[1st Edition] 9780128121948, 9780128120910

Table of contents :
Content:
Series PagePage ii
CopyrightPage iv
ContributorsPage vii
PrefacePages ix-xPeter W. Hawkes
Future ContributionsPages xi-xiii
Chapter One - Micro-XRF in Scanning Electron MicroscopesPages 1-60Michael Haschke, Stephan Boehm
Chapter Two - A Variational Approach for Simulation of Equilibrium Ion Distributions in Ion Traps With Regard to Coulomb InteractionPages 61-73Igor A. Kopaev, Dmitry Grinfeld, Mikhail A. Monastyrskiy, Roman S. Ablizen, Sergei S. Alimpiev, Andrei A. Trubitsyn
Chapter Three - Analytical Review of Direct Stem Imaging Techniques for Thin SamplesPages 75-184Ivan Lazić, Eric G.T. Bosch
Chapter Four - Quantum Nanooptics in the Electron MicroscopePages 185-235Luiz H.G. Tizei, Mathieu Kociak
Chapter Five - Component Identification and Interpretation: A Perspective on Tower of KnowledgePages 237-301Mai Xu, Jie Ren, Zulin Wang
IndexPages 303-309

Citation preview

EDITOR-IN-CHIEF

Peter W. Hawkes CEMES-CNRS Toulouse, France

Cover photo credit: Luiz H.G. Tizei and Mathieu Kociak Quantum Nanooptics in the Electron Microscope Advances in Imaging and Electron Physics (2017) 199, pp. 185–235. Academic Press is an imprint of Elsevier 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States 525 B Street, Suite 1800, San Diego, CA 92101-4495, United States The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom 125 London Wall, London, EC2Y 5AS, United Kingdom First edition 2017 Copyright © 2017 Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. ISBN: 978-0-12-812091-0 ISSN: 1076-5670 For information on all Academic Press publications visit our website at https://www.elsevier.com/books-and-journals

Publisher: Zoe Kruze Acquisition Editor: Poppy Garraway Editorial Project Manager: Shellie Bryant Production Project Manager: Magesh Kumar Mahalingam Cover Designer: Greg Harris Typeset by SPi Global, India

CONTRIBUTORS Roman S. Ablizen Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, Russia Sergei S. Alimpiev Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, Russia Stephan Boehm Bruker Nano GmbH, Berlin, Germany Eric G.T. Bosch FEI Company, Eindhoven, The Netherlands Dmitry Grinfeld Thermo Fisher Scientific (Bremen) GmbH, Bremen, Germany Michael Haschke Eggersdorf, Germany Mathieu Kociak Laboratoire de Physique des Solides, UMR 8502 CNRS and Universite Paris-Sud, Orsay, France Igor A. Kopaev Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, Russia Ivan Lazic FEI Company, Eindhoven, The Netherlands Mikhail A. Monastyrskiy Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, Russia Jie Ren School of Electronic and Information Engineering, Beihang University, Beijing, China Luiz H.G. Tizei Laboratoire de Physique des Solides, UMR 8502 CNRS and Universite Paris-Sud, Orsay, France Andrei A. Trubitsyn Ryazan State Radio Engineering University, Ryazan, Russia Zulin Wang School of Electronic and Information Engineering, Beihang University, Beijing, China Mai Xu School of Electronic and Information Engineering, Beihang University, Beijing, China

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PREFACE An account by M. Haschke and S. Boehm of micro-X-ray fluorescence (μ-XRF) opens this latest volume. This has become a useful technique in recent years with the arrival of X-ray optical systems capable of concentrating a small spot on a target. The authors first discuss the differences between μ-XRF and energy-dispersive spectrometry after which they describe the design of suitable X-ray sources. They then tell us how measurements are performed in practice and conclude with a selection of applications. Coulomb interactions between charged particles are a source of difficulty in many situations, ranging from multibeam sources and ultrafast electron microscopy to ion traps. The latter are the subject of the second chapter, by I.A. Kopaev, D. Grinfeld, M.A. Monastyrskiy, R.S. Ablizen, S.S. Alimpiev, and A.A. Trubitsyn (some of whom are no strangers to this series). Here, they describe a variational approach for simulating the distribution of charged particles in an ion trap, which has many merits compared with earlier attempts to solve this problem. A substantial chapter by I. Lazic and E.G.T. Bosch follows on the theory of image formation in the scanning transmission electron microscope. Although the subject has been examined in numerous articles and book chapters, there are still aspects that have not been thoroughly studied or simply neglected. In this long chapter, the authors reexamine the theory and give a very clear and convincing account of its many ramifications. We remain with the electron microscope in Chapter 4, in which L.H.G. Tizei and M. Kociak describe a new role for an old technique, cathodoluminescence imaging. This is now being employed in the scanning transmission electron microscope for the study of quantum nanooptics. The authors first describe the technique and the reasons for adopting it before turning to the interaction between electrons, photons, and the material target. They conclude with a description of some recent experimental work. I am sure that this lucid presentation of an unfamiliar area will be widely appreciated. The concluding chapter introduces us to a subject that has not been treated before in these pages. M. Xu, J. Ren, and Z. Wang introduce the notion of a Tower of Knowledge, a subject that greatly interested the late Maria Petrou, a regular contributor to these Advances. This belongs to the

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Preface

family of pattern recognition tasks, and M. Xu, J. Ren, and Z. Wang concentrate on component identification in images and on their identification. Let me conclude with thanks to all the contributors for sharing their knowledge with the readers of these Advances and for all the trouble they have taken to make their subjects accessible to a broad audience. PETER W. HAWKES

FUTURE CONTRIBUTIONS S. Ando Gradient operators and edge and corner detection J. Angulo Mathematical morphology for complex and quaternion-valued images A. Ashrafi Walsh functions and their applications D. Batchelor Soft x-ray microscopy E. Bayro Corrochano Quaternion wavelet transforms C. Beeli Structure and microscopy of quasicrystals C. Bobisch, R. M€ oller Ballistic electron microscopy F. Bociort Saddle-point methods in lens design K. Bredies Diffusion tensor imaging A. Broers A retrospective A. Cornejo Rodriguez, F. Granados Agustin Ronchigram quantification C. Edgcombe Electron phase plates J. Elorza Fuzzy operators R.G. Forbes Liquid metal ion sources P.L. Gai, E.D. Boyes Aberration-corrected environmental microscopy R. Herring, B. McMorran Electron vortex beams M.S. Isaacson Early STEM development

xi

xii K. Ishizuka Contrast transfer and crystal images K. Jensen, D. Shiffler, J. Luginsland Physics of field emission cold cathodes U. Kaiser The sub-A˚ngstr€ om low-voltage electron microcope project (SALVE) S.A. Khan Quantum methodologies in Maxwell optics O.L. Krivanek Aberration-corrected STEM M. Kroupa The Timepix detector and its applications B. Lencova´ Modern developments in electron optical calculations H. Lichte Developments in electron holography M. Matsuya Calculation of aberration coefficients using Lie algebra J.A. Monsoriu Fractal zone plates L. Muray Miniature electron optics and applications M.A. O’Keefe Electron image simulation V. Ortalan Ultrafast electron microscopy D. Paganin, T. Gureyev, K. Pavlov Intensity-linear methods in inverse imaging N. Papamarkos, A. Kesidis The inverse Hough transform H. Qin Swarm optimization and lens design Q. Ramasse, R. Brydson The SuperSTEM laboratory B. Rieger, A.J. Koster Image formation in cryo-electron microscopy P. Rocca, M. Donelli Imaging of dielectric objects

Future Contributions

Future Contributions

J. Rodenburg Lensless imaging J. Rouse, H.-n. Liu, E. Munro The role of differential algebra in electron optics J. Sa´nchez Fisher vector encoding for the classification of natural images P. Santi Light sheet fluorescence microscopy R. Shimizu, T. Ikuta, Y. Takai Defocus image modulation processing in real time T. Soma Focus-deflection systems and their applications I.J. Taneja Inequalities and information measures J. Valdes Recent developments concerning the Syste`me International (SI) J. van de Gronde, J.B.T.M. Roerdink Modern non-scalar morphology

xiii

CHAPTER ONE

Micro-XRF in Scanning Electron Microscopes Michael Haschke*,1, Stephan Boehm† *Eggersdorf, Germany † Bruker Nano GmbH, Berlin, Germany 1 Corresponding author: e-mail address: [email protected]

Contents 1. Introduction 2. Differences and Synergies of SEM-EDS and μ-XRF 2.1 Spot Size and Information Depth 2.2 Elemental Range and Limits of Detection 2.3 Spectral Background and Peak-to-Background Ratio 2.4 Sample Handling 2.5 Synergetic Effects on Spectra Evaluation 3. Design of an Microspot X-Ray Source for SEM 3.1 General Requirements 3.2 Excitation Unit 3.3 X-Ray Optics 3.4 Filters in the Primary Beam 3.5 Market Situation 4. Performing a Measurement 4.1 Sample Presentation in the SEM 4.2 Measurement Conditions 5. Applications 5.1 Trace Analysis 5.2 Accuracy of Analysis 5.3 Analysis of Light Elements 5.4 Coating Analysis 5.5 Distribution Analysis 6. Summary References

Advances in Imaging and Electron Physics, Volume 199 ISSN 1076-5670 http://dx.doi.org/10.1016/bs.aiep.2017.01.001

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2017 Elsevier Inc. All rights reserved.

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Michael Haschke and Stephan Boehm

1. INTRODUCTION Elemental composition determines or influences macroscopic properties like mechanic behavior (for example, hardness, elasticity, weight), electrical properties (for example, resistance), or chemical properties (for example, corrosion resistance). Therefore, it is necessary to control the elemental composition. For that purpose, several analytical methods are available, including wet chemical methods, and also spectroscopic methods like atomic absorption (AAS) (Cammann, 2000; Skoog & Leary, 1996; W€ unsch, 1976), optical emission (OES) (Slickers, 1992), inductive coupled plasma (ICP) (Cammann, 2000; N€ olte, 2002; Skoog & Leary, 1996), mass spectrometry (MS) (Nelms, 2005; Taylor, 2001), and X-ray spectroscopy (XRF) (Beckhoff, Kanngießer, Langhoff, Wedell, & Wolff, 2006; Br€ ummer, 1977; Erhardt, 1981; Hahn-Weinheimer, Hirner, & Weber-Diefenbach, 1995). All of these methods have advantages as well as drawbacks. AAS is very sensitive for traces, but the dynamic range is limited and typically it is a monoelement method. OES has a high sensitivity, but the dynamic range is also limited and the sample surface is damaged by the excitation with an arc. ICP has high sensitivity and is a multielement method, but the samples have to be prepared as a solution. MS also is extremely sensitive but requires a special excitation mode. XRF can handle a large range of concentrations and is a multielement method but its sensitivity is limited. All of these methods require a homogeneous sample, but the mentioned macroscopic properties depend on the structure and distribution of different components and materials. These nonhomogeneities can be both a lateral distribution and also perpendicular to the sample surface, i.e., as layer structures. The examination of such elemental distributions of nonhomogeneous materials requires position-sensitive analytical methods. Very well-known examples of nonhomogeneous materials are microelectronic circuitries or micromechanical tools. They are manufactured as highly structured materials, with structure sizes down into the μm or even the nm range. Also for other industries like automotive, machining, and consumer electronics the parts become smaller and smaller. Very often they have to be analyzed without preparation because, in particular, for failure analysis the samples have to be analyzed directly; sample preparation can destroy not only the part but also the failure. For that purpose analytical methods are required that can determine the elemental composition for small sample areas on irregularly shaped samples and if possible also for thin layers on the sample.

Micro-XRF in Scanning Electron Microscopes

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One well-established analytical method with a high spatial resolution are scanning electron microscopes equipped with an energy-dispersive X-ray spectrometer (SEM-EDS). This combines the imaging function of an SEM with the analytical function of an X-ray spectrometer. In that case the electrons of the electron beam in the SEM are not only scattered to create a surface picture of the specimen, but they also excite the sample for the emission of X-rays. This radiation can be analyzed with the X-ray spectrometer. The emitted radiation contains information about qualitative and quantitative composition of the excited part of the sample. This volume is determined by the diameter of the electron beam that can go down to the sub-μm range and the penetration depth of electrons into the material that is in the range of a few μm. The combination of imaging with elemental analysis is a powerful tool for characterization of nonhomogeneous material. Therefore, most of electron microscopes are equipped with EDS systems. However, the excitation of X-ray fluorescence with electrons has some disadvantages. The incident electrons do not only excite characteristic radiation but also generate a relatively high spectral background, limiting the sensitivity. Another limitation results from the limited excitation probability for elements with higher atomic number. Higher sensitivity for elemental analysis is possible in case of excitation with X-rays, but X-rays cannot be focused very well. Typical analyzed areas in conventional X-ray spectrometry are in the cm range and the information depth is determined by the absorption of characteristic radiation in the material of the sample. This is significantly less for electrons, and therefore, information depths are smaller for electron excitation. However, this excitation has a significant reduced spectral background, and therefore, it is possible to improve the sensitivity for traces by factors up to 100, in particular for heavier elements. The availability of modern X-ray optics allows the concentration of the exciting X-ray beam to small spots. These optics capture the X-rays from a source like a tube and focus them on the sample. In that way, it is possible to have both XRF analysis with spatial resolution—less than with electron excitation but sufficient to solve many analytical problems—and high sensitivity for trace analysis. This method is called micro-X-ray fluorescence (μ-XRF) (Haschke, 2014; Janssens, Adams, & Rindby, 2000) and was introduced in the middle of the 90th of last century with stand-alone instruments. For focusing of the excitation beam, different types of optics are available. Because typically a wide range of elements have to be analyzed, a continuous excitation spectrum is preferred. This can be generated in a small spot only by capillary optics. In that case, a large solid angle of the

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Michael Haschke and Stephan Boehm

tube radiation will be captured by multiple internal total reflection concentrated to the sample. Spot sizes down to few 10 μm are possible. Other optics like Bragg mirrors can also be used for focusing; however, they reflect only one energy and can therefore be used only for the analysis of a very limited elemental range. If a microspot X-ray source is installed on an SEM, several interesting analytical opportunities will be opened. In that case, the already available X-ray detector of the EDS system can be used for the detection of fluorescence radiation excited by the microspot source. The excitation with X-rays offers some advantages over the excitation with electrons. The higher sensitivity of X-ray fluorescence is only one of them. The larger penetration depth offers the possibility for coating analysis; thicker coatings than with EPMA and even multiple coatings can be analyzed. In addition, sample preparation is easier for X-ray excitation because the sample does not need to be electrically conductive. Additionally the stress of the sample is smaller caused by the reduced absorption of radiation and, therefore, reduced thermal stress of the sample. The main advantage is the possibility to iterate in between the results of both excitation methods for a better quantification result with regard to accuracy and complete material characterization. This chapter starts with a detailed discussion of the differences of the excitation of X-ray fluorescence with electrons and X-rays, describes the design and use of a μ-XRF excitation unit for SEM, and gives an overview of the quantification procedures for both excitation modes and the iteration in between both methods for a more accurate quantification. Finally, several examples for the application of this combination of analytical methods for the material characterization are demonstrated.

2. DIFFERENCES AND SYNERGIES OF SEM-EDS AND μ-XRF Excitations either with electrons or X-rays generate fluorescence radiation of the irradiated material. Their detection is performed with energy-dispersive detectors, nowadays mostly with silicon drift detectors. Signal collection and spectra presentation are identical, but quantification is different. However, there are some further important differences with regard to the analytical performance. These differences are summarized in Table 1.

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Micro-XRF in Scanning Electron Microscopes

Table 1 Differences Between Both Analytical Methods Parameter SEM μ-XRF

Analyzed volume

∅ and information depth: few ∅: 20–30 μm Information depth: few μm to μm, depending mainly on few mm, depending on electron energy analyzed element and matrix

Detectable elements

All with higher atomic number All with higher atomic number than 4 (beryllium) than 11 (sodium)

Concentration Approx. 1000 μg/g to 100% range

50 μg/g to 100%, depending on the analyzed element

Spectral background

Generated by continuous bremsstrahlung by electron excitation (first-order effect)

Generated by scattered tube radiation on the sample into the detector (second-order effect)

Sample preparation

Sample needs to be electrical conductive

Electrical conductivity not required

Sample stress by measurement

Heating due to absorbed electrons

Negligible

Quantification Standard based or standard less

Standard based or standard less

The different excitation modes have a few synergetic effects, in particular for the characterization of the investigated material mainly caused by the different detected elemental range and information depth. The reason for the differences and the opportunities for synergetic effects are discussed in detail in the following sections.

2.1 Spot Size and Information Depth The electron beam of an SEM can be focused down into the sub-μm range. But the analyzed volume is larger due to the scattering of electrons in the sample. The generated X-rays can penetrate deeper into the sample and generate secondary fluorescence. Therefore, the diameter of the analyzed volume is always larger than the diameter of the exciting electron beam and depends on the accelerating voltage. Typically it is in the range of few μm. The electrons will be stopped very rapidly in the material. Therefore, the information depth is in the range of only few μm and depends also mainly on the electron energy. This is demonstrated with Monte Carlo simulations for the positions of excited atoms as shown in Fig. 1A. Together with the secondary excited radiation they are emitted from a pear-shaped

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Michael Haschke and Stephan Boehm

B

X-rays characteristic and bremsstrahlung

Incident electrons with energy E0 Secondary electrons backscattered

Penetration depth Secondary fluorescence

Electron paths in Au for 30 keV

Excitation volume

Fig. 1 (A) Monte Carlo calculations for the positions of excited electrons. (B) Analyzed volume for electron excitation.

volume that contributes to the fluorescence signal. The volume segments of the different interactions which contribute to the excitation are shown in Fig. 1B. The radiation for X-ray excitation is generated by an X-ray tube, and this radiation is emitted divergently. In conventional X-ray spectrometers the beam is collimated to diameters between 20 and 40 mm. For μ-XRF smaller analyzed areas are required. Collimators have a too small captured solid angle of tube radiation; consequently the excitation intensity is low. Therefore, two possibilities for enhancing the excitation intensity are used: • The tube target can be positioned as close as possible to the sample. This is possible with transmission target tubes where the anode is close to the sample. There are special tubes available with the target at the end of a capillary. In these tubes the anode is at ground potential and the beam size can be defined by an small collimator—down to approx. 0.5 mm. • A large solid angle of tube radiation can also be captured by X-ray optics and then concentrated to the sample. In that case a high amount of tube radiation can be used for the sample excitation and spot sizes down to less than 20 μm are possible. Typically reflection is used for influencing the direction of X-rays. For optics both Bragg reflection and total reflection are possible. In the case of Bragg reflection only one energy of tube radiation is reflected in one direction. Typically the optics are designed for the reflection of the characteristic line of the anode material. But that means only elements with an absorption edge energy in a range of approx. 5 keV less than the

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Micro-XRF in Scanning Electron Microscopes

fluorescence line of the tube will be sufficiently excited. Curved or even double-curved crystals or synthetic multilayers are used for these optics. The curvature depends on the reflected energy which is necessary for focusing the divergent tube radiation. This bending also limits the captured solid angle of radiation. Further, it has to be considered that these optics are imaging systems. That means the spot size depends on the source size, i.e., the spot size on the tube. In case of total reflection the captured angle is determined by the critical angle of total reflection. This angle is very small but can be enlarged by using multiple reflection areas. This is the basic concept of polycapillary optics where thousands of glass capillaries with diameters down to 2 μm are arranged to a monolithic piece as shown in Fig. 2A. Every single capillary changes its thickness from thin to thick and again to thin; the same changes then are valid for the complete monolithic block as shown in Fig. 2B. All capillaries look to the source and capture the tube radiation from a small area. By multiple internal total reflection on the glass the direction of the beam in every capillary is changed. The radiation leaving the optic will then be concentrated at a spot with diameters down to few 10 μm. The advantage of these optics is that the complete spectrum will be propagated through the optic. The tube spectrum will be slightly changed, but all energies 8 mm. The contribution from the inner diameter of a single capillary has to be considered only for working distances in the range of