chapter 3 - electron energy loss spectroscopy in the electron … aiep... · 2019-07-16 ·...

CHAPTER THREE

Electron energy loss spectroscopyin the electron microscope✩

Christian ColliexLaboratoire de Physique des Solides, Université Paris-Sud, Orsay, Francee-mail address: [email protected]

Contents

1. Introduction 1882. Fundamentals of inelastic scattering 190

2.1 General instrumental considerations 1902.2 Some useful definitions 1922.3 The physics of elementary excitations 197

3. The low-energy loss region: plasmons and interband transitions 2053.1 Energy dependence 2063.2 Angular dependence 214

4. High-energy loss region: inner shell excitations 2184.1 Bethe theory for inelastic scattering by an isolated atom 2194.2 Fine structures due to various solid-state effects 2354.3 Some problems in the intermediate energy loss domain 249

5. Developments in instrumentation 2555.1 Classification of various systems 2565.2 The scanning transmission microscope 2575.3 Spectrometer design and coupling 2585.4 Detection unit 2665.5 Data acquisition and processing 270

6. EELS as a microanalytical tool 2716.1 Qualitative microanalysis 2726.2 Quantitative microanalysis 2766.3 Detection limits 2846.4 Environmental information 2886.5 Chemical mapping with energy filtered images 289

7. Miscellaneous 2937.1 Electron energy loss spectroscopy in high voltage microscopy 2937.2 Energy filtered images 2957.3 Energy losses on surfaces at glancing incidence 296

✩ Reprinted from Advances in Optical and Electron Microscopy, Volume 9, R. Barer andV. E. Cosslett (Eds.), Academic Press, London, New York, 1984.

Advances in Imaging and Electron Physics, Volume 211ISSN 1076-5670https://doi.org/10.1016/bs.aiep.2019.04.002

Copyright © 2019 Elsevier Inc.All rights reserved.

187

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https://doi.org/10.1016/bs.aiep.2019.04.002

188 Christian Colliex

Acknowledgements 297Post scriptum 297References 298Further reading 304

1. Introduction

Electron Energy Loss Spectroscopy (EELS) is now a common methodto investigate the spectrum of excitations in a solid. It reflects the responseof the electron population of the specimen under the impact of a primarybeam of monoenergetic electrons. All the available information is obtainedby an analysis of the angular and energy distributions of the scattered elec-trons. Transmission through thin films is mostly used in experiments withfast electrons of a few 10s of keV and more. On the other hand, electronreflection on solid surfaces of massive specimens is generally studied withlow-energy electrons, though there is nowadays an increased number of sit-uations departing from this overall classification. A very complete review ofthe present state of this technique, emphasizing the collective behaviour ofthe valence electrons in the bulk as well as on the surface, has recently beenwritten by Raether (1980). It contains all the useful information which hasbeen collected by this group in Hamburg together with a detailed set ofexperimental and theoretical references for many substances. It is an im-portant source of knowledge for everybody who wants to understand thephysical meaning of an energy loss spectrum, especially in the first 50 eVrange (“low-energy loss domain”).

However, several fields of interest are not convincingly covered by thatreview. It is the goal of the present paper to discuss the specificity and theusefulness of EELS carried out in the general environment of an electronmicroscope, as part of the new generation of high performance instrumentsgenerally designated “analytical electron microscopes”. The tendency is tocombine, within the same apparatus the possibilities of visualizing witha high spatial resolution (typically 0.3 to 0.4 nm) the topography andstructure of the specimen prepared as a foil less than a few hundreds ofnanometres thick, and of characterizing its electronic and chemical proper-ties with a nearly equivalent level of spatial definition. EELS has become inthis context an essential microanalytical tool, in which the elemental com-position of the specimen is deduced from the characteristic atomic featuresin the high-energy part of the loss spectrum. The second aspect of thiscontribution is therefore to emphasize the specific information conveyed

Electron energy loss spectroscopy in the electron microscope 189

in the core-loss signals, as a complementary technique to other deep-levelspectroscopies in the energy range from 100 eV to a few 1000 eV. A lastpurpose of this paper is to update a topic which has been covered in anearly volume of this series by Metherell (1971) under the title: “Energyanalysing and energy selecting electron microscopes”. This author reviewedthe principle and design of several energy analysing and selecting devicesand illustrated their potentialities with examples concerning the plasmoncontribution in image formation and its use for chemical analysis. At thattime no reference to core-loss signals was given.

The excitation of atomic levels had actually been recorded for thefirst time by Ruthemann (1942) and Hillier and Baker (1944) proposed,after a more detailed analysis of the K-edges in carbon, nitrogen andoxygen, to use them for chemical analysis. However, it was necessary towait at least two decades for this idea to be reconsidered. Some prelimi-nary measurements by Watanabe (1964) on the L2−3 edge of aluminiumanticipated the more systematic work, which has been devoted to core-loss spectra by Wittry, Ferrier, and Cosslett (1969), Colliex and Jouffrey(1970a, 1970b, 1972), and Isaacson (1972). These authors used very differ-ent types of instrumentation: two groups had fixed a simple magnetic spec-trometer below the column of a conventional microscope (Wittry, 1969)or of a dedicated STEM (Crewe, Isaacson, & Johnson, 1971). The Orsaygroup had adapted a mirror-prism device due to Castaing and Henry (1962)for the recording of some important edges located between 50 and 500 eV.

This was really the starting point of the revival of EELS as a micro-analytical tool, because the use of plasmon lines had been of limited success.These collective excitations probe the average density of conduction elec-trons and the related energy loss does not constitute an accurate way ofdiscriminating various elements. Apart from the pioneering work of ElHili (1966) concerning some well-defined aluminium based alloys, onecan find an evaluation of the possibilities of this technique in Williamsand Edington (1976). During the seventies, the number of papers deal-ing with electron energy loss spectroscopy in the electron microscopehas continuously increased and several authors, apart from those alreadymentioned, have greatly contributed to this development. Egerton has es-tablished the first systematic rules governing the quantitation of core-lossspectra (1975, 1978) while two more general papers due to Isaacson andJohnson (1975) and Colliex, Cosslett, Leapman, and Trebbia (1976) es-tablished the general frame in which EELS had to be considered for thedevelopment of a new and powerful analytical tool. Since then, EELS has


become a general subject of contributions and discussions at the differentsuccessive conferences and workshops dealing with the progress in electronmicroscopy. For instance, during the preparation of this manuscript, I havecounted up to 51 papers concerning various aspects of EELS, published inthe issues of Ultramicroscopy for the period 1976–1982. It is out of myscope to quote all the reviews dedicated to this subject in the proceedingsof the international conferences in Toronto (1978), The Hague (1980),Hamburg (1982) and of the successive SEM, EMSA, EMAG. . . meetings.Several books also contain well developed chapters on various aspects ofthis subject, among which a subjective choice consists in pointing out thewell-documented papers due to Joy, Johnson, Maher, and Silcox in “Intro-duction to Analytical Electron Microscopy” (Hren, Goldstein, & Joy, 1979).

Among this profusion of literature which, apart from its historical in-terest, provides the general framework for the instrumental, physical andtheoretical use and comprehension of EELS, the aim of the present text isto give a critical overview of the present and future state of the technique.

Things being what they are, I shall mainly illustrate it by the work doneby my colleagues and myself in Orsay.

2. Fundamentals of inelastic scattering

2.1 General instrumental considerationsIn the electron microscope, the quasimonochromatic beam of electrons ofprimary energy E0 interacts with the specimen so that most of the outgo-ing electrons have suffered changes in direction and in energy. The terminelastic event with an energy loss �E is used when the measured changein energy (�E) is larger than the smallest detectable one; in most practi-cal spectrometers, this lower limit is set by the width of the primary beamat about 0.3 eV when one uses a field emission gun and at about 1 eVwith a standard thermionic gun. The distribution in momentum q (or an-gular change θ) and energy �E of the transmitted (or reflected) electronscharacterizes the scattering properties of the target and reveals its static anddynamical behaviour. Moreover in the context of the electron microscope,a micro-analytical use of the inelastic electrons consists in recording thecurrent I(r, θ,�E) transmitted at a point r on the specimen, in the direc-tion θ and with an energy loss �E. Such a measurement is achievable bythe introduction of a device (energy loss spectrometer) at some level in theelectron microscope column. Because of evident considerations about themagnitude of the recorded signal and its statistical noise, it is not possible


simultaneously to reduce the windows in position, angle and energy defin-ing the experimental conditions. One of these three parameters has to bechosen for integration and another for selection. This choice gives rise tothe following formal classification:

Integrationparameter

Selectionparameter

Results Couplingmode

Working mode ofthe spectrometer

1 θ r Ir(�E)

SpectrumImage Analyser

2 r θ Iθ (�E)

SpectrumDiffraction Analyser

3 θ �E I�E(r)Filteredimage

Image Filter

4 r �E I�E(θ)

Filtereddiffractionpattern

Diffraction Filter

The following comments can be made.(a) In the analysing modes of the spectrometer (1 and 2), the results are

displayed as a spectrum, that is a distribution of intensity as a functionof the energy-loss scale—or practically, for digitally recorded data, asa histogram of number of counts in successive channels.In the filtering modes (3 and 4), the results consist of a bidimen-sional distribution of intensity; this distribution requires more storageand display capability than is required for the analysing modes. Thesimplest such capability is still the photographic plate. For the acqui-sition of these bidimensional pictures, one distinguishes two types ofEM configuration: CTEM and STEM. In the first case, the acquisi-tion is simultaneous over all picture elements (pixels), while it is timesequential, governed by a scan generator, in the second case.

(b) For microanalytical applications, image coupling modes are most use-ful. A local analysis is first recorded (1) and it reveals the main con-tributions in the energy loss spectrum. The filtered image (3) showsa map of the distribution of an element over an extended area of thespecimen, once a characteristic elemental information has been se-lected in the spectrum.

Fig. 1 defines the general parameters of an experimental device for en-ergy loss microanalysis in transmission geometry. The area localization canbe achieved either by focusing the exciting beam (microprobe method) or


Figure 1 Definition of the general experimental parameters for an EELS measurement.Three selection apertures (or slits) determine the selection in area, angle and energy.

Figure 2 The parameters in energy and momentum involved in an inelastic scatteringevent.

by a selection area method—shown in the drawing. Apertures are thereforeused for area selection (in r), angular collection (in θ ) and energy selection(in �E). In this last case, it is generally a slit located after the spectrometerand the spectrum is time sequentially scanned in front of it. We shall discusslater more recent possibilities of simultaneous acquisition of the spectrumwith an array of detectors.

2.2 Some useful definitionsIn the theory of collisions the scattering of a primary particle in the initialstate energy E0, wave vector k0 by a potential centre generates an outgoingparticle in the final state (energy E0 − �E, wave vector kn). Such a pro-cess is schematically presented in Fig. 2. The scattering centre itself (atom,molecule, solid) suffers a change in energy—it comes to an excited state of


energy En = �E above its fundamental state—and receives a momentumtransfer q = k0 − kn.

The probability of such an event is generally expressed in terms of adifferential cross-section:

d2σ

d�.d(�E)

for an inelastic scattering event, within the angular solid angle d� aroundthe final wave vector, and with an energy loss �E.

The important problem of understanding electron energy loss data is tocorrelate the recorded spectra with calculations of cross-sections performedin a given model. It is obscured by several effects which must be clearlypointed out. An electron transmitted through a specimen suffers elastic aswell as inelastic collisions, so that there is a non-negligible probability ofmultiple scattering with m elastic events (without energy loss) and n inelasticevents of different types (and total energy loss �E = ∑n

j=1 �Ei). This effectbecomes more and more important as the specimen thickness increases.As a consequence, the recorded signal within given solid angle and energywindow is the result of a rather complex mixture of elastic processes whichare mainly responsible for large-angle scattering and of inelastic processeswhich do not all carry the same level of characteristic information.

A preliminary remark concerns the definition of the relevant angulardomain which is not a trivial factor. When a problem requires a refined arealocalization, it is more efficient to focus the whole primary beam currenton the object of interest rather than to lose a great fraction of it irradiatingother features of the image (as is the case in the selected area mode depictedin Fig. 1—generally used in the CTEM). As a consequence, focusing canonly be achieved by enlarging the angular width of the incident beam onthe specimen (STEM imaging mode) to a value (α0) which minimizes thecontributions of the aberrations of the probe-forming lens to the spot size.Fig. 3 illustrates the practical angular situations which can be imagined atthe specimen level: the simple one is the CTEM case with a parallel inci-dent beam of negligible divergence and the acceptance of inelastic electronsin a cone of half angle α. The differential cross-section has to be integratedfrom 0 to α. The configuration depicted in Fig. 3B would correspond toa STEM-ray diagram with a very small collector aperture; clearly, the samescattering events have to be considered, integrated from 0 to α0, but the to-tal recorded intensity is roughly scaled by an efficiency factor (α/α0)

2 whichmakes this situation one of very poor collection capability. To improve thesignal, one must increase the size of the collection aperture at least to the


Figure 3 Typical angular conditions for recording the inelastically scattered beam inCTEM and STEM.

order of the illumination angle (α � α0). In this case, the recorded signalcan be calculated as a convolution of the primary angular distribution withthe differential cross-section for the elementary process. This effect will beconsidered for the quantitation of chemical analysis in various EM geomet-rical configurations. Back to elementary processes, it is important to definefor every type of scattering event:• the partially integrated cross-section:

σ(α) =∫ α

0

dσ

d�2πθdθ

corresponding to the experimental geometrical conditions definedabove;

• the total cross-section:

σtot =∫ π

0

dσ

d�2πθdθ

representing the total probability of occurrence for this event;• the mean free path defined as:

1�

= Nσ

when N = number of scattering centres per unit volume.


The statistics governing multiple scattering obey the Poisson law, thatis:

Pn = 1n!

(t�

)n

exp

(− t

�

)

where Pn is the probability for an incoming electron to suffer n similarevents of mean free path �, during its way through a specimen of thick-ness t. This probabilistic approach has led Misell (1973) to classify thevarious populations of transmitted electrons as function of scattering an-gle and of transferred energy. A summation rule can be written:

I0 = Iun + Iel + Iin

where:

Iun = unscattered beam = e−t/�t

where the total mean free path is:

1�t

= 1�e

+ 1�i

Iel = elastic beam = e−t/�i(1 − e−t/�e

)where the first term expresses the fact that there is no inelastic scattering

Iin = inelastic component = 1 − e−t/�e

It represents, as illustrated in Fig. 4, the pure inelastic processes and allmultiple elastic–inelastic combinations with at least one inelastic collision.

Fig. 4 is actually the representation of this classification on a chart with|�q| and �E axes (Colliex, Mory, & Trebbia, 1980). It does not distin-guish between the different energy loss mechanisms. Moreover it considersthe fact that elastic scattering occurs generally at larger angles than inelas-tic scattering. One knows the results in the Thomas–Fermi atomic modelwhich assumes that atomic orbital electrons exponentially screen the nu-clear charge:

dσe

d�(θ) = 4Z2

a20q4

[1

1 + (1/q2a2)

]2

= 4Z2

a20

a4

(1 + a2q2)2

where

a0 = Bohr radius


Figure 4 Schematic representation on a (q,�E) chart of the various types of electronstransmitted through the specimen: unscattered, elastic and inelastic beams. The dashedareas correspond respectively to the zero-loss peak collected in an aperture α and to theinelastic electrons contained in an energy window � around the energy loss �E, alsocollected within an angle α.

a = screening parameter = 0.885a0Z− 13

q = k0θ

or

Ie(θ)

Ie(O)= θ4

0

(θ20 + θ2)2

where

θ0 = 1k0a

= 1.2 × 10−2Z13 (rad)

for primary electrons of 100 keV. Notice also that Ie(θ) varies as Z23 for

small angles of scattering (θ → 0) and as Z2 for large angles of scattering(θ → π).

Fig. 5 shows some typical curves of elastic scattering angular distri-butions. They are typically 20 mrad broad at half-height. In the case ofa crystalline sample, the elastic scattering peaks at those angles satisfyingBragg’s condition (2θB = λ/d) where d is the lattice spacing, the form ofthe elastic peak is different but its overall width remains of the same magni-tude. The importance of elastic scattering is that it prevents the collectionof all the inelastically scattered electrons within an angle α, because thereis a chance that the electrons undergo multiple elastic and inelastic events.


Figure 5 Amplitude and phase components of the atomic scattering factor: f = |f |eiχ ,for B and Th, as a function of θ . The elastic cross section dσe/d�(θ) = |f |2 (courtesy ofD. Dorignac, Thesis, Toulouse, 1978).

This effect has practical consequences for quantitative measurements: thezero-loss peak in an energy loss spectrum actually contains both the un-scattered contribution and the elastic scattering within the angular limit α

which has been used to record the spectrum. All inelastic cross-sectionshave therefore to be deduced from ratios between inelastic contributionsand zero-loss peaks recorded within the same angular conditions. It is thebest way to take into account the loss of inelastic information due to elasticscattering outside the spectrometer entrance aperture (see Fig. 4).

2.3 The physics of elementary excitations2.3.1 General classification

An energy loss spectrum reflects the response of the electron populationof the solid to the external disturbance introduced by the incident particletravelling through the specimen. It is governed by long range Coulombfields more or less screened by the electron gas. Apart from the zero-losspeak already mentioned with its various contributions (unscattered beam,Bragg scattering, phonon scattering. . . ) which cannot be resolved in a stan-dard instrument, it is customary to distinguish two important domainsin the loss spectrum. They are respectively the “low-energy loss region”(extending typically from 1 or 2 eV to 50 eV) which corresponds to the ex-citation of the conduction, valence and moderately bound electrons whoseenergy states lie in the first tens of eV below the Fermi level, and the“high-energy loss region” (from 50 or 100 eV to several thousand eV)which contains the information relating to atomic-type core levels. It is a


Figure 6 The different contributions recorded in an energy loss spectrum of 100 keVelectrons transmitted through a thick layer (�70 nm) of Dy2O3. (A) refers to the low-energy loss domain and contains the plasmon peak and the contribution of the 5pelectrons of the dysprosium atoms, (B), (C) and (D) refer to the excitation of 4d, 3d elec-trons of dysprosium and 1s electrons of oxygen (courtesy of L. Brown, M. Gasgnier, &C. Colliex, 1983, unpublished).

standard simplification to attribute a solid state character to the first typeof excitations and an atomic one to the second: the first category of elec-trons corresponds to more or less delocalized orbitals extending over severalatomic sites, while the second one is due to excitations from well localizedorbitals on one atomic site and refers to this specific element.

The general features of an energy loss spectrum are illustrated inFigs. 6 and 7 for two very different substances: a rare-earth oxide thinfilm (Dy2O3) and hematin deposited on a thin carbon layer (Ottensmeyer,Baaett-Jones, & Adamson-Sharp, 1981). These examples are representativeof typical specimens in materials science and in biology. The main featuresare however similar. They consist of a dominant contribution between 15and 40 eV due to the collective excitation of the nearly free electrons in thesystem. In the first case, it concerns the 6s,5d lanthanide electrons mixedwith the 2p oxygen electrons for the plasmon at 16 eV; the second mainpeak at 35 eV is more due to the 5p electrons of the rare-earth ion whichlie below the Fermi level. In the hematin spectrum, the broad and impor-tant maximum at 25 eV is due to the collective excitation of all valenceelectrons and is rather similar for every organic substance mainly composed


Figure 7 Energy loss spectrum of hematin deposited on carbon, showing the relativeimportance of the molecular and atomic features (see text) (courtesy of Ottensmeyer etal., 1981).

of carbon. There exists an extra small feature at 3 eV corresponding to theoptical absorption of the porphyrin ring of the heme molecule. Similarfine structures in the 5 to 10 eV energy loss range have been recorded byIsaacson (1972), Johnson (1972), Hainfeld and Isaacson (1978). . . in differ-ent nucleic acids: cytosine, thymine. . . . They are due to molecular energylevels and are subject to severe radiation damage. They have therefore beenstudied more especially to determine critical radiation doses for disruptingsome specific molecular bonds (see for instance, Isaacson, 1977).

The spectrum intensity decays gradually away at higher energies: thisis generally called the background contribution. This regular decrease is,however, interrupted by intensity steps corresponding to the excitation ofsuccessive core levels: N4−5 of dysprosium at 155 eV, oxygen K-edge at532 eV and the double line of M5 and M4 levels of dy at 1295 and 1332 eVfor the rare-earth oxide specimen. In the hematin spectrum, the K-edgesof carbon, nitrogen and oxygen at respectively 284 eV, 401 eV and 532eV are seen, followed by the L2−3 edge of iron at 707 eV, these last threesignals being of small amplitude superposed on the high intensity tail of thecarbon K-edge. These two examples clearly illustrate how the backgroundcan be due either to the high-energy tail of valence electron excitations orof core-loss excitations lying at lower energy.


2.3.2 The recovery of single loss spectraThe above examples have been recorded for rather thin specimens and theoccurrence of multiple inelastic scattering is greatly reduced. This situa-tion is however rather seldom realized in practical circumstances. A greaterthickness has several effects on the shape of an energy loss spectrum, asa consequence of plural scattering. The relative intensities of the variousregions are altered; auxiliary peaks occur in the low-loss part, at energieswhich are a multiple of the plasmon fundamental energy. The signal tobackground ratio is substantially reduced in the neighbourhood of coreedges and supplementary structures are also visible above these edges, ob-scuring the more characteristic near-edge and extended fine structures. Allthese trends can be observed on the spectra shown in Figs. 8 and 9.

The interpretation of these effects depends on the probability of pluralinelastic scattering which follows the already mentioned Poisson distribu-tion. It is necessary to estimate these various contributions due to plurallow loss (plasmon) and high loss (core level) excitations, to recover thesingle scattering distribution which is more representative of the specimenelectronic and chemical properties.

Several methods have been proposed for removing the effects of multi-ple scattering from a spectrum and a recent review of this subject has beenwritten by Swyt and Leapman (1982). Preliminary work has been stimu-lated by Misell and Jones (1969), and Daniels, von Festenberg, Raether, andZeppenfeld (1970) who showed that the experimental spectrum ES(�E)

is actually a sum of convolutions of single scattering events. Johnson andSpence (1974) write it as:

ES(�E) =∑n=0

Cn−1

n! In(�E)

where

In(�E) = I1(�E) ∗ In−1(�E)

is the contribution of electrons suffering n loss processes. The scaling pa-rameter C is shown to be equal to 1/I0 where I0 is the area under thezero-loss peak. Two approaches have been developed to solve the requireddeconvolution equation. A recurrence method has been used by Colliex,Gasgnier, and Trebbia (1976), which consists in subtracting from the exper-imental spectrum an estimate of the double scattering, yielding a partiallycorrected spectrum. Having “removed” double scattering, it is then possi-ble to go on to higher orders of inelastic scattering “removing” as many as


Figure 8 Plasmon peaks in silicon specimens of increasing thickness.


Figure 9 L2−3 edges in silicon foils of different thickness, after background subtraction;for thicker specimens, there is a decrease of the intensity rise at the edge itself and astrong effect of oscillator strengths towards higher energy losses preventing a clear de-tection of extended fine structures.

is required. Stephens (1981) has discussed the validity of this method andshown that it can give results accurate to better than 5%, provided that thewidth of the zero-loss peak is less than one-third the width of the plas-mon peak. However problems are associated with determining when thesolution has sufficiently converged.


Another way of attacking this problem is to achieve the deconvolutionin Fourier space, where:

ES = I0. exp SS

and

SS = logESI0

SS = Fourier transform of the single-loss spectrum

I0 = Fourier transform of the zero-loss peak

ES = Fourier transform of the experimental spectrum.

This approach takes into account the instrument response through the termI0, but an additional convolution by a narrow symmetrical peaked functionM is required to reduce the noise. A trade-off between resolution increaseand declining signal to noise ratio has to be found by making a suitablechoice of M . An important application of deconvolution schemes lies in therecovery of the single-scattering distribution in the region of core edges fora more accurate quantitation of the data. Swyt and Leapman (1982) haveused the total single-scattering formulation for spectra with low-energycore losses of interest or those for which background cannot be extrapo-lated. They propose a simplified approach, following Egerton and Whelan(1974), of deconvolution by the unbroadened low loss distribution whenthe pre-edge background can be subtracted. An example of this procedureis shown in Fig. 10. It clearly shows to what extent the analyst needs decon-volution for elemental composition measurements in thicker specimens; itis rather important when edges of interest are close in energy. Moreover, itis very useful for extraction of fine and extended structures (see EXELFSdiscussion later).

In this description, the energy loss spectra have been considered tobe a function of energy alone. The possible different angular distribu-tion for multiple and single scattering events has been ignored. Stephens(1980, 1981) has calculated a correction factor μ(�E1,�E2) for several val-ues of energy losses �E1 and �E2 to be deconvoluted, when a collectionaperture of semi-angle α is introduced. The results show that an accuracy ofbetter than 10% is readily obtained for collection angles >10 mrad, exceptwhen one of the energy losses is very large (�E2 � 2000 eV, for instance).


Figure 10 Effect of deconvolution by the low-energy loss distribution on the oxygen Kand chromium L2−3 edges for two specimens of different thickness. The backgroundhas been stripped and the edges normalized on the height of the oxygen edge. (A)refers to the original spectra and (B) to the spectra after deconvolution (courtesy of Swyt& Leapman, 1982).

Conventional deconvolution in energy is therefore sufficient for most situ-ations in which the characteristic inelastic angles involved are smaller thanthe angular acceptance of the spectrometer.

Let us mention finally that a quite complete method of deconvolutiontaking into account scattering angles as well as energy losses, has been de-rived by Batson (1976) to establish inelastic scattering data as function of |q|and �E with good accuracy. This approach, requiring a lot of computation


time, cannot for the moment be routinely used for analytical applicationsand only applies to rather specific problems.

The next two sections will cover in more detail the specific propertiesof both domains in the energy loss spectrum, emphasizing for each casethe important characteristics of the solid which they probe. A followingsection will discuss developments in instrumentation which have recentlyestablished EELS as a powerful microanalytical tool in the general electronmicroscope environment. This more specific aspect of the technique willbe the topic of a special section devoted to its actual possibilities and limits,together with some examples of microanalysis. Some various aspects willconstitute the content of the last section.

3. The low-energy loss region: plasmons and interbandtransitions

When one considers the interaction between the swift electron andthe quasi-free electron gas of the target, it is very convenient to considerits response through the variations of the electron density in a jellium-typemodel:

ρr =∑

i

eδ(r − ri)

whose Fourier components are:

ρq =∫

ρre−iq.rdr =∑

i

e−iq.ri

They describe the screening induced by the medium on the travelling testcharge and Nozieres and Pines (1958) have pointed out the usefulness ofthe concept of macroscopic dielectric constant ε(q,ω) to give an accountof this effect. Generally a scattering process involves a transition betweenan initial state |0k0〉 and a final state |nkn〉 where 0 and n correspond to thefundamental and excited states of the target while k0 and kn are the wavevectors of the incident and scattered electrons. Introducing the energy lossfunction:

Im1

ε(q,ω)= −4πe2

�q2

∑n

∣∣(ρq)0n∣∣2{δ(ω − ωn0) − δ(ω + ωn0)

}


the cross-section can be expressed as:

d2σ

d(�E).d�= 1

N(eπa0)2 · 1q2 · Im

(− 1

ε(q,ω)

)

where a0 is the Bohr radius and N the number of free electrons per unitvolume.

In the case of small-angle scattering,

q2 � k2(θ2 + θ2E

)where θE = �E/2E0 is the characteristic inelastic angle for an energy loss�E. Typically θE = 10−4 rad for �E = 20 eV and E0 = 100 kV. Anotherassumption is to identify:

Im(

− 1ε(q,ω)

)� −Im

(1

ε(0,ω)

)= −Im

1ε(ω)

so that it is possible to compare energy loss data with optical measurements.In this case, the cross-section can be separated into independent terms inangle and energy:

d2σ

d(�E).d�= 1

2π2E0a0N· 1θ2 + θ2

E· Im

(−1

ε

)

3.1 Energy dependenceIn the small-angle scattering limit, it is possible to determine the behaviourof the energy loss function Im(−1/ε) from an experimental spectrum:

Im[− 1

ε(�E)

]= 1

K· SS(�E)

Fα(�E)

where:• K is a constant depending on the specimen thickness,• SS is the single scattering profile at energy loss �E, after deconvolution

of multiple losses,

• Fα(�E) =∫ α

0

2πθdθ

θ2 + θ2E

= π log

(1 + α2

θ2E

)when the angular width of the primary beam is negligible.As a consequence of the causality principle, the knowledge of

Im[1/ε(�E)] over the whole (0 → ∞) �E-range enables one to calcu-


late Re[1/ε(�E)] by Kramers–Kronig transformation.

Re1

ε(�E)= 1 − 2

πPP

∫ ∞

0Im

[− 1

ε(�E′)

]· �E′

�E′ 2 − �E2 d(�E′)

where P.P. means the principal part of the integral. Further simple mathe-matics provide ε1(�E), ε2(�E),n(ω),μ(ω),R(ω) . . . all functions which areroutinely handled in optical measurements (refractive index, absorption co-efficient, reflexion coefficient for the optical frequency ω = �E/�).

It is important to point out the origin of the plasmon frequencies (orenergies). They correspond to roots of the equation ε(ωp) = 0 and con-sequently to maxima in the energy loss function. This is the reason whyinelastic electron scattering experiments have been so useful for studyingthese excitations.

Let us summarize the following important properties of the plasmons.In the ideal situation of the free electron gas, or jellium (electrically neutral,non-magnetic and homogeneous plasma) which is used as a simple approx-imation to describe the metallic state, two types of solution can be foundfor the propagation of waves (in the Maxwell equations):

ε = 0 and B = 0

This is a transverse electromagnetic wavewith a dispersion relationship:

ω2 = c2

εq2

This is a longitudinal wave with a characteristicfrequency ωp such that ε(ωp) = 0

In a gas of N free electrons/volume unit, one calculates:

ε(ω) = 1 − ω2p

ω2

where

ω2p = Ne2

ε0m(MKS units)


Figure 11 Model behaviour of the dielectric functions ε1, ε2 and −Im( 1ε ) in the Drude

model of an ideal jellium.

In the Drude model with a relaxation time τ :

ε(ω) = 1 − ω2p

ω(ω + i/τ)

and if ε = ε1 + iε2 then

ε1(ω) = 1 − ω2p

ω2(1 + 1/ω2τ 2)

ε2(ω) = ω2p

ωτ.ω2(1 + 1/ω2τ 2);

−Im1

ε(ω)= ε2

ε21 + ε2

2= ω2

p .(ω/τ)

(ω2 − ω2p)

2 + (ω/τ)2

The behaviour of these three functions ε1, ε2 and −Im(1/ε) are shownschematically in Fig. 11 for the Drude model. The most famous example isaluminium for which �ωp = 15 eV, �/τ � 0.5 eV and [−Im(1/ε)]max � 30.


In an assembly involving Nf free electrons and Nb bound electrons withan eigenfrequency ωn, the dielectric constant can be written as:

ε(ω) = 1 − ω2p

ω[ω + (i/τ)] + Nbe2

ε0m· 1ω2

n − ω2 + (iω/τ)

where

ω2p = Nf e2

ε0m

The root of the equation ε = 0 is then ωp such as: ω2p = ω2

p/(1+χb) involvinga change of plasma frequency with respect to the free electron gas situation.Two extreme cases can be discussed:

(1) Influence of interband transitions with eigenfrequencies ωn > ω andωp (for instance, deeper levels with eigenenergies just above the free elec-tron plasma energy)

ω2p � ω2

p − Nbe2

mε0

ω2p

ω2n

The plasma frequency is lowered, because the polarization of the boundelectrons reduces the restoring force on a displaced free electron.

(2) Influence of interband transitions with eigenfrequencies ωn < ω andωp:

ω2p = ω2

p + Nbe2

mε0

The plasma frequency of the conduction electrons is shifted towards higherenergies, because the bound electrons are now able to act as free electronswhich increase the restoring force.

In the case of an insulator with Nf = 0 and all Nb electrons bound witha frequency ωn (this model corresponds to an insulator with a gap �ωn):

ω2p = ω2

n + Nbe2

mε0

The corresponding dielectric and energy loss functions are schematized inFig. 12, for such a “plasmon” associated with an interband transition. Itcorresponds to a peak at a frequency ωρ beyond the value for which ε1 = 0.Raether describes this mode of pronounced longitudinal excitation as a“travelling polarization wave” such as shown in Fig. 13.


Figure 12 Model behaviour of the dielectric function ε1, ε2 and −Im( 1ε ) for a gas of

bound electrons.

Figure 13 Schematic presentation of the polarization waves in crystals with bound elec-trons. Above: longitudinal wave. Below: transverse wave (courtesy of Raether, 1980).

Let us illustrate these general considerations by a practical situation: yt-trium metal and yttrium sesquioxide (Y2O3), studied by Brousseau-Lahaye,Colliex, Frandon, Gasgnier, and Trebbia (1975) and Frandon (1979).

Yttrium (Fig. 14). The plasmon energy is measured as 12.8 eV and thesimplified formula for a free electron gas and three valence electrons peratom gives a theoretical value of 11.2 eV. The slight shift towards highervalues is probably due to the influence of a non-resolved interband transi-tion around 7 eV, involving d band electrons. Lynch, Olson, and Weaver(1975) analysed optical reflectivity spectra in the same energy region (5 to10 eV) which exaggerated this contribution; they deduced the existence ofa second low-energy plasmon: ε1 would become zero twice and two intense


Figure 14 Energy loss function (−Im 1ε ) and dielectric constants ε1 and ε2 extracted

from energy loss measurements on an yttrium thin foil (courtesy of Frandon, 1979).

energy loss peaks at about 6 and 12 eV were deduced from these opticalmeasurements. Our experiments show only one zero of ε1 for �E = 12 eV,which is in contradiction with the hypothesis of two distinct plasmons inthis transition metal. The second important contribution appearing as arather large, symmetric and intense peak at 35 eV, will be discussed laterafter the description of inner-shell excitations.

Yttrium sesquioxide (Fig. 15). The important modifications with respectto metallic spectra concern the low-energy range below 20 eV while thestructures observed around 40 eV are rather similar to those recorded inthe yttrium case. It confirms the hypothesis that these latter peaks concernexcitation and rearrangement within the yttrium atoms. Y2O3 is an insu-lator with a band gap of 5.6 eV as measured by optical absorption. This isresponsible for the zero value of the loss function and of ε2 between 0 and�6 eV. There cannot be any excitation in this energy region. The peak inε2 at � 8 or 9 eV corresponds to the maximum of interband transitions.The peak in Im(−1/ε) at 15 eV is due to the plasmon type process; thedifference between the model curves shown in Fig. 12 and the real case


Figure 15 Energy loss function (−Im 1ε ) and dielectric constants ε1 and ε2 extracted

from energy loss measurements on a Y2O3 thin foil (courtesy of Frandon, 1979).

in Fig. 15 lies in the behaviour of ε1 which comes down to zero at about14 eV without crossing it.

Coming back to simple elements, the variation of the dominant vol-ume plasmon energy with atomic number is shown in Fig. 16, togetherwith some theoretical estimation within the free electron model. In thesecalculations, there exists some arbitrary decision concerning the number offree electrons per atom, particularly when one considers the contributionof the 3d-band electrons in the transition metals series. The major con-clusion of this compilation of results is that the plasmon energy roughlyreflects the average density of pseudofree electrons in the material and thatit is not a very sensitive tool to probe the chemical properties of the spec-imens.

There exists, however, a situation in which these collective modes canprovide interesting information about electronic properties, with high spa-tial resolution: they exist not only in the volume of a plasma but also inits boundary. Longitudinal waves of the surface-charge density run along


Figure 16 Chart of the measured plasmon energies for the most important elements(Z = 3 to Z = 32) and comparison with the corresponding energies calculated in thefree electron model.

the surface as polarization waves, which can be coupled with electromag-netic fields. Radiative as well as non-radiative surface plasmons can thusbe excited by incident electrons, the first type when very weak momen-tum is transferred to the surface. The probability of surface excitation hasgenerally been studied in the geometry corresponding to electrons crossingthe surface at normal incidence. In this case, one shows two effects, thefirst being the appearance of an extra peak when −Im[1/(1 + ε(ω))] = 0(the true surface term) and the second being a contribution to the volumeterm with an opposite sign. These specific surface terms are less and lessimportant as one uses larger collection apertures (the angular dependenceof the surface term behaves as θ/(θ2 + θ2

E)2 exhibiting a maximum of inten-sity at θE/

√3 and decreasing as θ−3 at larger angles), and thicker specimens

(the surface contribution does not depend on thickness while the volumeterm increases as t). Let us point out that in the jellium case the surfaceplasmon energy root of ε(ωs) = −1 corresponds to the well-known valueωs = ωp/

√2. When two media of dielectric constants εa and εb are joined,

this formula becomes:

ωs = ωp/√

(εa + εb)

This planar mode can be more suitably investigated in glancing incidencereflection experiments on clean surfaces, or more usefully in materials sci-


ence, on interfaces tilted parallel to the primary beam, see for instanceColliex, Krivanek, and Trebbia (1982).

Geometries have also been considered with non-planar interfaces forwhich different eigenfrequencies (the eigenvalue being an integer l) can beexcited. This situation concerns all kinds of problems in which a sphere ofradius r of a material of dielectric function ε(ω) is embedded in a dielectricmedium of ε0: the mode l = 1 has been detected in several experiments(for a review, see Raether, 1980, Chapter X). For a cavity in a metal, l = 1implies a surface mode ωs = ωp/

√3, which has been visualized for instance

in the filtered images of Henoc and Henry (1970).

3.2 Angular dependenceThe energy dependence has been discussed in terms of energy loss func-tion −Im1/ε, as dependent on energy alone. It is strictly valid in the limitof small scattering angles in which case the correspondence with opticalfunctions is straightforward: it essentially probes the direct vertical transi-tions between states of the same momentum (interband transitions) andthe collective response of the conduction electrons (plasmons). The angu-lar dependence of the inelastically scattered electrons is then governed bythe 1/q2 factor in the cross-section formula: there results a Lorentzian typedistribution

dσ(θ)

d�α

1θ2 + θ2

E

of full width at half maximum 2θE. For �E = 20eV and E0 = 100 keV, θE =10−4 rad which is rather small compared to the typical width θ0, alreadymentioned for the elastic angular distribution. It must however be pointedout (Egerton, 1976) that the smallness of this characteristic inelastic angledoes not totally reflect the quantitative behaviour of the inelastic angularwidth.

The total cross-section for an energy loss �E is obtained by integrationover the acceptance angle α. As a consequence, one easily calculates:

θ =∫ π

0θ.

dσ

d�d�

/∫ π

0

dσ

d�d� � 22θE, or

a mean inelastic scattering angle θ for which one half of the scatteringevents are concentrated in an angle θ < θ , that is:

∫ θ

0

dσ

d�d�

/∫ π

0

dσ

d�d� = 1

2⇒ θ � 10θE


These mean angles are an order of magnitude larger than θE itself, due tothe important tails of the Lorentzian distribution.

Similar arguments should as well be applied to the elastic angular dis-tribution when one wants to make quantitative comparison of the beamelastically scattered outside or within a given aperture, with respect to theprimary beam.

When the energy loss contains only one well-defined plasmon peak atenergy �Ep = �ωp, it is possible to describe in simple terms the behaviourof the energy loss function as a function of the transferred momentum �q(or the scattering angle θ � q/k0). There are two important results:

(a) Beyond a theoretical value of the wave vector, the critical wave vec-tor qc, collective excitations do not exist but only single electron-hole pairexcitations. Due to conservation equations, energy �ω and momentum �qcan be transferred to an individual electron if its state (ω, q) lies betweentwo curves:

�ωmax = �2

2m(q2 + 2qkF

)(A)

and

�ωmin = �2

2m(q2 − 2qkF

)(B)

(see Fig. 17). This continuum represents the spectrum of possible single-electron excitations. One of the solutions is the excitation of an electroninitially at rest, this is the “Compton” line (C), �ω = (�2/2m)q2. The decayof the plasmon of frequency ωp is only possible for q > qc such that:

�ωp = �2

2m(q2

c + 2qckF)

which is sometimes simplified as:

qc ∼ ωp

vFwhen qc � kF

vF is the Fermi velocity of the electron gas. Practically, one calculates in thefree electron gas model important parameters shown in Table 1.

(b) For q < qc, one also finds a small variation of ωp as a function of q.This q dependent plasmon peak position is obtained theoretically by in-troducing a q dependent ε into the loss function. The free electron casehas been discussed in the random phase approximation by Lindhard (1954),


Figure 17 Dispersion curve for the excitation of plasmon merges in the continuum ofindividual excitations for a critical wave vector qc.

Table 1Substance n (e−/atom) N e−/cm3 kF (Å−1) ��ωp (eV) qc (Å−1)Lithium 1 4.6 × 1022 1.11 8.0 0.7Beryllium 2 24.2 × 1022 1.93 18.4 1.0Aluminium 3 18.0 × 1022 1.74 15.8 0.9Silicon 4 19.9 × 1022 1.80 16.7 0.9

leading to a dispersion relationship for the plasmon:

�ωp(q) = �ωp(0) + �2

mαq2

where

α = 35

EF

�ωp(0)

This dispersion law has been tested in various substances, either polycrys-talline or monocrystalline and the results are in rather good agreement withthis simple model. Refinements have to be made to describe correctly thesituation when the plasmon curve merges into the electron-hole excitationcontinuum: the value of qc quoted in the table above has to be modifiedto take into account this better description of the plasmon dispersion. Forinstance qc in Al is shown to be of the order of 1.3 Å−1. More refined ex-periments have tested the dependence of the structure of the loss spectrumon the q direction. Theoretical improvement with respect to the Lindhardfree electron case must include the effect of the periodic potential of thelattice involving local field correction and band structure effects. If theseconsiderations are important for understanding the properties of plasmonsthey remain of limited quantitative importance for most applications in theelectron microscope.


Table 2Substance σp (cm−2) �p (nm)Lithium 7.6 × 10−19 286Beryllium 3.0 × 10−19 138Aluminium 3.3 × 10−19 159Silicon 3.3 × 10−19 152

The total cross-section for inelastic scattering by the valence electronscan be calculated by integration over the energy loss and the scatteringangle. In the case of a spectrum with a well-defined plasmon peak at energy�Ep = �ωp, the energy loss function is the limit, for τ → ∞, of the Drudecurve already mentioned, that is:

−Im1

ε(ω)= π

2ωp.δ(ω − ωp)

the integral of which is:∫ ∞

0−Im

1ε(ω)

d(�E) = π

2�ωp

The Dirac function in the energy loss allows one to calculate the angularintegral for a given θE value corresponding to �Ep/2E0, to an upper limitdefined by θc. The result is:

σp = θE

Na0log

(θc

θE

)

expressed in cm2 or Å2. The mean free path for plasmon excitation definedby

�pNσp = 1

is therefore

�p = 1Nσp

= a0

θE

(log

θc

θE

)−1

Numerical values for the substances already mentioned are summarized inTable 2. Values refer to a primary energy E0 = 100 keV and no relativisticcorrection is included in these estimations (see the modifications involved athigh energies by the relativistic effects in the last section). Numbers for thecross-section refer per free electron per atom, they have to be multiplied by


Figure 18 Schematic representation of a core-loss excitation within the band-structuremodel: an electron initially on an atomic inner-shell level |0〉 is promoted to a vacantstate |n〉 above the Fermi level.

the number of free electrons per atom. As a consequence, the cross-sectionper aluminium atom at 100 keV is 10−18 cm2.

4. High-energy loss region: inner shell excitations

Over the continuously decreasing background extending roughlyfrom 50 to a few thousand eV, characteristic contributions appear as moreor less sharp intensity steps. They correspond to ionization processes inwhich an electron initially in a well-defined atomic orbital is promoted toa vacant state above the Fermi level or in the continuum, through inter-action with an incident electron. The understanding of such an excitation,schematized in Fig. 18, requires a satisfactory knowledge of the initial andfinal states of the excited particle. If the former is truly atomic-like, thelatter is actually an electronic wave function in the solid. Consequently thefeatures observed near an ionization edge provide information at differentlevels of refinement:(a) The chemical composition of the specimen relates to the nature of the

involved edge. It is useful to discuss in a first approach its basic physicsas an atomic phenomenon.

(b) The valence state of the excited atom, and its average environmentis seen from a study of the near and extended structures above theedge. Such considerations require a more elaborate approach in termsof solid-state physics which will be developed in Section 4.2.


4.1 Bethe theory for inelastic scattering by an isolated atom1

The probability of excitation in the first Born approximation involves thematrix element of the Coulomb interaction potential between the incidentelectron and the atomic electrons, that is:

Vi =Z∑

j=1

e2

|r − rj|

between the initial state wave function |ψi〉 = |0,k〉 and |ψf 〉 = |n,kn〉 that ofthe final state (normalized per unit energy range in the continuum). Bothincident and scattered electrons are treated as plane waves.

∣∣〈ψf |Vi|ψi〉∣∣2 =

∣∣∣∣∣〈n|Z∑

j=1

e2

|r − rj| eiq.r|0〉

∣∣∣∣∣2

= 4πe2

q2

Z∑j=1

∣∣〈n|eiq.rj |0〉∣∣2

This expression is directly correlated to the Generalized Oscillator Strength(GOS), defined as:

f0n(q) = 2mω0n

�q2

∣∣∣∣〈n|∑

j

eiqrj |0〉∣∣∣∣2

for a transition between two discrete states |0〉 and |n〉.Practically, one refers to a specific transition between an initial state of

principal n and angular momentum l quantum numbers, and a final statewith continuum energy ε and angular momentum l′. The energy loss isrelated to ε by �E = ε − Enl where Enl is the binding energy of the initialstate with respect to the vacuum level in an atom (and is negative).

dfnl(�E, q)d(�E〉 = 2m�E

�2q2

∑l′

∣∣⟨ε, l′∣∣eiq.r

∣∣n, l⟩∣∣2

This generalized oscillator strength is an extension of the well-known op-tical oscillator strength to which it is identical in the q → 0 limit. Thisremark has some very important consequences. In the small-angle scatter-ing situation there is again identity between the oscillator strengths probed

1 For a more complete theoretical discussion, see Inokuti (1971).


by optical techniques (X-ray absorption for instance) and by EELS. More-over, cross-sections for inelastic scattering of fast electrons can be estimatedfrom photoabsorption data (Powell, 1976).

A three-dimensional plot of df (q,�E)/d(�E) in the coordinate system(q,�E) is known as the Bethe surface. As this surface embodies all the in-formation concerning the inelastic scattering of charged particles by atoms,many experimental investigations as well as theoretical calculations of theGOS have been performed in atomic and plasma physics. Following theoriginal work by Bethe (1933), numerous calculations of photo-ionizationcross-sections (Fano & Cooper, 1968; Manson, 1976) and of secondaryelectron ejection by charged particles (Inokuti, 1971) have contributed toour better knowledge of the intra-atomic effects involved in such process.Some of them have been adapted to typical electron microscopy situations(Leapman, 1978; Inokuti, 1978).

Coming back to the cross-section, it can be expressed as:

d2σ(θ,�E)

d(�E).d�= e4

E0.�E· 1θ2 + θ2

E· df (q,�E)

d(�E)

where q2 = k20(θ

2 + θ2E).

4.1.1 Angular distribution

In the small angle limit, one develops eiq.r = 1+ iq.r+· · · and the GOS canbe extrapolated into its small q limit:

q2.|x0n|2 = q2∣∣〈n|u.r|0〉∣∣2

where u is the unit vector in the q direction.The dipole matrix element is q-independent and:

d2σ(θ,�E)

d(�E)d�= 4

a20k

20|x0n|2. 1

θ2 + θ2E

The angular distribution behaves again as 1/(θ2 + θ2E) for any inelastic tran-

sition in an atomic collision.At large angles, deviations from this Lorentzian profile are introduced by

the q behaviour of the GOS. The best available computations for the mo-ment are due to Leapman, Rez, and Mayers (1980) in a Hartree Slater cen-tral field model. The initial state is a one-electron Herman–Skillman wavefunction and the final states are found by solving the radial Schrödinger


Figure 19 Computed GOS for the boron K-edge as a function of q (courtesy of Leapmanet al., 1980).

equation with the same central field for the continuum energies:

[�

2

2md2

dr2 − V (r) + ε − l′(l′ + 1)�2

2mr2

]φεl′(r) = 0

The results of their calculations for the excitation into the continuum fromthe 1s shell of boron are shown in Fig. 19. (The binding energy is 188 eVand energies on the curves refer to �E = ε + 188 eV.) For small ε, thecurves are peaked at q = 0 due to the dominance of dipole s → p tran-sitions. At larger ε, the optically forbidden channels become importantfor non-zero q with the occurrence of a clearly resolved Bethe ridge atε � 100 eV.

A useful simpler approach is due to Egerton (1979): a hydrogenic modelwith Zener screening constant is used to calculate GOS for K-shell ion-ization. The results are shown in a very convenient fashion for use in theelectron microscope context. Fig. 20 is the GOS for carbon K-excitation


Figure 20 The Bethe surface for K-shell ionization in carbon, calculated from the hydro-genic model (courtesy of Egerton, 1979).

as a function of �E and log(qa0)2. The individual curves in this figure qual-

itatively show the angular dependence of K-shell scattering, for differentamounts of energy loss. Just above the threshold value EK , this scattering isforward peaked whereas for large energy loss (several times EK ) the scatteredelectrons are concentrated around an angle given by

(qa0)2 = �E

R

where

a0 = �2

me2 = Bohr radius = 0.0529 nm

R = me4

2�2 = Rydberg constant = 13.6 eV


Let us notice that this angular value of the Bethe ridge corresponds to:

θa =(

�EE0

) 12

The limit is equivalent to the Compton line already mentioned in the caseof individual electron excitations for an electron primarily at rest. For ener-gies well above the typical binding energy, the same angular behaviour canbe predicted. Since the total angular distribution is weighted by the term1/(θ2 + θ2

E), it remains forward peaked but its width increases and a sec-ondary maximum can be detected for this specific Bethe ridge angle. Thisbehaviour has been detected for the first time in the study of the angularbehaviour of background electrons just below the occurrence of K-shellexcitations by Wittry et al. (1969). It has been more extensively studied byEgerton (1975) and Leapman and Cosslett (1977) in the same experimen-tal conditions. These results confirm the model that the origin of a greatproportion of background electrons in carbon at about 250 eV is due toexcitations of conduction electrons towards high-energy states in the con-tinuum. These electrons can reasonably be considered as free because theirbinding energy is small compared to the recoil energy which they get inthe collision.

More recently, Williams and Bourdillon (1982) used this effect to de-velop a new approach to Compton scattering, by studying the broadeningof this distribution around the Bethe ridge. Measurements are made at agiven scattering angle (of about 5 degrees). An important Compton profilecontribution peaks in the energy loss spectrum at about 1 keV. This spec-trum is converted to momentum space, and Fourier transformed to obtainthe reciprocal form factor B(r), which is the autocorrelation function ofthe ground state wave function. This technique of handling data to studyelectron momentum densities is directly developed from well establishedhigh energy photon scattering experiments.

4.1.2 Energy distribution

The number of electrons scattered as a result of an inner shell excitationinto angles less than α and with an energy loss �E can be expressed as anenergy differential cross-section dσα(�E)/d(�E). The hydrogenic modeldeveloped by Egerton predicts a saw-tooth profile, that is a steep edge atthe threshold energy followed by a regular decrease towards higher energies


obeying a model law:

dσα(�E)

d(�E)∝ �E−s

where s is the downward slope on a log–log plot. The value of s dependsconsiderably on α.

dσα(�E)

d(�E)=

∫ α

0

2πθ

θ2 + θ2ε

· df (θ,�E)

d(�E)dθ

For most of the commonly used angles of acceptance, the Bethe ridgedoes not come into account and a rapid examination of the set of curvesdisplayed in Fig. 20 shows that one can reasonably assume

df (θ,�E)

d(�E)= df (�E)

d(�E)

over the angular domain of integration. As a consequence, the only depen-dence on α is due to the factor

hα(�E) =∫ α

0

2πθdθ

θ2 + θ2E

= π log

(1 + α2

θ2E

)

This term measures the proportion of electrons inelastically scattered withan energy loss �E into a solid angle α. When α is very small, one checksthat hα(�E) ∝ �E−2 and for very large α,hα(�E) = constant. The depen-dence in �E is then determined by the shape of df (�E)/d(�E), whichaccording to Rau and Fano (1967), can be written as �E−γ . Altogether,the exact determination of γ defines the behaviour of the parameter s. Forγ = 3 which constitutes an average value, s varies between 4 for a largeangle α of collection and 6 for a very small one. This behaviour has beenexperimentally recorded for most K-edges.

This simple theory does not, however, apply to all observed edges andit is necessary to classify them as a function of the important following pa-rameters introduced in standard atomic text books. Z is the atomic numberof the element, n, l, j = l + s are the quantum numbers describing the sub-shell on which an electron has been excited. Selection rules for dipolarelectric transitions (valid at small angle scattering) determine the dominanttransitions to be observed:

�j = 0,±1

�l = ±1


As a consequence, only allowed transitions from occupied states towardsvacant states of correct symmetry lying above the zero level of energy canbe easily observed. An old spectroscopy notation is responsible for the gen-erally used symbols:

K excitation for 1 s electronsL1 excitation for 2 s electronsL2 excitation for 2 p 1

2electrons

L3 excitation for 2 p 32

electronsM1 excitation for 3 s electronsM2 excitation for 3 p 1

2electrons

M3 excitation for 3 p 32

electronsM4 excitation for 3 d 3

2electrons

M5 excitation for 3 d 52

electronsN1 excitation for 4 s electronsN2 excitation for 4 p 1

2electrons

N3 excitation for 4 p 32

electronsN4 excitation for 4 d 3

2electrons

N5 excitation for 4 d 52

electronsN6 excitation for 4 f 5

2electrons

N7 excitation for 4 f 72

electronsO1 excitation for 5 s electronsO2 excitation for 5 p 1

2electrons

O3 excitation for 5 p 32

electrons

Among these lines, only a few transitions can be practically recorded.They are tabulated in Table 3. For each pure element we point out theedges of interest in the energy range �30 eV to �2500 eV, together withthe energy position of the corresponding threshold and with a rough clas-sification into five categories for their shape. This classification can onlybe approximate and for several cases there may be some uncertainty in theattribution of this label. This classification, which omits the fine structurefound close to the edge, can be understood in terms of atomic description.Fig. 21 shows a schematical display of the following types of edgeshape:

(a) Means a saw-tooth profile, such as calculated in the hydrogenicmodel.

(b) Means a delayed edge (or a “sleeping whale” profile) and is a con-sequence of a relatively large transfer of the oscillator strength to higherenergies, due to the effective centrifugal barrier. This happens mainly for


Table 3Z Element Edge Position of edge (eV) Shape of edge1 H K 13, 6 a2 He K 24, 6 a3 Li K 54, 5 a4 Be K 111, 0 a5 B K 188 a6 C K 284 a7 N K 401 a8 O K 532 a9 F K 685 a10 Ne K 867 a11 Na K 1072 a12 Mg K 1305 a13 Al K 1560 a

L23 72 b14 Si K 1839 a

L23 99 b15 P K 2150 a

L23 136 b16 S K 2472 a

L23 165 b17 Cl L23 201 b18 A L23 245 a19 K L2 296 c

L3 293 cM23 �20 d

20 Ca L2 350 cL3 347 cM23 �25 d

21 Sc L2 406 cL3 402 cM23 ∼33 d

22 Ti L2 460 cL3 454 cM23 ∼36 d

23 V L2 520 cL3 513 cM23 ∼40 d

(continued on next page)


Table 3 (continued)Z Element Edge Position of edge (eV) Shape of edge24 Cr L2 584 c

L3 575 cM23 ∼45 d

25 Mn L2 651 cL3 640 cM23 49 a

26 Fe L2 720 cL3 707 cM23 54 a

27 Co L2 794 cL3 779 cM23 60 a

28 Ni L2 872 cL3 855 cM23 68 a

29 Cu L2 951 Poorly definedin metal betterin oxides

L3 931M23 74

30 Zn L23 1020 bM23 ∼87 Invisible

31 Ga L23 1120 bM23 ∼103 Very weak

32 Ge L23 1218 bM45 ∼30 d

33 Se L23 1435 bM45 57 e

35 Br L23 1550 bM45 70 e

36 Kr L23 1675 aM45 89 e

37 Rb L2 1864 cL3 1804 cM45 111 e

38 Sr L2 2007 cL3 1940 cM45 133 b

39 Y L2 2156 cL3 2080 cM45 160 bN23 ∼26 d



Table 3 (continued)Z Element Edge Position of edge (eV) Shape of edge40 Zr L2 2307 c

L3 2222 cM45 180 bN23 ∼32 d

41 Nb L2 2456 cL3 2370 cM45 205 bN23 ∼35 d

42 Mo L2 2625 cL3 2520 cM45 230 bN23 ∼35 d

43 Tc ?44 Ru M45 280 b

N23 ∼45 d45 Rh M45 308 b

N23 ∼48 d46 Pd M45 308 b

N23 ∼48 d47 Ag M45 ∼370 b

N23 ∼60 Very weak48 Cd M45 ∼405 b

N23 ∼65 Very weak49 In M45 ∼450 b

N23 ∼80 Very weak50 Sn M45 495 b

N23 ∼90 Very weak51 Sb M45 530 b

N45 ∼32 d52 Te M45 573 a

N45 ∼40 d53 I M45 620 a

N45 ∼50 Very weak54 Xe M45 675 a

N45 ∼65 b55 Cs M4 740 c

M5 725 cN45 ∼80 b

56 Ba M4 796 cM5 781 cN45 ∼90 b



Table 3 (continued)



Table 3 (continued)Z Element Edge Position of edge (eV) Shape of edge80 Hg M45 2300

N67 InvisibleO23

81 Tl M45 2400 aO45 �18 d

82 Pb M45 2500 aO45 ∼25 d

83 Bi M45 2600 aO45 ∼35 d

90 Th O45 85 d92 U O45 95 d

Figure 21 Schematic representation of the five main families of edge shape introducedin the classification of Table 3 (see text for discussion).

final states of large l′ quantum number. The continuum wave function seesan effective potential such as:

Veff = V (r) + l′(l′ + 1)�2

2mr2

in which the second term, the “centrifugal potential” dominates. The dif-ference between the energy of the maximum of the cross-section and thethreshold varies from typically 20 eV for the L23 edges for Mg, Al, Si. . . to100 eV for the same edges in Se, Br. . . .


(c) Applies generally to very clearly spin–orbit split levels which appearas narrow and intense peaks over the background. They have already beendesignated as “white lines” in the literature. This is a type of hydrogenictransition towards vacant bound states and the most famous examples are:• The L2–L3 edges in the first series of transition metals from Ca to Ni

(transition 2p → 3d). The experimental situation has been extensivelystudied by Leapman and Grunes (1980), Leapman, Grunes, and Fejes(1982).

• The L2–L3 edges in the second series of transition metals from Sr to Pd(transition 2p → 4d).

• The M4–M5 edges in Cs, Ba and lanthanides (transition 3d → 4f ).Results have been reported by Krivanek (1982) and they are presently beingsystematically investigated by Brown, Gasgnier, and Colliex.2

The variation of the L3/L2 or M5/M4 relative intensities can only be un-derstood by considering selection rules applying to the j quantum number.They do not reflect only the relative population between both initial states,that is (2j + 1) 3

2/(2j + 1) 1

2= 2 for the 2p case and (2j + 1) 5

2/(2j + 1) 3

2= 3

2for the 3d case.

(d) Applies to nearly all edges lying in the low-energy range (20 to50 eV). They appear rather as a large symmetric plasmon peak than as atrue edge. This behaviour is very clear for all edges associated with quiteintense oscillator strengths: 3p → 3d in the transition metals; 4p → 4d in theseries Y to Pd (see Figs. 14 and 15); 5p → 5d in the lanthanides. It will bediscussed a little more extensively in a later paragraph.

(e) Is a special case of a delayed edge with a mixture of a transitiontowards a bound state at a threshold (marked by a peak) and a delayedcontinuum appearing as a second weaker maximum at about 100 eV abovethe onset.

These general behaviours can be roughly understood by examinationof the electronic configuration of each element. For instance, it appears, asone covers the periodic table, that the only relevant edges are those corre-sponding to an initial state of maximum occupied l for a given n shell. Forinstance, one has to look for 1s,2p,3d signals when they exist, because the2s and 3s,3p contributions will be an order of magnitude smaller. More-over non-dipole transitions such as s → d can only be observed when onecollects inelastic electrons at large scattering angle.

2 Published as Colliex, Manoubi, Gasgnier, & Brown (1985). Scanning Electron Microscopy, II,489–512.


This compilation is essential for microanalytical work. Very importantsystematic studies have been consequently made during the last year byseveral groups of workers to obtain complete libraries of EELS spectra, themost prominent being due to Zaluzec (1982) and especially to Krivanekand Ahn (1982). Anyone involved in this type of analysis requires the per-manent availability of one of these libraries close to his microscope.

4.1.3 Partially integrated cross-sections

For quantitative use of these signals, it is necessary to know partial cross-sections corresponding to the probability of inner-shell scattering throughangles up to α with energy losses covering a range � above Ec, that is:

σc(α,�) =∫ Ec+�

Ec

dσα(�E)

d(�E)d(�E)

This has been done in the hydrogenic model by Egerton (1979, 1981a)for K excitations and by Egerton (1982a) for L2−3 and L1 excitations. Thislatter edge is not clearly visible but must not be omitted in cross-sectionevaluation for analysis because it can contribute a few % of the total signalwhen integrated over a large energy window. The programs now availableas Sigmak and Sigmal programs, can be implemented on minicomputersand are currently used in many laboratories.

The Hartree–Slater calculations are more accurate and can be adaptedto any edge, but they cannot be handled as easily and require large amountsof data to be stored (Rez, 1982). This author has compared some results ofHartree–Slater calculations with those of hydrogenic models and proposeda scheme for parametrization so that the more accurate H.S. cross-sectionscan be used under a compressed format for routine microanalysis.

Some numerical values referring to standard working conditions andcommon elements are gathered in Table 4 (extracted from Sigmak andSigmal programs). Results are expressed in cm2/atom.

The total cross-sections for a given core-loss excitation are straightfor-wardly obtained by further integration to the cut-off angle θa = (�E/E0)

12

= (2θE)12 and to an infinite energy window above the edge. The carbon

K-edge has been the goal of several measurements and the results are sum-marized together with some available theoretical calculation in Fig. 22.Other edges such as Ti L2−3, Fe L2−3, Gd N4−5 have been investigated byTrebbia (1979). Another way to estimate the total cross-section is to use an


Table 4E0 = 100 kV α (mrad) 5 10 20CarbonK-edge(284 eV)

� = 50 eV 2.46 × 10−21 4.01 × 10−21 5.50 × 10−21

� = 100 eV 3.72 × 10−21 6.15 × 10−21 8.58 × 10−21

NitrogenK-edge(401 eV)

� = 50 eV 9.34 × 10−22 1.69 × 10−21 2.48 × 10−21

� = 100 eV 1.49 × 10−21 2.74 × 10−21 4.08 × 10−21

OxygenK-edge(532 eV)

� = 50 eV 4.10 × 10−22 8.23 × 10−22 1.29 × 10−21

� = 100 eV 6.81 × 10−22 1.38 × 10−21 2.20 × 10−21

AluminiumK-edge(1560 eV)

� = 100 eV 1.69 × 10−23 5.32 × 10−23 1.26 × 10−22

� = 200 eV 2.9 × 10−23 9.3 × 10−23 2.2 × 10−22

SiliconK-edge(1839 eV)

� = 100 eV 8.97 × 10−24 2.98 × 10−23 7.56 × 10−23

� = 200 eV 1.6 × 10−23 5.3 × 10−23 1.3 × 10−22

AluminiumL2−3-edge(73 eV)

� = 50 eV 8.92 × 10−20 1.10 × 10−19 1.22 × 10−19

� = 100 eV 1.25 × 10−19 1.59 × 10−19 1.83 × 10−19

SiliconL2−3-edge(99 eV)

� = 50 eV 5.06 × 10−20 6.52 × 10−20 7.43 × 10−20

� = 100 eV 7.55 × 10−20 1.00 × 10−19 1.19 × 10−19

TitaniumL2−3-edge(454 eV)

� = 50 eV 2.10 × 10−21 3.93 × 10−21 5.77 × 10−21

� = 100 eV 3.54 × 10−21 6.74 × 10−21 1.01 × 10−20

IronL2−3-edge(707 eV)

� = 50 eV 4.86 × 10−22 1.09 × 10−21 1.83 × 10−21

� = 100 eV 8.70 × 10−22 1.99 × 10−21 3.37 × 10−21

NickelL2−3-edge(855 eV)

� = 50 eV 2.54 × 10−22 6.21 × 10−22 1.11 × 10−21

� = 100 eV 4.65 × 10−22 1.15 × 10−21 2.08 × 10−21

efficiency factor method such as:

σ(α,�) = σtotη(α).η(�)

η(α) corresponds to the use of a limited angular acceptance;η(�) corresponds to the use of a limited energy window above the edge.


Figure 22 Comparison of a few measurements of the K-shell cross-section in carbonwith simple models (courtesy of Trebbia, 1979).

Starting from the models described above, one finds:

η(�) = 1 −(

Ec + �

Ec

)1−s

η(α) = log(1 + α2/θ2E)

log(2/θE)

where the mean inelastic angle θE corresponds to the average energy lossin the energy window. This efficiency factor method is however of ratherlimited accuracy because:• the calculation of η(�) requires the knowledge of s which is α-depen-

dent.• the calculation of η(α) requires the knowledge of θE which is

�-dependent.It is therefore more advisable to calculate first σc(α) = σc(α,�)/η(�) thenσtot = σc(α)/η(α) because η(�) is more sensitive to α variations than η(α)

to � variations. Finally, the results can be compared to total cross-sectionsmeasured by Auger and X-ray techniques (see for discussion Powell, 1976).

There exists a general method to test the validity of various cross-sectionmeasurements or calculation. It results from rewriting the cross-section for-mula in the Bethe theory:

σc = πe4

Eθ .Ec· Zc.bc log

∣∣∣∣ ccE0

Ec

∣∣∣∣


where

E0 = primary energy

Ec = core loss energy

Zc = number of electrons in the initial orbital

bc and cc represent phenomenologically the average number of electronsinvolved in the excitation and their average energy loss. Introducing Uc =E0/Ec, this expression becomes the Fano plot:

σcE2c Uc

6.51 × 10−14Zc= bc[log Uc + log Cc]

By varying E0, one obtains on a log–log plot a line whose slope and in-terception give bc and cc. From Powell’s survey article, one expects valuesfor bc ranging from 0.45 to 0.70 (bK) and from 0.25 to 0.55 (bL). Such anapplication of the Fano plot to EELS in STEM has been recently publishedby Liu (1982).

4.2 Fine structures due to various solid-state effects4.2.1 Generalities

An experimental edge recorded from a solid specimen actually displays amore complex structure than those discussed in simplified atomic terms.This is particularly true for most K- and L2−3-edges which can be studiedin the standard accessible energy loss range 50 to 1000 eV. Moreover, thedetailed profile of such edges depends on the allotropic variety or com-pound nature in which this element is involved.

The most famous example clearly showing these effects is the carbonK-edge at 284 eV. Fig. 23 shows spectra recorded with our instrumentfor the three important sorts of carbon: amorphous carbon, graphite anddiamond, together with some examples of the modifications of the finestructures at the edge itself in six types of common nucleic acid bases (fromthe work of Isaacson, 1979). They can be used to define the various modi-fications induced by the solid-state environment on the shape of a core-lossspectrum:

(1) At the threshold itself, one can measure a displacement of the edge,known as “chemical shift” and a variation of the onset slope and structures.These effects are related to the position and nature of the vacant states atthe Fermi level with respect to the initial state. For instance, they are very


Figure 23 (A) Examples of near edge and extended fine structures for the K-edge of vari-ous sorts of carbon: amorphous, graphite and diamond. (B) Comparison of the thresholdof the carbon K-shell in six types of nucleic acid bases (courtesy of Isaacson, 1979).


Figure 23 (continued)

sensitive to the modifications of band structure, such as the existence of aband gap if the element is present in an insulator instead of a metal.

(2) The second type of solid-state contribution lies in the structures de-tected in the energy domain 10 to 50 eV above the edge. A few years ago(Colliex, Cosslett, et al., 1976) it was customary to describe them as bandstructure effects and this was the type of approach followed by Colliex andJouffrey (1972), Egerton and Whelan (1974) to interpret the profiles ob-served in this domain. The underlying simple idea is to use a one-electrontransition model between the initial state and a vacant state in the con-duction band, and the intensity in the spectrum is estimated from a simplemodel:

I(�E) ∝ N(ε)T(�E)


where N(ε) represents the density of states for an energy ε = (�E − Ec)

above the Fermi level, and T(�E) means the probability of a transitionobeying the selection rules already mentioned. This model seems now in-sufficient and recent developments introduced by people in the synchrotronphysics area have to be considered for the interpretation of EELS spectra.For equivalence with the XANES (X-ray Absorption Near Edge Struc-tures) common terminology, we propose to designate them as ELNES(Energy Loss Near Edge Structures). Some first comments on these effectshave been published by Colliex (1982a), Taftø and Zhu (1982) and themost complete work in this field is certainly due to Leapman et al. (1982),and Grunes, Leapman, Wilker, Hoffmann, and Kunz (1982).

(3) The last type of environmental effect is now better established. Itconcerns the extended oscillations which are superposed on the decayingpart typically between 50 and a few hundred eV above the edge. Theseoscillations were recognized a long time ago in high-energy X-ray absorp-tion spectra but it is mainly from the work of Sayers, Stern, and Lytle (1971)that EXAFS (Extended X-ray Absorption Fine Structures) have emergedto occupy nowadays a great number of optical lines around synchrotronfacilities. The possibility of similar features in core-loss EELS spectra hadbeen pointed out by Colliex and Trebbia (1975) and the first simple analy-sis of what would be later called EXELFS is due to Leapman and Cosslett(1976). The best EELS spectra have been recorded by Kincaid, Meixner,and Platzman (1978) on a machine dedicated to EELS studies. In the E.M.environment, many experiments have been done during the last two yearsand a satisfactory review can also be found in the papers of Leapman,Grunes, Fejes, and Silcox (1981), and of Csillag, Johnson, and Stern (1981)published in a book on EXAFS spectroscopy (Teo & Joy, 1981). We shallnow discuss these three types of solid-state contributions.

4.2.2 Chemical shift and edge shape

For well-defined edges, the threshold energy is defined as the position ofthe inflexion point on the steep rise in intensity. Several effects are actuallyresponsible for its non-verticality: instrumental broadening, finite lifetimeof the inner-shell core. The chemical shift refers to the variation in energyof this threshold when the same element is investigated in various com-pounds.

A similar chemical shift is well known in photoelectron spectroscopy(XPS). In a single-electron transition scheme, one measures the excitationof a core electron (let us say a 2p state) towards a final state which is gen-


Figure 24 Energy levels involved in XPS and EELS measurements of the 2p level excita-tion energies in the corresponding metal and oxide (transition metal series). The variouscontributions to the chemical shift are pointed out (courtesy of Leapman et al., 1982).

erally an excited electron with large kinetic energy (see Fig. 24). In thiscase the metal-oxide chemical shift, for instance, is a measure of the dif-ference in energy between the respective 2p core levels, assuming that thefinal state is unchanged in the metal and in the oxide. This condition hasclearly been pointed out by Leapman et al. (1982). Upon oxidation, valenceelectron charge is transferred from metal to oxide, the atomic potential ismore attractive because the shielding of the 2p orbitals is less efficient. Con-sequently, one records an increase in the oxide core level energy. On theother hand, EELS is a more complex spectroscopy: at threshold, it inves-tigates simultaneously the changes in the initial state and the changes inthe final state, which is the lowest unoccupied state above the Fermi level.Consequently, the EELS chemical shift is due to the combination of a core-level shift and band-gap creation, and of exciton production. It is difficultto explain it in simple terms. Leapman et al. (1982) have tabulated in fulldetail the comparison of L3 binding energies in oxides and correspondingmetals determined from EELS and XPS measurements. They suggest anexplanation in terms of many-body relaxation effects which can be of dif-ferent intensity in the XPS case (the excited electron is ejected to energiesfar above the Fermi level leaving the core-hole bare) and in the EELS case(the excited electron is promoted to a localized 3d state contributing to thescreening of the core-hole and reducing the relaxation energy).

Other chemical shifts are well known and they constitute a clear tool toinvestigate the oxidation state of an element. For instance the Al L2−3 edgeshifts from 73 to 77 eV when one compares Al metal and Al2O3. Similarly


Figure 25 Comparison of the L2–L3 edges in: (A) Sc and Sc2O3 (courtesy of L. Brown,M. Gasgnier, & C. Colliex, 1983, unpublished). (B) Ti and TiO2 (courtesy of Leapman et al.,1982). (C) Cu and CuO (courtesy of Leapman et al., 1982).

the Si–L2−3 edge shifts from 99.5 eV in Si to 103 eV in SiO and 106 eV inSiO2 (see, for instance, a use of this chemistry sensitive change in the nearedge fine structure for the investigation of the Si–SiO2 interface; Krivanek,1981). A last example worth mentioning is the K-edge case which has beenshown for illustration (Fig. 23). The sharp peak at 284 eV in amorphouscarbon and graphitized carbon corresponds to transitions towards a π∗ stateat the Fermi level. On the other hand, the steep rise lies at 288 eV for theK-edge in diamond. This 4 eV shift corresponds to the occurrence of animportant gap in this case.

Changes at threshold do not concern only the energy position of theedge; in addition fine structure variations can also be observed. One firstexample has already been shown for the carbon K-edge in the differenttypes of nucleic acid bases (Fig. 23). They are not yet explained by a prioricalculations and can only be used as a kind of fingerprint for the recognitionof molecular structures.

Another very important situation concerns 2p edges in transition metals.Let us illustrate it by three examples Sc and Sc2O3, Ti and TiO2, Cu andCuO, the last two being extracted from the paper of Leapman et al. (1982)while the first has been studied in our laboratory (see Fig. 25). In eachcase the spin orbit splitting between the L3 and L2 edges is clearly resolved.Moreover, one detects a second splitting for each of the L3 and L2 whitelines in oxide with respect to metal in Sc and Ti: these two components are



separated by 1.6 eV in Sc2O3 and 2.5 eV in TiO2. A preliminary interpreta-tion of this effect lies in a cluster molecular orbital approach (Fischer, 1970):the octahedral coordination of Ti atoms with oxygen splits the degenerateunoccupied 3d states into two lower energy 2t2g and a higher 3eg molecularlevels. If this model seems reasonable for the localized states in the oxides it


is clear that a detailed comparison of the shape and width of the observedpeaks requires a more complete band calculation theoretical support.

The situation in Cu and CuO is also very interesting: in the metal the2p edge does not appear very clearly. This is due to the fact that the 3dband is filled and lies just below the Fermi level. As a consequence thestrong 2p → 3d transitions do not occur and no “white line” can be seen.In CuO, electron transfer between Cu and O atoms produces some unfilledd states and the Fermi level is lowered into the Cu d bands. A clear L3 whiteline can then be detected at the edge.

For practical purposes, the oxygen K near-edge fine structure requiressome further comments. It is a fundamental edge which can be studiedrather easily by EELS techniques since synchrotron radiation is of poor ef-ficiency in this energy range (532 eV). Grunes et al. (1982), Colliex andTrebbia (1982) have published some results. Striking variations are reportedeither for selected 3d transition metal oxides or for SiO2, Al2O3 samples.Two characteristic examples are shown in Fig. 26 for SiO2 and Fe3O4.There does not exist now a complete and clear theory giving a satisfactoryaccount of all observed features. Qualitatively, these transitions originatingfrom a 1s level probe final states of p symmetry. They are very intense inSiO2 and Al2O3 and the main peak at the edge can be due to one-electronexcitations towards these vacant levels. In transition metals the different finestructures at the edges (splitting, occurrence of a pre-ionization peak) can-not be explained in such simple terms, and solutions have to be sought inmore complete band structure calculations or core exciton schemes. Thisproblem remains open for discussion but it surely contains important infor-mation concerning the symmetry of the site and the environment of theexcited atom.

4.2.3 Band structure effects and ELNES

This subject has already been partly covered in the above paragraph becausethere is no clear distinction between edge and near-edge effects. Solutionsfor the interpretation of oxygen K near-edge structures can also be foundin ELNES (or XANES) theories. Apart from examples already mentioned,one can quote the differences in fine structures covering the first 30 eVabove the edges for the L2−3 edges of Si in SiO2, Si3N4 (Colliex, 1982a), forthe K edges of Mg, Al and Si in various octahedral or tetrahedral environ-ments (spinel, olivin, feldspar—see Taftø and Zhu, 1982). A general result isthat ELNES are significantly modified not only by valence variations, butalso by changes in symmetry. The problem studied with EELS concerns


Figure 26 Comparison of the ELNES structures for the oxygen K-edge in SiO2 (α quartz)(specimen kindly prepared by M. Pascucci) and in Fe3O4 magnetite.

generally core levels less deep than those covered by XANES in photoab-sorption measurements. However the physical phenomena involved in bothcases are rather similar. The main conclusions extracted from XANES canbe applied to ELNES, and it is useful to refer for instance to the proceedingsof the International Conference on EXAFS and Near Edge Structures heldin Frascati (1982). There is, however, an important difference concerningthe existence of multiple scattering (core loss + plasmon) which has alreadybeen mentioned. In this energy range it is important to get rid of them byan appropriate deconvolution technique.


For the future, one can see that the observed ELNES features are re-lated to structural details of the absorbing site such as its chemical valence,its coordination geometry and the type of ligand. It will be a useful tool forchoosing between different structural models, when the comparison withreference compounds is possible. From the theoretical point of view, theband structure constitutes a first satisfactory approach but is not sufficient.It is unsuitable for applications to disordered materials or to crystals withcomplicated unit cells; corrections for the changed potential of the ionizedatom are omitted. One has to adapt the theory developed for EXAFS, totake into account multiple scattering. Durham, Pendry, and Hodges (1981)have established the foundations of such a model. The atoms are classifiedinto shells surrounding the absorbing one, and the cross-section for theexcitation of an electron orbital on the central atom is calculated by usingthe total reflection matrix due to all surrounding atoms and considering allmultiple scattering within and between the atomic shells. This point willbe expressed more clearly after the discussion on EXAFS theory.

To illustrate the type of tenuous difference between a simple bandtheory interpretation and the more elaborate multiple scattering theoryrequired a practical situation can be considered: the K-boron and nitrogenedges in the spectrum of hexagonal boron nitride which is one of the fa-mous test specimens (see Fig. 27). One distinguishes similarities in positionwith respect to the edge, of the main contributions which can be inter-preted in terms of transitions towards the respective π∗, σ ∗ sub-bands witha non-negligible contribution of multiple scattering at higher energies (25and 40 eV above the edge). This model has been confirmed by orientationdependence measurements due to Leapman and Silcox (1979) who excitedpreferentially the π∗ antibonding orbitals parallel to the c axis or the σ ∗

antibonding ones perpendicular to it, by choosing carefully the angle ofscattering with respect to a specimen in a 45° tilted position. Both coreedges correspond to transition from an initial 1s state and investigate there-fore the same final states made up from 2s and 2p orbitals. The differences inrelative intensity of the various features of the core edges of boron and ni-trogen also pointed out by Hosoi, Oikawa, Inoue, Matsui, and Endo (1982)therefore reflect a difference in final state density seen from a 1s state local-ized on the nitrogen and on the boron atom which have the same symmetryenvironment. This is why we suggest that a more quantitative fit betweentheory and experiment should be sought for in recent XANES models.

To conclude this discussion of fine structure effects in the first tens ofeV above the edge it is important to note they can only be investigated


Figure 27 ELNES structures for the boron and nitrogen K-edges in boron nitride hexag-onal thin flakes. Comparison of the position of the different features and of their relativeintensity with a schematic band structure model pointing out the main features of theunoccupied conduction band: one vacant state in the 2pz − π∗ band and three va-cant states in the 2px 2py 2s-hybridized σ ∗ band. For the boron K-edge: a = 191 eV,b = 198 eV, c = 204 eV, d = 215 eV, e = 229 eV. For the nitrogen K-edge: a = 400 eV,b = 406 eV, c = 413 eV, d = 425 eV, e = 439 eV. The dashed areas in the spectra roughlycorrespond to transitions towards the π∗ and σ ∗ band, while the dotted areas aremainly due to multiple effects (convolution with plasmon losses).

with a spectrometer of refined energy resolution (1 eV or better at losses ofseveral hundred eV).

4.2.4 Extended fine structures (EXELFS)

Recent experiments have shown that the weak oscillations superposed onthe high-energy tail of a core-loss spectrum can be recorded with suffi-ciently high counting rates so that they can be analysed in similar terms as


the extended fine structures on X-ray absorption edges. This is the basis ofthe analogy between EXAFS and EXELFS performed at small q and theformalism established for the first case can be used for the analysis of EELSdata. The main formula for interpreting EXAFS data is the following. Theoscillatory component of the cross-section can be written as:

χ(k) =∑

j

fj(k)nje−rj/λ

kr2j

e−σ 2j (k2/2) sin

[2krj + 2ηj(k)

]

where

k = wave vector for ejected electron = [(2m/�2)(�E − Ec)] 12

fj(k) = backscattered amplitude on neighbour atomsrj = distance from absorbing atom to the j th coordination shell

e−rj/λ represents damping due to inelastic losses suffered by theejected electron with λ being the electron mean free path forelectrons of energy (�E − Ec)

e−σ 2j (k2/2) represents damping due to thermal vibrations and static

disorderηj(k) is a phase shift containing contributions from both the

absorber and the backscatter

The sinusoidal oscillation is therefore a function of interatomic distances(2krj) and of the phase shift ηj(k). This expression has been formulated inthe generally accepted short range, single-electron, single scattering theory.Application to EELS data requires the following procedures (see Leapmanet al., 1981):• Subtraction of the background intensity preceding the edge by a fit to

an inverse power law = A.�E−r .• Modelling of general profile after the edge by fitting to a polynomial.• Transform the energy of the final state above threshold to a wave vector

scale.• Multiply by k2 or k3 to take account of attenuation by the backscatter-

ing amplitude function fj(k).• Truncate the intensity modulations at kmin to avoid band structure ef-

fects and at kmax set by the energy at which noise begins to dominateor another edge occurs.

• Calculate the Fourier transform to extract the radial distribution func-tion F(rj) = nj/r2

j from which the nearest neighbour distance can bemeasured.


• Make phase shift corrections for each pair of central and backscatteringatoms.As a conclusion one obtains the interatomic distances, with a resolution

mainly limited by the truncation k window. The two first near-neighbourdistances can then be measured with relative confidence, while it is difficultto deduce approximate information about the next ones and the coordina-tion numbers.

Clear advantages of the EXELFS method can be summarized as follows,with respect to EXAFS:• It can be applied to low Z elements because for counting rate statistics

it is at present limited to energy losses of 2 or 3 keV at maximum, whileX-ray absorption data are most easily obtained at energies above 2 or 3keV.

• Electrons can be focused into small probes and with modern equipmentsuch an analysis can be performed on sample areas as small as 10 nm,which is very useful for non-uniform specimens (see for instance theanalysis by Batson and Craven (1979) with a probe diameter of 1.5 nmon a 10 nm graphite film).

• EXELFS can be combined in situ with microdiffraction on the samearea, within an analytical electron microscope.

• The data collection time is comparable to that of synchrotron sources.• One can study the momentum transfer dependence of the inelastic scat-

tering cross section. A very elegant application has been shown recentlyby Disko, Krivanek, and Rez (1982), which probed the near-neighbouratomic environment in graphite in two perpendicular directions, usingconditions such that the momentum transfer q lies parallel and per-pendicular to the graphite c axis. The spectra and the magnitudes ofthe Fourier transforms are shown in Fig. 28. Maxima in F(rj) occurnear 0.36 nm for q‖c and 0.14 nm for q ⊥ c as predicted. These resultsprove that “it is intrinsically possible to analyse the near-neighbour en-vironment of a particular type of atom in a particular crystallographicdirection”. The authors add “at a particular crystal site” and this aspectwill be discussed later.

On the other hand EXELFS suffers severe limitations:• Thickness requirements below typically a few tens of nm to avoid plural

scattering effects which add their own modulation and are difficult toremove.

• Edges below 2 keV only can be analysed and at these low energies,it is more difficult to avoid overlapping edges such as L1 over L23 for


Figure 28 (A) Carbon K-edges with background removed, for momentum transfer q par-allel and perpendicular to the graphite c-axis. E0 = 120 kV, α0 � α � 0.3 mrad; an 8 μmdiameter region of a 30 nm thick graphite flake is sampled in each case. (B) Magnitudesof the Fourier transforms of the χ(k) functions. The EXELFS orientation dependence isclearly shown (courtesy of Disko et al., 1982).


instance or other atomic species contribution. Very few situations existfor which the energy range available for EXELFS data analysis is greaterthan 200 or 300 eV. A good problem to be considered would be thecase of a light atom in a heavier matrix with no edge pile-up.If one wants to summarize now the practical results obtained by EX-

ELFS, they have remained of limited success with respect to new structuralinformation. They have been more aimed at demonstrating intrinsic capa-bilities of the method (see Batson & Craven, 1979 or Disko et al., 1982)than at solving problems in more complex materials. This is the reason whyit is important to consider the whole environmental information conveyedin the core-loss fine structures, ELNES as well as EXELFS. The formerrequires better resolution, more complete theoretical interpretation in theway followed by Durham et al. (1981) of a multiple scattering extensionof the single scattering theory used for EXELFS. On the other hand, thesecond method can be achieved with a moderately poorer energy reso-lution but requires very drastic conditions on counting rates (106 to 108

counts/channel is essential), because the noise due to the strong underlyingbackground prevents an accurate determination of the useful oscillatorypart.

4.3 Some problems in the intermediate energy loss domain4.3.1 Background

The characteristic core-loss signals are superposed on a regularly decreasingbackground. It is very important to be capable of modelling this non-characteristic contribution so that the specific signal can be extracted froman energy loss spectrum.

To solve this problem, a pragmatic approach has been followed up tonow. It originates from a suggestion due to Egerton (1975) who displayedhis results on a log–log plot. The energy dependence of the backgroundappears then as straight lines of slope varying with collection angle α andspecimen thickness t. As a consequence, one has generally used a simplepower law to model the background:

B(�E) = A.�E−r

where r is a measure of the downward slope of this profile with a value be-tween 3 and 5. However, the fit between an experimental profile and sucha model with a given r value is satisfactory only for limited energy win-dows. One notices a gradual evolution of the r parameter towards higher


values for increasing energy losses, though this is not completely systematic.A practical conclusion is that, for each situation and each edge, a fit has tobe made over an energy window typically 80 to 100 eV wide before theedge and that the same model can be extended over �100 eV after theedge. A total energy window of 200 eV practically constitutes the largestover which a power-law fit with a single r value can be considered valid.

Several methods have been proposed for this fitting procedure. Recentdevelopments are due to Egerton (1980a) and to Colliex, Jeanguillaume,and Trebbia (1981). The former determines the parameters A and r byusing the following equations:

r = 2log(I1/I2)

log(E2/E1)

and

A = (I1 + I2)(1 − r)E1−r

2 − E1−r1

where the fitting window extending from �E = E1 to �E = E2 halves therespective integrals I1 and I2. This approach is interesting because theseformulae give rather accurate values of �r/r � 1% in minimum computingtime. The precision of A is, however, dependent on the precision of r andno values of uncertainties σA and σR are provided.

Starting from these Egerton formulae a program of least square fitting,Curfit program, has been written by Trebbia, immediately derived from aFortran Curfit program described in Bevington (1969). It provides the fol-lowing final results: A, σA, r, σr, χ

2 and χ2v . A comparison of the final value

of χ2 with a standard table enables one to say whether the final fitting func-tion describes with sufficient accuracy the unknown parental distributionof an ideal experiment performed during an infinite counting time.

Using this procedure routinely, one has been able to measure the slope rparameter for many practical situations and the following main behaviourshave been recorded:• Decrease of r with increasing α (for instance r drops from about 4.5 to

3.5 when α increases from 3 to 34 mrad—for energy windows of 100eV below the carbon K-edge at 284 eV).

• Decrease of r with increasing thickness t.• Increase of r with the mean value of �E covered by the fitting window

when �E � 700–800 eV; then one notices a stabilization of r.Altogether, it is not possible to define a priori the r value suitable for a

given specimen area and well-determined experimental conditions. It must


be determined in each case and this effect has important consequences inmicroanalysis for recording maps of the chemical distribution with the helpof energy filtered images of characteristic losses (see Section 6). This gener-ally observed behaviour of r can only be understood qualitatively by usingsome arguments already mentioned. Several mechanisms are responsible forthe existence of this background:• High energy tail of the excitation spectrum of the valence and conduc-

tion electrons. As long as the Bethe ridge (or Compton line on freeelectrons) is not intercepted by the collector aperture, the behaviour ismainly controlled by the high energy tail of:

Im1

ε(ω)� ε2(ω) ∝ 1

ω3

multiplied by the yield factor hα(ω) already mentioned. Altogether,this involves a general behaviour of r(α) varying between 5 for smallcollection angles to 3 for large collection angles.

• High energy tail of a lower-lying edge—this is the case for most edgesin compounds. The r parameter for the background is equivalent tothe s parameter for the dominating core-loss contribution under theedge of interest. This is illustrated in the example of Fig. 29 relative toa typical biological specimen: a section 70 nm thick of macrophageembedded in epon. The four spectra are displayed with the back-ground estimation respectively for the prominent carbon K-edge, andfor the N–K , O–K and Fe–L2−3 edges. The values of r determined bythe Curfit program in these four extrapolations are 2.89 (C–K), 3.52(N–K), 3.81 (O–K) and 3.70 (Fe–L2−3).

• Multiple scattering of lower energy losses. The probability of singlescattering increases as t, while it is t2 for double scattering, t3 for triplescattering. . . . Consequently the background intensity does not increaselinearly with thickness, contrary to the characteristic core-loss intensity.This effect has been clearly discussed by Johnson (1981) as one of thelimiting factors in the use of EELS core-loss signals for chemical anal-ysis. There exists an optimum thickness determined as a compromisebetween the t/λ�E term where λ�E is the mean free path for the energyloss region of interest and e−t/λT where λT is the mean free path for allscattering events.Another important operating parameter is the angle of collection α. In-

creasing α is responsible for a more intense characteristic signal (with typicalinelastic angle θE = (�E/2E0) but with a still quicker rise of the back-


Figure 29 Typical spectra for a biological tissue (rat bone marrow) section embedded inepon. Thickness is �70 nm. The main contribution is the carbon K-edge, followed by theN–K , O–K and Fe–L2−3 edges. The background fit is achieved with Curfit program over35 channels preceding the edge and the results are displayed in graphs A, B, C and D.

ground signal. This is due to the fact that background events are peakedat larger scattering angles as a consequence of the Bethe ridge alreadymentioned. There exists again an optimum α determined as a compro-mise between signal and background limiting factors. This αopt has beenstudied experimentally by Joy and Maher (1978) and will be discussed inmore detail in the context of quantitative microanalysis.



In several cases, the fit with a simple power-law model has completelyfailed: for instance, on the tail of an intense 3p edge in transition metals.Grunes and Leapman (1980) have fitted the background intensity beforeand after the M1 peak to a cubic polynomial in a way rather similar to back-ground subtraction in X-ray analysis. Bentley, Lehman, and Sklad (1982)have developed a modified background form which uses a polynomialfit to the logarithm of electron intensity and energy loss, to extract theboron signal over the 3p tail of titanium and nickel in TiB2–Ni ceramics.Colliex et al. (1981) have pointed out that a background model with sev-eral parameters A, r1, r2 could be handled by the Curfit program for finding


the χ2 minimum value in the (χ2,A, r1, r2) hypersurface. Finally, EXELFSstructures can in certain circumstances prevent satisfactory modelling ofthe background when one reaches the limits of detection for an elementwhose characteristic edge lies on the high energy tail of the matrix coreloss.

4.3.2 Core loss excitations in the 20–50 eV energy loss domain

In the general classification of core-loss shapes, a special category (D) hasbeen reserved for some edges associated with moderately deep energy lev-els, between 20 and 50 eV, which exhibit a “plasmon-like” profile. Onesuch example is the excitation of the 4p electrons in yttrium metal andsesquioxide shown in Figs. 14 and 15; there is a large, symmetrical and in-tense peak at �35 eV, which is rather similar in Y and Y2O3. The N2−3

edge is at 25 eV and appears only as a weak structure. It seems that theexcitation of these p electrons covers a large domain of energy with a max-imum at about 10 eV above the threshold. A similar behaviour has beenobserved for all excitations of p electrons in alkaline earth materials, and inthe first elements of the transition series: 3p in the first row (see Colliex& Trebbia, 1974; Wehenkel & Gauthe, 1974a, 1974b), 4p in the secondand 5p in the third row (see Colliex, Gasgnier, et al., 1976). The originof this effect does not seem to have been completely elucidated at present.It can be considered either as an extension of the plasmon concept asso-ciated with high energy interband transitions corresponding therefore tocollective resonant excitation of all electrons lying on orbital levels at lowerenergies; or as a special case of correlation effect on one-electron transi-tions within an “atomic” model. This second type of analysis would seemmore appropriate because of the lack of sensitivity of such excitations asa function of the environment (gases, compounds. . . ). This behaviour canonly be observed when there exists a very intense probability of transitionbetween moderately deep p level and vacant d states at the Fermi level (thecross-section per atom is �10−18 cm2, of the order of the plasmon excita-tion cross-section). Consequently, important rearrangements of the initial psubshell of the atom have to be considered, such as some authors have triedto define this resonant-type excitation as a kind of collective excitation ofthe p subshell. Extending the dielectric formulation to this energy domain,the maximum in ε2 corresponding to interband transitions from the p elec-trons, is associated with a dip in the εi function. This problem thereforeremains open for discussion.


5. Developments in instrumentation

Referring back to the general instrumental classification introducedin Section 2, we shall now consider the development of systems capable ofproducing EELS results in the analysing mode, that is as an energy spec-trometer, and in the filtering mode, that is as an energy filter. In the firstworking mode, STEM has proved to be superior for producing high qual-ity spectra, directly available for quantification and recorded from highlyspatially resolved specimen areas. On the other hand, when one is inter-ested in the elemental distribution over many picture elements, the overalladvantage of STEM with respect to CTEM is not as clear. The latter typeof instrument can compensate partially its limited access to quantificationby its large storage capability (a standard photographic plate correspondsto about 107 pixels). Assuming that a given dose on a pixel is necessaryto record a significant signal—of any type—the primary flux available ina probe delivered from a field emission gun in a STEM configuration isabout 105 times higher than the flux in a conventional microscope, andtherefore the sequential acquisition is superior to simultaneous recording(CTEM) when the total number of pixels is less than �105. There stillremains an advantage in using CTEM equipped with convenient energyfilters for recording the elemental information over large specimen areas.Taking into account future developments, it is evident that in a CTEM onecan only record a single energy filtered image at a time while the availabilityof parallel detection systems in a STEM will allow the recording of severaldifferent energy filtered images simultaneously.

As a consequence, it seems evident that already the STEM configu-ration offers strong advantages for the use of multisignal information andhigh spatial microanalytical work and constitutes the most promising wayof development for high performance “nano-analytical” instruments in thefuture. On the other hand, when one contemplates the development ofEELS during the past few years, it is evident that CTEM with a CastaingHenry filter (or their magnetic equivalents) have largely contributed to thedefinition of our present knowledge of the subject.

It is impossible to discuss the recent developments in instrumentationin terms of spectrometer and detection unit only; they must be consideredas part of a whole instrument which is capable of delivering the requiredprobe of electrons on to the feature of interest in the specimen, of collectingand analysing it and of providing at the end the useful information in asatisfactory format which can be of direct interest for the user, either amaterial scientist or a biologist.


5.1 Classification of various systems5.1.1 CTEM with energy-loss filters

With a CTEM, the energy-selecting device transfers an image of the spec-imen into an achromatic stigmatic conjugate plane. The energy discrim-ination is achieved by introducing a selection slit in the plane containingthe energy-loss spectrum (real stigmatic plane). It is well suited for record-ing energy-loss images, but much less convenient for energy-loss analysisfrom a selected area. The first satisfactory device has been developed byCastaing and Henry (1962) who used a combination of magnetic prismand electrostatic mirror; their system has been thoroughly described in theliterature (see for instance Metherell, 1971). Various improvements of thisoriginal instrument have been used by Colliex (1970), Henkelman andOttensmeyer (1973), Egerton, Philip, Turner, and Whelan (1975), Kihn,Zanchi, Sevely, and Jouffrey (1976), Ottensmeyer and Andrew (1980). Oneimportant modification is to ramp the energy-loss voltage on the primaryvoltage so that electrons of constant kinetic energy are travelling throughthe filter and analysed through the selection slit.

The difficulty of handling electrostatic mirrors and the relevant high-voltage power supplies have convinced several authors to design purelymagnetic equivalents of this device. Various solutions have been investi-gated and used, with a symmetry plane in the middle of the system: theseare the three magnets �-filter in the 1-MeV Toulouse microscope (Zanchi,Perez, & Sevely, 1975) and the four magnets filter on a 100-kV microscopeat Berlin (Krahl & Herrmann, 1980). Better corrections of second-orderaberrations according to calculations by Rose and Pejas (1979) are nowbeing tested (Krahl, 1982).

The best performance attained with such a filtering device is quoted byOttensmeyer et al. (1981): attainment of a spatial resolution of 0.3 nm inelastically energy selected images and of equivalent resolution (0.3–0.5 nm)

using an atom specific characteristic inner-shell excitation (phosphorusL2−3 at 150 eV). This last claim must, however, be treated with a criticalattitude because it seems subject to controversy due to chromatic aberrationconsiderations imposed by the objective lens and to localization effects (seediscussion in Section 6).

Another type of experimental system is the combination of a CTEMmicroscope with a retarding Wien filter spectrometer (Curtis & Silcox,1971). An entrance slit selects electrons according to their scattering angleand the spectrometer disperses them in a direction perpendicular to the slit.


A two-dimensional pattern results, corresponding to the map of the scat-tered electron intensity as a function of energy loss and scattering angle.A very good angular resolution has been achieved at the expense of a poorspatial definition. Very elegant applications of this instrument concern ei-ther the study of the dispersion of radiative surface plasmons at very small qvector (Vincent & Silcox, 1973; Pettit, Silcox, & Vincent, 1975) or of theplasmon dispersion at large wave vector (Batson, Chen, & Silcox, 1976).

5.1.2 STEM with energy-loss spectrometers

This is by far the most abundant family of presently operating systems, ei-ther on a dedicated STEM or on a mixed CTEM/STEM instrument. Mostmanufacturers have now developed their own instrumental attachment orthey are selling a compatible device. The commonly used solution consistsin interfacing a simple magnetic prism at the end of the column and thiscan be achieved at reduced cost. It offers a very versatile possibility of op-eration in all modes (mentioned in the table of Section 2). Moreover, it hasproved to be the most sensitive system in terms of detection limits, as shownby Colliex et al. (1981, 1982). As an example of recent developments ininstrumentation, the experimental system in operation in Orsay consistingin the combination of dedicated FEG-STEM Vacuum Generators3 HB501with the spectrometer designed by Krivanek and manufactured by Gatan,4

has been described by Colliex and Trebbia (1982). It is well suited for re-solving analytical problems with a high spatial definition at the nanometrelevel. We shall discuss the main factors which are responsible for this highlevel of attainable performance.

5.2 The scanning transmission microscopeThe design and characteristics of the electron gun and illumination systemdetermine the properties of the primary beam impinging on the speci-men. In the case of the VG-HB501, described by Wardell (1981) the probeforming system made of two condensers and a high excitation objectivelens focuses a current of the order of a few 10−10 to a few 10−9 A in aspot on the specimen. Its size is determined by a complex superposition ofGaussian image size (carrying the current) and of aberration contributionsof the objective lens (diffraction, spherical aberration, chromatic aberra-tion). In practical terms, the generally used apertures of 50 and 100 µm

3 Vacuum Generators Ltd, Charlwoods Road, East Grinstead, Sussex, England.4 Gatan Inc, 780, Commonwealth Drive, Pittsburgh, PA 15086, USA.


Figure 30 Parameters involved in the definition of the interaction of the STEM primarybeam with the specimen. The difference between the volume analysed in EELS andX-ray emission is clearly displayed.

correspond to half angles of illumination of 7.5 and 15 mrad and to probediameters of �0.6 nm and �1.5 nm respectively. Characterization tech-niques on the nanometre scale can be contemplated as a consequence ofthis high-brightness beam available on the specimen surface. Fig. 30 il-lustrates the geometry of the currently performed analysis with such aninstrument. Depending on the probe size and specimen thickness, totalvolumes of the order of 1 nm3 to 400 nm3 can be analysed, correspond-ing to a total number of atoms between �100 and 40 000 involved in theanalysis in a fixed probe mode. It offers the counterpart of delivering a veryintense dose of electrons on the specimen, together with its consequencesin terms of radiation damage.

5.3 Spectrometer design and couplingThis high-performance system of illumination can be useful only if atten-tion is paid to the design of a device capable of collecting and analysingwith high efficiency the information conveyed by the inelastically scatteredelectrons.


Figure 31 Parameters involved in the design of a homogeneous magnetic field spec-trometer.

5.3.1 Qualities of a spectrometer: Theory and application

Following the work of Enge (1967), several efforts have been madeto calculate and realize a magnetic uniform prism corrected for sec-ond order aberrations (Parker, Utlaut, & Isaacson, 1978; Shuman, 1980;Egerton, 1980b; Isaacson, 1981; Krivanek & Swann, 1981). The basic prin-ciple of such a design can be understood with simple geometric arguments.The spectrometer is actually an electron optical transfer system which trans-forms a given distribution of electrons I0(x0,y0, t0,u0, γ ) in the object planeof coordinate z0 along the curved trajectory into a distribution of electronsIi(xi,yi, ti,ui, γ ) in the image plane in coincidence with the energy selectingslit—see Fig. 31 for definition of the notations. The spectrometer is charac-terized by its radius of curvature R0, its angle of deflection (generally π/2),the tilt angles β1 and β2 of the entrance and exit faces, the radius of curva-tures R1 and R2 of these faces, the gap D. Using Shuman’s (1980) notation,Jeanguillaume (1982) has calculated the main properties of a magnet to beinstalled on the VG microscope column. First-order focusing is achieved bysetting (xi/t0) and (yi/u0) = 0. The linear magnification is then determinedby its radial (xi/x0) and axial (yi/y0) coefficients and the dispersion is gov-


Figure 32 Results of the calculation of the tilt angles (β1,β2) of the entrance and exitfaces of a magnetic spectrometer to achieve first order focusing at an image distance l2when l1 is fixed (courtesy of Jeanguillaume, 1982).

erned by (xi/γ ). This last factor measures the ability of the spectrometerto discriminate along xj in the image plane, electrons of different energies(γ parameter = �E/2E0). Extending the calculation to second order, onehas to consider a (4 × 15) matrix of type (x/x2, . . .) of which only 30 termsare non-zero due to symmetry considerations. The main ones are thosewhich define the angular aberration coefficients (x/t2) and (x/u2) and thefactor (x/γ t) which is associated with the inclination angle of the dispersionplane with respect to the electron trajectory.

The calculation of a satisfactory magnetic prism must follow the steps:Choose a priori α = total deviation angle and l1 = distance between the

object and the entrance surface of the spectrometer.Vary l2 = distance between the image and the exit surface of the spec-

trometer, over the range of possible solutions.For each l2 value calculate the angles β1 and β2 for first order focusing.

Fig. 32 shows the results for l1 = 3.835 in reduced units l1/R0. An extendedfringing field calculation with shunted faces has been used. Two sets ofsolution (β1, β2) and (β∗

1 , β∗2) are possible.

For these conditions, calculate R1 and R2 which cancel (x/t2) and(x/u2). The two sets of solutions (R1,R2) and (R∗

1,R∗2) corresponding to

the previous calculation are shown in Fig. 33.Finally, study the behaviour of (x/tγ ) as a function of l2 which is respon-

sible for the final choice of l2 and the solution in β1, β2,R1,R2 (Fig. 34).


Figure 33 Results of the calculation of the radius of curvature (R1,R2) of the entranceand exit faces of a magnetic spectrometer to achieve second-order aberration correc-tion, at an image distance l2 when l1 is fixed (courtesy of Jeanguillaume, 1982).

Figure 34 Results of the calculation of the parameter x/tγ defining the tilt angleof the dispersion plane. There exists one solution for which it is zero (courtesy ofJeanguillaume, 1982).

As a conclusion, one has thus calculated a double focusing spectrometer,with correction of second-order aberration and a dispersion plane perpen-dicular to the trajectory. One can check that the Gatan spectrometer, whencoupled to the VG-HB501 microscope, approximately satisfies these calcu-lated properties (Krivanek & Swann, 1981).


The energy resolution can be estimated from a knowledge of the abovetransfer coefficients as shown by Egerton and Lyman (1975). In the generaldefinition:

�x ={

l2 + (D.δE0)2 +

[(xx

)rm

]2

+[(

xt

)θm

]2

+ · · · +[(

xt2

)θ2

m

]2

+ · · ·} 1

2

one recognizes the various contributions:• l width of the selecting slit.• D.δE0 corresponds to the natural width δE0 of the primary beam.• rm and θm represent the spatial and angular distributions of the beam at

the object level.• (x/x) . . . (x/t2) . . . are the different first- and second-order Enge coeffi-

cients.A reduced useful formula consists in combining all second-order importantcoefficients in a single C factor:

�x ={(D.δE0)

2 +[(

xx

)rm

]2

+ (Cθ2

m

)2} 1

2

in the case of negligible slit width. As a consequence, the energy resolu-tion δE = �x/D does not only depend on the spectrometer parameters butalso on the properties of the scattered beam which has to be analysed. Tocharacterize the energy resolution by a number, for instance 0.5 eV, doesnot mean anything, if the conditions of spectrum recording are not indi-cated. A spectrometer can be very good for given circumstances (diffractionmode) and very poor in others (image mode).

5.3.2 Coupling of the spectrometer to the microscope column

It is often necessary to introduce between the specimen and the spectrom-eter an optical transfer system for three main reasons:

(i) Generally, a spectrometer has only two pairs of stigmatic points,so that it is important to bring into coincidence the object plane of thespectrometer, either with the specimen (image coupling mode) or with itsdiffraction plane (diffraction coupling mode).

(ii) An optical system of variable magnification can realize a satisfac-tory equilibrium between the angular and spatial extension of the objectsource of the spectrometer, contributing therefore to optimizing the en-ergy resolution for a given collection efficiency. This can be illustrated as


Figure 35 Schematic representation of the isoresolution curves (δε = Ct) for variousconditions (rm, θm) of the intensity distribution at the entrance of the spectrometer.A and B refer to two practical conditions which can be connected by an optical transfersystem, at constant rmθm (courtesy of Jeanguillaume, 1982).

follows. In the simple model introduced above, one can define the resolu-tion R = δE/E0 as:

R = δEE0

= 1DE0

[(Brm)2 + (

Cθ2m

)2] 12

and calculate the equation of the isoresolution curves in a diagram of(rm, θm) as in Fig. 35.

θm = 1√C

[(DR − Brm)(DR + Brm)

] 14

If A corresponds to the emittance parameters of the beam at the specimenlevel (very small rm and large θm—that is image mode in STEM with largeacceptance conditions to collect high-energy losses), it is responsible forrather poor performance of the spectrometer. The introduction of transferoptics would displace A towards a characteristic point B on the same graph,while remaining on the constant emittance hyperbola rmθm = Ct (whileneglecting aberrations of the transfer lenses). One can then define the best


Figure 36 Definition of the optimum coupling conditions between the microscope andthe spectrometer, obtained when the isoemittance curves are tangential to the isores-olution curves (courtesy of Jeanguillaume, 1982).

coupling condition for B, determined when the hyperbola is tangential tothe best isoresolution curve. Fig. 36 shows that, in this simple model, theoptimal coupling conditions lie on the parabola of equation:

θm = 1

214

[Brm

C

] 12

(iii) Even for the best calculated prism, it is often convenient to achievethe final alignment with auxiliary coils and to refine the second- and third-order aberrations by use of multipolar elements (see, for instance, Isaacson,1981; Tang, 1982).

For all these reasons, it has appeared very useful to consider in more de-tail the possibilities of optimal coupling between the spectrometer and themicroscope column. In a CTEM, this function is, of course, achieved bythe magnifying lenses of the column. Egerton (1980c) and Johnson (1980)have investigated simultaneously these possibilities, pointing out a solutionin which an optimal M value should exist which minimizes the size of thespectrometer image and thus maximizes the energy resolving power of thesystem. Johnson has also shown that the figure of merit F = πα2

0(E0/δE)


introduced by Isaacson and Crewe (1975), can increase from the standardvalue of 1 for an uncorrected spectrometer to 12 and even 40 at the opti-mum magnification.

In the STEM case, Crewe (1977a) has pointed out the advantages ofpost-specimen lenses to satisfy the requirements mentioned. The completesuggested solution consists in three post-specimen lenses (PSL), an objec-tive lens, a field lens and a third lens to refocus the spectrometer imageto a more convenient location or to make it the required size. Even witha conventional spectrometer, this would make values of F of the order of100 attainable. It would be even better with a second-order corrected spec-trometer, the general design of which was also investigated by Crewe in afollowing paper (Crewe, 1977b). This important idea of matching selectedportions of the distribution of scattered electrons leaving the specimen todetectors of fixed angular acceptance or physical size, with specific applica-tions to EELS and diffraction patterns, has been taken up again by Cravenand Buggy (1981), Craven, Buggy, and Ferrier (1981), Buggy and Craven(1982). They have realized in collaboration with Vacuum Generators a sys-tem of three PSL for a HB-501 microscope. The last lens is focused sothat its cross-over is fixed with respect to the entrance of the spectrome-ter. These authors have studied how a quantitative analysis of a spectrumrecorded with this system must take into account both the convolution ofthe angular distribution of current in the incident probe with the angulardistribution of the inelastic scattering and the chromatic effects in the PSL.As a consequence, one has to measure carefully the dependence of collec-tion efficiency on energy loss due to the fact that these lenses do not focusequivalently electrons of different energy loss.

Another approach has been used for interfacing the Gatan spectrom-eter to the VG microscope in our laboratory (see Krivanek & Swann,1981; Jeanguillaume, 1982). It uses the post-specimen field in the high-excitation objective lens as a weak converging lens with a magnificationfactor M dependent on the objective excitation current. M has beenshown to increase from �5 to �12 for NI/

√V ∗ varying from 19.2 to

21.5. A quadrupole is then used to adjust the spectrometer focusing onthe z-dependent object position and a sextupole to compensate slightly theradius of curvature R1 of the spectrometer entrance face so that the second-order aberration terms can be cancelled. The schematic representation ofthe coupling geometry used in Orsay is shown in Fig. 37. The properties ofthe spectrometer itself, the spectrometer quadrupole and the spectrometerplus quadrupole plus post-specimen converging lens have been practically


Figure 37 Schematization of the coupling optics used between the STEM-HB 501 andthe Gatan spectrometer at Orsay.

studied (Jeanguillaume, 1982). The second-order aberrations have beenanalysed using the alignment figures proposed by Egerton (1981b)—seeJeanguillaume, Krivanek, and Colliex (1982). As a practical consequence,an energy resolution �0.35 eV has been recorded with an effective collec-tion angle of 7.5 mrad at the specimen (measured as the FWHM of theelastic peak for an aluminium specimen). It is mainly controlled at this levelby the width of the primary field emission beam (Fig. 38). On the otherhand, an energy resolution of the order of �1 eV can be maintained forlarge 25 mrad angles of collection at the specimen, necessary to record corelosses with sufficient signal/noise ratio (see the spectra of Scandium L2−3 inFig. 25).

5.4 Detection unitIn most existing EELS systems, the recording of spectra is still achieved byserially ramping the inelastic electron distribution in front of the detectionslits. Several solutions have been practically used: the energy-loss scan canbe governed either by a deflection coil before or after the magnet, or by thevariation of the magnet current itself for relatively slow scans, or by an ab-solute voltage scan when applying a reference voltage to the insulated drifttube within the magnet (Batson, Pennycook, & Jones, 1981). The variationof the primary voltage mostly used for CTEM energy filters has been for-


Figure 38 Illustration of the energy resolution capabilities of the Orsay system, mea-sured on the full width at half maximum of the elastic peak (see also the Gatan brochureconcerning the spectrometer 607 model).

saken for STEM because of the high sensitivity of the probe-forming lensworking conditions to variations in primary voltage.

The detector is located several centimetres behind the slits. For largeelectron signals, a simple analog amplification of the electron current canbe converted into a digital signal with a commercial ADC or V/F con-verter. For very low currents, direct counting of electron events is required.A surface barrier solid-state detector provides very good dark current dis-crimination but is limited to �104 c/s (Trebbia, Ballongue, & Colliex,


1977). To accommodate the large dynamic range of electron fluxes in anenergy-loss spectrum, a widely-used solution lies in a combination of plasticscintillator and photomultiplier coupled to a threshold discrimination sys-tem. The scintillator NE 160, the properties of which have been describedby Engel, Christen, and Michel (1981), provides single-electron capabili-ties and saturates at about 2 MHz. The photomultiplier delivers pulses oftypically 8 ns which can be best discriminated from the noise when 1200 Vare applied on the PM tube. A highly convenient automatic gain changehas been included in the Gatan signal processor so that it can be used fora single energy-loss spectrum scan, in current mode for the high intensitypart of the spectrum (elastic peak and first plasmon peak for instance) andin pulse mode for the lower intensity part (high-energy losses). Overall adynamic range of >108 is accessible, which is quite useful for a posterioriquantitative handling of the data.

Such a sequential acquisition of the spectrum represents, however, aconsiderable waste of signal and solutions using multiarray simultaneousdetectors have been tested in recent years. The general principles of paralleldetection systems for EELS have been discussed by Egerton (1981c) andMonson, Johnson, and Csillag (1982). Energy-loss spectra can be recordedin parallel at the spectrometer image plane, either by exposing a suitabledetector directly to the electrons or by placing a converter there to trans-form the spectrum of electron energies to a spectrum of photointensitieswhich is optically transferred to a photon detector. The simplest meansof electron parallel detector is still the photographic plate, which suffersstrong limitations, however: reduced dynamic range, no immediate accessto spectrum evaluation, need for a posteriori densitometry. . . , so that its usefor quantitative work is nowadays fairly restricted.

More recently, semiconductor detectors have been used to recordenergy-loss spectra in parallel both via direct electron exposure and by indi-rect photoconversion. They are the charge coupled devices (CCD) and thephotodiode arrays which are basically similar but differ in the read-out pro-cess. Recent progress on each type of device has been discussed by Jones,Walton, and Booker (1982), Jones, Rossouw, and Booker (1982) for self-scanned photodiode arrays and by Chapman, Glas, and Roberts (1982) forCCD. The various design options for using these arrays as electron detec-tors are summarized in Fig. 39, due to Egerton (1981c). The main problemsassociated with this new type of electron detector are the following:• Degradation in energy resolution. In the Fairchild CCD, the cell size

is of the order of 15 µm. In the IPL-1D selfscanned silicon photodi-


Figure 39 Some design options for using photodiode or charge-coupled diode arraysas electron detectors (courtesy of Egerton, 1981c).

ode, the centre-to-centre spacing is 100 µm. Compared to the energydispersion of a standard spectrometer (�2 µm/eV), it requires a magni-fication system after the spectrometer. Another way of improving theresolution, suggested by Egerton, is to tilt the array (or the phosphorscreen, for indirect exposure) away from normal incidence, and thebest situation would be to approximate this tilt angle to the dispersionplane tilt of the spectrometer. The calculations developed in Section 5.3above, for zero-angle tilt of the dispersion plane are, of course, not validfor this application.

• Limitation of the dynamic range. This is generally of the order of a fewhundred and it has been increased to greater than 1000:1 by reducingthe temperature. The detector collects charge for a variable integrationtime τ (∼1 ms to ∼10 s) and the spectrum is then read out and displayedon an oscilloscope screen in ∼100 µs. By varying τ , one can recordboth low-energy and high-energy spectra. In the indirect method, therecorded dynamic range may be increased by use of a half-plane filterin the optical path.

• Deterioration of performance after prolonged irradiation. Various re-ports have been published. It seems now that most of the radiation


damage can be removed by thermal annealing at �650 K for severalhours. With simple masking and sensible use, degradation is not a se-rious problem, and is insignificant for medium to low electron currentdensity. Similarly to standard detection systems, the output is in theform of an electric signal, which can then be digitalized and processedby a minicomputer.As a conclusion, parallel detection which has been mentioned for sev-

eral years as an important potential improvement in EELS spectroscopy, hasprogressed more slowly than expected due to severe technological prob-lems. The situation seems now so developed that it is possible to considerit as a major step forward to be awaited during the next two years.

5.5 Data acquisition and processingInterfacing with a minicomputer has been achieved for several years. It hasnow become routinely available, and it constitutes an important develop-ment for data acquisition and processing. The first task of the computeris to control the spectra-recording conditions. At present, it governs theunit which scans the inelastic electrons in front of the detection slit. In thefuture, it will define the read-out process of the parallel detection system.The more flexible is the program of acquisition, the more useful it is. Onecan change the acquisition time between different energy-loss domains,superpose successive spectra, select reduced energy ranges around featuresof interest for longer acquisition periods, fix a given energy-loss value torecord a filtered image. All these processes are now incorporated in EELSsoftware packages.

On the other hand, multiple processing tasks have to be developed asexplained in Sections 2, 3 and 4. One can mention deconvolution of mul-tiple scattering, Kramers–Kronig transformation of the low-loss spectrumto obtain dielectric constants, background fitting and extrapolation belowan edge of interest, simple calculations of cross-sections, modelling of high-energy tails and extraction of EXELFS to obtain the radial distribution. . . .Needs for new and more sophisticated programs are currently involved bymajor developments in understanding the energy-loss features. The situa-tion is at present very diversified; there exist well-developed home-madelibraries adapted to a given system and using different languages. Manu-facturers, on the other hand, propose their own packages (see for instanceStatham, 1982a). The attitude is therefore different for people who wantto develop the potentialities of EELS and those who want to use themfor characterization problems. Let us mention, finally, practical approaches,


such as described by Joy (1982), consisting in developing simple programswhich can be handled rapidly on a microcomputer or even on a pocketcalculator, for quantitation of energy-loss data to give elemental concentra-tions or elemental ratios in a compound. As it makes quantitative analysiswith EELS a simple matter, this approach is very important because it bringsit into the hands of numerous new users. However it is also dangerous be-cause these procedures for handling data are generally oversimplified andmay become misleading in some circumstances.

6. EELS as a microanalytical tool

During the past few years, the impact of EELS in the world of elec-tron microscopists has increased. It has left the domain of spectroscopicmethods dedicated to solid-state physics investigations and has moved intobecoming a powerful tool for elemental analysis with high spatial resolu-tion. This was the result of the main aspects of instrumental developmentdescribed in the previous section: a good insertion into the electron mi-croscope and systematic quantitative recording of core-loss edges. As aconsequence, our knowledge of the basic phenomena has been regularlyimproved by systematic studies on well-defined systems. The method couldthen be applied to more complex substances as shown by various examples(sections of human lung poisoned by asbestos particles, or segregations ofimpurities in minerals. . . ). The application of EELS for elemental analysishas been covered by many review papers during the last few years (Maher,1979; Maher & Joy, 1980; Joy, 1981; Egerton, 1982b; Egerton, 1982c;Colliex, 1982a). Moreover, all the important physical properties requiredfor defining how to use it, have been discussed in the previous sections.Consequently, the following will constitute a short survey of the microan-alytical capabilities of EELS.

Characterization of solid thin films with high spatial resolution is nowachieved in a STEM, by a combination of:• High-resolution imaging, better than 1 nm in the dark-field image

mode; it allows one to see and to track the object of interest (smallparticle, defect. . . ).

• Convergent microdiffraction pattern; it reflects the crystallographicstructure of the analysed volume (amorphous or crystalline, orienta-tion relationships, and in the extreme case of a coherent electron probesmaller than the crystal unit, sensitivity to the contents of the unit cell).


• X-ray analysis of the emitted photons generally detected now by anenergy-dispersive X-ray detector (EDX); the characteristic elementalinformation is distributed in a set of lines superposed over a backgroundof low intensity.

• Finally, electron energy-loss spectroscopy. The chemical analysis is dueto the appearance of core-loss signals for all elements (Z > 2). Moreparticularly, as seen from Table 3, the low Z elements exhibit sim-ple edges of strong intensity in the high energy loss domain (50 to2000 eV), which have been the goal of complete cross-section calcu-lations. As a consequence, borides, carbides, nitrides, oxides constitutean increasing population of specimens well suited to EELS, as com-pared to EDX which is rather insensitive to these low Z elements.A second important property of EELS is that the localization of theinelastic event along the beam trajectory (see Fig. 30) is favourablefor the study of situations with typical lateral dimensions down tothe nanometre range. Precipitation and segregation phenomena overthose characteristic distances constitute important domains of applica-tion. The following topics will be successively discussed:• qualitative microanalysis,• quantitative microanalysis,• limits in sensitivity,• environmental information,• chemical mapping.

The first four aspects deal with EELS in an analysing mode, while the lastdiscusses recent developments in the filtering mode.

6.1 Qualitative microanalysis6.1.1 Library of useful edgesTable 3 has listed all useful edges for all elements in the periodic table, to-gether with data on their energy position and general profiles. The librariesdue to Zaluzec (1982) and Krivanek and Ahn (1982) are also quite useful.Most elements can be detected by one and often two edges in the accessibleenergy range �50 to 2000 eV. If all the lightest ones from Li (Z = 3) toNi (Z = 28) are very easy to recognize, there exist some cases where themethod does not seem so well suited, i.e. the metals at the end of the d pe-riod (noble metals Cu, Ag, Au, or Zn, Cd. . . ). However, Fig. 40 presentstwo examples in which such elements have been analysed by one of theircharacteristic edges: Pd particle on an Al2O3 support, and a Zn-rich lamel-lar phase among other phyllosilicates which do not contain Zn.


In the library of Krivanek, H and He K-edges have been recorded fromgases in an electron microscope equipped with an environmental chamber(Burgner, Krivanek, & Swann, 1982). The problem of detection of hy-drogen in a solid is a more complex problem because the H-electron isinvolved in solid-state orbitals so that it cannot be detected by its K-edgeat 13.6 eV. Rare-earth and transition metal hydrides have been the sub-ject of several experimental investigations (Colliex, Gasgnier, et al., 1976;Stephens & Brown, 1980; Zaluzec, Schober, & Westlake, 1981; Stephens,1981). When the hydrogen enters a metallic lattice, it is not clear whetherits electron is kept by the hydrogen nucleus (in which case a K loss shouldbe visible, maybe shifted in energy) or it is given to the conduction bandof the lattice. The absence of an atomic-like K-edge of H in the spectraspeaks for the second solution in which case the extra hydrogen electronmodifies the metallic conduction band and shifts the Fermi level. In rare-earth dihydrides (LnH2) a shift of plasmon energy towards higher values hasbeen interpreted in this general model and the results have been discussed interms of the effective number of free electrons involved in the collective ex-citation. For transition metals MHx a general behaviour has been observedconcerning the shift in plasmon peak energy �Ep for the hydride relative tothe metal. When displaying the data as �Ep/H with H/M = 1 (that is theshift expected for monohydrides), it decreases linearly from group 3 (Sc, Y)to group 4 (Ti,Zr,Hf) and 5 (V,Nb,Ta). Schober et al. (unpublished) sug-gest that these phenomena result from the changing electron density as oneadds hydrogen. For transition metals with few outer electrons (group 3) theaddition of hydrogen with its one electron/atom increases the net electrondensity. This effect reverses for transition metals that have a large number ofvalence electrons (�Ep/H → 0 between groups 5 and 6). Finally one mustpoint out the results of Stephens and Brown who have detected an extrapeak at �7 eV for β-vanadium hydride (for which the composition lies inthe range VH0.45–VH0.7 at room temperature) and at 4.2 eV in β-niobiumhydride in the composition range NbH0.7 to NbH1.05 at room temperature.They propose, following the general theory developed by Cazaux (1971)and by Liang and Cundy (1969), an explanation in terms of resonant plas-mon excitation in a two-band model, in which the effect of hydrogenwould be to introduce an energy gap into the valence band of the matrixmetal. Summarizing all these results, it is obvious that the search for hydro-gen does not obey a single and simple solution; it must rather be consideredthrough the modifications of the band structure induced by the introduc-


tion of hydrogen in the matrix. Consequently the limits of detection areseveral orders of magnitude worse than those discussed below.

6.1.2 Examples of applicationsMany examples of qualitative applications of EELS have now appeared invarious domains: the presence of a given element in a selected area is deter-mined by the appearance of its characteristic edges. Biological applicationshave been reviewed by Somlyo, Shuman, and Somlyo (1982) and Egerton(1982c). An obvious field of immediate interest concerns the identifica-tion of elements present in mineral deposits within tissue sections, see forinstance, Jouffrey, Kihn, Perez, Sevely, and Zanchi (1978).

In material sciences, the number of contributions in which EELS is usedas an aid in solving a local characterization problem is regularly increasingin the different meeting proceedings. Some examples concern the analy-sis of crystalline inclusions in amorphous silicon (Craven, Lynch, Brown,& Mistry, 1980) segregation in rare-earth oxides (Dexpert, Pennycook, &Brown, 1980), measurement of carbon in V(C,N) precipitates extractedfrom HSLA steels on aluminium replicas (Garratt-Reed, 1981), structureand chemical properties of iron oxide thin films (Pennycook, Batson, &Fisher, 1980), segregation and chemical changes in crystalline and amor-phous phases in ceramics (Herrmann, Krahl, Rühle, & Kirn, 1980). Thislist is far from being exhaustive.

Finally, a promising new domain of application lies in the earth sciencesmaterials, because they are mainly composed of rather complex oxides.EELS is the only available method for probing the local change in oxy-gen content. Work is presently being done systematically on phyllosilicates(Steinberg et al., see examples in Colliex, 1982a, 1982b) olivine (Vaughanand Colliex, unpublished) at 100 kV primary voltage. With 1 MeV elec-trons, a similar analysis has been performed by Sevely et al. (1981) to revealthe heterogeneous distribution of elements in Mn- and Zn-mixed sulphideswith a lateral resolution of �0.2 µm in a specimen of �0.2 µm thickness.

Figure 40 Two examples of detection of elements with rather badly defined edges.(A) Pd M45 edge (threshold at 335 eV but maximum at �420 eV) in a volume of3 × 4.5 × 8 nm3 of a catalytic cluster deposited on an aluminium flat support parti-cle. The edges of aluminium (L23) and oxygen (K) are also visible (specimen courtesyof E. Freund and J. Lynch). (B) Zn L23 edge (at 1020 eV) from a sauconite lamellar crys-tallite among a mixture of halloysite ones. One also sees the edges of oxygen (K) andaluminium (K) (specimen courtesy of M. Rautureau and M. Steinberg). (C) and (D) Thecontribution of the these two edges Pd M45 and Zn L23 after background removal.


6.2 Quantitative microanalysis6.2.1 Definitions: Signal and cross-section

Microanalysis by EELS is rather easy to quantify, since one is concernedonly with the primary ionization process, in comparison with EDX wherevarious corrections (atomic number, absorption, fluorescence) have to betaken into account. The basic formulae and corrections have been es-tablished by Egerton (1978) who clearly pointed out how the effects ofcollecting the inelastic electrons within an angle α and measuring the signalover an energy window � after the edge have to be considered.

The core-loss signal is defined as the difference, in the energy loss regionof interest, between the actually recorded intensity and the backgroundintensity, deduced by extrapolation for energies >Ec of the curve recordedat energies <Ec:

Sc(α,�) =∫ Ec+�

Ec

[I(�E) − B(�E)

]d(�E)

Sc(α,�) = I(α,�) − B(α,�)

The problem of background stripping has already been discussed in Sec-tion 4.3. One generally uses a model curve I(�E) = A.�E−r which is validover a maximum energy window �200 eV (including both the fitting win-dow below the edge and the extrapolation window above it). Egerton hasestablished that the number N of atoms of the element present per unitarea of the specimen giving rise to the core-loss structure of interest, canbe deduced from the equation:

N = 1σc(α,�)

· Sc(α,�)

I0(α,�)(a)

where Sc(α,�) is the signal under the undeconvoluted spectrum, andI0(α,�) measures the area of the low-energy domain spectrum up to anenergy loss (�) including the elastic peak (see Fig. 41A). This constitutesan approximation, taking into account multiple inelastic scattering, of theformula:

N = 1σc(α,�)

· S′c(α,�)

I ′0(α)

(b)

where S′c(α,�) is the area under the deconvoluted inner-shell spectrum,

I ′0(α) is the measured area under the zero-loss peak and α is the angular

range (see Fig. 41B).


Figure 41 Schematic models of the quantities involved in the microanalytical quantita-tive use of EELS spectra: (A) non-deconvoluted spectrum; (B) deconvoluted spectrum(see text).

Eq. (a) has been shown to be accurate within about 10% for sampleswhich are sufficiently thin to give good EELS data (Egerton, 1981d). In thecase of a BN specimen, the ratio SB

K/SNK remains constant to a maximum

thickness tm ∼ λp (for E0 = 100 keV, λp = 90 nm in BN ). A larger valueof � increases the range of validity of the above formula, similarly to anincrease of α. This is quite natural because the validity of the approximationinvolved in using limited α and �, improves as these parameters increase.When one wants to extend the simplified method due to Egerton, it ispossible to use two correction terms, calculated by Stephens (1980): thefirst, called the plasmon shift correction, estimates the loss of collectionefficiency after a shift in energy caused by multiple scattering, while thesecond, the angular collection correction, arises from the convolution of


angular collection efficiencies. These effects have already been discussed inSection 2.3.2.

In most practical situations, one is not particularly interested in the ab-solute number of atoms of a given species but rather in ratios of elementalconcentration. The Egerton formula can then be rewritten as:

NA

NB= SA

c (α,�)

SBc (α,�)

· σBc (α,�)

σAc (α,�)

which means that EELS can be used as a convenient standardless method forquantitative analysis. All the useful information is contained in one singleenergy loss scan.

Use of the ratio method requires good measurement of the signals,and good knowledge of the cross-sections involved. Considering the signalitself, the various methods of background fitting and the validity of mod-elling the shape of the background with a power law have already beendiscussed. The statistical uncertainty in the signal determination is in thesuperposition of the noise on the total number of counts in I(α,�), thatis roughly

√I for Poissonian statistics, and the uncertainty in background

subtraction. It can be expressed following Bevington (1969) as:

σ 2s = σ 2

I + σ 2B

according to the general rule of propagation of errors. When one uses theCurfit program for background fitting:

σ 2s = I(α,�) + [

B(α,�)]χ2

v

where χ2v is the reduced chi-square value which estimates the goodness of

the fit. Let us consider another situation in which the fitting is made fromonly two measurements I1 and I2 in two channels located at E1 and E2

below the edge. One determines analytically:

r = (log I1/I2)/ log(E2/E1)

A = I1Er1 = I2Er

2

S = I3 − AE−r3

where I3 is the content of the channel located at E3 after the edge. Onecalculates:

�r = 1log(E2/E1)

[�I1

I1+ �I2

I2

]


where

�I1 = √(I1), �I2 = √

(I2)

�BB = 1log(E2/E1)

[�I1

I1log

(E3

E2

)+ �I2

I2log

(E3

E1

)]

and

�S = √(I3) +

(E1

E3

)r[√(I1)

log E3/E2

log E2/E1+ I1√

(I2)

log E3/E1

log E2/E1

]

In the RHS of this last equation, the first term corresponds to the ran-dom noise in counting I3 and the second to the uncertainty due to thebackground extrapolation. When one inserts typical numbers for an exper-iment, it appears that this second contribution can be several times greaterthan the first one. Great care must be taken to reduce it. A different wayof presenting these considerations is due to Egerton (1982d) who performsthe background fitting in logarithmic coordinates. He expresses finally thenoise on the signal as:

σ 2s = S + hB

where h is a parameter which can be calculated as a function of the width �

of the fitting region and of the width � of the integration region. The gen-eral conclusion is that the most suitable choice of both � and � involves acompromise between systematic and random errors; practically, � = 100 eVand � between 50 and 100 eV constitute a very satisfactory solution, forwhich h � 4 to 6.

The second source of error in quantitative data lies in the choice ofadequate cross-section values. As has already been discussed there are threemain methods of cross-section determination (Maher, 1979):

(a) Efficiency factor method: the total ionization cross-section is multi-plied by two efficiency factors (in energy and angle)—see Section 4.1.3:

η� = 1 −(

Ec

Ec + �

)s−1

ηα = log(1 + α2/θE2)

log(2/θE)

The exponent s describing the high energy tail of the edge varies with col-lection angle, involving serious errors in quantitation. Following Isaacson


(1980), a poor man’s approach consists in parametrization of the importantcoefficients. Joy (1982) proposes:

s(α,�E) = H + J logα

θE

where

H = 5.31

J = −0.336for K edges 3 < Z < 15

and

H = 4.92

J = −0.332for L edges 13 < Z < 30

Moreover, the saturation cross-section is written as

σ = F log[G(E0/Ec)]E0.Ec

where

F = 1.6 × 10−13 cm2/atomG = 0.0557

}for K edges such as 55 < Ec < 1850 eV

F = 4.51 × 10−13 cm2/atomQ = 0.0562

}for L edges such as 99 < Ec < 1000 eV

E0 and Ec are expressed in eV.Concerning the partial cross-section this simple pocket calculator calcu-

lation gives results within 20% of the more complete direct atomic partialcross-sections.

(b) Measurement of the relevant cross-section from a standard: this re-quires too many specimens of known composition and accurately calibratedin thickness so that it has remained very unattractive for general use. It canonly be contemplated when the two other methods seem suspicious (thatis for a high l quantum number edge in a heavy material, for instance O4−5

in uranium!).(c) Partial cross-section calculations from atomic models either in a

hydrogenic model (Egerton Sigmak and Sigmal programs) or with Hartree–Slater wave functions (Rez, 1982). The first are easy to handle and provide


useful results for the important K and L edges, while the more completesecond calculations are of limited access because of the large storage capa-bilities required. Good agreement between both theories has been foundfor the K-edges while some discrepancies are detected for the L2−3 edge.They are far superior to the efficiency factor method, more especially whena small � window is used. For all these theoretical approaches, an atomicmodel has been used, which neglects modifications in the cross-sectionsproduced by the solid-state environment. It is a satisfactory assumptionwhen one integrates over large energy windows which average the contri-bution of EXELFS oscillations. However, there exist certain points whichrequire further study. ELNES are associated with transitions towards finalstates of given symmetry. There may be redistributions of final state sym-metry due to bonding, and the use of limited energy windows would bemore sensitive to these effects.

A practical microanalytical test has been carried out on a type 304 steelusing EDX and EELS methods by Collett, Brown, and Jacobs (1981). TheFe:Cr:Ni weight composition ratios in the steel are calculated from peakareas in the X-ray spectra and from edge areas in the energy loss spectra.Composition ratios are found to agree to within 10%. This is a favourablesituation for EELS quantitation because the edges are of the same type andlie in the same energy range. Taking into account the possibility of testingthe stability of the results as a function of variable collection angles α andenergy windows �, one can expect total accuracies better than 5% on suchquantitative measurements. On the other hand, when one has to measureratios of elements due to different edge-types such as K,L2−3 and M4−5,it is clear that the results do not present the same character of reliabilityand an accuracy �15 to 20% is at present a satisfactory goal. One mustfinally notice that the main objective of this technique is to investigate thechemical nature of very small volumes, so that the total number of atomsis very limited. For statistical reasons, it is obvious that a highly accurateconcentration measurement does not mean anything, the ultimate situationbeing the case of single atom identification for which there are only twopossibilities: 0 and 100%.

6.2.2 Specimen induced effects

The validity of the above measurements can also be limited by propertiesof the specimen itself.

(i) Thickness. Very thin specimens have always been defined as suitabletest situations for quantitative elemental analysis by the EELS technique. All


previous discussions have clearly pointed out how multiple scattering couldinduce important failure of the validity of Egerton’s formulae, prevent asatisfactory definition of the characteristic signal, increase the backgroundunder the edge and superpose extra noise. When no deconvolution ofthe plasmon satellite on core-loss spectra is undertaken, a maximum valuetm � λp must be used. It seems possible, however, to extend the range ofvalidity of these quantitative estimations by careful deconvolution, as hasbeen shown by Swyt and Leapman (1982)—see Fig. 10.

Increasing the specimen thickness has another consequence, it deteri-orates the spatial resolution of the method, as a consequence of the beamspreading through the foil. However, there is an advantage with EELS:only the electrons scattered within an angle α can be detected, so that thisangular window induces a collimation effect and reduces the total lateralextension of the probed volume. On the other hand, in EDX, photonsissuing from the whole volume covered by the scattered electrons can bedetected (see Fig. 30). A practical estimation of the broadening due tobeam spreading in EELS is therefore: 2ρ � t.α + 2ρ0 which corresponds to2.5 nm for α = 25 × 10−3 rad and t � 100 nm. It remains of acceptablemagnitude with respect to the size of the primary beam spot, contrary towhat has been detected in EDX analysis of the segregation profile near agrain boundary (Fries, Imeson, Garratt-Reed, & Vandersande, 1982) where2ρ = βt

32 + 2ρ0.

(ii) Orientation effects. The above theory has been developed for an amor-phous solid model; the cross-section for the solid can be calculated as thesum of the cross-sections for all constituent atoms without regard to possibleeffects caused by the crystalline nature of the specimen. One has thereforeto consider the influence of diffraction conditions on energy loss analysis.

Rossouw and Whelan (1980) have pointed out the two types of possibleinfluence of diffraction conditions on energy-loss analysis. They can affect:

(i) The change in core-loss excitation with crystallographic orientation.This is more easily understood as a channelling effect on characteristic loss(an equivalent of the Borrman effect in X-rays).

(ii) The variation in diffraction contrast between core-loss and other(low-loss) electrons which have not created deep-level holes. For instancean apparent increase in the measured value of Nc as Sc(α,�)/I0(�,α)σc canoccur in areas for which strong extinction of the elastic beam occurs whilesignificant transmission of the core-loss signal may be preserved. There aretwo possible mechanisms responsible for these apparent discrepancies be-tween elastic and core-loss extinction; the first is the smearing out of the


diffraction contrast caused by the angular spread of the inelastic electrons(this effect has been considered by Craven and Colliex (1977) in calculatinginelastic images of lattice fringes). The second is the destruction of diffrac-tion contrast caused by inelastic interbranch transition. So it is clear that forquantitative microanalysis, one has to avoid orientation situations in whicha strong dynamic reflection is excited. Moreover with the large angular pri-mary probe generally used in a high resolution STEM, one integrates thediffraction conditions over α0 so that these critical angular configurationsare less sensitive.

Returning to channelling effects, they are of little influence in mostcases because precise angular conditions have to be fulfilled to show them.They are a consequence of the propagation of Bloch waves through thecrystal which distributes the density of electrons either on atomic sites orbetween them; in a compound, it can be preferentially on a set of planescontaining a given element or another one. If the inelastic scattering pro-cess is sufficiently localized, that is within a typical L distance smaller thand/2, one can expect a variation of the core-loss signal when one changesthe crystal orientation on either side of the Bragg condition. Preliminaryresults by Taftø and Lehmpfuhl (1982) have shown a weak dependence ofthe K-loss of Mg in MgO monocrystals. This is the first support for thelocalization arguments due to Craven, Gibson, Howie, and Spalding (1978)who estimate a typical interaction distance L � 2λE0/�E which decreasesas �E increases (L � 0.4 nm for �E = 1500 eV). For lower-energy losses,it is hopeless to detect clear orientation effects when one measures the for-ward inelastic electrons.

A more complete study is due to Taftø and Krivanek (1982a), Spence,Krivanek, Taftø, and Disko (1982), who show that for the specific K-lossesof Al and Mg, the localization increases rapidly with scattering angle. Thedivergence angles of the incident beam and the collector angle of thespectrometer are much smaller than the Bragg angle. In a natural spinelMgAl2O4 ((100) planar orientation), two different types of atomic planesare seen along the (100) direction. One type contains all the Al and Oatoms while the planes midway have all the Mg-atoms. Very clear chan-nelling and blocking effects have been obtained by comparing the Mg andAl–K losses while varying independently the diffraction conditions and lo-calization. A next step has been taken by Taftø and Krivanek (1982b) whocombined this site-sensitive technique with the determination of the va-lence of an atom by its chemical shift. It has been applied to the study ofthe location of Fe2+ and Fe3+ ions in a mixed valence spinel.


This crystallographic type of information in EELS spectra is onlyrecorded in well-collimated angular conditions, that is again at the expenseof good spatial resolution.

6.3 Detection limitsThe theoretical framework required to make predictions concerning theultimate capabilities of EELS elemental analysis has been established byIsaacson and Johnson (1975). They have introduced the useful conceptsof minimum detectable mass (MDM) and minimum detectable mass frac-tion (MMF) and evaluated them in simple calculations. Their paper alsocontains the first experimental investigations obtained by extrapolation of afew recorded spectra.

Following the same general guidelines, Colliex and Trebbia (1979), Joyand Maher (1980) have written the equations governing the detectablelimits, when inner-shell edges are used for microelemental analysis in atransmission electron energy loss experiment. The ultimate goal is theidentification of a single atom, which appears to be within the realm ofpracticality as pointed out by Isaacson and Utlaut (1979).

In 1975, the STEM used by Isaacson and Johnson was not particu-larly optimized for microanalysis, but has proved to be capable of detectingmasses of less than 10−18 g. Since that time the advances in microscope andspectrometer technologies discussed in Section 5 have pushed these limitsdown by two or three orders of magnitude (Colliex et al., 1982; Colliex,1982a, 1982b).

6.3.1 Minimum detectable mass

The basic formula is again:

S(α,�) = J0Nσ(α,�)ητ

where:• J0 is the primary electron current density expressed in e−/cm2 (J0(α,�)

introduced by Egerton �J0 when one analyses an infinitely small masswhich does not scatter at large angles nor introduce appreciable inelasticscattering).

• N is the number of analysed atoms.• σ(α,�) is the cross-section for the process under consideration and the

experimental conditions used.


• η is the efficiency of collection for the spectrometer and detection unit(�1).

• τ is the effective counting time (dwell-time per channel in sequentialdetection, total time in simultaneous detection).The MDM is then:

MDM = Smin

Jσητ

Since η and σ cannot be varied, the MDM varies as (Jτ)−1. It can be con-tinuously decreased as one uses higher density electron beams and longercounting times. The limitations are then:• The instabilities of the various components of the microscope.• The radiation damage induced by this very intense primary dose of

electrons.• The localization parameter which means that atoms lying within a crit-

ical distance L from the beam trajectory can be excited on an innershell. A rough estimation of this impact parameter is L � 2λ.(�E/E0)

(Howie, 1981) and the recent experiments on channelling and block-ing effects mentioned in Section 6.2.2 have already provided significantproof of its validity.

The work of Colliex et al. (1982) concerning the energy-loss spectra andfiltered images on the O4−5 edge of uranium, for a specimen consisting ofvery small uranium clusters deposited on a thin amorphous carbon layer,shows a practical MDM of �10 uranium atoms, that is a few 10−21 g. Thelimiting factor is attributed to the localization parameter, which estimatesthe full width of a uranium atom image formed with the U–O4−5 elec-trons to be of the order of 6 nm, in forward scattering conditions. Anotherimportant factor is the permanent migration of the uranium atoms on thesurface of the carbon foil, the origin of which is the superposition of ther-mal and collisional effects.

The other limitation therefore lies in the beam induced damage, whichhas been well known to biologists for a long time. In an organic specimen,one has detected structural changes and chemical changes. The latter caseis of interest for microanalysis: it can mean total mass loss or selective massloss. Very clear examples have been shown by Isaacson, Collins, and Listvan(1978). The ratio of the number of fluorine atoms to the number of carbonatoms decreases with a critical dose of 8 to 15 e−/Å2 in fluorine analogsof nucleic acid bases; it corresponds to the detection of 10−13 g of fluorinewith no apparent loss of material. More systematic radiation damage studies


Figure 42 Schematic representation of an energy-loss spectrum with definition of themain quantities, signal and background involved in the detection of the MMF of ele-ment B within a matrix of element A (see Colliex, 1982b).

have been carried out by Egerton (1980d, 1980e) in various beam sensitivesubstances and as a function of temperature. The characteristic dose forremoval of oxygen by 80 keV electrons ranges from a few to a few hundrede−/Å2.

These effects have been largely ignored by materials scientists up to now.However, in an experiment aimed at measuring the oxygen content of verysmall precipitates along dislocation cores in germanium, Bourret, Colliex,and Trebbia (1983) have observed a radiation induced desorption of oxygenfor doses of 106–107 e−/Å2. Many more studies of this type are required fora more comprehensive view of such limitations.

6.3.2 Minimum detectable mass fraction (MMF)

Applying the basic definition of the signal as a function of cross-section,flux of primary electrons and number of atoms, to the situation depictedin Fig. 42 for the detection of element B in a matrix A, we obtain thefollowing result:

xmin = k√

BB

SA· σA

σB

where k is a factor used in the visibility criterion of Rose:

SB > k√

BB


This is an approximation in which the only source of uncertainty is thenoise due to the Poissonian statistical distribution of counts. This detectionlimit criterion had been originally written in a slightly different way byIsaacson and Johnson (1975): MMF = MF × k/(P/

√B) when one detects a

known mass fraction MF, with a signal to noise ratio P/√

B under a givenset of experimental conditions. A more rigorous treatment would followthe approach due to Bevington (1969) and Colliex et al. (1981), that is:σs is the uncertainty in SB and �[2BB] 1

2 for the case illustrated in Fig. 42.A test of confidence for the existence of a true signal SB is:

SB = kσS

where k = 0.68 involves 50% probability of presence for the element B,k = 1 corresponds to 68% and k = 1.96 corresponds to 95%. Combiningthese two equations implies that a value k = 3 in the Rose criterion isroughly equivalent to a probability of 95% for the presence of element B.BB and SA are determined by recording an energy-loss spectrum on thematrix and σA and σB are cross-sections which can be calculated by Sigmakor Sigmal programs. It can, therefore, be seen that the minimum detectableconcentration depends on the edges under consideration through σA andσB, while the experimental conditions come into account through thefactor

√(BB/SA) which roughly varies as (JτN)− 1

2 . For a given primaryelectron density J0 and counting time τ , the MMF behaves therefore asN− 1

2 . Several practical examples have been investigated by Colliex (1982b).All the results lie in the range 0.5 to 1% when the total analysed vol-ume contains typically 105 to 106 atoms. They have been collected in asingle graph which tries to correlate the minimum detectable concentra-tion xmin as a function of the analysed volume (Fig. 43). Let us commenton the main trends of this chart. The general behaviour as N− 1

2 in thelow-concentration region is due to background constraints imposed by thematrix. On the contrary, the N−1 behaviour in the very small volume limitis due to noise in the signal. This is only an illustrative representation ofthe capabilities of the method. It points out the fact that EELS does notconstitute a technique well adapted to the detection of very small concen-trations; this is a consequence of the strength of the background whichunderlies any characteristic signal. It is more suited to the study of verysmall volumes of matter and consequently to the detection of high con-centrations: as a conclusion one should use it for the study of segregationor precipitation phenomena over characteristic distances of one or severalnanometres.


Figure 43 Typical results of EELS microanalysis gathered on a chart xmin(N). (a) Towardsthe detection limit of single uranium atoms. (b) Analysis of a uranium cluster on a carbonthin foil. (c) Analysis of oxygen along a dislocation core in germanium. (d) Detection ofnitrogen in a section of kidney. (e) Detection of titanium in a microcrystal of biotile. Seetext for comments concerning the illustrative set of curves N−1/2 and N−1 (see Colliex,1982b).

6.4 Environmental informationSection 4.2 has extensively discussed how various solid-state environmentparameters could be revealed through the analysis of fine structures on theedges. They concern the chemical shift and threshold shape, the near edgefine structures (ELNES) and the extended structures (EXELFS). The firsteffect is more connected with the valence state or electronic affinity ofthe atom under investigation, the second seems more governed by thesymmetry of the site and the third by the short-order environment. Thisconstitutes a very complete characterization and it is obvious that the studyof EELS spectra carries much more complete information for chemicalmicroanalysis than X-ray spectra do. However, this discussion still remainsrather speculative because such applications have been very limited untilnow. This is due to two types of problems:• Experimental limitations, because the use of EXELFS structures needs

counting regimes of 106 or 107 counts per channel to satisfy the sta-tistical requirements for a satisfactory analysis of the oscillations. On


the other hand, ELNES can be clearly recorded with counting regimesof 104 to 105. This is about three orders of magnitude smaller thanfor EXELFS, but requires a much better energy resolution, better than1 eV, which has been achieved only recently, apart from the work ofIsaacson (1979) concerning the fine structure at the carbon K-edge innucleic acids. Consequently, with an efficient spectrometer capable ofgood energy resolution with closed slits, it is relatively easier to satisfythis energy resolution condition for ELNES analysis than the inten-sity criterion for EXELFS analysis (by opening the slits to about 10 or20 eV).

• Theoretical problems, because the interpretation of EXELFS structuresseems nowadays satisfactorily developed within the framework of theshort-range, single-electron, single-scattering model. But the choice ofphase shifts and zeroes of kinetic energies nevertheless introduces someuncertainty in the final result, when the structure is not initially wellknown. On the contrary, the theory required for the interpretation ofELNES still needs to be elaborated before it can be used for a priori sitesymmetry determinations. It is now restricted to the comparison of therecorded spectra with standard traces and the approach has remainedphenomenological. It is one of the important goals for the next fewyears to improve the understanding of these features.

6.5 Chemical mapping with energy filtered imagesWhen one is interested in the variation of concentration of an elementover an extended specimen area, it is more useful to display an imagerecorded with the corresponding characteristic signal. An image is actuallya grid made of N × N picture elements (pixels). The useful information iscontained in the N2 spectra which would be acquired by positioning suc-cessively the probe of size d2 on the N2 adjacent pixels. This suggests firstthe recording conditions for correct specimen sampling: one must select amagnification M such that d = L/MN where L is the size of the final image(this is a typical description in STEM mode for which L is the dimension ofthe display screen). The situation is equivalent in the CTEM mode becauseat some stage in the data processing the image must be digitalized with agiven step increment.

Using the language of computer image processing, a standard image of128 × 128 pixels digitalized in 8 bits (= 1 byte = 256 grey levels) formatrequires a storage capacity of 16 Kbytes. Similarly an image 256 × 256corresponds to 64 Kbytes, and 512 × 512 to 256 Kbytes. These numbers


provide a quick estimate of the memory size necessary for manipulatingsuch a great quantity of information.

The content number in each pixel must be correlated to the number ofatoms of a given species in the analysed volume (that is roughly d2t) or perunit area. As a consequence, it has to be proportional to:

NA = SA(α,�)

I0(α,�).σA(α,�)

The problem is twofold:• Extract for each pixel, the characteristic signal SA in the minimum

recording time.• Normalize it by reference to the low-loss intensity I0(α,�) to obtain

an absolute value of the number of atoms A, or by reference to anothersignal SB(α,�) to study the relative fluctuations of one element withrespect to another.The following discussion refers primarily to the extraction of the useful

signal SA for any pixel element and reference has to be made to the spectradisplayed in Fig. 29 which are typical of a medium thick biological section.When one wants to form an image with either the nitrogen, oxygen, oriron signal, the main difficulty is to get rid of the existence of a strongbackground due to the carbon K-loss which is the dominant element inthe studied section.

The first possibility is to make an image subtraction between an imagerecorded before (I1) and after (I2) the characteristic edge, that is for eachpixel, to calculate S = I2 − I1. This method is obviously very bad, becauseit underestimates the signal, and can even lead to negative signals when itis very weak. An improved two-image method (I1 before the edge, I2 afterthe edge) has been used by Ottensmeyer and Andrew (1980), Bazett-Jonesand Ottensmeyer (1982). It assumes that the parameters A and r describingthe background are the same over the whole image field. It allows a betterdefinition of the signal, by introducing a correction factor k′ such that, forall pixels:

k′I1 = I2 = A.E−r2 and k′ =

(E1

E2

)r

The signal is then calculated as:

S = I2 − k′I1


Figure 44 Definition of the three energy spectroscopic images of E1,E2 and E3 requiredfor performing a chemical map with the characteristic signal S superposed on the non-characteristic background B.

With this method of processing, energy filtered images around the phos-phorus L2−3 edge have been recorded for strands of bulk chromatin nu-cleosomes. The authors develop this technique to display in colour thephosphorus distribution image over the original nucleosome image shownin grey. They suggest that approximately two supercoil turns of DNA,revealed by the spectroscopic phosphorus image, are wound about the nu-cleosome core.

However, this method seems insufficient, because it can confuse changesin thickness, orientation (when considering crystalline specimens) and scat-tering power, with changes in chemical composition. To avoid these mis-leading effects, Jeanguillaume, Trebbia, and Colliex (1978) pointed out thatit was necessary to record at least three images, two I1 and I2 before theedge, and one I3 after this edge. It is then possible to estimate for each pixelthe values of r and A defining the background:

r = log(I1/I2)/ log(E2/E1)

A = I1.Er1 = I2.Er

2

and consequently:

B = A.E−r3

S = I3 − B


Figure 45 Annular dark-field image (top) and “true” iron-loss image (bottom) of a vac-uole in a macrophage section embedded in epon (average thickness �70 nm). Thewhite spots in the iron image are probably due to single ferritin molecules distributedthrough the biological section.

(see Fig. 44 for the definition of the energy window used and the sig-nals). The necessary handling of energy filtered images can be carried outeither from digitalized images recorded in a CTEM (Krahl, 1982) or bycomputer driven on-line acquisition with a STEM. This method has beenrealized practically by several authors: Statham (1982b), Butler, Watari, andHiggs (1982), Rez and Ahn (1982), Oikawa, Sasaki, Matsuo, and Kokubo(1982), Jeanguillaume (1982), Jeanguillaume, Tencé, Trebbia, and Colliex(1983). But it seems that, at the present time, only Butler et al. (1982) andJeanguillaume et al. (1983) have performed satisfactory spectroscopic chem-ical processing, with three images. One typical example, extracted from the


work of the Orsay group on biological sections, is shown in Fig. 45. It con-cerns the analysis of iron distribution in a vacuole located at the peripheryof a macrophage. One can compare the standard annular dark-field imagewith the characteristic iron image recorded at E3 = 708 eV, after subtrac-tion of the background estimated from two images recorded respectively at559 eV and 678 eV, below the iron L2−3 edge at 705 eV. Only the smallaggregates are visible in the iron image; they can be individually comparedwith the equivalent bright dots in the dark-field image. It is reasonableto estimate that they correspond to single ferritin molecules of average size5 nm distributed throughout the 70 nm thick biological section. Discussionof the accuracy of the method together with an investigation of possible im-provements are at present under development at Orsay, and the results willbe published shortly.

To conclude this survey of the microanalytical capabilities of energyfiltered images, it must be pointed out that concentration variations of �5%can be detected with a spatial definition of 2 nm, for a primary dose ofthe order of a few 103 e−/nm2. Three images have to be recorded, andfor practical considerations, a satisfactory compromise is used in Orsay:it consists in recording the same line in the image successively with thethree relevant energies. This procedure reduces the effect of any shift inthe image and of fluctuations in the emission, while maintaining the totaltime of recording within a reasonable 10 min, for a 256 × 256 image and auseful core-loss edge of about 500 eV. Once again, however, it seems thatradiation damage will be the main limiting factor for future developments,more particularly in biological specimens.

7. Miscellaneous

In concluding this review, it seems worthwhile to mention brieflysome aspects of electron energy loss spectroscopy which are currently un-der promising development. This list is far from being exhaustive and it isclear that some other interesting features will appear in the near future asa consequence of the permanently increasing effort devoted to this generalsubject.

7.1 Electron energy loss spectroscopy in high voltagemicroscopy

Apart from some work due to Considine, Smith, and Cosslett (1970) andto Shirota, Doi, Izui, and Tomimitsu (1974), the main contribution in this


field is due to the Toulouse group which has successively developed energyanalysing and filtering devices for their 1 and 3 MeV electron microscopes:Perez, Zanchi, Sevely, and Jouffrey (1975), Zanchi et al. (1975), Sevely,Perez, Zanchi, Kihn, and Jouffrey (1982). These systems have brought in-teresting results concerning the physics of elementary excitations under theimpact of highly relativistic electron beams. In spite of a poorer energy res-olution, plasmon peaks and inner-shell excitations (down to the K-edge ingermanium at �11500 eV) have been recorded.

The general behaviour of the mean free path � (or total cross-section)of different features in the spectrum, plasmon or core-loss, has been studiedas a function of the primary voltage up to E0 = 1.2 MeV (Perez, 1976) andmore recently to E0 = 3 MeV. A first interesting result is the confirma-tion of the saturation of �p at high voltage, in good agreement with theAshley–Ritchie formula:

1�p

= e2

�2c2· �Ep · 1

β2 · log

(�qccβ

1.132�Ep

)

where β = v/c (see Fig. 46). There exists generally an increase of �p by afactor of �3 when the primary voltage is varied from 100 kV to 1 MV.

Concerning the dependence of the cross-section for an atomic level as afunction of E0, the Bethe model modified by relativistic effects to become:

1�c

= 2πe4nc

mc2· Fc

β2 · 1�Ec

[log

θ2max

θ2E

+ log1

1 − β2 − β2]

seems valid at least to E0 = 1 MeV (Perez, 1976; Jouffrey, 1978).In this formula:

• nc is the number of atoms per unit volume;• Fc is the oscillator strength;• �Ec = 3

2�Ec assuming a variation in Fc such that [dFc/d(�E)] ∼ �E−3

above the edge;• θmax is the angle of collection;• θE is the characteristic inelastic scattering angle defined relativistically

as:

θE = γ.�Ec

(γ 2 − 1) mc2

The behaviour of �c at energies greater than 1 MeV, which is expected todecrease slightly, has not yet been confirmed experimentally (Sevely, privatecommunication).


Figure 46 Measured and calculated mean free paths for plasmon excitation in carbonand aluminium, as a function of the primary voltage (up to 2.5 MeV) (courtesy of Sevely,Gout, Kihn, & Zanchi, 1983).

The major interest, reported up to now, of using this type of very highvoltage is the improvement of the jump ratio S/B at an inner-shell edgefor equal thickness (Zanchi, Sevely, & Kihn, 1981). A factor of five to tenhas been measured between 80 and 1000 kV on the carbon K-edge, for anaverage thickness of 200 to 300 nm. This suggests a great interest for usinghigh-voltage primary beams for the analysis of specimens in this thicknessrange, by reducing the effect of multiple scattering. It has been checkedexperimentally for qualitative analysis of mineralogical specimens (Sevely etal., 1983). On the contrary, in the limit of very thin specimens the situationseems inverted because of the general decrease of the characteristic signalwhen the primary voltage is increased.

7.2 Energy filtered imagesThe possible use of energy filtered images has already been largely describedin the section devoted to the microanalytical capabilities of EELS. It consistsin selecting in the energy-loss spectrum a specific feature which can beconnected to the presence of a given element in the analysed area. Thisis actually one of the many possibilities which are opened by the use ofinelastic electrons.

More generally, energy filtering offers great advantages for image con-trast improvement and it is worthwhile to summarize some of these possi-bilities:


(a) For relatively thin specimens, there is the advantage of eliminatingthe whole inelastic contribution and to keep the pure elastic informa-tion. It extends the range of validity of phase contrast theory towardshigher thickness (better contrast of lattice fringes—see Craven & Col-liex, 1977; improvement of the study of Lorentz images of magneticwalls—see Mory & Colliex, 1976).

(b) For very thick specimens, it is useful to select the inelastic electronsthat have suffered the most probable energy-loss defined by Landau toincrease the contrast in bright field images (Pearce-Percy & Cowley,1975; Kihn et al., 1976).

(c) Finally, a very efficient mode of contrast improvement is the ratioimage developed by Crewe, Langmore, and Isaacson (1975), whichis known nowadays as Z-contrast. It consists in displaying an imagewhich is proportional to the elastic signal, collected by an annulardark-field detector, divided by the inelastic component of the bright-field signal; it takes advantage of the specific configuration of detectorsin a STEM which allows one to measure simultaneously the varioussignals arising from the specimen-beam interaction. This ratio inten-sity has been shown, at least for low thickness, to be insensitive toweak variations in mass thickness but very dependent on the localatomic number of the specimen. This method has been primarily usedwith great success to visualize single heavy atoms or atom clustersdeposited on thin carbon foils. Recent applications have concernedcatalyst particles or metal aggregates on supports (Treacy, Howie, &Wilson, 1978; Treacy, Howie, & Pennycook, 1980) and unstained bi-ological sections (Carlemalm & Kellenberger, 1982). As a practicalpromising domain of use, the ultrastructure of the septate junctionshas been studied and compared in both stained and unstained prepa-rations (Garavito, Carlemalm, Colliex, & Villiger, 1982).

7.3 Energy losses on surfaces at glancing incidenceA new subject has recently emerged from experiments due to Cowley(1982a, 1982b) and Marks (1982). It concerns the characteristic featuresrecorded in spectra obtained when a beam of electrons travels parallel toa crystal surface. There exists a coupling with the surface plasmons whoseassociated electric fields extend outside of the crystal. There seems also tobe an indication of transition radiation due to the oscillatory motion of theelectrons being channelled along the surface (Cowley). It actually consti-tutes a special manifestation of the more general emission of radiation by


fast electrons channelled through crystals. This radiation, which should alsobe observed in energy-loss spectra, is due to the periodic transverse motionof the channelled particles along the atomic strings or atomic particles (seeBird, 1982, for discussion of the theory).

In summary, this survey has covered many aspects of the impact of EELSin the environment of the electron microscope. Its interest lies far beyondthe well-known microanalytical capabilities of the method, which seemsto be at present one of the most sensitive in terms of minimum detectablemass (except the combination of field ion microscopy and atom probe). Itdeals with the physics of interactions between a beam of particles and a solidand this technique can be competitive in many situations with the more es-tablished tools for spectroscopy: synchrotron radiation at zero-momentumtransfer, neutron scattering at zero-energy transfer. It is a more complexmethod probing inelastic effects with transfer of both energy and momen-tum. The various results which have been obtained will stimulate the effortof research in this field during the next few years, so that one can anticipatethat it will be extremely difficult in the future to cover the whole of thesubject in one review paper.

AcknowledgementsThe contents of this paper reflect many collaborative efforts in experimental devel-opments as well as in theoretical discussions of the results. It has been stimulated bythe daily help of P. Trebbia, C. Jeanguillaume, C. Mory, P. Ballongue and M. Tencé,all members of the Orsay Group in electron microscopy. The highly efficient equip-ment has been obtained with the help of CNRS, DGRST, DRET, University ofParis-Sud grants. I want to acknowledge more particularly the very stimulating col-laboration with O. Krivanek and L. M. Brown during their stays in our laboratory.Many ideas originated also from fruitful discussions with R. Egerton, R. D. Leapmanand J. Sevely. Thanks are due to C. Fradin and A. Touchant for their very efficientcontribution to the preparation of this manuscript. I am finally very grateful to V. E.Cosslett for his critical reading of the text.

Post scriptum

The above text has been written in the years 1983–1984. It is there-fore illustrated with figures and results dating back from these years andbefore, and they evidently carry a historical character. Since then, theinstrumentation and theory of EELS in the electron microscope have spec-tacularly progressed and opened this technique to wide and diversified newfields of applications. In the domain of instrumentation, I can quote the


parallel electron detectors and associated spectrum-imaging mode in theEELS STEM mode, the aberration correctors delivering on the specimenelectron probes smaller than 1 Angström, the monochromators offering aspectral resolution down to below 10 meV, the digital acquisition and pro-cessing of big-data sets. Consequently the spatial resolution has jumped intothe sub-interatomic distances and energy resolution into the infra-red do-main giving access to the spectroscopy of phonon modes. The identificationof single individual atoms has been demonstrated as well as the mapping ofEELS core-loss fine structures at the atomic column level. Recent reviewsrevisiting the topics described in Sections 3 and 4 of the present text cannowadays be found in the following references:(i) Colliex, Kociak, & Stéphan (2016). Electron energy loss spectroscopy

imaging of surface plasmons at the nanometer scale. Ultramicroscopy,162, A1–A24.

(ii) Gloter et al. (2017). Atomically resolved mapping of EELS fine struc-tures. Materials Science in Semiconductor Processing, 65, 2–17.

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Further readingEgerton, R. F., & Egerton, M. (1983). In Scanning electron microscopy 1983: Vol. I

(pp. 119–142). An electron energy loss bibliography containing approximately 700 en-tries till 1983.

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