bragg position of the lattice planes with reciprocal lattice vector g.

V.2.1.2. Applications

In SEM, it is well known that the electron channelling contrast can be used in two basic ways [Wilkinson 1997]: i) Electron channelling patterns (ECP) performed at low magnifications by rocking the beam through a range of incident angles relative to the crystal planes, which causes a variation in the signal [Joy 1982]. Thus, it gives access to many channelling conditions over a wide angular range, and giving rise to 'Kikuchi-like bands' produced by backscattered electrons (figure V.3a). Thus, it is can be used to determine the crystal orientation. However, ECP is less and less unused and replaced by EBSD because of its simplified experimental set-up and automatic indexing process for orientation and phase determination [Kamaladasa 2010]. ii) Electron channelling contrast imaging (ECCI) performed at magnifications high enough to allow a specific orientation, through a specific channelling condition, to be isolated. Thus, a perfect crystal in this case shows no contrast or rather a constant signal. Contrarily, the presence of a defect (like a dislocation) may block the channel and scatter more electrons back towards the detector, or 'open' a channel and let the electrons penetrate deeply, reducing the number of electrons scattered towards the detector. Both situations lead to an increase of the dislocation contrast (see figure V.3b, c) via electron channelling effects. However, as the optimum diffraction contrast for ECCI is achieved by orientating the crystal exactly into Bragg condition for a selected set of diffracting lattice planes (see subsection V.2.2.2 for detail), a preparative experiment is necessary to determine the relative orientation between the incoming electron beam and the sample either by ECP [Kamaladasa 2011] or EBSD [Gutierrez-Urrutia 2013]. As illustrated in figure V.4, when ions are aligned to low index crystallographic planes, the depth of ion penetration (channelling) will be large, that decreases both the sputtering yield and secondary electron yield. Inversely, when ions are aligned obliquely to low index crystallographic plane, the ions are stopped closer to surface, that enhances the sputtering yield and secondary electron yield. As a result, ion channelling is interrelated to the relative contrast between different grain orientations.

The channelling of low energy gallium ions (30 keV) for the case of FIB can be modelled mathematically by the Lindhard-Onderdelinden approximation [Lindhard 1964] [Onderdelinden 1966]. It describes the directional effects of charged particles moving through single crystals lattices in sputtering (emission of SEs), to determine the channelling contrast. Whenever an incident beam is aligned with a direction [uvw] of a row or a string of atoms with an interval t uvw in crystal lattice and within a critical angle fΨ c (1 < f < 2), the beam inside the crystal can be divided into two beams (figure V.4): an aligned beam of fraction (1-χ 0 uvw ) with angles Ψ ≤ fΨ c and a random or non-aligned beam of fraction χ 0 uvw with angles Ψ ≥ fΨ c . For ion energies smaller than E' (given in equation V.3), the non-channelled fraction χ 0 uvw normal to a surface with direction [uvw] is expressed by equation V.4, which is based on a Thomas-Fermi screened Coulomb potential between the interacting ion and target atoms of atomic numbers Z 1 and Z 2 , respectively.

𝐸 ′ = !! ! ! ! ! ! ! !"# !!! ! ! ! (V.3) 𝜒 !"# ! = 𝜋𝑁𝑡 !"# !/! !! ! ! ! ! ! ! ! !!! ! ! !/! (V.4)
In above two equations, N is the atomic density, t uvw is the distance between atom position along [uvw]; A is the Thomas-Fermi screening length; Z 1 , Z 2 are the atomic number of the ion and target, respectively; e is the elemental charge (1.6 × 10 -19 C); ε 0 is the permittivity (8.85 × 10 -12 C 2 /Nm 2 ); E is the incident ion energy. And the Ψ c is given by equation V.5.

! ! ! !! ! ! ! ! ! ! ! !!! ! !! !"# ! !!! (V.5)
However, all above theory considers only the case of single crystal and needs to be verified for the case of crystals with different type of atoms along a row or a string.

V.2.2.2. Applications

The ion channelling contrast of SE images is related to the ion penetration depth which controls the secondary electron emission [Giannuzzi 2011]. As shown in figure V.5, the contrast is better for 'ioninduced' SE images than for conventional 'electron-induced' ones; then, it is pertinent to use a FIB to optimize an orientation-dependent imaging mode which could complete or even replace the classical EBSD approach in order to quantify the distribution of the grains orientation in a polycrystal (see figure V.5) or microstructures (see figure V.6). Obviously, a strong limitation of any possible approach would be ion induced damaging because of the heavier ions as compared to electrons for ion channelling [Alimadadi 2013]. Also, any quantitative approach should rely on a comprehensive analysis of the origin of the channelling contrast; as an example, figures V.5a and b) show respectively ion ('channeling-in') and electron ('channeling-out') effects giving rise to inverse contrasts for a large number of grains [Giannuzzi 2013].

V.3. Crystal orientation from channelling contrast V.3.1. Existing works

From equations V.4 and V.5, the critical angles and non-channelled fraction can be calculated for the case of 30 keV Ga + into aluminium (shown in table V.1 and illustrated by figure V.7), with an upper ion energy limit of 2.3 Mev [Kempshall 2001] [Silk 2010]. While the polar angle from the normal along a channelling direction [uvw] is Ψ, the non-channelled fraction is expressed as:

! !"# ! ! !"# ! !! !!! !"# ! ! ! !! ! ! (V.6)
The plot of this function according to <100> tilt directions of Ga + ions to aluminium alloy [Silk 2010] is shown in figure V.8a. A similar form of expression in stereographic projection (see figure V.8b) shows the calculated positions of the channelling minima of a FCC crystal with SE imaging.

The variation of the channelling contrast by imaging the induced secondary electron yield has the same variation = uvw as the variation of sputtering with lattice orientation (see figure V.8a)and thus should be useful to determine the lattice orientation.

V.3.2. New approach for crystal orientation mapping

All above previous publications [Yahiro 2004] [Silk 2010] [Veligura 2012] on the evolution of SE contrast due to channelling contrast, were trying to compare the theoretical maxima or minima contrast value on the specific plane or angle according to the Lindhard-Onderdelinden approximation (see figure V.8b). However, nobody tried to index the crystallographic orientation from the channelling contrast. The question to be asked is: can we find the Euler angles from this evolution in a SE image series?

The answer is evidently that it should be possible. As reported in section V.2, these variations of grey level in SE image series (peaks of the SE intensity profile in figure V.8a) are linked to the presence of dense planes at a low crystallographic index. We show in this section that we can simulate all the SE intensity for different Euler angle (0 > -1 , -2 > 360°, 0 > . > 180° in general case of triclinic crystal symmetry and no sample symmetry) and crystal lattice (by considering principal reflected planes). When we correlate the experimental intensity profile with the theoretical ones, the best match corresponds to its Euler angle. This method is a little same to commercial EBSD indexing process with Hough transform, which compares angles between Kikuchi lines to the theoretical angles between different crystal lattice (see section II.3.3 for details of indexing Kikuchi patterns in EBSD).

a) b)

More detailed process for the construction of theoretical intensity profiles and comparison with experimental ones is reported in following sections. From this idea, we have developed a fast acquiring software for image series and a post-mortem treating software to determine the Euler angle from intensity profiles.

The test sample is a TiN alloy with known crystal structure (FCC), which gives good crystallographic contrast in EBSD experiment. The stereographic projection allows the geometry between the primary beams and the sample to be clearly visualized. In the sample referential, the sample tilt and rotation with respect to the incident fixed electron beam are transformed as a beam movement; the centre of projection corresponds to the projection of primary beams (either ion or electron) while the sample surface is normal to it (no tilt), see figure V.9.

V.3.2.1. SE image series acquisition a) Experimental geometry

We started our experiments by getting image series with an increasing tilt angle, as it was performed in the publications mentioned above. Doing so, we are facing an indexing problem due to the 180° ambiguity: because of the symmetry, an orientation cannot be distinguished from the equivalent one formed by a mirror around the plane in which the beam is moving (shown by dotted blue lines in figure V.9). It intersects the same dense planes for the cases in figure V.9a and figure V.9b, thus the SE evolution intensity profile is the same. Moreover, because the angle between the sample surface normal and the detector always changes during tilting, the SE image has to be continuously equilibrated in contrast and brightness during the acquisition. As a result, a rotation has been applied which can avoid most of problems: i) no more compensation of contrast and brightness is required for the acquisition of SE images; ii) the incident beam can cross these main dense planes, so that there is the evolution in the intensity profile from image series; iii) The incident beam insects these planes at different points for each orientation and then is rotated, so that the 180° ambiguity interpretation problem no long exists. In this rotation setup, the sample is tilted always at same angle (40° here; the dotted black circle at the centre in figure V.9 describes the positions of beam) with respect to the incident primary beam. An image is acquired at every rotation step.

b) Semi-automatic acquisition of images

In order to accelerate the acquisition process, we have developed a semi-automatic acquisition program of image series using Carl ZEISS API as illustrated in figure V.10. It starts with the choice of the channelling source (ion or electron) to be used for inducing SE contrast. The mode of changing the angle between incident beam and crystal lattice (by tilting or rotation) and the step of angle change are then defined. The sample being placed at the coincidence point of ion and electron beams (eucentric position), ion channelling and electron channelling images are acquired in a manual procedure (the user has to click a '+' button to increment the rotation angle; at this stage it could be easy to perform this rotation automatically but we did not develop such a routine for security reasons, i.e. to avoid any collision of the stage with any internal part of the microscope chamber if something goes wrong). At the end, image series are acquired according the conditions listed in table V.2. In addition, an EBSD map is also obtained on the same area as reference for comparison.

V.3.2.2. Crystal orientation analysis

Once the series of ion-induced images has been obtained, both tilt and rotation corrections are applied, and the stack is aligned with the plugin 'MultiStackReg' in Fiji software. From the aligned series (see '1' in figure V.11), the intensity evolution of each pixel ('2' in figure V.11) can be plotted. and the corresponding stereographic projection is also plotted.

At this point, we have two strategies to link the intensity profile (frame '2' of figure V.11) with the crossing of crystal planes during the sample rotation.

The first method, probably the most elegant, would be to calculate directly the Euler angles according to geometrical and crystallographic calculations in order to correlate maxima and minima (and angular distances between these extrema) to a succession of planes, or poles in the stereographic projection. From a practical point of view, this method requires a normalization of the intensity. Furthermore, the indexing of peaks is not straightforward and we found this task rather complicated and not very accurate.

A second method would rely on the comparison of the experimental intensity profiles with a calculated database containing simulated profiles for a large set of possible trajectories with Euler angles ranging in the intervals 0 > -1 > 360°, 0 > -2 , . > 90° (sufficient in the case of the cubic system because of the symmetry of crystal). Obviously, these calculated profiles will essentially be 'pseudo-binary' profiles since the intensity has no obvious meaning here (see further explanations just below). This method has been applied in the present work; we will briefly describe the two main steps: (i) the generation of the profile database, (ii) the comparison between the experimental and calculated profiles.

The construction of the theoretical database is done via a computer routine written by C. Langlois [Langlois 2014] according to the following principle: the space is discretized into <uvw> directions considered every 2 or 3° degrees on the Euler angles (3° for -1 , 2° for ., and 2° for -2 ). For each of these directions, the crossing of {hkl} planes are calculated when describing a conical rotation with an angle corresponding to that used experimentally: at each plane angular position, a 'peak' of intensity is associated, the magnitude of which is proportional to its kinematical diffracted intensty F 2 (hkl). According to the previous literature (see subsection V.2.2.1), this profile can be refined by associating a Gaussian width to this 'peak'. In the present state of the program, this width W hkl can be parameterized according to the match of the calculated profiles with the experimental ones obtained on beam positions where the crystallographic orientation is known from the reference EBSD map. This approach is illustrated in figure V.12. For a chosen orientation (defined through its Euler angles in frame '1' of figure V.12), the experimental intensity profile of the corresponding imaged grain along the rotation path superimposed as a dotted circle on the stereographic projection in figure V.12 is displayed (orange empty symbols in frame '4'). On this plot, vertical bars show the positions of main {hkl} planes (3 different colors for the {100}, {110} and {111} families). At present, the full width at half maximum (FWHM) and the scale factor of each Gaussian curve is determined empirically by tuning the empirical parameters in frame '3' in order to adjust the calculated profile (red curve in frame '4' to the experimental by a quick eye inspection. Obviously, in the perspective of matching the experimental profile with calculated ones in reality, another parameter is here missing: the angular point where the rotation trajectory is started; thus, each profile is used to generated news profiles by translating them by a 2° increment.

The identification part of our approach consists in matching the experimental intensity profiles with calculated ones. To minimize the search time, we first scan the database with a binning of two to obtain a coarse solution of (-1 , ., -2 ) by minimizing the Euclidian distance between the two curves; the search is then refined in the vicinity of these angles. At the present time, the correlation algorithm for searching the best match between experimental and calculated profiles is rather rough and take 5 seconds for a single point; it requires then about 3 hours to obtain an orientation map on a multi-core PC for an image of 264 " 186 pixels. It is highly probable that optimizing the search algorithm though neuronal network or Monte-Carlo methods could easily considerably reduce the computing time, and allow the angular accuracy to be significantly improved. Figure V.13 summarizes the results obtained on a convenient ceramic material consisting in a polycrystalline titanium nitride (TiN has a f.c.c., Na-Cl type structure, with a 6 0.4 nm). The acquired area was 264 " 186 pixels in size, the rotation range was 360° (full range) with an angular step of 1°, which requires about 40 minutes for the acquisition (according to the semi-automatic method where the user has to click each step to get the new position, see figure V.10). The orientation map reconstructed by the profile method from the ion-induced SE image series (see figure V.13a) has been obtained by applying a unique set of Euler angles in each single grain. This map shows a very good match with the 'solution' as determined by conventional EBSD (figure V.13b). This EBSD map was initially 400x300 pixels over a slightly larger area than that cropped for the present analysis; it was acquired in 40', which represent an true acquisition time of 16' for the current ROI of 264 " 186 pixels. As shown in figure V.13b, most grains in the ROI show a disorientation of about 2.5°, and only three grains are identified with a disorientation larger than 5°.

At the same time, it is meaningful to compare the intensity profile on a random grain with fixed crystal orientation, obtained from experiment (image series), EBSD and simulation in TiN sample. Figure V.14 illustrates a typical profile match as was presented in figure V.12. The stereographic plot shows only the {100}, {110} and {111} great circles since these three families are sufficient to describe most of the ion channelling effect in the TiN cubic system. In the previous sub-section, the acquisition was run over 360° with an angular step of 1°; one may wonder whether it is necessary to work with a so large set of experimental images which directly defines the acquisition 'beam' time. As indicated above, the EBSD map corresponds here to a 16' acquisition time whereas the semi-automatic acquisition of the SEM series took about 40'.

A first reduction of the acquisition time consists in dividing it by 4 by considering a rotation range of 180° and an angular step of 2°, or a rotation range of 360° and an angular step of 4°. Figure V.15 shows the reconstructions performed according to these parameters; it clearly indicates that the most important parameter is the range of rotation (the larger the more accurate the orientation map).

Accordingly, we can still increase the angular step and maintain a reasonable accuracy of the method: figure IV.16, shows the result obtained with an angular step of 10°, which leads to an acquisition time as short as 5 minutes with only 36 images.

V.4. Conclusions

V.4.1. Summary of the channelling approach of crystalline orientation

As evoked in the introduction, EBSD is an accurate technique in order to map the crystallographic orientation of a polycrystalline grains in a SEM or a FIB-SEM for respectively 2D and 3D approaches. When applicable (in terms of quality of the polished surface, resolution regarding the size of the microstructural details to be investigated), its main limitation remains the time of acquisition.

Developing an alternative method for fast orientation mapping was one motivation of the approach presented in this chapter; another obvious one is the availability of an EBSD system on the microscope to be used. Tracking the evolution of the electron or ions channelling contrast when tilting or rotating the sample under the ion or electron beam is the basis of this approach. Main conclusions can be summarized as follows:

-To move the sample under the beam, both tilt or rotation procedures are available. The possible 180° ambiguity due to the crystal symmetry is a severe limitation for the tilting strategy, therefore it is much preferable to rotate the sample under the beam (after having applied a fixed pre-tilt).

a) b)

-Classical SEM are acquired by rotating the sample over a given amplitude with a given rotation step; elementary image manipulations are performed in order to equalize their contrast and correct them form the tilting geometrical factor before their treatment. -Intensity profiles measured in each point are compared to calculated profiles stored in a database generated for the crystal structure of interest. A set of programs have been developed (by C. Langlois at MATEIS), which runs at the present time in the cubic case; they include the generation of the database and the quantitative comparison between experimental and calculated profiles to estimate the orientation of each pixel of the ROI through the determination of its Euler angles. -The method has been tested on a model sample consisting in a polycrystalline, well-polished TiN ceramic sample. Very good results were obtained as compared to the 'exact' orientation map obtained by conventional EBSD. Optimisation of the experimental conditions (angular range and step) has allowed the beam time of the experiment to be reduced to about 5 minutes, while still maintaining a reasonable accuracy in the range of 2-2.5° of disorientation. The most important parameter is here the angular range rather the incremental step, and it is advised to rotate the sample over a full 360° amplitude.

Without any specific optimization during the acquisition step (performed here in a semi-automatic way), the method can be faster than EBSD: a reasonable accuracy was obtained with a 5' acquisition time where the EBSD took about 16'. We can emphasize that a fully automatic acquisition routine can easily reduce the time by a factor 2. We then believe that this method can easily be one order of magnitude faster than EBSD, which may present a great advantage for acquiring large map in terms of the microscope occupancy. However, EBSD remains largely competitive and superior since it offers several other advantages in terms of angular resolution.

V.4.2. Perspectives

This work here is a first step showing the feasibility of obtaining Euler angles from channelling contrast. Further work to explore the potentiality of this method is listed below:

-It is needed to optimize the searching algorithm in the database of theoretical intensity profiles in order to obtain fast match of the experimental profiles. At the present time, each elementary operation takes a fraction of second, which leads to high computing time for reasonably large maps (16 hours for a 120000 pixels² map on the quad-core personal PC). -Further tests are to be undertaken to check the applicability of the method to non-cubic systems; also, multiphase materials should be rapidly considered in order to evaluate the real potentiality of the method. -Another advantage, in principle, of the channelling approach is its resolution, since it should be possible to access easily to information in the range of, or below 10 nm, which is attainable only in the best cases with EBSD.

The final important perspective is to test the method with electrons channelling. Due to the context of the whole thesis, we focused our efforts on the FIB and the use of the ion beam which produces strong channelling effects, well-adapted to develop this new approach. From a practical (and economical) point of view, it would be very interesting to be able to run the method on a conventional SEM without any EBSD attachment.

Conclusions & perspectives

VI.1. General conclusion

This dissertation, which is in collaboration with the German electron microscope constructor -Carl ZEISS, is initially oriented to optimize the current available commercial 3D EBSD processes in FIB (with the option '3D-EBSD' in 'Fast Acquisition' software for the case of Oxford Instrument). This software suffers from both its proper technical problem (piloting the ion beam for accurate machining and repositioning precisely the ROI between the milling position and the EBSD position) and the theoretical limits (large electron-solid interaction volume for EBSD and FIB milling effects). Thus, it is so challenging to apply this routine for the study of nanoscale microstructures with its poor spatial resolution -(50 nm) 3 .

The possible solution for theoretical difficulty of classical 2D EBSD is to combine other type of contrast with high spatial resolution (like channeling contrast, either ion introduced electron contrast, or electron channelling contrast imaging), or to apply other methods (like t-EBSD in a SEM or TEM) with a small electron-solid interaction. At the same time, the classical EBSD method suffers its onesided view like other 2D methods to investigate globally the microstructures.

From these above points, a new approach for 3D EBSD is developed. In this method, the sample is placed alternatively, at the milling position for accurate milling with ion beam and high resolution imaging with electron beam in low accelerating voltage; and at the EBSD position for crystal orientation mapping with EBSD detector in high accelerating voltage. By comparison to current 3D EBSD software, this method combines well the high resolution mapping capacity of standard FIB-SEM tomography (a few nanometers for X, Y and Z directions) and the obtaining crystal orientation capacity of EBSD technique.

Moreover, all analysis from 3D FIB tomography requires a correct, dedicated post-mortem treatment of serial SEM images. We focus on the alignment issue in this thesis, which point is easily ignored for general application. With a dedicated experiment, it is shown that the usually direct crosscorrelation on primarily unknown microstructures can introduce artificial error for the 3D virtual reconstruction. Two additional alignment methods either with the topography of sample surface or with a drilled hole which crosses the ROI are developed. By comparison to classical alignment ways, the topography of sample exhibits as a good reference to align the image stack of SEM from the tomography in X, Y and Z (typical difficult point) directions.

Finally, in collaboration with Cyril Langlois (assistant professor at Mateis laboratory of INSA Lyon), a new procedure for crystal orientation mapping from the ion or electron channeling contrast is built. By comparison to current EBSD technique, this procedure shows its advantages: no requirement of additional EBSD detector and dedicated preparation of sample surface, high acquiring speed for large area mapping and high spatial resolution up to a few nanometers.

VI.2. Synthesis of chapters

VI.2.1. FIB-SEM instrument and EBSD technique

The FIB and SEM column are composed principally by charged particle sources (ions and electrons), condenser and objective. Contrary to ion column, electron column has been specially designed to reduce the negative effects (aberrations of optics and stigmatism) on final probe (especially for low voltage imaging). A dual-beam FIB is typically made up of a Ga + LMIS based ion beam and a Schottky FEG based electron beam. The largest difference between the FIB and the SEM is that the high mass ion allows to mill away materials from the sample.

A homogenous and high-brightness source is the basis to obtain a high performance with a fine final probe size for either FIB milling or SEM imaging. Nowadays, an energy-spread of around 5 eV and a brightness of about 5 × 10 9 A m -2 sr -1 for the ion source can give a final probe size of about 3 nm, while an energy-spread of around 0.5 eV and a brightness of about 10 12 A m -2 sr -1 for electron source can give a final probe size of about 1 nm. Just because the high mass ion needs huge magnetic optics to be focused, the electrostatic lenses are generally adapted for ion beam while the electromagnetic lenses are typically used for electron beam. For the ZEISS GEMINI electron column, a complementary 8 keV voltage is maintained by the beam booster throughout the electron column) to reduce the traverse chromatic aberration and further effect on imaging resolution.

The EBSD technique is a standard tool in SEM for crystal orientation mapping by interpreting the Kikuchi patterns with Hough transform. The electron backscatter mechanism to form Kikuchi patterns leads to a large electron-solid interaction volume, which cause its low spatial resolution. In addition, because of the live interpreting of Kikuchi patterns, its acquiring speed is not so high. By comparision 3D EBSD with classical 2D EBSD, it shows the real microstructures, which avoids possibly false impression of different features. In order to achieve 3D EBSD, serial sectioning with FIB is the most powerful way for its well-controlled milling accuracy of nanometres.

VI.2.2. Post-mortem alignment for FIB-SEM tomography

FIB-SEM tomography is a serial-sectioning based method. Its concept is not complicated: alternative machining of thickness fixed layers with the ion beam and imaging of fresh layers with the electron beam after the preparation of working area. Even though the FIB offers already high accuracy of nanometres for machining, compared to other sectioning methods (based on etching, sputtering and grinding, etc.), the predefined constant thickness of each layer to mill away is difficult to reach. Moreover, the drifts in X and Y direction frequently presents during the acquisition.

Since the tomography in FIB is a constructive way, how can we recover correctly the original microstructural features from the virtually reconstructed volume? The issue for alignment of stack image is little discussed in literature. The average eroded layer thickness (drift in Z direction) is often estimated from different features (markers on the sample surface or microstructural features of sample). However, because of the damage of ion beam on these features, this method is not so accurate. At the same time, the cross-correlation on different references (interface between protected layer, markers on this layer and the ROI, etc.) is typically performed to correct the drifts in X and Y direction. However, this can drags in artificial errors, which are demonstrated by a dedicated experiment.

In order to resolve these problems, two different references are introduced to align correctly the stack images: the topography of sample surface and the FIB drilled hole. In comparision to classical methods, the topography of sample can correct the drifts in X and Y directions with high precision, and further evaluate the individual thickness of each layer.

VI.2.3. Dedicated 3D-EBSD in FIB with high spatial resolution

The reasons for the low spatial resolution of 3D-EBSD in FIB are discussed for two points of view. Technically, the ROIs are located alternatively by recognizing markers using cross-correlation. However, these markers are imaged in low magnification for working correctly, which limits especially the high accurate milling by FIB. Even so, the obtained result can be so bad because of impossible recognization of markers, which are clearly seen. The serial sectioning in 3D-EBSD is achieved by moving a wider (3 times larger than desired width, which is advised by Oxford Instruments) milled objet in a constant thickness (desired width of each layer), which also resists also the high accurate milling by FIB; Theoretically, EBSD woks always with backscattered electrons for Kikuchi patterns, which requires relatively high SEM accelerating voltage and current for enough signal. And this causes larger electron-solid interaction volume and low EBSD spatial resolution. Moreover, by the simulation in SRIM, the Ga + ion presents widely near the fresh milled sample surface after the FIB machining in high voltage, which reduces the intensity of Kikuchi patterns and thus the EBSD mapping quality.

Different from commercial 3D-EBSD software, a new program is developed, which is based on FIB-SEM tomography in low SEM voltage and additional EBSD mapping in high SEM voltage. This method integrates the high spatial resolution mapping of nano-tomography and the crystal orientation mapping of EBSD. Thus, diverse sub-routines (recalling the stage between milling position and EBSD position, positioning the ROIs for two positions, recalling the different electron column for two positions and pausing, resuming the FIB-SEM tomography) are written in ZEISS API, which are launched in order by a super manager program. For highest quality of positioning repetitively the ROIs for FIB milling and SEM imaging at milling position and EBSD mapping at EBSD position, three images in different magnifications are captured (the magnification of the first image is in the same order to the one in commercial software of 3D EBSD).

In the first result with this routine, a high accurate abrasion with FIB has been performed, where 5 µm is asked to remove for 500 slices and about 4.9 µm is calculated from prepared markers. Moreover, the 3D morphology of nanoscale structures (like precipitates) are shown at the same time with the substrate orientation. The grain boundary is refined comparing to the reconstruction of commercial software. These small grains, which exhibited only as some discontinuous points in the EBSD maps, are also reconstructed. In a word, the ultimate physical limit of current FIB-SEM instrument for spatial resolution has been attained in this way.

VI.2.4. Crystal orientation mapping from channelling contrast

The electron channelling contrast of SE image is directly linked to the backscatter of electron at the sample surface, while the ion channelling contrast of SE image is related to the ion stopped range and corresponding secondary electron yield. The classical theory to describe the electron channeling and ion channeling is by considering electrons as wave and ions as charged particles, respectively.

It is shown in literature that the evolution of image contrast from serial tilted sample is linked directly to crystal orientation. Because of the well-known 180° ambiguity for interpreting the orientation in tilted method, a rotated method is adapted to evolve the SE contrast.

From the evolved intensity in serial SE images, the crystal orientation can be determined from the simulated evolution of intensity with different Euler angle. By comparison to EBSD result on the same area, an angular step of 10° and a rotation range of 180° for a serial ionic imaging allows already a determination of crystal orientation with a disorientation of 4°.

VI.3. Perspectives

i) Drifts for 3D FIB acquisition: The procedure for tomography with the ZEISS SmartSEM ® system is typically 'Pause Mill for Imaging', which means that the ion beam is blanked while the electron beam acquires an image. Then the ion beam is re-operating to prepare the next slice. This discontinuous operating mode may produce slice thickness variations which can be corrected during the post-mortem treatment. Alternatively, the ATLAS-3D package (external generator proposed by the Carl ZEISS and Fibics companies) provides another 'continuous milling' mode, which means that electron images are acquired simultaneously during milling and while the ion beam is progressing through the slice. This mode has the greatest sample stability by nearly constant charge distribution overtime, so that the slice thickness is more possible constant. Furthermore, this mode is the most time efficient. However, this mode may not be acceptable because the presence of ion beam causes sample vibration or loss of imaging contrast, or the imaging time is very large.

ii) Plasma ion sources 33, 34 and statistic geometry for standard 3D EBSD acquisition: To get a feasible geometry for the 3D EBSD acquisition, a long time is required for the preparation of ROI with Ga+ LMIS based FIB. Furthermore, the milling process in 3D EBSD varies from 1 min to 3 min. The FIB milling rate can be improved 50 times with plasma ion sources according to the constructors, because of their higher current (limited to about 50 nA in Ga + LMIS and 2000 nA in plasma ion sources) and higher ion mass (atomic number: 34 for Ga and 54 for Xe). In the tilt geometry for 3D EBSD, the movements of stage between EBSD and milling position introduce and locating repetitively the ROIs introduces firstly the additional time for the acquisition and secondly the instability of stage. The statistic geometry without stage movements can avoid these problems.

iii) Large area imaging: In current FIB imaging software (SmartSEM ® for our case of ZEISS), the imaging size is limited to 3072 × 2304 pixels (2048 × 1536 pixels in the 3D case for avoiding redeposition effects). This means the largest area is about a few dozens of µm 2 with a pixel size of 10 nm for example. It is obvious that the new developed program for dedicated 3D EBSD is much more interesting with a much larger area for the representability of bulk sample from local working area. Up to now, the ATLAS-3D package offers only an imaging option of 32k × 32k pixels, which indicates that a larger area is possible with current machine. Moreover, Fibics company is developing their API like ZEISS. Maybe the current sub-routines based on ZEISS API, can be adapted to Fibics API, which owns some useful ready options like 'auto-stig' for FIB-SEM tomography. iv) Simultaneous 3D EBSD and EDX mapping: 33 http://www.tescan.com/en/products/fera 34 http://www.fei.com/products/fib/vion/ The principal constructor of microanalysis (like Oxford Instruments, Bruker and EDAX) have started to build software for simultaneous 2D EBSD and 2D EDX mapping (AZtec for our case of Oxford Instrument). These features, with similar crystal structure but different chemical components, will be much easier to be separated. Moreover, Oxford Instruments offers officially API for AZtec, which can be integrated easily in the new developed 3D EBSD software.

In order to speed up the drift correction procedure, we chose to align binned images (the expected time is proportional to the square of the binning factor). After the (X, Y) drifts measurements, the correction amplitude is re-multiplied by the binning factor in order to be correctly applied to the experimental images. Obviously this choice limits the accuracy of the method but we simply intend not to lose the ROI during the acquisition (a final accurate and post-mortem alignment will remain necessary after all). The second step is the core of the process: it consists in the measurement of drift ($X, $Y) between an image n and the image n-1 (or all precedent images), and in the application of a correction which anticipate the drift on the image n+1. In order to measure drifts between two images, the plugin 'StackReg' [Thevenaz 1998] of Fiji is used. A slight improvement of this plugin is 'MultiStackReg', which allows the shifting values between treated images to be stored in a text file. These two procedures are illustrated in figure A1.4.

A1.2 Details of auto-focusing

As discussed above, the focusing may be lost during the 3D FIB/SEM tomography experiment due to undesired instabilities. The essential idea to retrieve a sharply focused image is deduced from the dynamic focusing procedure applied to a highly inclined imaged surface [Reichelt 2007].

We have developed a VB6 application using the ZEISS API in SMARTSTEM, as illustrated in figure 1.12. The auto-focusing procedure starts by getting the actual Working Distance (WD: Zposition of the top surface of the specimen, linked to the height stage). Then a range of WDs within an interval [WD -n$WD, WD + n$WD], is applied to a predefined reduced area at the centre of image (green rectangle in figure 1.12a) which can be modified by the user. Then, the best focusing conditions were found by searching the image among the stack of 2n+1 images were the overall contrast s maximum. In a first approach the scanned area was vertically cut into 2n parts in which a different focusing condition was applied (i.e. a ramp of focus from top to bottom applied in one run), but this was not satisfactory in terms of robustness (the maximum of contrast was location-dependent and un-optimized focus could easily be found according to the microstructural features in the image, as shown in Figure 1.12b). Once a first 'rough' focus condition was measured, the operation can be repeated in an iterative way to refine its value in a smaller 2m$'WD. In practice, A full two-iterations procedure take about 10 seconds; the next figures 1.

Figure I. 1 .

 1 Figure I.1. Presentation of the Carl ZEISS Nvision 40 FIB workstation located at CLYM and its related applications (* courtesy by Fulcrand R., ILM -UMR CNRS 5306).

Figure II. 1 .

 1 Figure II.1. The Carl ZEISS Nvision 40 dual-beam FIB workstation located at the Microscope Centre of Lyon (CLYM). It is equipped with a SII Zeta ion gun (Ga LMIS), a ZEISS Gemini ® FEG, a SII Gas inject system (W, SiO x , C, H 2 O, XeF 2 ), a flood gun, multi-detectors (SESI, Inlens, EsB, STEM), an Oxford Instruments 50mm 2 SDD EDX detector, an Oxford Instruments Nordlys F + EBSD camera, two KlockeNanotechnik micromanipulators and a Fibics external scan generator.

Figure II. 2 .

 2 Figure II.2. Manipulator in form of a clutching, which can perform task in radioactive areas where no human can enter [Feynman 1960].

Figure

  Figure II.3. a) Schema of an working blunt-needle LMIS [Forbes 2009a]; b) A typical liquid metal ion source substrate showing a W needle and a spiral reservoir spot welded to a heating loop (Courtesy by FEI Company), where the red rectangle part corresponds to the blunt-needle in a).

Figure II. 4 .

 4 Figure II.4. The evolution of a liquid Ga Taylor cone by applying regularly raised voltage from an in-situ TEM imaging at 2.5 MeV: a) I e < 1 !A, V e = 4.63 kV; b) I e = 2 !A, V e = 4.63 kV; c) I e = 5 !A, V e = 4.7 kV; d) I e = 14 !A, V e = 5 kV; e) I e = 30 !A, V e = 5.5 kV; f) I e = 40 !A, V e = 6.2 kV; g) I e = 80 !A, V e = 5.1 kV; h) I e = 100 !A, V e = 5.4 kV; i) I e > 100 !A, V e = 5.6 kV [Benassayag 1985].

Figure II. 6 .

 6 Figure II.6. Illustration of the Ga + LMIS setup for the SII Zeta ion gun (courtesy by FIB team of CLYM) a) and the ion beam operation interface of ZEISS SmartSEM ® software b) in our ZEISS Nvision 40 FIB system.

Figure

  Figure II.7. a) Basic setup of GFIS, consisting of cryogenically cooled emitter, applied high extracted voltage and gas supplying (adapted from [Ward 2006]); b) illustration of the local physical phenomena at the apex of a helium (He) field ion emitter, where these operating gas atoms (not shown in figure II.7b) are weakly bound to a rarified layer on the top of the needle tip [Forbes 2012].

Figure II. 8 .

 8 Figure II.8. Schema of SII Zeta ion column [Reyntjens 2001] a); and ZEISS GEMINI ® I electron column b) (courtesy by Carl ZEISS Company) in a Nvision 40 dual-beam FIB system.

Figure II. 9 .

 9 Figure II.9. Main electron detectors around the objective lens of the ZEISS GEMINI ® I column.

Figure II. 11 .

 11 Figure II.11. Angular dependence of sputtering yield as a function of incidence angle: a) for 30 keV Ga + into Si by comparing the theory of Sigmaund and Yamamura with experiment [Orloff 2003]; b) for Ar and Ga ions on Au and Si target by comparing the SRIM simulated result with experiment [Tseng 2007].

Figure II. 12 .

 12 Figure II.12. Energy dependence of sputtering yield as a function of incidence energy for Ga and Ar ions into Au and Si targets at normal incidence, comparing the SRIM simulated result with experiment [Tseng 2007].

Figure

  Figure II.13. a) Description of the interactions between an incident primary electrons (PE) and matter (adapted from [Plummer 2001]); b) Energy distribution of emitted electrons after the interaction (SE: secondary electrons, BSE: backscatter electrons, AE: Auger electrons, LLE: low loss electrons; non-linear energy scale on horizontal axis); c) Schematized view of SE generation: generated SE with an escape depth of ', which can leave the solid and contribute to the image formation [Utke 2012].

Figure II. 14 .

 14 Figure II.14. Significantly reduced size of the interaction volume as obtained by changing the electron voltage from 15 kV a) to 1.5 kV b); the blue trajectories represent the track of penetrating electrons and the red trajectories represent the BSE. The escape depths of BSE (indicated by the length between blank arrows) are also clearly reduced from ~300 nm to ~12 nm (Simulation performed with the Casino 19 software [Drouin 2007]: 100 000 electrons penetrate into Cu layer with a thickness of 1000 nm, tilt of specimen 0°).

  Figure II.15. Energy distribution of the interaction in figure II.14b. By a selection of energy about1.35 kV, only the electrons generated in the central area with high energy will be collected. As a result, the theoretical lateral resolution (in direction of X and Y, indicated by the length between the arrows in a) is around 4 nm and the theoretical depth resolution in direction of Z, indicated by the length between the arrows in b) is around 5 nm.

Figure II. 16 .

 16 Figure II.16. Increase of the backscattering coefficient with the sample tilt increase, i.e. with an increasing electron incidence angle (from [Reimer 1998]).

Figure

  Figure II.17. a) Formation of TKP with an angular distance of 2* B [Randle 2010]; b) formation of backscattered Kikuchi (or Kossel) lines on EBSD camera with an angular distance of 2* B [Randle 2010]; c) real form of backscattered Kikuchi patterns -Kikuchi cones [Schwarzer 2009]; d) a diffraction pattern (Kikuchi lines) from nickel collected at beam voltage of 20 kV and beam current of 1.5 nA, exposure time of 1.5 seconds, without no binning of detector [Dingley 2004].

  very small volume inside the crystal. Secondly, those electrons which impinge upon lattice planes hkl at the Bragg angle interact elastically according to the Bragg law:

Figure

  Figure II.18. a): experimental EBSD pattern of molybdenum, and b): the corresponding many-beam dynamical simulation.In the calculation, a total of 1200 reflections were considered; on average 150 reflections were treated exactly, the others were included by perturbation. A lattice constant equal to 3.147 Å was used[Winkelmann 2010].

Figure II. 19 .

 19 Figure II.19. The experimental set up for EBSD in a SEM: a) diagram of principal components of an EBSD system; and b) typical experimental arrangement (screen and electron beam parallel).

Figure II. 20 .

 20 Figure II.20. Spatial resolution of EBSD on nickel as a function of accelerating voltage in a tungsten-filament SEM [Randle 2010].

Figure II. 21 .

 21 Figure II.21. The Radon transform of a straight line in the image space a) into a point b) in the Radon space [Schwarzer 2009].

Figure II. 22 .

 22 Figure II.22. Schematic representation of the Hough transform. a) Line with three points in the original image; b) corresponding three Hough-transformed curves from points in a) and their intersection in one point in the Hough space, whose coordinates , and * then represent the original line; c) original gray-tone image with two bands of distinct width; d) Hough-transformed image, showing the characteristic butterfly shape of transformed EBSD bands [Randle 2010].

Figure II. 23 .

 23 Figure II.23. Application of the Hough transform on an experimental EBSD pattern prior to the determination of the crystal orientation from calculated angles: a) original EBSD pattern with identified bands, represented as line in color; b) pattern after the Hough transform with identified bands, represented as points in color [Randle 2010].

Figure

  Figure II.24. a) An example of blurred BKP due to inadequate sample preparation and b) after a more dedicated surface preparation in a lead-silver alloy. Both EBSPs are obtained on Pb matrix at 20 keV without binning of EBSD camera [Brodusch 2013b].

Figure

  Figure II.25. EBSD patterns showing the improved contrast by energy filtering. The primary electron beam energy is 15 keV; a), b) and c) are unfiltered patterns from silicon, iron and iridium; d), e) and f) are corresponding patterns with the energy cut-off set to 14.5 keV [Eades 2009].

Figure II. 26 .

 26 Figure II.26. Typical experimental set-up for a t-EBSD experiment using a pre-tilted EBSD sample holder; the TEM foils held in a micro-clamp in a horizontal position and the EBSD detector [Trimby 2012].

Figure II. 27 .

 27 Figure II.27. Comparison of t-EBSD with conventional EBSD at a beam energy of 28 keV: a) -b) two images of the EBSD pattern with ultrathin nickel film specimen in a conventional EBSD geometry (70° tilt towards detector) where no indexing is reasonably possible; c)-d) two images of the same specimen in t-EBSD geometry (20° tilt away from detector), where identifiable reflections are observed [Keller 2012].

  Figure II.29 illustrates well interepration errors that can be made by a basic 2D EBSD analysis: a single boundary between 2 grains produces multiple traces on various single sectioned layers, giving the appearance of more than 2 grains or more than one boundary in some innappropriate 2D sections. If we compare all these four images, we found that all of the highlighted boundary traces in figure II.29a-d are parts of a single 03 boundary shown in figure II.29e) separating just two grains as a medium-sized twinned crystal embedded in a much larger grain (labeled 2).

Figure II. 28 .

 28 Figure II.28. Comparison of the interaction volume for the case of conventional EBSD and t-EBSD calculated by Monte-Carlo simulation. Red trajectories indicate electrons backscattering out of the incident beam entrance surface and blue ones indicate electrons that have either been transmitted through or stopped within the specimen [Keller 2012].

Figure

  Figure II.29. (a-d) Four successive aligned EBSD images from a 3D analysis of a steel sample (with an increasing sectioning depth from a) to d)), demonstrating a single complex-formed 03 boundary (arrows) separating only two grains (labeled 1 and 2), even though grain 1 appears as a 'double' grains in c) and d); (e) perspective view of the identified boundary traces defining this single 03 boundary [Reed 2012].

Figure

  Figure II.30. Publications and Citations obtained from SCI search on key words 'EBSD' a), b) and '3D EBSD' c), d) for the last 20 years.

III. 1 .

 1 Introduction ............................................................................................................................. III.2. History of serial sectioning tomography .............................................................................. III.3. Details of dual-beam FIB/SEM serial sectioning tomography .........................................

III. 6 .

 6 Discussion and conclusions ................................................................................................. Reference -Chapter III ...................................................................................................................

Figure III. 1 .

 1 Figure III.1. Comparison of 3D FIB/SEM tomography with other 3D information acquired techniques. As demonstrated, this technique shows a good capacity of analyse: a larger volume of material with a better spatial resolution [Cantoni 2014].

Figure III. 2 .

 2 Figure III.2. Automatic 3D serial sectioning device for micro-level precision: a,b) based on microtome and c) based on precision mechanical system and automatic optical microscope.

  Figure III.3. Illustration of single beam FIB serial sectioning tomography. a) local deposition of a protective layer over the ROI. b) drilling of reference markers. c,d) milling of cross section with a high current. e,f) imaging of freshly milled cross-section with a low current by tilting by a given angle * about the x-axis [Inkson 2001a].

Figure

  Figure III.4. a) Initial ROI without protected layer and b) the ROI with deposited protective layer.

Figure

  Figure III.6. GIS nozzle presented in the FIB chamber in a global view a) and with mounted sample b).

Figure

  Figure III.7. Increase of amorphous layer thickness in a sidewall of Si as a function of Ga + energy [Gautier 2013].

Figure

  Figure III.8. a): 'U-shape' trench for 3D FIB-SEM nano-tomography; b): 'Stair-case' type in the FIB 'lift-out' TEM sample preparation[Giannuzzi 1999] (the top of the thin foil -entrance surface of the ion beam -is shaded); this geometry minimizes the quantity of matter to be removed.

  9a) is about two figure (section II.1.3-sputtering, figure II.11).

Figure III. 9 .

 9 Figure III.9. In the standard geometry, the specimen is tilted 2. A clearly visible brightness gradient though Inlens detector due to shadowing effect of the bottom of the section according to the position of Inlens detector (sample: of LGL laboratory).

Figure

  Figure III.10. Schematic representation of variants of the milling geometry in FIB/SEM tomography: a) standard geometry; b) oblique milling geometry where the pre-trimmed sample surface is parallel to the ion beam [Hazekamp 2011].

Figure III. 11 .

 11 Figure III.11. Comparison of a) SE and b) BSE images (EHT: 1.5 kV, aperture size: 60 !m, high current, pixel size: 2 nm, acquiring time: 4 min, image size: 2048 " 1536 pixels) from the same area of a silicate sample (olivine with iron-nickel precipitates) of ZEISS Nvision 40 DB FIB system (sample courtesy of Harrisson R., Cambridge University, UK).

  Figure III.12. Inlens detector collected SE contrast of different phases in a complex Cu alloy (sample courtesy of Cazottes S., Mateis).

Figure

  Figure III.13. Monte-Carlo simulation of excited backscattered electron (BSE) and X-rays in a multi-layer SiO 2 -C sample with different primary electron accelerating voltages in oblique incident angle. The size of this interacted volume is closely connected to electron accelerating voltage and stage tilted angle. Moreover, an asymmetric form of interaction volume is produced by the oblique incident angle, thus the exact volume is smaller than whole interaction volume [Holzer 2012].

Figure III. 14 .

 14 Figure III.14. Prepared cross-section with 30 kV, 300 pA a) and 5 kV, 300 pA b).

Figure III. 15 .

 15 Figure III.15. Illustration of the SEM and FIB scanning 'grids' (respectively green -(X,Y) plane -and red -(X,Z) plane -) in a 3D experiment; the FIB and SEM pixel sizes are not necessarily identical.

Figure III. 16 .

 16 Figure III.16. Relationship between the volume size and the 3D reconstructed image voxel size with different image stored resolution; Relationship between the experimental acquiring time and volume size, voxel size with fixed image stored resolution (Courtesy by FIB team for the CNRS training program 'Microscopie à balayage double faisceaux (FIB/SEM): un outil analytique' in 2013).

Figure III. 18 .

 18 Figure III.18. Recording of the beamshifts LBSX and LBSY in a) and working distance WD in b) during a 3D FIB/SEM tomography experiment.

Figure

  Figure III.19. Comparison of 3D reconstructed surface of a grain with and without complete spatial drift correction of source data, which showing the necessity of post-mortem alignment [Schaffer 2007].

Figure III. 20 .

 20 Figure III.20. Procedure of alignment of two images with a cross-correlation algorithm.

Figure III. 21 .

 21 Figure III.21. Alignment of sequential cross-sections and reconstructed objet (adapted from [Inkson 2001b]).

Figure III. 22 .

 22 Figure III.22. Bibliographical alignment reference markers for successive images of FIB tomography: a) a set of drilled hole, by which the uncertainties of alignment on each slice in X and Y directions are estimated to 30nm and 70nm [Inkson 2001a]; b) milled cross[Lasagni 2008]; c) milled line[Nagasekhar 2010], which is parallel to Z direction; d) milled crossing diagonals[Iwai 2010]; e) drilled hole on the imaging surface[Uchic 2009]; d) specifically prepared marker[Lepinay 2013], which is viewed with different contrast in the SEM, in order to facilitate the aligning procedure.

  Figure III.23. a) 'Overview' and b) 'detail' of BSE contrast on the working area [Schaffer 2007].

Figure III. 24 .

 24 Figure III.24. Cross pattern milled on the side of ROI to measure the sectioning thickness consistency in a) global view and b) presented in individual slice [Groeber 2007].

Figure

  Figure III.25. a) Thicknesses of milled slices (nominal 500nm) measured from aligned successive images, which vary from 290nm to 640nm [Schaffer 2007]; b) SEM image on ROI with the presence of fiducial markers (in red rectangle) in low magnification [Kotula 2006].

Figure III. 26 .

 26 Figure III.26. Illustration of a wrong alignment produced by a cross-correlation approach in the case of an inclined (according to horizontal plane) object in the volume of interest: for clarity, this 'object' is considered to be a cylindrical hole, of inclusion in the material. The top line shows the expected successive sections in the ideal case where no re-alignment is required; the bottom line shows how the cross-correlation will align the successive elliptical sections with respect to the reference image (chosen here as the central image), thus creating a wrong microstructure.

Figure

  Figure III.27. a) SEM view of the micro-volume extracted from a bulk sample (serpentine) just before 'lift-out' with the help of a micro-manipulator; b) montage of the micro-volume on an eroded Cu support; c) wedgeshaped block, once glued on the Cu support before starting the slice-and-view procedure; d): markers realized on the lateral surface: trenches were milled and filled by tungsten deposition in order to get a good contrast. Note that the region of interest to be imaged in SEM has been prepared with the FIB and is ready for the acquisition of the 3D series.

  Results are shown in figure III.28 where the different alignments are illustrated by the side view of the surface where the specific markers were machined. Surprisingly, none of the reference area gives a satisfactory result. The most simple reference area to use (number 1) leads to an alignment totally controlled by the isotropy of the microstructure. As a whole the alignment is roughly correct but presents fluctuations owing to specific features in the microstructure, although the eye inspection of the reconstructed volume does not reveal any discontinuity, and gives a strong feeling that the microstructure is really isotropic. All other reference areas, which include edges (intersection of surfaces) lead to more 'straight' alignments, but clearly flawed alignments. This simply attests that those edges are not perpendicular to the viewing Z direction, which produces the same effect than what was illustrated in figure III.26: inclined lines are just re-aligned by the cross-correlation.

Figure III. 28 .

 28 Figure III.28. Post-mortem alignment of the test experiment using different areas for cross-correlation. In each case, the results are illustrated by showing the reconstructed surface on which the lateral markers were machined.

  ] [Piazzesi 1973] as permitted, for example, by the commercial MEX software. The MEX program (Alicona SARL, Les Ulis, France) is well-known by SEM users 26 . The method to measure the 3D topography of the surface of a sample is to acquire three images of the sample inclined at, typically, -10°, 0° and 10°, as shown in figure III.29a. The surface reconstruction is obtained from simple trigonometric calculations retrieving the height of any detail at the surface from the differently inclined projections. The result is shown in figure III.29b for our 'test' serpentine sample.

Figure III. 29 .

 29 Figure III.29. Reconstruction of the surface topography of a sample (serpentine used in section III.4.2) by using the stereoscopic approach (MEX software): a) SEM images taken at different tilt angles: -10°, 0° and 10°; b) 3D view of the reconstructed surface.

  Figure III.30. a) Example of part of a reconstructed sample surface with the MEX software; where the dark-red line shows the position at which the lower profile (blue curve in b)) has been extracted.

Figure

  Figure III.31. a) Front image of the 3D FIB-SEM sequence showing the 4 lateral references at the right-hand side (bright features); b) local cropped area showing the topography of the sample surface clearly revealed by the W-layer (high intensity) during the slice-and-view process (i.e. at a given Z), and c) corresponding surface profile obtained after easy thresholding and used for the alignment routine.

Figure III. 32 .

 32 Figure III.32. Principle of the comparison of a FIB profile (schematic, in blue) with all MEX profiles (in green) ; according to the numerical comparison, the best match is found (in the present case with profile MEX 2).

Figure

  Figure III.33. a) The first FIB profile (blue curve) of the image stack and its matching MEX profile (green curve) with BM(1)=378 are shown together with the values of the resulting shifts along x and y, the correlation coefficient and the Euclidian error between both profiles; b) same for the second FIB profile: it is seen that the best matching MEX profile is the same than in a).

Figure III. 35 .

 35 Figure III.35. Correspondence between the FIB and MEX profiles (see text for details).

  Figure III.36. a) Measurement of different characteristics distances from 4 milled fiducial markers on the right side of ROI before the slice-and-view acquisition; note that the angle between the crossing lines at the bottom is equal to 30° (360-329.8°); b): same view after the topographic reconstruction: the previous angle is measured at 27 ± 3°; c): same view after reconstruction assuming a cubic voxel size during the FIB acquisition (i.e. 10 nm/pixel in all directions). The yellow markers will be discussed in the text.

  27 http://www.fibics.com/

Figure

  Figure III.37. a) Reconstruction of 4 markers on the side where the alignment is based on the topography of sample surface; b) comparison of reconstructed sample surface after the alignment (red) with MEX reconstructed surface (green).

Figure

  Figure III.38. a) Reconstruction of 4 markers on the side where the alignment is based on two upper parallel lines; b) comparison of the reconstructed sample surface after the alignment (red) with MEX reconstructed surface (green).

Figure

  Figure III.39. a) Reconstruction of 4 markers on the side where the alignment is based on the interface between deposited layer and sample surface; b) comparison of reconstructed sample surface after the alignment (red) with MEX reconstructed surface (green).

  Figure III.38a shows a very good alignment of the two top parallel lines 28 , which does not lead to a better alignment (comparing the error factors reported in 28 note however that the oscillations of the bottom intersecting lines, attributed to fluctuations in the scan process (see end of section III.5.1.3) are present, as well as in all other reconstructed volumes.

Figure

  Figure III.40. a) Reconstruction of 4 markers on the side where the alignment is based on the central area of ROI; b) comparison of reconstructed surface after the alignment (red) with MEX reconstructed surface (green).

Figure III. 42 .

 42 Figure III.42. Schematic views of a drilled hole seen from the front (a) and a lateral side of the ROI (b). The green layers represent the successive slices in the Z direction , and the angle between the hole and the top surface can be measured post-mortem from simple trigonometric relations using the points A, C', C'',…, as indicated.

Figure III. 43 .Figure

 43 Figure III.43. Drilled hole as seen before (a) and after (b) the 3D sectioning sequence; a top view is shown in c) at the end of the experiment.

Figure

  Figure III.45. a) Reconstructed drilled hole and sample surface after aligning the image stack by using the surface topography; b) comparison of the reconstructed top surface after the alignment (red) with the initial reference surface reconstructed using MEX (green, idem figure III.44).

Figure

  Figure III.46. a) Reconstructed drilled hole and sample surface after aligning the image stack by a crosscorrelation over a selected region including the interface with the top surface: b) comparison of the reconstructed top surface after the alignment (red) with the initial reference surface reconstructed using MEX (green, idem figure III.44-45).

Figure

  Figure III.48. a) Lateral (Z,Y) views of the median section of the hole corresponding to figure III.44 (alignment using hole sections). The average inclination of the hole has been forced to be the expected value, i.e. 36°. b): same as a) corresponding to figure III.45 (alignment using the top surface topography); c): same as a) corresponding to figure III.46 (alignment using the cross-correlation method); angle values are the mean inclination of the hole axis (see text for details).

Figure

  Figure III.49. Top-view of the top surface of the sample after alignment using the cross-correlation method applied in figure III.46a. The deformed reconstructed surface shows again the danger of cross-correlation even it shows an apparent acceptable result.

Figure IV. 1 .

 1 Figure IV.1. Microstructure of Ni-based super-alloy, A) Grain map after EBSD acquisition, with an step size of about 250 nm; B) grain map after grain approximation; c) ion beam induced SE image; and D) binary image of the grain boundaries for improved stereology measurements [Groeber 2006].

Figure IV. 2 .

 2 Figure IV.2. Different geometrical set-up between FIB, SEM column and EBSD camera in a FIB-EBSD: a) rotation set-up; b) tilt set-up; c) static set-up [Zaefferer 2008].

Figure IV. 3 .

 3 Figure IV.3. Geometrical setup for 3D EBSD in the FIB (ZEISS / Oxford Instruments configuration). A 180° rotation around the inclined axis allow to change from the EBSD to the FIB position.

  29 http://www.tescan.com/en/news/static-acquisition-geometry-true-3d-eds-and-3d-ebsd

Figure IV. 4 .

 4 Figure IV.4. Geometrical arrangements for the FIB (a) and EBSD (b) positions showing the difference in the WD value (adapted from [Mateescu 2007]).

  Figure IV.5. Different sectioning strategies in 3D FIB-EBSD: a) the grazing-incidence 'Edge Milling' method and b) the low-incidence 'Surface Milling' method [Zaefferer 2009].

Figure IV. 6 .

 6 Figure IV.6. Views of ROIs to be defined in a 3D EBSD experiment: a) in the FIB position (ion-induced image), b) same as a) but true SEM image, c) in the EBSD position (SEM image). The cross-hairs, in the centre of red circle, are used as reference for repositioning the ROI; they correspond to markers described in the text, and respectively labelled "2" in a-b), and "1" in c).

Figure IV. 7 .

 7 Figure IV.7. Illustration of the limited resolution of EBSD map (2D case) as compared to low voltage SEM imaging (Ni super-alloy sample); a) 1.5 keV SEM Image, b) noise-cleared EBSD map. Because of the low spatial resolution of EBSD, many microstructural features cannot be revealed correctly: small-sized precipitates (areas 1 and 2); exact grain shape (area 3).

Figure IV. 8 .

 8 Figure IV.8. Verification of alignment process during a 3D-EBSD acquisition: a) indication of successful repositioning of ROI (option 'Drift correction' in ZEISS SmartSEM ® software); b-c) indication of the working windows in 'HKL Fast Acquisition', used to move respectively the electron and ion beams (according to the ROI). The cross-hairs (shown in figure IV.5) are imaged at low magnification during the last two steps b) and c).

Figure

  Figure IV.10. Improved EBSD spatial resolution on a TWIP steel obtained by lowering the SEM accelerating voltage: a) with the same step size, a narrow twin, located by two black points at 15 keV, is reasonably wellidentified at 7.5 keV; b) diagram showing the evolution of the Hough peak intensity during a linescan across a boundary (white dotted points in c) [Steinmetz 2010].

  the 'physical resolution' (unless specified): how far from a large-angle grain boundary one obtains diffracted intensities from both crystals. The 'effective resolution' is how accurately an orientation microscopy system may resolve a large-angle grain boundary after using software algorithms to deconvolve overlapping patterns; typically, the effective resolution depends on physical resolution whereas being usually better.

Figure IV. 11 .

 11 Figure IV.11. Comparison of the quality of EBSD Kikuchi patterns as a function of the electron accelerating voltage, although the exposure time has been increased for the lower voltages [Steinmetz 2010].

Figure IV. 12 .

 12 Figure IV.12. Backscatter Kikuchi patterns of a diamond surface milled with different ion energies. The SEM is set at 20 kV with a probe current of 9.5 nA for the collection of these patterns. The quality of the patterns is decreased because of the increased surface defect density [De Winter 2011].

Figure IV. 13 .

 13 Figure IV.13. EBSD maps acquired on a surface of a complex oxide milled at 30 and 5 kV (respectively a) and b)). The improvement of pattern quality is clearly seen by eye inspection and further revealed by the detection of smaller grains at low voltage (circled area in b) [Saowadee 2013].

Figure IV. 14 .

 14 Figure IV.14. Definition of the longitudinal projected range (R p ), the lateral projected range (R y ) and the radial range (R r ) for one single ion with an incidence angle * i treated in the SRIM software.

Figure IV. 15 .

 15 Figure IV.15. SRIM simulation of a Ga ion trajectories in Cu for different ion energies, 5 kV, 10 kV, 20 kV and 30 kV respectively (incidence angle of 89.9°).

Figure IV. 16 .

 16 Figure IV.16. Electron exit depth for Si, simulated with a 15 kV beam and 70° sample tilt (intensity relative levels shown in gray scale) [Deal 2008].

Figure IV. 17 .

 17 Figure IV.17. Projection of energy distribution in the geometry of EBSD as obtained from 'Casino' simulations (see section II.2.5) for a Cu sample (sample tilted at 70°, high value of the SEM voltage -30 keV -).

Figure IV. 18 .

 18 Figure IV.18. Schematic diagram showing the result of the depth of penetration on atomic number (fcc metals) for 30 kV Ga+ ions nearly parallel to the EBSD highly tilted surface (3D EBSD case; SRIM and Monte-Carlo calculations). The evolution of the EBSD quality of indexing (IQ) with the atomic number (Z) is also plotted [Mateescu 2007].

Figure IV. 19 .

 19 Figure IV.19. FIB prepared cross-section imaged with different conditions: a) InLens detector at 15 kV; b) EsB detector at 15 kV; c) InLens detector at 1.5 kV; d) EsB detector at 1.5 kV.

Figure IV. 21 .

 21 Figure IV.21. Automatic modification of user-defined 'Height' (0.1 !m) value by microscope during the preparation of 3D EBSD: if the imaging mode is changed from FIB to SEM and then to FIB, the height is modified by the system (here 0.41 !m, which seems connect to actual FIB milling pixel size: 81.26 nm / 2 = 40.63 nm).

Figure IV. 22 .

 22 Figure IV.22. Synoptic schema of the successive steps in a 3D EBSD process; left: automatic process managed by HKL Fast Acquisition software of Oxford Instruments (the EBSD maps are acquired systematically after each FIB erosion, without any possible action of the user); right: presently developed program, which allows the user to launch a EBSD map every 'n' times of FIB erosion (n = 10 for example).

  Figure IV.24a shows the interface window before the acquisition and figure IV.24b shows all parameters defined by the user, as well as the indication of the activated subroutine.

Figure IV. 23 .

 23 Figure IV.23. Synoptic schema of diverse steps for a complete cycle during the FIB-SEM / EBSD 3D sequence.

Figure IV. 24 .

 24 Figure IV.24. Interface of the 'MAITRE' program; a): preparing the whole procedure, b): acquisition parameters. a) b)

Figure IV. 25 .

 25 Figure IV.25. Schema of dedicated support for 3D EBSD experiment (reproduced at scale 1).

Figure IV. 26 .

 26 Figure IV.26. Working windows of saving and recalling two positions (EBSD and milling).

Sample

Figure IV. 27 .

 27 Figure IV.27. Different positions of the 3D EBSD support as visualised and captured by the infrared camera (signal TV in SmartSEM ® software, symmetrical to the real position because of the camera position); a): EBSD position with inserted EBSD camera; b): same position after a safe displacement -Y; c): after a rotation of 180°; d): after the correction of height (WD, typically from 10 mm to 5 mm); e): support at milling position; f): other view of the position b) if the EBSD camera would have not be retracted (green lines).

Figure IV. 28 .

 28 Figure IV.28. Possible large stage positioning error (measured as about 10 !m in X direction) even after the stage backlash (the red lines are markers indicating a given detail in the initial position of the ROI (a); b) recovered stage position after the FIB-EBSD cycle.

Figure

  Figure IV.29. Executing window for multi-regional recognition: manual mode permits user to define 3 different magnifications for precise location of the ROI and automatic mode uses 3 predefined magnifications. The manual mode is suggested to adapt the size of the ROI.

Figure IV. 30 .

 30 Figure IV.30. View of the ROI after repositioning the stage with different levels of accuracy: MAG1 -a) and b); MAG2 -c) and d); MAG3 -e) and f) (SEM imaging at low voltage in the milling position).

  Figure IV.31. Captured screens from typical 'recipes': a) in the Zeiss SmartSEM ® software (recipe test1.EMRCP showing different saved parameters); b) recipe file opened in Notepad showing the values of different parameters saved during the creation of recipe; c) recalling a recipe from a Macro in SmartSEM ® .

Figure IV. 32 .

 32 Figure IV.32. Typical starting SE images acquired with the Inlens (a) and EsB (b) detectors; c) and d) are the corresponding images obtained when recalling the imaging conditions rigorously saved from cases a) and b) respectively but after having modified some parameters such as WD, EHT,…

Figure IV. 33 .

 33 Figure IV.33. Crystal structure of a) 8 and b) 8'.

Figure IV. 34 .

 34 Figure IV.34. Typical microstructure of the Ni-based super-alloy: a) SEM image with an EsB detector, b) with an Inlens detector, c-d) crystallographic EBSD maps from the white rectangles in a-b) before and after noise reduction (respectively c) and d); the red lines delimitate grain boundaries with disorientation larger than 10° between two neighbour grains. Note that the larger central grain presents a twin which is not perceptible in the SEM images of the top row.

Figure IV. 35 .

 35 Figure IV.35. Preparation process of the sample for a dedicated 3D EBSD acquisition: a) captured image from the infrared camera showing the top-surface above the ROI parallel to ion beam (orientation close to the EBSD position); b) FIB view of the well-cleaned and flat top-surface; c) delicately machined markers for the postmortem treatment (image acquired before the deposition of the final protective C layer); d)

Figure IV. 36 .

 36 Figure IV.36. Typical EsB images used to verify the mean thickness of each eroded layer: a) first image and b) last image of the tomography experiment.

Figure

  Figure IV.37. 3D visualisation of precipitates 1 (in pink) & 2 (in green) within a volume of 16 " 13 " 1 !m 3 .

  Figure IV.38. Size distribution of precipitates -type 1 in a) and type 2 in b) -in nanometres from the reconstruction of 100 successive images in FIB-SEM tomography, shown in figure IV.37.

Figure IV. 40 .

 40 Figure IV.39. Example of indexing precipitate families 1 and 2 in EBSD, shown in a) InLens, b) EsB images; c) raw crystal orientation images (without any noise reduction procedure). Black areas in circle A and B of a) are precipitates 1; White areas in the circle C and D of a) are precipitates 2.

Figure

  Figure IV.41. a) InLens image with grain boundaries underlined by hand according to different greyscale with the help of b) EsB image and noise-reduced EBSD result on the same ROI in c): orientation map (same colour legend as figure IV.39c); d) band contrast map, where red, yellow and blue lines correspond to an misorientation of 10°, 5° and 2° respectively between adjacent grains; e) -f) manually labelled and coloured grains (according to EBSD orientation map in c) for size measurement.

  Figure IV.42. Reconstruction of two 8 matrix grains (same colour legend as figure IV.39c) from a) serial 101SEM images and b) serial 11 EBSD maps, where the voxel size is 10 nm " 10 nm " 10 nm and 50 nm " 50 nm " 100 nm, respectively.

Figure IV. 43 .

 43 Figure IV.43. Comparison of histograms for the grain size distribution obtained from 2D images a) and 3D reconstructions b) respectively for the SEM and EBSD imaging modes: a) histogram for a single 2D SEM image (shown in figure IV.41a), and a single EBSD map (shown in figure IV.41c); b) similar SEM histogram from the tomographic SEM volume and the tomographic EBSD volume.

Figure

  Figure V.1. Evolutional intensity (grey level) in FIB secondary electron contrast of 4 grains, which is a function of variation from the normal incidence as the specimen (aluminium alloy) is tilted with respect to gallium ion beam[Phaneuf 1999].

Figure V. 2

 2 Figure V.2. a)The Bloch wave mode for an electron flux in a crystal. The current can be resolved into two components: Bloch wave I, which has its maxima between the planes, and Bloch wave II, which has its maxima on the line of atom centres. b) Changes in geometry of an incident beam during scanning, which gives the changes in backscattering signal[Joy 1982].

Figure

  Figure V.3. a) ECP showing how the beam direction can be identified with respect to the crystal orientation (a: the incident beam within a channelling band -the beam incidence on the lattice planes is less than the Bragg angle -; b-c: the beam is respectively oriented on the edge and outside of the channelling band. And their relative positions are linked to emitted signal as shown in figure V.2b) [Simkin 1999]; ECCI of dislocation cells and mechanical twins in a tensile deformed Fe-22Mn-0.6C Twin-induced plasticity steels at low b) and high c) magnification [Gutierrez-Urrutia 2009].

  Figure V.4. The particle model for channelling: two different beam-crystal orientation showing a nonchannelling (left) and a channelling (right) situation [Newbury 1986].

Figure V. 5 .

 5 Figure V.5. Comparing of ion introduced SE image a), electron introduced SE image b) and EBSD map c) on a polycrystalline Cu from the same area [Giannuzzi 2013].

Figure V. 6 .

 6 Figure V.6. Cross-section of a nanotwinned microstructure investigated with different methods: a) EBSD orientation map; b) EBSD image quality (IQ) map (pixel size: 20nm); c) ion channelling image (pixel size: 6.25nm).As illustrated, ion channelling image shows a better capacity to detect twin lamella than obtained in IQ map. Some twin lamellae can be misinterpreted from the IQ map and orientation map even not resolve most part of them[Alimadadi 2013].

Figure V. 7 .

 7 Figure V.7. Schema showing critical channelling directions on (110) plane of an Al FCC single crystal, where the unit cell of Al in (110) plane is highlighted. The [115] direction here shows a high fraction of nonchannelling owing to collisions with arranged atoms (blue) [Silk 2010].

Figure

  Figure V.8. a) Normalised grey level and incident ion beam angle of three different grains compared with <100> theoretical tilt directions. The intensity profiles of grains j, d and bg have been rotated 10°, 6° and 10° respectively to match the sputtering yield peaks [Silk 2010]; b) Calculated map of different channelling directions in a fcc crystal. The colour coding interprets quantitatively the width and depth of the scattering minima [Veligura 2012].

Figure V. 9 .

 9 Figure V.9. An example case of symmetry (cubic crystal) for a same SE intensity showing in stereographic projection (black lines: plane family (100), orange line: plane family (110), and red line: plane family (111)). The Euler angle is -1 = 30°, . = 41°, -2 = 25° for a) and -1 = 330°, . = 41°, -2 = 65° for b) respectively.

Figure V. 10 .

 10 Figure V.10. Program interface for the semi-automatic serial images acquisition (ZEISS API routine).

Figure V. 11 .

 11 Figure V.11. Interface to extract SE intensity profile (rectangle 2) from image series (rectangle 1).

  Figure V.12. Matching a calculated profile with an experimental known one (according to the knowledge of the exact orientation from the EBSD reference map).

  Figure V.13. a) Reconstructed orientation map from a full set of images (intensity profiles with 1° angular step and 360° rotation range); b) EBSD orientation map in the same region of interest for comparison; c) Disorientation between reconstructed and EBSD orientation expressed in colour levels.

  Figure V.14. First result of crystal orientation determination on a TiN sample with calculated value (rectangle 1) and theoretical value (rectangle 2) of Euler angles; and comparison (rectangle 3) of theoretical intensity profile from EBSD (blue curve), experimental profile (plotted by orange points) and found profile (red curve).

Figure V. 16 .

 16 Figure V.16. Reconstructed orientation map on the same ROI as in figure V. 13 with a rotation range of 360° and an angular step of 10°. The acquisition time here is about 5 minutes.

Figure A1. 4 .

 4 Figure A1.4. Main window of two Fiji plugins: the 'StackReg' (at left) and 'MultiStackReg' (at right) which is useful to align these successive images of FIB/SEM tomography.

Figure A1. 5 .

 5 Figure A1.5. Executed window (hidden to user) of programmed 'macro' in Fiji.

  Figure A1.5 shows all parameters, hidden for user, that Utilized Option to align those images Saving the text of 'MultiStackReg' 'ON' or 'OFF' (figure A1.8 and figure A1.9 respectively). The [beam shifts] applied to the SEM image are monitored to check the behaviour and good working conditions of the procedure (see figure A1.10).

Figure A1. 8 .

 8 Figure A1.8. Sub-stack (chosen at random) of images recorded with the live dynamic drift correction 'ON' (each two images); red lines are fixed markers for reference. We note a slight uncorrected drift between the initial and final images of this series but roughly the ROI is well preserved.

Figure A1. 10 .

 10 Figure A1.10. Recorded beam shifts (LBSX and LBSY in %) concerning the SEM column as a function of time (in seconds) during the test experiment illustrated by figure A1.8 and figure A1.9. point P in the display corresponds to the moment of deactivation of drift correction program (i.e. the correction is 'ON' on the lefthand side and 'OFF' on the right-hand side with respect to P). The right part of curves corresponds with figure III.17 (normal beam shift evolution during 3D experiment with activated 'Track WD' option). The left part of curve shows clearly the effect our program (correction frequency and general trend of the [beam shifts] vs. time curves).

Figure A1. 11 .

 11 Figure A1.11. Reconstructed volume without further treatment of above stack image with (figure A1.8) and without (figure A1.9) dynamic live drift correction. Clearly, the ROI is disappearing without correction.

Figure A1. 12 .

 12 Figure A1.12. GUI of the autofocus procedure (a); b): 'focus ramp' approach (the arrow indicate the identified 'best focus' according to the maximum of contrast).

  Figure A1.13. Autofocusing (central image) of a starting out-of-focus area (left, serpentine sample) as compared to the manual focus determined by eye-inspection (right).

Figure A1. 14 .

 14 Figure A1.14. Initial defocused (a)-b), left column) and final auto-focused (c)-d) right) images of two areas, respectively with high contrast (top line, serpentine sample) and poor contrast (bottom line, Si sample).

Table II . 1 .

 II1 List of available ion beam current/accelerating voltage in SII Zeta ion column

	Current (pA)	45000	27000	13000	6500	3000	1500		700	300	150
	Voltage (keV)	30	30	30	30	30	30		30	30	30
	Probe size (nm) 5100	2500	900	360	170	107		59	38	29
	Current (pA)	80	40	10	1	< 0.3	< 0.15	15000	6500	3000
	Voltage (keV)	30	30	30	30	30	30		20	20	20
	Probe size (nm) 22	19	13	7	5	4		450	20	20
	Current (pA)	700	45	100	20	200	100		100	50	100
	Voltage (keV)	20	16	10	8	5	5		2	2	1
	Probe size (nm) 40	45	8	20	14	10		10	-	-
	Table II.2. List of available electron beam currents (10 kV without high current) according to aperture diameters
	in ZEISS GEMINI	® electron column
	Current (pA)		20	30	130	300	1200	4500
	Aperture diameter (µm)	7.5	10	20	30	60	120

Table II .

 II 3. Reasons to choose Ga as ion source and corresponding proprieties[START_REF] Bozack | Materials considerations in liquid metal ion source development[END_REF]].

	Proprieties	Reasons
	Low melting point (29.8 °C)	Minimises reaction between liquid and substrate
	Low volatility at melting point	Conserves supply of metal; promotes long source
		lifetime
	Low surface free energy	Promotes wetting and flow of liquid on substrate
	Low solubility of liquid metal in substrate	Dissolution of liquid metal in substrate in liquid alters
		its resistivity and hence heating characteristics
	Low solubility of substrate in liquid metal	Dissolution of substrate in liquid metal alters its
		composition and increases the melting temperature
	Mechanical, electrical and vacuum properties of
	emitter substrate

Emitter must be electrically conductive, able to withstand high electric fields (~ 10 V/nm), have low power consumption and be able to operated in less than ultimate high vacuum conditions

Emission characteristics

High angular intensity (~ 25 µA/sr, I e = 2 µA),

Small energy spread (~ 5 eV, I e = 2 µA)

Table II . 5 .

 II5 Comparison of performances for different field emission electron source at 20 kV[Goldstein 2003]

	Property	Brightness	Lifetime	Virtual source size	Energy-spread (FWHM)	Beam current stability
	Source / Unit	A m -2 sr -1	h	nm	eV	(%/h)
	Cold field emission	10 12	> 1000	< 5	0.3	2
	Thermal field emission	10 12	> 1000	< 5	1	2
	ZrO/W Schottky field emission	10 12	> 1000	15 -30	0.3 -1.0	~ 1

Table II . 6 .

 II6 Comparison of modern mainly applied sources (adapted from[START_REF] Forbes | The Theory of Bright Field Electron and Field Ion Emission Sources[END_REF]

	Property	Unit	ZrO/W Schottky	Ga LMIS	He GFIS
			(SEM)	(FIB)	(SIM)
			Value	Value	Value
	Typical extraction voltage	kV	~ 5	~ 5	20
	Energy-spread (FWHM)	eV	0.6	5	0.35
	Source optical radius	nm	20	25	< 0.08
	Typical angular intensity	!A sr -1	~ 400	10	2.5
	Reduced Angular intensity	A sr -1 V -1	~ 7 " 10 8	2 " 10 -9	10 -10
	Source brightness Reduced source brightness	A m -2 sr -1 A m -2 sr -1 V -1	~ 5 " 10 11 ~10 8	5 " 10 9 10 6	> 10 14 5 " 10 9
	Typical emission current	!A	40 -400	2	0.5 -0.8
	Typical probe current	pA	variable	variable	variable
	Typical probe voltage	keV	variable	variable	variable
			(0.1 -30 for ZEISS)	(1 -30 for SII)
	Best probe radius	nm	0.5	3	0.12

  Cho 2011] Cho B. S., Oh H. J., Uhm H. S., Kang S. O., Kim C., Choi Y., Choi E. H. Ion emission and electric field characteristics in the liquid metal ion source with a new suppressor electrode. Current Applied Physics, 2011, vol. 11, pp. s172-176. Claessens B. J., Reijnders M. P., Taban G., Luiten O. J., Vredenbregt E. J. D. Cold electron and ion beams generated from trapped atoms. Physics of Plasmas, 2007, vol. 14, 093101. Deans S.R. Hough Transform from the Radon Transform. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1981, vol. PAMI-3, pp. 185-188.

	[Clampitt 1975] Clampitt R., Aitken K.L., Jefferies D.K. Abstract: Intense fiedemission ion source of
	liquid metals. Journal of Vacuum Science & Technology, 1975, vol. 12, pp. 1208.
	[Deans 1981] [Deans 1983] Deans S.R. The Radon transform and some of its applications. Wiley, New York, 1983,
	289 p.
	[Engler 1996] Engler O., Escher C., Gottstein G. Single Grain Orientation Measurements Applied to
	the Formation and Growth of Recrystallization Nuclei. Textures and Microstructures, 1996, vol. 26-27,
	pp. 337-359.

[Claessens 2007]

[Dey 2006] Dey S. R., Morawiec A., Bouzy E., Hazotte A., Fundenberger J. J. A technique for determination of gamma/gamma interface relationships in a (alpha(2)+gamma) TiAl base alloy using

TEM Kikuchi patterns. Materials Letters, 2006, vol. 60, pp. 646-650

. [Dingley 2004] Dingley D. J., Nowell M. M. The use of electron backscatter diffraction for the investigation of nano crystalline materials and the move towards orientation imaging in the TEM. Microchimica Acta, 2004, vol. 147, pp. 157-165. [Driesel 1996] Driesel W., Dietzsch C., Muhle R. In situ observation of the tip shape of AuGe liquid alloy ion sources using a high voltage transmission electron microscope. Journal of Vacuum Science & Technology B

, 1996, vol. 14, pp. 3367-3380.

[Drouin 2007] Drouin D., Couture A. R., Joly D., Tastet X., Aimez V., Gauvin R. CASINO V2.42 -A fast and easy-to-use modeling tool for scanning electron microscopy and microanalysis users.

Scanning, 2007, vol. 29, pp. 92-101.

[Dudarev 1995] Dudarev S.L., Rez P., Whelan M.J. Theory of electron backscattering from crystals. Physical Review B-condensed matter and materials

physics, 1995, vol. 51, pp. 3397-3412.

[Eades 2009] Eades A., Andrew D., Bhattacharyya A., Hooghan T. Energy Filtering in EBSD. In: Electron Backscatter Diffraction in Materials Science (Second Edition), eds. Schwarzer A. J., Kumar M.,

Adams B. L., Field D. A., Springer, New York, 2009, 403

p.

[Escher 2006] Escher C., Thomann S., Andreoli C., Fink H. W., Toquant J., Pohl D. W. Vacuum ion emission from solid electrolytes: An alternative source for focused ion beams. Applied Physics

Letters, 2006, vol. 89, 053513.

. Complement on the alignment procedure

  ... III.3.1. Preparation of the working area ......................................................................................... III.3.2. Parameters for the acquisition of 3D FIB/SEM tomography .............................................. III.3.2.1. SEM imaging parameters ........................................................................................... III.3.2.2. FIB milling parameters ................................................................................................ III.3.3. Acquisition of 3D FIB/SEM tomography ............................................................................ III.3.4. Bibliographical approaches of alignment ........................................................................... III.4.1. Issues of commonly used alignment methods ................................................................... III.4.2. Demonstration of the inaccuracy of cross-correlation methods for aligning a series of images during a 3D FIB-SEM experiment .................................................................................... III.5.2. Drilled tube .........................................................................................................................

	III.4

........................................................................... III.5. Developed methods for alignment ........................................................................................ III.5.1. Using the topography of sample surface for accurate alignment ...................................... III.5.1.1. Reconstructing the topography of the sample top surface ......................................... III.5.1.2. Comparing top surface profiles obtained by FIB and from the reconstructed topography ................................................................................................................................ III.5.1.3. Comparing the 'topographic' alignment with other alignment methods ......................

Table III . 1 .

 III1 Experimental conditions for a study case in order to test the accuracy of alignment procedures based on cross-correlation.

	FIB		SEM
	FIB pixel size	50 nm	SEM pixel size	12.5 nm
	Milling probe	700 pA	Image resolution 2048 " 1536 pixel
	Milling resolution 2048 " 1536 Aperture size	60 !m
	Step in Z	25 nm	High current	On
	Depth	15 !m	Detectors	Inlens, EsB
	FIB EHT	30 kV	SEM EHT	1.5 kV

Table III .

 III

	2. Experimental conditions for topographic experiment
	FIB		SEM
	FIB pixel size	30 nm	SEM pixel size	10 nm
	Milling probe	700 pA	Image resolution	2048 " 1536 pixels
	Milling resolution	6144 " 4608	Aperture size	60 !m
	INC STYLE	10 nm	High current	On
	Depth	15 !m	Detectors	Inlens, EsB
	FIB EHT	30 kV	SEM EHT	1.5 kV

Table III .4. Experimental conditions for drilled tube experiment

 III

	FIB		SEM
	FIB pixel size	30 nm	SEM pixel size	10 nm
	Milling probe	700 pA	Image resolution	2048 × 1536 pixels
	Milling resolution	6144 × 4608	Aperture size	60 µm
	Step in Z	5 nm	High current	On
	Depth	15 µm	Detectors	Inlens, EsB
	FIB EHT	30 kV	SEM EHT	1.5 kV

  30 , plugin of MTEX 31 and open-EBSD 32 in Matlab ® ), the manufactories Oxford Instruments and EDAX propose commercial programs respectively 'HKL 3D viewer', 'OIM™ 3D Data Analysis and Visualization' for 3D EBSD data treatment. These programs 30 http://dream3d.bluequartz.net/ 31 https://code.google.com/p/mtex/ 32 http://code.google.com/p/open-ebsd/

Table IV .

 IV 1. Comparison of classical Hough transform based EBSD resolution in a FEG type SEM

			Spatial Resolution*		Experimental Condition
	Reference	X (lateral resolution # x , nm)	Y (longitudinal resolution # y , nm)	Z (depth resolution # z , nm)	Step Size (nm)	Sample	EHT (keV)
		50			50	Ni	10
	[Isabell 1997]	100			50	Ni	20
		150			50	Ni	30
	[Humphreys 1999]	9 (effective)	14 (effective)			#-Cu	20
	[Dingley 2004]	6-9 (effective)	6-9 (effective)		3	Pt	25
	[Keller 2004]	10 (effective)	35 (effective)		10	GaAs	15
	[Zaefferer 2007]	35	90	2		Fe	15
	[Steinmetz 2010]	10			10	Fe	7.5
	[Chen 2011]	34.4	44.7	1.91		Cu (monocrystal)	10

Table IV

 IV

		Voltage (keV)	5	10	20	30
		R p (A)	14	21	32	42
	Cu	R y (nm)	29	44	71	96
		R r (nm)	32	49	78	105
		R p (A)	22	32	50	66
	Al	R y (nm)	70	107	173	233
		R r (nm)	73	112	180	242

.2. SRIM calculations of the penetrations of Ga ions into Cu and Al (99999 ions with an incidence angle of 89.9°).

Table IV .3

 IV Parameters for FIB-SEM imaging and EBSD mapping

		FIB-SEM	EBSD
	EHT (keV)	1.5	20
	Aperture size (!m) 60	120
	High current	Yes	Yes
	WD (mm)	5	12
	Detectors	EsB, Inlens	EBSD
	Voxel size (nm 3 )	10 "10 " 10	50 "50 " 100
	Voxel number	2048 " 1536 "500 300 " 300 " 50

Table V . 1 .

 V1 Calculated critical angle, Ψ c and non-channelled fraction χ uvw of 30 keV Ga + ions to aluminium for selected channelling orientations (adapted from[Silk 2010] by ordering the non-channelled fraction).

	Direction Atom spacing	T uvw /d Angle from	Ψ c 𝛘 𝐮𝐯𝐰 𝟎
		T uvw (nm)		[100]
	[110]	0.29	0.71	90	7.85 0.14
	[100]	0.41	1.00	0	6.05 0.23
	[112]	0.50	1.22	35.3	5.20 0.31
	[130]	0.64	1.58	18.4	4.29 0.46
	[111]	0.70	1.73	54.7	4.01 0.53
	[114]	0.86	2.12	19.4	3.44 0.72
	[120]	0.91	2.24	26.6	3.31 0.78
	[150]	1.03	2.55	11.4	3.00 0.94
	[113]	1.34	3.32	25.2	2.46 1.40

Table V .2. Experimental

 V conditions for ion, electron induced SE imaging and EBSD mapping

		Ion	Electron	EBSD
	EHT/aperture 30 kV/ 3 nA 30 kV/60 µA 30 kV/120 µA
	Detectors	Inlens	Inlens	EBSD

  principal de ce travail est d'optimise la tomographie par coupe sériée dans un microscope 'FIB', en utilisant soit l'imagerie électronique du microscope à balayage (tomographie FIB-MEB), soit la diffraction des électrons rétrodiffusés (tomographie dite EBSD 3D). Dans les 2 cas, des couches successives de l'objet d'étude sont abrasées à l'aide du faisceau ionique, et les images MEB ou EBSD ainsi acquises séquentiellement sont utilisées pour reconstruire le volume du matériau. En raison de différentes sources de perturbation incontrôlées, des dérives sont généralement présentes durant l'acquisition en tomographie FIB-MEB. Nous avons développé une procédure in situ de correction des dérives afin de garder automatiquement la zone d'intérêt (ROI) dans le champ de vue. Afin de reconstruire le volume exploré, un alignement postmortem aussi précis que possible est ensuite requis. Les méthodes actuelles utilisant la corrélation-croisée, pour robuste que soit cette technique numérique, présente de sévères limitations car il est difficile, sinon parfois impossible de se fier à une référence absolue. Ceci a été démontré par des expériences spécifiques ; nous proposons ainsi 2 méthodes alternatives qui permettent un bon alignement. Concernant la tomographie EBSD 3D, les difficultés techniques liées au pilotage de la sonde ionique pour l'abrasion précise, et au repositionnement géométrique correct de l'échantillon entre les positions d'abrasion et d'EBSD, conduisent à une limitation importante de la résolution spatiale avec les systèmes commerciaux (environ 50 nm)3. L'EBSD 3D souffre par ailleurs de limites théoriques (grand volume d'interaction électrons-solide et effets d'abrasion). Une nouvelle approche, qui couple l'imagerie MEB de bonne résolution en basse tension, et la cartographie d'orientation cristalline en EBSD avec des tensions élevées est proposée. Elle a nécessité le développement de scripts informatiques permettant de piloter à la fois les opérations d'abrasion par FIB et l'acquisition des images MEB et des cartes EBSD. L'intérêt et la faisabilité de notre approche est démontrée sur un cas concret (superalliage de nickel). En dernier lieu, s'agissant de cartographie d'orientation cristalline, une méthode alternative à l'EBSD a été testée, qui repose sur l'influence des effets de canalisation (ions ou électrons) sur les contrastes en imagerie d'électrons secondaires. Cette méthode corrèle à des simulations la variation d'intensité de chaque grain dans une série d'images expérimentales obtenues en inclinant et/ou tournant l'échantillon sous le faisceau primaire. Là encore, la méthode est testée sur un cas réel (polycritsal de TiN) et montre, par comparaison avec une cartographie EBSD, une désorientation maximale d'environ 4° pour les angles d'Euler. Les perspectives d'application de cette approche, potentiellement beaucoup plus rapide que l'EBSD, sont évoquées.MOTS-CLES :Sonde ionique focalisée (FIB), Diffraction des électrons rétrodiffusés (EBSD), cartographie d'orientation cristalline, tomographie électronique, FIB-MEB, dérives, alignement par corrélation croisée, topographie de surface, EBSD 3D, résolution spatiale, canalisation.

	FOLIO ADMINISTRATIF
	THESE SOUTENUE DEVANT L'INSTITUT NATIONAL DES SCIENCES APPLIQUEES
		DE LYON
	NOM : YUAN	DATE de SOUTENANCE : 15/12/2014
	Prénoms : Hui
	TITRE : Analyse 3D morphologique et cristallographique des matériaux par microscopie FIB
	NATURE : Doctorat	Numéro d'ordre : 2014ISAL0134
	Ecole doctorale : Matériaux de Lyon (ED 34)
	Spécialité : Science et Génie des Matériaux
	RESUME :
	L'objectif Laboratoire(s) de recherche : MATEIS (UMR CNRS 5510) & LGLTPE (UMR CNRS 5276)
	Directeur de thèse: Thierry Epicier
	Président de jury : Marc Legros

Composition du jury : Marco Cantoni, Smail Chalal, Thierry Epicier, Marc Legros, Nicolas Menguy, Bertrand Van de Moortèle †

http://www.clym.fr/

A first thesis mainly based on the use of the FIB has already been defended at MATEIS on a

3D microstructural study of polymer nanocomposites [Liu 2013]. Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2014ISAL0134/these.pdf © [H. Yuan], [2014], INSA de Lyon, tous droits réservés

A first thesis mainly based on the use of the FIB has already been defended at MATEIS on a

3D microstructural study of polymer nanocomposites[Liu 2013]. Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2014ISAL0134/these.pdf © [H. Yuan], [2014], INSA de Lyon, tous droits réservés

Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2014ISAL0134/these.pdf © [H. Yuan], [2014], INSA de Lyon, tous droits réservés

This thesis was financially supported in two ways: a Carl ZEISS S.A.S. funding for 2.3 years, and a temporary research position (ATER) at MATEIS laboratory and first cycle department of INSA Lyon for 1 year. Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2014ISAL0134/these.pdf © [H. Yuan], [2014], INSA de Lyon, tous droits réservés

http://www.oxford-instruments.com/products/microanalysis/ebsd/ebsd-detector-nordlysmax

http://www.edax.com/Products/EBSD/Hikari-XP-EBSD-Camera.aspx

http://www.bruker.com/products/x-ray-diffraction-and-elemental-analysis/eds-wds-ebsd-sem-micro-xrf-andsem-micro-ct/quantax-ebsd/technical-details.html Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2014ISAL0134/these.pdf © [H. Yuan], [2014], INSA de Lyon, tous droits réservés

http://smt.zeiss.com/semiconductor-manufacturing-technology/en_de/home.html

SII NanoTechnology has become a wholly owned subsidiary of Hitachi High Technology Corporation on January 1st, 2013, which changed its name to "Hitachi High-Tech Science Corporation". http://www.hitachihitec-science.com/en/ Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2014ISAL0134/these.pdf © [H. Yuan], [2014], INSA de Lyon, tous droits réservés

http://forums.zeiss.com/microscopy/community/forumdisplay.php?f=15 Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2014ISAL0134/these.pdf © [H. Yuan], [2014], INSA de Lyon, tous droits réservés

http://microscopy.zeiss.com/microscopy/en_de/products/multiple-ion-beam.html

It means the pressure of gas distant from the emitter in thermodynamic equilibrium, while enclosure (filled with ionizing gas) walls are at the same temperature.

It corresponds to the GFIS best source field (BSF) at which the probe can be focused most sharply, when other parameters are set to 'best focus'.

There is an upper limit of gas pressure, due to the onset of charge-exchange collisions between emitted ions and neutral gas atoms (away from the emitter). As a result slow ions entering the column cannot be properly focused.Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2014ISAL0134/these.pdf © [H. Yuan], [2014], INSA de Lyon, tous droits réservés

http://www.srim.org/ Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2014ISAL0134/these.pdf © [H. Yuan], [2014], INSA de Lyon, tous droits réservés

http://www.vsg3d.com/

http://www.adcis.net/

http://www.exelisvis.com/

http://fiji.sc/Fiji Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2014ISAL0134/these.pdf © [H. Yuan], [2014], INSA de Lyon, tous droits réservés

In this work, preliminary reconstructions were performed using an old version acquired by the LaMCoS laboratory at INSA of Lyon; the presented reconstructions were finally obtained using a demo version provided by courtesy by the MEX Company.

Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2014ISAL0134/these.pdf © [H. Yuan], [2014], INSA de Lyon, tous droits réservés Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2014ISAL0134/these.pdf © [H. Yuan], [2014], INSA de Lyon, tous droits réservés

Although a robust focus correction was developed (see below, section A1.2), it has not be included in the present version of the software. The astigmatism has not yet been treated. Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2014ISAL0134/these.pdf © [H. Yuan], [2014], INSA de Lyon, tous droits réservés

Then, I'm grateful to Jean-Claude

During FIB-SEM tomography experiments, an intuitive requirement is to keep the working area, or Region of Interest (ROI), in a 'good shape' in the field of view. If one imagine that the volume to be reconstructed is aimed at being about 10 !m thick, with a desired Z-resolution of, say, 10 nm, this means 1000 slices which could easily demand a time acquisition of about 10 hours with an elementary step of

image acquisition and ion milling step of 30 seconds. This means, the image must remain in a 'good shape' from the point of view of focus and astigmatism, and must stay in the field of view whatever any perturbation or unexpected drift. These perturbations may have very various origins: the sample itself (charging effects, deformation due to irradiation), the mechanics of the stage (although not probable), external stray fields (acoustic, electro-magnetic,…). Indeed, it is highly probable that any user having carried out FIB/SEM tomography has been facing at least once this problem of the global stability of the stack of images. Instead of staying permanently in front of the instrument, of checking it periodically to correct any undesirable drift, it is obviously preferable to use an automatic routine which unsure the tracking of these settings and corrects any damageable variation.

At the time of the present work, there was no commercial routine permitting this on a ZEISS machine and we thus decided to develop a solution regarding the main and more common problem, which is the image drift illustrated in figure A1.1.

Figure A1.2 shows the GUI of our program, initially intended to allow focus, astigmatism and drift corrections to be performed periodically at the user's convenience 35 . Any arbitrary frequency of dynamic correction can thus be activated, for example, every 50 images for focusing and every 10 images for drift correction in X-Y direction for example. Furthermore, thee settings can be re-adjusted in real time during the acquisition. The next section gives some technical details about the program.

Details of dynamic drift correction in X-Y directions

We have developed a computer routine compatible with the ZEISS Application Programming Interface (API) integrating in the FIB/SEM operating software (SmartSEM ® ). We choose to program a mixture of VB6 TM and ImageJ Java plugin (indeed its Fiji version with more plugins [Schindelin 2012]): VB6 constitutes the master program driving the microscope and calling the Fiji subroutine performing the live alignment. The drift correction is then composed by three successive steps (shown in figure A1.3) once an image storage folder and the correction frequency have been chosen:

-Preparation of images -Drift calculation between successive images -Application of correction Appendix 1 control the macro-command that pilots the procedure MultiStackReg (They include a binning value, the pixel size in nm that is read from images, and other data relative to the number of image to be aligned and the frequency of the drift correction). The exported text file, named 'TransformationMatrices.txt', is shown in figure A1.6. This text file contains drifts in pixels of image m according to image n (2 to 1 in the figure), in fact, these drifts $x and $y are calculated from the coordinates of centres of both images ((x r , y r ) and (x a , y a ) in pixels for the reference and current images respectively):

$x = x a -x r , $y = y a -y r The 'TransformationMatrices.txt' file is read by a VB6 application, and the shifts in pixels are converted into distances (in nm or !m) knowing the imaging magnification and the pixel size (deduced form the SEM magnification). To be re-injected in the microscope, the drifts have to be converted into [beam shift values] (%), the SmartSEM ® parameters allowing the image to be moved in both X and Y directions. A preliminary calibration procedure has been performed to rely accurately the beam shifts values to the desired displacement in nm (or !m), see figure A1.7.

To check the performance of our dynamic drift correction, a tomographic acquisition has been performed on a test Nickel alloy; during this experiment, the automatic correction was randomly set to Coordinates x r , y r in pixel of the centre of reference image (image 1 in this example)

Coordinates x a , y a in pixel of the centre of image to align (image 2 in this example) Appendix 1 Figure A1.9. Sub-stack (chosen at random) of images recorded with the live dynamic drift correction 'OFF' (each two images); red lines are fixed markers for reference. We note that the ROI has drifted with a much greater amplitude as compared to figure A1.8.